Author name code: nakariakov ADS astronomy entries on 2022-09-14 author:"Nakariakov, Valery" ------------------------------------------------------------------------ Title: Two-Spacecraft Detection of Short-period Decayless Kink Oscillations of Solar Coronal Loops Authors: Zhong, Sihui; Nakariakov, Valery M.; Kolotkov, Dmitrii Y.; Verbeeck, Cis; Berghmans, David Bibcode: 2022arXiv220901917Z Altcode: Decayless kink oscillations of an ensemble of loops are captured simultaneously by the High Resolution Imager (HRI) of the Extreme Ultraviolet Imager (EUI) and the Atmospheric Imaging Assembly (AIA) from 22:58 UT on 5 November to 00:27 UT on 6 November 2021. Oscillations are analysed by processing image sequences taken by the two instruments with a motion magnification technique. The analysed loops are around 51 Mm in length, and oscillate with short periods of 1-3 min (1.6 min in average) and displacement amplitudes of 27-83 km. The signals recorded by AIA are delayed by 66 s as compared to HRI, which coincides with the light travel time difference from the Sun to each instrument. After correction of this time difference, the cross-correlation coefficient between the signals from the two data varies from 0.82 to 0.97, indicating that they are well consistent. This work confirms that HRI sees the same oscillations as AIA, which is the necessary first step before proceeding to the detection of shorter time scales by EUI. In addition, our results indicate the robustness of the de-jittering procedure in the study of kink oscillations with HRI. Title: Probing the Density Fine Structuring of the Solar Corona with Comet Lovejoy Authors: Nisticò, Giuseppe; Zimbardo, Gaetano; Perri, Silvia; Nakariakov, Valery M.; Duckenfield, Timothy J.; Druckmueller, Miloslav Bibcode: 2022arXiv220904051N Altcode: The passage of sungrazing comets in the solar corona can be a powerful tool to probe the local plasma properties. Here, we carry out a study of the striae pattern appearing in the tail of sungrazing Comet Lovejoy, as observed by the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatory (SDO) during the inbound and outbound phases of the comet orbit. We consider the images in EUV in the 171 Å bandpass, where emission from oxygen ions O$^{4+}$ and O$^{5+}$ is found. The striae are described as due to a beam of ions injected along the local magnetic field, with the initial beam velocity decaying because of collisions. Also, ion collisional diffusion contributes to ion propagation. Both the collision time for velocity decay and the diffusion coefficient for spatial spreading depend on the ambient plasma density. A probabilistic description of the ion beam density along the magnetic field is developed, where the beam position is given by the velocity decay and the spreading of diffusing ions is described by a Gaussian probability distribution. Profiles of emission intensity along the magnetic field are computed and compared with the profiles along the striae observed by AIA, showing a good agreement for most considered striae. The inferred coronal densities are then compared with a hydrostatic model of the solar corona. The results confirm that the coronal density is strongly spatially structured. Title: Seismology of the solar corona and extensions to stellar coronae Authors: Nakariakov, Valery Bibcode: 2022cosp...44.2498N Altcode: Wave motions detected in the upper part of the solar atmosphere, the corona, become a commonly used tool for probing physical conditions in the waveguiding plasma structures. Properties of the waves are sensitive to macroscopic parameters of the plasma, as well as transport coefficients and geometry and directivity of the magnetic field. Waves observed in the corona are of the magnetohydrodynamic (MHD) type, and are well described by MHD wave theory. The combination of high-precision observations with an array of spaceborne and ground-based instruments, and state-of-the-art theoretical modelling gives us estimations of physical parameters which are not open to direct observations, such as the absolute value of the magnetic field and its twist and free magnetic energy, electric currents, fine perpendicular structuring, the coronal heating function, and channels of the slow solar wind. A specific interest is paid to quasi-periodic (QPP) processes in flaring energy releases, as, on one hand it is natural to search for oscillatory processes in the vicinity of impulsive energy releases and, on the other, the enhanced radiation power can significantly improve the signal-to-noise ratio. We discuss possible links of QPP in solar and stellar flares with MHD wave processes, and implications of these links to plasma diagnostics. Title: Probing the solar corona with sungrazing comets: magnetic field and coronal density estimates from the EUV striae in the tail of Comet Lovejoy Authors: Nisticò, Giuseppe; Nakariakov, Valery; Zimbardo, Gaetano; Perri, Silvia; Duckenfield, Timothy; Druckmüller, Miloslav Bibcode: 2022cosp...44.2501N Altcode: The transit of Comet Lovejoy C/2011 W3 across the solar atmosphere in December 2011 offers us the opportunity to probe the physical conditions of the solar corona at distances that are still inaccessible to current spacecraft. The tail of Comet Lovejoy, as observed in EUV with the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO), appeared in the form of striae caused by the emission of cometary ions injected along the local coronal magnetic field lines intersected by the comet. We studied the spatial and time evolution of such striae as observed in the channel at 171 \AA~ of SDO/AIA to acquire information on the local magnetic field and plasma density. The striae are modelled as a beam of oxygen ions, with the injection beam velocity decaying because of collisions. Also, oxygen ions spread in space because of collisional diffusion. Both the collision time for velocity decay and the diffusion coefficient depend on the ambient plasma density. We developed a probabilistic description of the ion beam density along the magnetic field. In such a model, the beam position is determined by the velocity decay and the spreading of diffusing ions is described by a Gaussian probability distribution. Profiles of the ion density along the magnetic field are computed and conveniently compared with the 171 \AA~ intensity profiles along the striae to constrain the values of the local plasma density. Furthermore, transverse displacements of the striae observed in the data are interpreted in terms of propagating kink waves, whose properties allow us to estimate the magnitude of the local magnetic field. Title: A new look at the frequency-dependent damping of slow-mode waves in the solar corona Authors: Kolotkov, Dmitrii Y.; Nakariakov, Valery M. Bibcode: 2022MNRAS.514L..51K Altcode: 2022MNRAS.tmpL..51K; 2022arXiv220505346K Being directly observed in the Doppler shift and imaging data and indirectly as quasi-periodic pulsations in solar and stellar flares, slow magnetoacoustic waves offer an important seismological tool for probing many vital parameters of the coronal plasma. A recently understood active nature of the solar corona for magnetoacoustic waves, manifested through the phenomenon of wave-induced thermal misbalance, led to the identification of new natural mechanisms for the interpretation of observed properties of waves. A frequency-dependent damping of slow waves in various coronal plasma structures remains an open question, as traditional wave damping theories fail to match observations. We demonstrate that accounting for the back-reaction caused by thermal misbalance on the wave dynamics leads to a modification of the relationship between the damping time and oscillation period of standing slow waves, prescribed by the linear theory. The modified relationship is not of a power-law form and has the equilibrium plasma conditions and properties of the coronal heating/cooling processes as free parameters. It is shown to readily explain the observed scaling of the damping time with period of standing slow waves in hot coronal loops. Functional forms of the unknown coronal heating process, consistent with the observed frequency-dependent damping, are seismologically revealed. Title: High frequency waves in chromospheric spicules Authors: Bate, William; Nakariakov, Valery; Jafarzadeh, Shahin; Jess, David; Stangalini, Marco; Grant, Samuel; Keys, Peter; Christian, Damian; Keenan, Francis Bibcode: 2022cosp...44.2548B Altcode: Using high cadence observations from the Hydrogen-alpha Rapid Dynamics camera imaging system on the Dunn Solar Telescope, we present an investigation of the statistical properties of transverse oscillations in spicules captured above the solar limb. At five equally separated atmospheric heights, spanning approximately $4900-7500$~km, we have detected a total of $15{\,}959$ individual wave events, with a mean displacement amplitude of $151\pm 124$~km, a mean period of $54\pm 45$~s, and a mean projected velocity amplitude of $21\pm 13$~km{\,}s$^{-1}$. We find that both the displacement and velocity amplitudes increase with height above the solar limb, ranging from $132\pm 111$~km and $17.7\pm 10.6$~km{\,}s$^{-1}$ at $\approx4900$~km, and $168\pm 125$~km and $26.3\pm 14.1$~km{\,}s$^{-1}$ at $\approx7500$~km, respectively. Following the examination of neighboring oscillations in time and space, we find 45% of the waves to be upwardly propagating, 49% to be downwardly propagating, and 6% to be standing, with mean absolute phase velocities for the propagating waves on the order of $75-150$~km{\,}s$^{-1}$. While the energy flux of the waves propagating downwards does not appear to depend on height, we find the energy flux of the upwardly propagating waves decreases with atmospheric height at a rate of $-13{\,}200\pm6500$~W{\,}m$^{-2}$/Mm. As a result, this decrease in energy flux as the waves propagate upwards may provide significant thermal input into the local plasma. Title: Long-term evolution of decayless kink oscillations of solar coronal loops Authors: Zhong, Sihui; Nakariakov, Valery M.; Kolotkov, Dmitrii Y.; Anfinogentov, Sergey A. Bibcode: 2022MNRAS.513.1834Z Altcode: 2022MNRAS.tmp.1009Z Long-term evolution of instantaneous parameters of decayless kink oscillations of six solar coronal loops observed for longer than 2 h each is studied. The oscillations are analysed by processing sequences of 171 Å images obtained with the Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) in the time interval from 2020 December till 2021 June, with the motion magnification technique. It is established that decayless kink oscillations could exist for more than 30 or 40 oscillation cycles. Neither the loop brightness nor instantaneous parameters of the oscillations show a monotonic increase or decrease during the oscillation. The observed instantaneous oscillation periods and amplitudes are found to vary randomly in time, with distributions around the mean values that resemble Gaussian profiles. Mean values of the oscillation periods and amplitudes are consistent with previous observations of this phenomenon. A power-law dependence of the oscillation period on the displacement amplitude is found, with the power-law index of 0.41 and with the 95 per cent confidence interval of [0.39, 0.71]. In general, we established the lack of correlation between instantaneous oscillation parameters and loop brightness. One exception is an event with relatively strong anticorrelation of the amplitude and the loop's brightness, with the cross-correlation coefficient of about -0.81, but this effect requires a further study. Fourier power spectra of the envelopes of the time-evolving instantaneous amplitudes and periods are white noise, indicating that consecutive values of the instantaneous parameters are independent of each other. The results obtained provide an empirical ground for validating and comparing existing and future theoretical models of decayless kink oscillations of coronal loops. Title: Kink Oscillation of a Flux Rope During a Failed Solar Eruption Authors: Kumar, Pankaj; Nakariakov, Valery M.; Karpen, Judith T.; Richard DeVore, C.; Cho, Kyung-Suk Bibcode: 2022ApJ...932L...9K Altcode: 2022arXiv220503480K We report a decaying kink oscillation of a flux rope during a confined eruptive flare, observed off the solar limb by the Solar Dynamics Observatory's Atmospheric Imaging Assembly (AIA), which lacked a detectable white-light coronal mass ejection. The erupting flux rope underwent kinking, rotation, and apparent leg-leg interaction during the event. The oscillations were observed simultaneously in multiple AIA channels at 304, 171, and 193 Å, indicating that multithermal plasma was entrained in the rope. After reaching the overlying loops in the active region, the flux rope exhibited large-amplitude, decaying kink oscillations with an apparent initial amplitude of 30 Mm, a period of about 16 minutes, and a decay time of about 17 minutes. We interpret these oscillations as a fundamental standing kink mode of the flux rope. The oscillation polarization has a clear vertical component, while the departure of the detected waveform from a sinusoidal signal suggests that the oscillation could be circularly or elliptically polarized. The estimated kink speed is 1080 km s-1, corresponding to an Alfvén speed of about 760 km s-1. This speed, together with the estimated electron density in the rope from our differential emission measure analysis, n e ≍ (1.5-2.0) × 109 cm-3, yields a magnetic-field strength of about 15 G. To the best of our knowledge, decaying kink oscillations of a flux rope with nonhorizontal polarization during a confined eruptive flare have not been reported before. These oscillations provide unique opportunities for indirect measurements of the magnetic-field strength in low-coronal flux ropes during failed eruptions. Title: Slow Magnetoacoustic Oscillations in Stellar Coronal Loops Authors: Lim, Daye; Nakariakov, Valery M.; Moon, Yong-Jae Bibcode: 2022ApJ...931...63L Altcode: 2022arXiv220511750L Slow magnetoacoustic oscillations in stellar coronal loops with gravitational stratification are analyzed with a numerical solution of the boundary value problem for eigenvalues and eigenfunctions. In this study, we only focus on the resonant periods. The effects of the gravitational stratification, star mass, loop temperature, and loop length on the properties of slow magnetoacoustic oscillations are investigated. It is shown that the discrepancy between stratified and nonstratified loops is higher in density perturbations than in velocity perturbations. When the star has a larger mass, higher coronal temperature, and longer loop, the density perturbations in the stratified loop are significantly different from the harmonic functions. The periods in the stratified loop are slightly longer than in the nonstratified loop. The periods calculated in our model (14-644 minutes) are consistent with the periods of stellar quasi-periodic pulsations observed in both soft X-rays (2-70 minutes) and white lights (8-390 minutes). Title: High-frequency Waves in Chromospheric Spicules Authors: Bate, W.; Jess, D. B.; Nakariakov, V. M.; Grant, S. D. T.; Jafarzadeh, S.; Stangalini, M.; Keys, P. H.; Christian, D. J.; Keenan, F. P. Bibcode: 2022ApJ...930..129B Altcode: 2022arXiv220304997B Using high-cadence observations from the Hydrogen-alpha Rapid Dynamics camera imaging system on the Dunn Solar Telescope, we present an investigation of the statistical properties of transverse oscillations in spicules captured above the solar limb. At five equally separated atmospheric heights, spanning approximately 4900-7500 km, we have detected a total of 15,959 individual wave events, with a mean displacement amplitude of 151 ± 124 km, a mean period of 54 ± 45 s, and a mean projected velocity amplitude of 21 ± 13 km s-1. We find that both the displacement and velocity amplitudes increase with height above the solar limb, ranging from 132 ± 111 km and 17.7 ± 10.6 km s-1 at ≍4900 km, and 168 ± 125 km and 26.3 ± 14.1 km s-1 at ≍7500 km, respectively. Following the examination of neighboring oscillations in time and space, we find 45% of the waves to be upwardly propagating, 49% to be downwardly propagating, and 6% to be standing, with mean absolute phase velocities for the propagating waves on the order of 75-150 km s-1. While the energy flux of the waves propagating downwards does not appear to depend on height, we find the energy flux of the upwardly propagating waves decreases with atmospheric height at a rate of -13,200 ± 6500 W m-2/Mm. As a result, this decrease in energy flux as the waves propagate upwards may provide significant thermal input into the local plasma. Title: Editorial to the Topical Collection: Oscillatory Processes in Solar and Stellar Coronae Authors: Nakariakov, Valery M.; Banerjee, Dipankar; Li, Bo; Wang, Tongjiang; Zimovets, Ivan V.; Falanga, Maurizio Bibcode: 2022SSRv..218...13N Altcode: No abstract at ADS Title: The dynamics and observability of circularly polarized kink waves Authors: Magyar, N.; Duckenfield, T.; Van Doorsselaere, T.; Nakariakov, V. M. Bibcode: 2022A&A...659A..73M Altcode: 2021arXiv211214951M Context. Kink waves are routinely observed in coronal loops. Resonant absorption is a well-accepted mechanism that extracts energy from kink waves. Nonlinear kink waves are know to be affected by the Kelvin-Helmholtz instability. However, all previous numerical studies consider linearly polarized kink waves.
Aims: We study the properties of circularly polarized kink waves on straight plasma cylinders, for both standing and propagating waves, and we compare them to the properties of linearly polarized kink waves.
Methods: We used the code MPI-AMRVAC to solve the full 3D magnetohydrodynamic equations for a straight magnetic cylinder, excited by both standing and propagating circularly polarized kink (m = 1) modes.
Results: The damping due to resonant absorption is independent of the polarization state. The morphology or appearance of the induced resonant flow is different for the two polarizations; however, there are essentially no differences in the forward-modeled Doppler signals. For nonlinear oscillations, the growth rate of small scales is determined by the total energy of the oscillation rather than the perturbation amplitude. We discuss possible implications and seismological relevance.

Movies associated to Figs. 1, 2, and 5 are available at https://www.aanda.org Title: Hot Jets in the Solar Corona: Creating a Catalogue of Events Based on Multi-Instrumental Observations Authors: Kaltman, T. I.; Stupishin, A. G.; Anfinogentov, S. A.; Nakariakov, V. M.; Loukitcheva, M. A.; Shendrik, A. V. Bibcode: 2021Ge&Ae..61.1083K Altcode: We present a catalogue of solar coronal plasma jets with a temperature above 0.5 MK, which includes primary information about the events, parameters of the diagnosed jets, as well as related eruptive phenomena. The catalogue (https://solar.sao.ru/coronal-jets-catalog/) contains data obtained using the spaceborne EUV high-precision telescope SDO/AIA and ground-based radio telescopes and spectrometers, including RATAN-600, SRH and NoRH. For a number of events data on the reconstructed magnetic field is also presented. The purpose of the catalogue is to provide summary information on coronal jets for further statistical analysis, determination of characteristic parameters of jets, and for in-depth study of the individual events by all interested researchers. Title: Multiwavelength Quasi-periodic Pulsations in a Stellar Superflare Authors: Kolotkov, Dmitrii Y.; Nakariakov, Valery M.; Holt, Robin; Kuznetsov, Alexey A. Bibcode: 2021ApJ...923L..33K Altcode: 2021arXiv211207734K We present the first multiwavelength simultaneous detection of quasi-periodic pulsations (QPPs) in a superflare (more than a thousand times stronger than known solar flares) on a cool star, in soft X-rays (SXRs, with XMM-Newton) and white light (WL, with Kepler). It allowed for the first ever analysis of oscillatory processes in a stellar flare simultaneously in thermal and nonthermal emissions, conventionally considered to come from the corona and chromosphere of the star, respectively. The observed QPPs have periods 1.5 ± 0.15 hr (SXR) and 3 ± 0.6 hr (WL), and correlate well with each other. The unique relationship between the observed parameters of QPPs in SXR and WL allowed us to link them with oscillations of the electric current in the flare loop, which directly affect the dynamics of nonthermal electrons and indirectly (via ohmic heating) the thermal plasma. These findings could be considered in favor of the equivalent LCR contour model of a flare loop, at least in the extreme conditions of a stellar superflare. Title: The solar corona as an active medium for magnetoacoustic waves Authors: Kolotkov, D. Y.; Zavershinskii, D. I.; Nakariakov, V. M. Bibcode: 2021PPCF...63l4008K Altcode: 2021arXiv211102370K The presence and interplay of continuous cooling and heating processes maintaining the corona of the Sun at the observed one million K temperature were recently understood to have crucial effects on the dynamics and stability of magnetoacoustic waves. These essentially compressive waves perturb the coronal thermal equilibrium, leading to the phenomenon of a wave-induced thermal misbalance. Representing an additional natural mechanism for the exchange of energy between the plasma and the wave, thermal misbalance makes the corona an active medium for magnetoacoustic waves, so that the wave can not only lose but also gain energy from the coronal heating source (similarly to burning gases, lasers and masers). We review recent achievements in this newly emerging research field, focussing on the effects that slow-mode magnetoacoustic waves experience as a back-reaction of this perturbed coronal thermal equilibrium. The new effects include enhanced frequency-dependent damping or amplification of slow waves, and effective, not associated with the coronal plasma non-uniformity, dispersion. We also discuss the possibility to probe the unknown coronal heating function by observations of slow waves and linear theory of thermal instabilities. The manifold of the new properties that slow waves acquire from a thermodynamically active nature of the solar corona indicate a clear need for accounting for the effects of combined coronal heating/cooling processes not only for traditional problems of the formation and evolution of prominences and coronal rain, but also for an adequate modelling and interpretation of magnetohydrodynamic waves. Title: The high-energy Sun - probing the origins of particle acceleration on our nearest star Authors: Matthews, S. A.; Reid, H. A. S.; Baker, D.; Bloomfield, D. S.; Browning, P. K.; Calcines, A.; Del Zanna, G.; Erdelyi, R.; Fletcher, L.; Hannah, I. G.; Jeffrey, N.; Klein, L.; Krucker, S.; Kontar, E.; Long, D. M.; MacKinnon, A.; Mann, G.; Mathioudakis, M.; Milligan, R.; Nakariakov, V. M.; Pesce-Rollins, M.; Shih, A. Y.; Smith, D.; Veronig, A.; Vilmer, N. Bibcode: 2021ExA...tmp..135M Altcode: As a frequent and energetic particle accelerator, our Sun provides us with an excellent astrophysical laboratory for understanding the fundamental process of particle acceleration. The exploitation of radiative diagnostics from electrons has shown that acceleration operates on sub-second time scales in a complex magnetic environment, where direct electric fields, wave turbulence, and shock waves all must contribute, although precise details are severely lacking. Ions were assumed to be accelerated in a similar manner to electrons, but γ-ray imaging confirmed that emission sources are spatially separated from X-ray sources, suggesting distinctly different acceleration mechanisms. Current X-ray and γ-ray spectroscopy provides only a basic understanding of accelerated particle spectra and the total energy budgets are therefore poorly constrained. Additionally, the recent detection of relativistic ion signatures lasting many hours, without an electron counterpart, is an enigma. We propose a single platform to directly measure the physical conditions present in the energy release sites and the environment in which the particles propagate and deposit their energy. To address this fundamental issue, we set out a suite of dedicated instruments that will probe both electrons and ions simultaneously to observe; high (seconds) temporal resolution photon spectra (4 keV - 150 MeV) with simultaneous imaging (1 keV - 30 MeV), polarization measurements (5-1000 keV) and high spatial and temporal resolution imaging spectroscopy in the UV/EUV/SXR (soft X-ray) regimes. These instruments will observe the broad range of radiative signatures produced in the solar atmosphere by accelerated particles. Title: Motion Magnification in Solar Imaging Data Sequences in the Sub-pixel Regime Authors: Zhong, Sihui; Duckenfield, Timothy J.; Nakariakov, Valery M.; Anfinogentov, Sergey A. Bibcode: 2021SoPh..296..135Z Altcode: The capability of the motion-magnification technique for the detection of transverse oscillations, such as kink oscillations of solar coronal loops observed with an imaging telescope, in the sub-pixel regime is investigated. The technique is applied to artificial-image sequences imitating harmonic transverse displacements of the loop, observed in the optically thin regime. Motion magnification is found to work well on the analysis of sub-pixel, ≥0.01 pixel oscillations, and it is characterised by linear scaling between the magnified amplitude and input amplitude. Oscillations of loops with transverse density profiles of different steepness are considered. After magnification, the original transverse profiles are preserved sufficiently well. The motion-magnification performance is found to be robust in noisy data, for coloured noise with spectral indices ranging from 0 to 3, and additional Poisson noise with a signal-to-background-noise ratio down to unity. Our findings confirm the reliability of the motion-magnification technique for applications in magnetohydrodynamic seismology of the solar corona. Title: Kink Oscillations of Coronal Loops Authors: Nakariakov, V. M.; Anfinogentov, S. A.; Antolin, P.; Jain, R.; Kolotkov, D. Y.; Kupriyanova, E. G.; Li, D.; Magyar, N.; Nisticò, G.; Pascoe, D. J.; Srivastava, A. K.; Terradas, J.; Vasheghani Farahani, S.; Verth, G.; Yuan, D.; Zimovets, I. V. Bibcode: 2021SSRv..217...73N Altcode: 2021arXiv210911220N Kink oscillations of coronal loops, i.e., standing kink waves, is one of the most studied dynamic phenomena in the solar corona. The oscillations are excited by impulsive energy releases, such as low coronal eruptions. Typical periods of the oscillations are from a few to several minutes, and are found to increase linearly with the increase in the major radius of the oscillating loops. It clearly demonstrates that kink oscillations are natural modes of the loops, and can be described as standing fast magnetoacoustic waves with the wavelength determined by the length of the loop. Kink oscillations are observed in two different regimes. In the rapidly decaying regime, the apparent displacement amplitude reaches several minor radii of the loop. The damping time which is about several oscillation periods decreases with the increase in the oscillation amplitude, suggesting a nonlinear nature of the damping. In the decayless regime, the amplitudes are smaller than a minor radius, and the driver is still debated. The review summarises major findings obtained during the last decade, and covers both observational and theoretical results. Observational results include creation and analysis of comprehensive catalogues of the oscillation events, and detection of kink oscillations with imaging and spectral instruments in the EUV and microwave bands. Theoretical results include various approaches to modelling in terms of the magnetohydrodynamic wave theory. Properties of kink oscillations are found to depend on parameters of the oscillating loop, such as the magnetic twist, stratification, steady flows, temperature variations and so on, which make kink oscillations a natural probe of these parameters by the method of magnetohydrodynamic seismology. Title: Fast magnetoacoustic wave trains: from tadpoles to boomerangs Authors: Kolotkov, Dmitrii Y.; Nakariakov, Valery M.; Moss, Guy; Shellard, Paul Bibcode: 2021MNRAS.505.3505K Altcode: 2021arXiv210513696K Rapidly propagating fast magnetoacoustic wave trains guided by field-aligned plasma non-uniformities are confidently observed in the Sun's corona. Observations at large heights suggest that fast wave trains can travel long distances from the excitation locations. We study characteristic time signatures of fully developed, dispersive fast magnetoacoustic wave trains in field-aligned zero-β plasma slabs in the linear regime. Fast wave trains are excited by a spatially localized impulsive driver and propagate along the waveguide as prescribed by the waveguide-caused dispersion. In slabs with steeper transverse density profiles, developed wave trains are shown to consist of three distinct phases: a long-period quasi-periodic phase with the oscillation period shortening with time, a multiperiodic (peloton) phase in which distinctly different periods co-exist, and a short-lived periodic Airy phase. The appearance of these phases is attributed to a non-monotonic dependence of the fast wave group speed on the parallel wavenumber due to the waveguide dispersion, and is shown to be different for axisymmetric (sausage) and non-axisymmetric (kink) modes. In wavelet analysis, this corresponds to the transition from the previously known tadpole shape to a new boomerang shape of the wave train spectrum, with two well-pronounced arms at shorter and longer periods. We describe a specific previously published radio observation of a coronal fast wave train, highly suggestive of a change of the wavelet spectrum from a tadpole to a boomerang, broadly consistent with our modelling. The applicability of these boomerang-shaped fast wave trains for probing the transverse structuring of the waveguiding coronal plasma is discussed. Title: Diagnostics of plasma jets in the solar corona Authors: Anfinogentov, Sergey; Kaltman, Tatyana; Stupishin, Alexey; Nakariakov, Valery; Lukitcheva, Maria Bibcode: 2021STP.....7b...3A Altcode: The paper discusses the diagnostics of plasma jets in the solar corona with the use of data from modern space- and ground-based telescopes observing the Sun in the extreme ultraviolet (EUV) and micro- wave bands. We examine observational parameters of EUV and radio emission in events associated with plasma jets, depending on the mechanism of formation, initiation conditions, and evolution of the jets. The opportunities provided by the study of plasma jets, which relies on simultaneous observations in different bands, are highlighted. For a number of jets, we have measured their primary parameters; and in this paper we present preliminary results of statistical processing of the data obtained. Microwave observations of several specific events, made by ground-based instruments RATAN-600, SRH, and Nobeyama Radioheliograph, are considered in detail. The diagnostic capabilities of these instruments for studying coronal jets are shown. To analyze the three-dimensional structure of the coronal magnetic field, we have used SDO/HMI data, which allowed for the reconstruction of the field in the lower corona. The information gained is compared with the results of diagnostics of the magnetic field at the base of the corona according to RATAN-600 data. The purpose of the methods developed is to determine the physical mechanisms responsible for the generation, collimation, and dynamics of plasma jets in the solar atmosphere. Title: Spectroscopic Detection of Alfvénic Waves in the Chromosphere of Sunspot Regions Authors: Chae, Jongchul; Cho, Kyuhyoun; Nakariakov, Valery M.; Cho, Kyung-Suk; Kwon, Ryun-Young Bibcode: 2021ApJ...914L..16C Altcode: Transverse magnetohydrodynamic waves often called Alfvénic (or kink) waves have been often theoretically put forward to solve the outstanding problems of the solar corona like coronal heating, solar wind acceleration, and chemical abundance enhancement. Here we report the first spectroscopic detection of Alfvénic waves around a sunspot at chromospheric heights. By analyzing the spectra of the Hα line and Ca II 854.2 nm line, we determined line-of-sight velocity and temperature as functions of position and time. As a result, we identified transverse magnetohydrodynamic waves pervading the superpenumbral fibrils. These waves are characterized by the periods of 2.5 to 4.5 minutes, and the propagation direction parallel to the fibrils, the supersonic propagation speeds of 45 to 145 km s-1, and the close association with umbral oscillations and running penumbral waves in sunspots. Our results support the notion that the chromosphere around sunspots abounds with Alfvénic waves excited by the mode conversion of the upward-propagating slow magnetoacoustic waves. Title: Could Switchbacks Originate in the Lower Solar Atmosphere? II. Propagation of Switchbacks in the Solar Corona Authors: Magyar, Norbert; Utz, Dominik; Erdélyi, Robertus; Nakariakov, Valery M. Bibcode: 2021ApJ...914....8M Altcode: 2021arXiv210410126M The magnetic switchbacks observed recently by the Parker Solar Probe have raised the question about their nature and origin. One of the competing theories of their origin is the interchange reconnection in the solar corona. In this scenario, switchbacks are generated at the reconnection site between open and closed magnetic fields, and are either advected by an upflow or propagate as waves into the solar wind. In this paper we test the wave hypothesis, numerically modeling the propagation of a switchback, modeled as an embedded Alfvén wave packet of constant magnetic field magnitude, through the gravitationally stratified solar corona with different degrees of background magnetic field expansion. While switchbacks propagating in a uniform medium with no gravity are relatively stable, as reported previously, we find that gravitational stratification together with the expansion of the magnetic field act in multiple ways to deform the switchbacks. These include WKB effects, which depend on the degree of magnetic field expansion, and also finite-amplitude effects, such as the symmetry breaking between nonlinear advection and the Lorentz force. In a straight or radially expanding magnetic field the propagating switchbacks unfold into waves that cause minimal magnetic field deflections, while a super-radially expanding magnetic field aids in maintaining strong deflections. Other important effects are the mass uplift the propagating switchbacks induce and the reconnection and drainage of plasmoids contained within the switchbacks. In the Appendix, we examine a series of setups with different switchback configurations and parameters, which broaden the scope of our study. Title: Probing the solar corona magnetic field with sungrazing comets Authors: Nisticò, Giuseppe; Nakariakov, Valery M.; Duckenfield, Timothy; Druckmüller, Miloslav; Zimbardo, Gaetano Bibcode: 2021EGUGA..2314653N Altcode: Space telescopes of the SoHO, STEREO and SDO missions have occasionally acquired observations of comets, providing an interesting opportunity to investigate the structure and dynamics of the heliospheric plasma. Cometary plasma tails exhibit a wave-like motion, which is believed to be a response to the physical conditions of the local interplanetary medium. Furthermore, sungrazing comets diving in the solar atmosphere provide us with an unprecedented way to diagnose the coronal plasma at distances which are unaccessible from the current spacecraft. Here, we present observations of Comet Lovejoy C/2011 W3 from SDO/AIA, which was seen to cross the EUV solar corona in December 2011. The cometary ions produced by the sublimation of the comet nucleus were channelled along the magnetic field lines forming some filamented structures. Such structures appear to show small amplitude kink oscillations, which are used to determine the magnitude of the coronal magnetic field by coronal seismology. Title: Kinematic Oscillations of Post-CME Blobs Detected by K-Cor on 2017 September 10 Authors: Lee, Jae-Ok; Cho, Kyung-Suk; Nakariakov, Valery M.; Lee, Harim; Kim, Rok-Soon; Jang, Soojeong; Yang, Heesu; Kim, Sujin; Kim, Yeon-Han Bibcode: 2021JKAS...54...61L Altcode: We investigate 20 post-coronal mass ejection (CME) blobs formed in the post-CME current sheet (CS) that were observed by K-Cor on 2017 September 10. By visual inspection of the trajectories and projected speed variations of each blob, we find that all blobs except one show irregular "zigzag" trajectories resembling transverse oscillatory motions along the CS, and have at least one oscillatory pattern in their instantaneous radial speeds. Their oscillation periods are ranging from 30 to 91 s and their speed amplitudes from 128 to 902 km/s. Among 19 blobs, 10 blobs have experienced at least two cycles of radial speed oscillations with different speed amplitudes and periods, while 9 blobs undergo one oscillation cycle. To examine whether or not the apparent speed oscillations can be explained by vortex shedding, we estimate the quantitative parameter of vortex shedding, the Strouhal number, by using the observed lateral widths, linear speeds, and oscillation periods of the blobs. We then compare our estimates with theoretical and experimental results from MHD simulations and fluid dynamics experiments. We find that the observed Strouhal numbers range from 0.2 to 2.1, consistent with those (0.15-3.0) from fluid dynamics experiments of bluff spheres, while they are higher than those (0.15-0.25) from MHD simulations of cylindrical shapes. We thus find that blobs formed in a post-CME CS undergo kinematic oscillations caused by fluid dynamic vortex shedding. The vortex shedding is driven by the interaction of the outward-moving blob having a bluff spherical shape with the background plasma in the post-CME CS. Title: Could Switchbacks Originate in the Lower Solar Atmosphere? I. Formation Mechanisms of Switchbacks Authors: Magyar, Norbert; Utz, Dominik; Erdélyi, Robertus; Nakariakov, Valery M. Bibcode: 2021ApJ...911...75M Altcode: 2021arXiv210303726M The recent rediscovery of magnetic field switchbacks or deflections embedded in the solar wind flow by the Parker Solar Probe mission lead to a huge interest in the modeling of the formation mechanisms and origin of these switchbacks. Several scenarios for their generation were put forth, ranging from lower solar atmospheric origins by reconnection, to being a manifestation of turbulence in the solar wind, and so on. Here we study some potential formation mechanisms of magnetic switchbacks in the lower solar atmosphere, using three-dimensional magnetohydrodynamic (MHD) numerical simulations. The model is that of an intense flux tube in an open magnetic field region, aiming to represent a magnetic bright point opening up to an open coronal magnetic field structure, e.g., a coronal hole. The model is driven with different plasma flows in the photosphere, such as a fast up-shooting jet, as well as shearing flows generated by vortex motions or torsional oscillations. In all scenarios considered, we witness the formation of magnetic switchbacks in regions corresponding to chromospheric heights. Therefore, photospheric plasma flows around the foot-points of intense flux tubes appear to be suitable drivers for the formation of magnetic switchbacks in the lower solar atmosphere. Nevertheless, these switchbacks do not appear to be able to enter the coronal heights of the simulation in the present model. In conclusion, based on the presented simulations, switchbacks measured in the solar wind are unlikely to originate from photospheric or chromospheric dynamics. Title: On the Nature of Propagating Intensity Disturbances in Polar Plumes during the 2017 Total Solar Eclipse Authors: Cho, Kyung-Suk; Cho, Il-Hyun; Madjarska, Maria S.; Nakariakov, Valery M.; Yang, Heesu; Choi, Seonghwan; Lim, Eun-Kyung; Lee, Kyung-Sun; Seough, Jung-Jun; Lee, Jaeok; Kim, Yeon-Han Bibcode: 2021ApJ...909..202C Altcode: 2021arXiv210202085C The propagating intensity disturbances (PIDs) in plumes are still poorly understood, and their identity (magnetoacoustic waves or flows) remains an open question. We investigate PIDs in five plumes located in the northern polar coronal hole observed during the 2017 total solar eclipse. Three plumes are associated with coronal bright points, jets, and macrospicules at their base (active plumes), and the other two plumes are not (quiet plumes). The electron temperature at the base of the plumes is obtained from the filter ratio of images taken with the X-ray Telescope on board Hinode and the passband ratio around 400 nm from an eclipse instrument, the Diagnostic Coronagraph Experiment. The phase speed (vr), frequency (ω), and wavenumber (k) of the PIDs in the plumes are obtained by applying a Fourier transformation to the spacetime (r - t plane) plots in images taken with the Atmospheric Imaging Assembly (AIA) in three different wavelength channels (171, 193, and 211 Å). We found that the PIDs in the higher-temperature AIA channels, 193 and 211 Å, are faster than that of the cooler AIA 171 Å channel. This tendency is more significant for the active plumes than the quiet ones. The observed speed ratio (∼1.3) between the AIA 171 and 193 Å channels is similar to the theoretical value (1.25) of a slow magnetoacoustic wave. Our results support the idea that PIDs in plumes represent a superposition of slow magnetoacoustic waves and plasma outflows that consist of dense cool flows and hot coronal jets. Title: The effect of the magnetic field on the damping of slow waves in the solar corona Authors: Duckenfield, T. J.; Kolotkov, D. Y.; Nakariakov, V. M. Bibcode: 2021A&A...646A.155D Altcode: 2020arXiv201110437D Context. Slow magnetoacoustic waves are routinely observed in astrophysical plasma systems such as the solar corona, and they are usually seen to damp rapidly. As a slow wave propagates through a plasma, it modifies the equilibrium quantities of density, temperature, and the magnetic field. In the corona and other plasma systems, the thermal equilibrium is comprised of a balance between continuous heating and cooling processes, the magnitudes of which vary with density, temperature and the magnetic field. Thus the wave may induce a misbalance between these competing processes. Its back reaction on the wave has been shown to lead to dispersion, and amplification or damping, of the wave.
Aims: This effect of heating and cooling misbalance has previously been studied in the infinite magnetic field approximation in a plasma whose thermal equilibrium is comprised of optically thin radiative losses and field-aligned thermal conduction, balanced by an (unspecified) heating process. In this work we extend this analysis by considering a non-zero β plasma. The importance of the effect of the magnetic field in the rapid damping of slow waves in the solar corona is evaluated and compared to the effects of thermal conduction.
Methods: A linear perturbation under the thin flux tube approximation is considered, and a dispersion relation describing the slow magnetoacoustic modes is found. The dispersion relation's limits of strong non-adiabaticity and weak non-adiabaticity are studied. The characteristic timescales were calculated for plasma systems with a range of typical coronal densities, temperatures, and magnetic field strengths.
Results: The number of timescales characterising the effect of the misbalance is found to remain at two, as with the infinite magnetic field case. In the non-zero β case, these two timescales correspond to the partial derivatives of the combined heating and cooling function with respect to constant gas pressure and with respect to constant magnetic pressure. The predicted damping times of slow waves from thermal misbalance in the solar corona are found to be of the order of 10-100 min, coinciding with the wave periods and damping times observed. Moreover, the slow wave damping by thermal misbalance is found to be comparable to the damping by field-aligned thermal conduction. The change in damping with plasma-β is complex and depends on the coronal heating function's dependence on the magnetic field in particular. Nonetheless, we show that in the infinite field limit, the wave dynamics is insensitive to the dependence of the heating function on the magnetic field, and this approximation is found to be valid in the corona so long as the magnetic field strength is greater than approximately 10 G for quiescent loops and plumes, and 100 G for hot and dense loops.
Conclusions: A thermal misbalance may damp slow magnetoacoustic waves rapidly in much of the corona, and its inclusion in our understanding of slow mode damping may resolve discrepancies between the observations and theory relying on compressive viscosity and thermal conduction alone. Title: Three-dimensional Simulations of the Inhomogeneous Low Solar Wind Authors: Magyar, N.; Nakariakov, V. M. Bibcode: 2021ApJ...907...55M Altcode: 2020arXiv201200811M In the near future, the Parker Solar Probe will put theories about the dynamics and nature of the transition between the solar corona and the solar wind to stringent tests. The most popular mechanism aimed to explain the dynamics of the nascent solar wind, including its heating and acceleration, is magnetohydrodynamic (MHD) turbulence. Most of the previous models focused on nonlinear cascade induced by interactions of outgoing Alfvén waves and their reflections, ignoring effects that might be related to perpendicular structuring of the solar coronal plasma, despite overwhelming evidence for it. In this paper, for the first time, we analyze through 3D MHD numerical simulations the dynamics of the perpendicularly structured solar corona and solar wind, from the low corona to 15 R⊙. We find that background structuring has a strong effect on the evolution of MHD turbulence, on much faster timescales than in the perpendicularly homogeneous case. On timescales shorter than nonlinear times, linear effects related to phase mixing result in a 1/f perpendicular energy spectrum. As the turbulent cascade develops, we observe a perpendicular (parallel) energy spectrum with a power-law index of -3/2 or -5/3 (-2), a steeper perpendicular magnetic field than velocity spectrum, and a strong build-up of negative residual energy. We conclude that the turbulence is most probably generated by the self-cascade of the driven transverse kink waves, referred to previously as "uniturbulence," which might represent the dominant nonlinear energy cascade channel in the pristine solar wind. Title: Solar Bayesian Analysis Toolkit—A New Markov Chain Monte Carlo IDL Code for Bayesian Parameter Inference Authors: Anfinogentov, Sergey A.; Nakariakov, Valery M.; Pascoe, David J.; Goddard, Christopher R. Bibcode: 2021ApJS..252...11A Altcode: 2020arXiv200505365A We present the Solar Bayesian Analysis Toolkit (SoBAT), which is a new easy to use tool for Bayesian analysis of observational data, including parameter inference and model comparison. SoBAT is aimed (but not limited) to be used for the analysis of solar observational data. We describe a new IDL code designed to facilitate the comparison of a user-supplied model with data. Bayesian inference allows prior information to be taken into account. The use of Markov Chain Monte Carlo sampling allows efficient exploration of large parameter spaces and provides reliable estimation of model parameters and their uncertainties. The Bayesian evidence for different models can be used for quantitative comparison. The code is tested to demonstrate its ability to accurately recover a variety of parameter probability distributions. Its application to practical problems is demonstrated using studies of the structure and oscillation of coronal loops. Title: Effect of Higher Radial Harmonics in Sausage Oscillations in Coronal Loops Authors: Lim, D.; Nakariakov, V. M.; Moon, Y. J.; Yu, D. J.; Cho, I. H. Bibcode: 2020AGUFMSH0290006L Altcode: Impulsively excited sausage oscillations of a plasma cylinder with a smooth radial profile of Alfvén speed are analyzed with a numerical solution of the initial-value problem for a partial differential equation of the Klein-Gordon type, describing linear magnetoacoustic oscillations with a fixed axial wavelength and an azimuthal mode number. The range of analyzed ratios of Alfvén speeds outside and inside the cylinder is from 2 to 10. Both trapped and leaky regimes of the oscillations are considered. It is shown that even in the long-wavelength limit, i.e., for axial wavenumbers much smaller than the cutoff values, damping times of higher radial sausage harmonics could be significantly greater than the oscillation periods, i.e., several oscillation cycles could be present in the signal. The quality factors decrease with decreasing ratios of Alfvén speeds outside and inside the cylinder. Oscillation periods of the second and third radial harmonics remain practically independent of the axial wavelength even when the wavelength is shorter than the radius of the cylinder. The ratios of oscillation periods of fundamental and higher radial and axial harmonics are found to be significantly different, up to a factor of two in the long-wavelength limit. It is concluded that higher radial harmonics could be responsible for the departure of observed sausage oscillation signals from a harmonic shape, especially during the first several cycles of the oscillation. Even in the absence of spatially resolved data, higher axial and radial harmonics can be distinguished from each other by the period ratios.

This work was supported by Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (2018-0-01422, Study on analysis and prediction technique of solar flares). Title: Seismological constraints on the solar coronal heating function Authors: Kolotkov, D. Y.; Duckenfield, T. J.; Nakariakov, V. M. Bibcode: 2020A&A...644A..33K Altcode: 2020arXiv201003364K
Aims: The hot solar corona exists because of the balance between radiative and conductive cooling and some counteracting heating mechanism that remains one of the major puzzles in solar physics.
Methods: The coronal thermal equilibrium is perturbed by magnetoacoustic waves, which are abundantly present in the corona, causing a misbalance between the heating and cooling rates. As a consequence of this misbalance, the wave experiences a back-reaction, either losing or gaining energy from the energy supply that heats the plasma, at timescales comparable to the wave period.
Results: In particular, the plasma can be subject to wave-induced instability or over-stability, depending on the specific choice of the coronal heating function. In the unstable case, the coronal thermal equilibrium would be violently destroyed, which does not allow for the existence of long-lived plasma structures typical for the corona. Based on this, we constrained the coronal heating function using observations of slow magnetoacoustic waves in various coronal plasma structures. Title: Accelerating and Supersonic Density Disturbances in Solar Polar Plumes Authors: Cho, I. H.; Moon, Y. J.; Nakariakov, V. M.; Lee, J. Y.; Yu, D. J.; Cho, K. S. F.; Yurchyshyn, V.; Lee, H. Bibcode: 2020AGUFMSH0290003C Altcode: Propagating intensity disturbances in solar coronal holes are often considered as wave propagations or mass flows. By applying the differential emission measure technique for the extreme ultraviolet images taken by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory, we analyze the propagation speed of density disturbances of plume structure in an off-limb coronal hole for a given temperature. We construct the map of cross-correlation between density profile for a given height and the profile at the height of 50 Mm. The evolution of density disturbances is well fitted by the second-order polynomial. The acceleration is calculated to be 36 m s-2. The initial speed is 134 km s-1 which is comparable with the sound speed given by the DEM-weighted temperature. Hence, density disturbances are accelerating and supersonic at around the base of the solar corona. The excess speed relative to the sound speed is ∼ 30 km s-1 at the height of 1.23 solar radii, which is consistent with the Doppler speeds and Doppler dimming speeds observed by different instruments. The extrapolated sonic distance of the excess speed is ∼ 2.16 solar radii which is consistent with those of solar winds. The lower limit of the mass flux corresponds to 7% of the global solar wind. Hence, we interpret that the observed density disturbances are slow magnetoacoustic waves propagating in subsonic and accelerating solar winds. Title: The Solar Orbiter magnetometer Authors: Horbury, T. S.; O'Brien, H.; Carrasco Blazquez, I.; Bendyk, M.; Brown, P.; Hudson, R.; Evans, V.; Oddy, T. M.; Carr, C. M.; Beek, T. J.; Cupido, E.; Bhattacharya, S.; Dominguez, J. -A.; Matthews, L.; Myklebust, V. R.; Whiteside, B.; Bale, S. D.; Baumjohann, W.; Burgess, D.; Carbone, V.; Cargill, P.; Eastwood, J.; Erdös, G.; Fletcher, L.; Forsyth, R.; Giacalone, J.; Glassmeier, K. -H.; Goldstein, M. L.; Hoeksema, T.; Lockwood, M.; Magnes, W.; Maksimovic, M.; Marsch, E.; Matthaeus, W. H.; Murphy, N.; Nakariakov, V. M.; Owen, C. J.; Owens, M.; Rodriguez-Pacheco, J.; Richter, I.; Riley, P.; Russell, C. T.; Schwartz, S.; Vainio, R.; Velli, M.; Vennerstrom, S.; Walsh, R.; Wimmer-Schweingruber, R. F.; Zank, G.; Müller, D.; Zouganelis, I.; Walsh, A. P. Bibcode: 2020A&A...642A...9H Altcode: The magnetometer instrument on the Solar Orbiter mission is designed to measure the magnetic field local to the spacecraft continuously for the entire mission duration. The need to characterise not only the background magnetic field but also its variations on scales from far above to well below the proton gyroscale result in challenging requirements on stability, precision, and noise, as well as magnetic and operational limitations on both the spacecraft and other instruments. The challenging vibration and thermal environment has led to significant development of the mechanical sensor design. The overall instrument design, performance, data products, and operational strategy are described. Title: Accelerating and Supersonic Density Fluctuations in Coronal Hole Plumes: Signature of Nascent Solar Winds Authors: Cho, Il-Hyun; Nakariakov, Valery M.; Moon, Yong-Jae; Lee, Jin-Yi; Yu, Dae Jung; Cho, Kyung-Suk; Yurchyshyn, Vasyl; Lee, Harim Bibcode: 2020ApJ...900L..19C Altcode: 2020arXiv200807848C Slow magnetoacoustic waves in a static background provide a seismological tool to probe the solar atmosphere in the analytic frame. By analyzing the spatiotemporal variation of the electron number density of plume structure in coronal holes above the limb for a given temperature, we find that the density perturbations accelerate with supersonic speeds in the distance range from 1.02 to 1.23 solar radii. We interpret them as slow magnetoacoustic waves propagating at about the sound speed with accelerating subsonic flows. The average sonic height of the subsonic flows is calculated to be 1.27 solar radii. The mass flux of the subsonic flows is estimated to be 44.1% relative to the global solar wind. Hence, the subsonic flow is likely to be the nascent solar wind. In other words, the evolution of the nascent solar wind in plumes at the low corona is quantified for the first time from imaging observations. Based on the interpretation, propagating density perturbations present in plumes could be used as a seismological probe of the gradually accelerating solar wind. Title: Magnetohydrodynamic Waves in the Solar Corona Authors: Nakariakov, Valery M.; Kolotkov, Dmitrii Y. Bibcode: 2020ARA&A..58..441N Altcode: The corona of the Sun is a unique environment in which magnetohydrodynamic (MHD) waves, one of the fundamental processes of plasma astrophysics, are open to a direct study. There is striking progress in both observational and theoretical research of MHD wave processes in the corona, with the main recent achievements summarized as follows: Both periods and wavelengths of the principal MHD modes of coronal plasma structures, such as kink, slow and sausage modes, are confidently resolved. Scalings of various parameters of detected waves and waveguiding plasma structures allow for the validation of theoretical models. In particular, kink oscillation period scales linearly with the length of the oscillating coronal loop, clearly indicating that they are eigenmodes of the loop. Damping of decaying kink and standing slow oscillations depends on the oscillation amplitudes, demonstrating the importance of nonlinear damping. The dominant excitation mechanism for decaying kink oscillations is associated with magnetized plasma eruptions. Propagating slow waves are caused by the leakage of chromospheric oscillations. Fast wave trains could be formed by waveguide dispersion. The knowledge gained in the study of coronal MHD waves provides ground for seismological probing of coronal plasma parameters, such as the Alfvén speed, the magnetic field and its topology, stratification, temperature, fine structuring, polytropic index, and transport coefficients. Title: Excitation of Negative Energy Surface Magnetohydrodynamic Waves in an Incompressible Cylindrical Plasma Authors: Yu, D. J.; Nakariakov, V. M. Bibcode: 2020ApJ...896...21Y Altcode: 2020arXiv200413552Y Negative energy wave (NEW) phenomena may appear in shear flows in the presence of a wave decay mechanism and external energy supply. We study the appearance of negative energy surface waves in a plasma cylinder in the incompressible limit. The cylinder is surrounded by an axial magnetic field and by a plasma of different density. Considering flow inside and viscosity outside the flux tube, we derive dispersion relations and obtain analytical solutions for the phase speed and growth rate (increment) of the waves. It is found that the critical speed shear for the occurrence of the dissipative instability associated with NEWs and the threshold of Kelvin-Helmholtz instability (KHI) depend on the axial wavelength. The critical shear for the appearance of sausage NEW is lowest for the longest axial wavelengths, while for kink waves the minimum value of the critical shear is reached for the axial wavelength comparable to the diameter of the cylinder. The range between the critical speed of the dissipative instability and the KHI threshold is shown to depend on the difference of the Alfvén speeds inside and outside of the cylinder. For all axial wavenumbers, NEW appears for the shear flow speeds lower than the KHI threshold. It is easier to excite NEW in an underdense cylinder than in an overdense one. The negative energy surface waves can be effectively generated for an azimuthal number m = 0 with a large axial wavenumber and for higher modes (m > 0) with a small axial wavenumber. Title: Standing Kink Waves in Sigmoid Solar Coronal Loops: Implications for Coronal Seismology Authors: Magyar, N.; Nakariakov, V. M. Bibcode: 2020ApJ...894L..23M Altcode: 2020arXiv200414083M Using full three-dimensional magnetohydrodynamic numerical simulations, we study the effects of magnetic field sigmoidity or helicity on the properties of the fundamental kink oscillation of solar coronal loops. Our model consists of a single denser coronal loop, embedded in a plasma with dipolar force-free magnetic field with a constant α-parameter. For the loop with no sigmoidity, we find that the numerically determined oscillation period of the fundamental kink mode matches the theoretical period calculated using WKB theory. In contrast, with increasing sigmoidity of the loop, the actual period is increasingly smaller than the one estimated by WKB theory. Translated through coronal seismology, increasing sigmoidity results in magnetic field estimates that are increasingly shifting toward higher values, and even surpassing the average value for the highest α value considered. Nevertheless, the estimated range of the coronal magnetic field value lies within the minimal/maximal limits, proving the robustness coronal seismology. We propose that the discrepancy in the estimations of the absolute value of the force-free magnetic field could be exploited seismologically to determine the free energy of coronal loops, if averages of the internal magnetic field and density can be reliably estimated by other methods. Title: Quasi-Periodic Pulsations in Solar and Stellar Flares. Review Authors: Kupriyanova, Elena; Kolotkov, Dmitrii; Nakariakov, Valery; Kaufman, Anastasiia Bibcode: 2020STP.....6a...3K Altcode: 2020SZF.....6a...3K This paper provides an overview of the state-of-the-art studies of oscillatory processes in solar and stellar flares, based on modern observational data from ground-based and space-borne instruments with high temporal, spatial, and spectral resolution in different bands of the electromagnetic spectrum. We examine the mecha-nisms that generate flare emission and its quasi-periodic modulation. We discuss similarities and differences between solar and stellar flares, and address associated problems of superflares on the Sun and space weather. Quasi-periodic pulsations (QPPs) of flare emission are shown to be an effective tool for diagnosing both the flare processes themselves and the parameters of flaring plasmas and accelerated particles. We consider types of QPPs, their statistical properties, and methods of analysis, taking into account the non-stationarity of the QPP' parameters. We review the proposed mechanisms of QPPs and summarize open questions. Title: Higher Radial Harmonics of Sausage Oscillations in Coronal Loops Authors: Lim, Daye; Nakariakov, Valery M.; Yu, Dae Jung; Cho, Il-Hyun; Moon, Yong-Jae Bibcode: 2020ApJ...893...62L Altcode: Impulsively excited sausage oscillations of a plasma cylinder with a smooth radial profile of Alfvén speed are analyzed with a numerical solution of the initial-value problem for a partial differential equation of the Klein-Gordon type, describing linear magnetoacoustic oscillations with a fixed axial wavelength and an azimuthal mode number. The range of analyzed ratios of Alfvén speeds outside and inside the cylinder is from 2 to 10. Both trapped and leaky regimes of the oscillations are considered. It is shown that even in the long-wavelength limit, I.e., for axial wavenumbers much smaller than the cutoff values, damping times of higher radial sausage harmonics could be significantly greater than the oscillation periods, I.e., several oscillation cycles could be present in the signal. The quality factors decrease with decfreasing ratios of Alfvén speeds outside and inside the cylinder. Oscillation periods of the second and third radial harmonics remain practically independent of the axial wavelength even when the wavelength is shorter than the radius of the cylinder. The ratios of oscillation periods of fundamental and higher radial and axial harmonics are found to be significantly different, up to a factor of two in the long-wavelength limit. It is concluded that higher radial harmonics could be responsible for the departure of observed sausage oscillation signals from a harmonic shape, especially during the first several cycles of the oscillation. Even in the absence of spatially resolved data, higher axial and radial harmonics can be distinguished from each other by the period ratios. Title: Magnetic Connectivity between the Light Bridge and Penumbra in a Sunspot Authors: Feng, Song; Miao, Yuhu; Yuan, Ding; Qu, Zhongquan; Nakariakov, Valery M. Bibcode: 2020ApJ...893L...2F Altcode: 2020arXiv200303976F A light bridge is a prominent structure commonly observed within a sunspot. Its presence usually triggers a wealth of dynamics in a sunspot and has a lasting impact on sunspot evolution. However, the fundamental structure of light bridges is still not well understood. In this study, we used the high-resolution spectropolarimetry data obtained by the Solar Optical Telescope on board the Hinode satellite to analyze the magnetic and thermal structure of a light bridge at AR 12838. We also combined the high-cadence $1700\,\mathring{\rm A} $ channel data provided by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to study the dynamics on this bridge. We found a pair of blue and red Doppler shift patches at two ends of this bridge; this pattern appears to be the convective motion directed by the horizontal component of the magnetic field aligned with the spine of the bridge. Paired upward and downward motions imply that the light bridge could have a two-legged or undulating magnetic field. Significant 4 minute oscillations in the emission intensity of the $1700\,\mathring{\rm A} $ bandpass were detected at two ends, which overlapped the paired blue- and redshift patches. The oscillatory signals at the light bridge and the penumbra were highly correlated with each other. Although they are separated in space at the photosphere, the periodicity seems to have a common origin from underneath the sunspot. Therefore, we infer that the light bridge and penumbra could share a common magnetic source and become fragmented at the photosphere by magnetoconvection. Title: Editorial: Magnetohydrodynamic Waves in the Solar Atmosphere: Heating and Seismology Authors: Van Doorsselaere, Tom; Nakariakov, Valery M.; Li, Bo; Antolin, Patrick Bibcode: 2020FrASS...6...79V Altcode: No abstract at ADS Title: Excitation of decay-less transverse oscillations of coronal loops by random motions Authors: Afanasyev, A. N.; Van Doorsselaere, T.; Nakariakov, V. M. Bibcode: 2020A&A...633L...8A Altcode: 2019arXiv191207980A Context. The relatively large-amplitude decaying regime of transverse oscillations of coronal loops has been known for two decades and has been interpreted in terms of magnetohydrodynamic kink modes of cylindrical plasma waveguides. In this regime oscillations decay in several cycles. Recent observational analysis has revealed so-called decay-less, small-amplitude oscillations, in which a multi-harmonic structure has been detected. Several models have been proposed to explain these oscillations. In particular, decay-less oscillations have been described in terms of standing kink waves driven with continuous mono-periodic motions of loop footpoints, in terms of a simple oscillator model of forced oscillations due to harmonic external force, and as a self-oscillatory process due to the interaction of a loop with quasi-steady flows. However, an alternative mechanism is needed to explain the simultaneous excitation of several longitudinal harmonics of the oscillation.
Aims: We study the mechanism of random excitation of decay-less transverse oscillations of coronal loops.
Methods: With a spatially one-dimensional and time-dependent analytical model taking into account effects of the wave damping and kink speed variation along the loop, we considered transverse loop oscillations driven by random motions of footpoints. The footpoint motions were modelled by broad-band coloured noise.
Results: We found the excitation of loop eigenmodes and analysed their frequency ratios as well as the spatial structure of the oscillations along the loop. The obtained results successfully reproduce the observed properties of decay-less oscillations. In particular, excitation of eigenmodes of a loop as a resonator can explain the observed quasi-monochromatic nature of decay-less oscillations and the generation of multiple harmonics detected recently.
Conclusions: We propose a mechanism that can interpret decay-less transverse oscillations of coronal loops in terms of kink waves randomly driven at the loop footpoints. Title: Quasi-periodic Pulsations of Gamma-Ray Emissions from a Solar Flare on 2017 September 6 Authors: Li, D.; Kolotkov, D. Y.; Nakariakov, V. M.; Lu, L.; Ning, Z. J. Bibcode: 2020ApJ...888...53L Altcode: 2019arXiv191201145L We investigate quasi-periodic pulsations (QPPs) of high-energy nonthermal emissions from an X9.3 flare (SOL2017-Sep-06T11:53), the most powerful flare since the beginning of solar cycle 24. The QPPs are identified as a series of regular and repeating peaks in the light curves in the γ- and hard X-ray (HXR) channels recorded by the Konus-Wind, as well as the radio and microwave fluxes measured by the CALLISTO radio spectrograph during the impulsive phase. The periods are determined from the global wavelet and Fourier power spectra as 24-30 s in the HXR and microwave channels, which are associated with nonthermal electrons, and ∼20 s in the γ-ray band related to nonthermal ions. Both nonthermal electrons and ions may be accelerated by repetitive magnetic reconnection during the impulsive phase. However, we could not rule out other mechanisms, such as magnetohydrodynamic oscillation in a sausage mode. The QPP detected in this study is useful for understanding the particle acceleration and dynamic process in solar flares and also bridging the gap between stellar and solar flares because the energy realm of the X9.3 solar flare is almost comparable to a typical stellar flare. Title: Observational signatures of the third harmonic in a decaying kink oscillation of a coronal loop Authors: Duckenfield, T. J.; Goddard, C. R.; Pascoe, D. J.; Nakariakov, V. M. Bibcode: 2019A&A...632A..64D Altcode:
Aims: An observation of a coronal loop standing kink mode is analysed to search for higher harmonics, aiming to reveal the relation between different harmonics' quality factors.
Methods: Observations of a coronal loop were taken by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). The loop's axis was tracked at many spatial positions along the loop to generate time series data.
Results: The distribution of spectral power of the oscillatory transverse displacements throughout the loop reveals the presence of two harmonics, a fundamental at a period of ∼8 min and its third harmonic at ∼2.6 min. The node of the third harmonic is seen at approximately a third of the way along the length of the loop, and cross correlations between the oscillatory motion on opposing sides of the node show a change in phase behaviour. The ratio of periods P1/3P3 was found to be ∼0.87, indicating a non-uniform distribution of kink speed through the loop. The quality factor for the fundamental mode of oscillation was measured to be ∼3.4. The quality factor of the third harmonic was measured for each spatial location and, where data was reliable, yielded a value of ∼3.6. For all locations, the quality factors for the two harmonics were found to agree within error as expected from 1d resonant absorption theory. This is the first time a measurement of the signal quality for a higher harmonic of a kink oscillation has been reported with spatially resolved data. Title: A Blueprint of State-of-the-art Techniques for Detecting Quasi-periodic Pulsations in Solar and Stellar Flares Authors: Broomhall, Anne-Marie; Davenport, James R. A.; Hayes, Laura A.; Inglis, Andrew R.; Kolotkov, Dmitrii Y.; McLaughlin, James A.; Mehta, Tishtrya; Nakariakov, Valery M.; Notsu, Yuta; Pascoe, David J.; Pugh, Chloe E.; Van Doorsselaere, Tom Bibcode: 2019ApJS..244...44B Altcode: 2019arXiv191008458B Quasi-periodic pulsations (QPPs) appear to be a common feature observed in the light curves of both solar and stellar flares. However, their quasi-periodic nature, along with the fact that they can be small in amplitude and short-lived, makes QPPs difficult to unequivocally detect. In this paper, we test the strengths and limitations of state-of-the-art methods for detecting QPPs using a series of hare-and-hounds exercises. The hare simulated a set of flares, both with and without QPPs of a variety of forms, while the hounds attempted to detect QPPs in blind tests. We use the results of these exercises to create a blueprint for anyone who wishes to detect QPPs in real solar and stellar data. We present eight clear recommendations to be kept in mind for future QPP detections, with the plethora of solar and stellar flare data from new and future satellites. These recommendations address the key pitfalls in QPP detection, including detrending, trimming data, accounting for colored noise, detecting stationary-period QPPs, detecting QPPs with nonstationary periods, and ensuring that detections are robust and false detections are minimized. We find that QPPs can be detected reliably and robustly by a variety of methods, which are clearly identified and described, if the appropriate care and due diligence are taken. Title: A New Type of Jet in a Polar Limb of the Solar Coronal Hole Authors: Cho, Il-Hyun; Moon, Yong-Jae; Cho, Kyung-Suk; Nakariakov, Valery M.; Lee, Jin-Yi; Kim, Yeon-Han Bibcode: 2019ApJ...884L..38C Altcode: 2019arXiv191009737C A new type of chromospheric jet in a polar limb of a coronal hole is discovered in the Ca II filtergram of the Solar Optical Telescope on board the Hinode. We identify 30 jets in a filtered Ca II movie with a duration of 53 minutes. The average speed at their maximum heights is found to be 132 ± 44 km s-1 ranging from 57 to 264 km s-1 along the propagation direction. The average lifetime is 20 ± 6 ranging from 11 to 36 s. The speed and lifetime of the jets are located at end-tails of those parameters determined for type II spicules, hence implying a new type of jets. To confirm whether these jets are different from conventional spicules, we construct a time-height image averaged over a horizontal region of 1″, and calculate lagged cross-correlations of intensity profiles at each height with the intensity at 2 Mm. From this, we obtain a cross-correlation map as a function of lag and height. We find that the correlation curve as a function of lag time is well fitted into three different Gaussian functions whose standard deviations of the lag time are 193, 42, and 17 s. The corresponding propagation speeds are calculated to be 9 km s-1, 67 km s-1, and 121 km s-1, respectively. The kinematic properties of the former two components seem to correspond to the 3-minute oscillations and type II spicules, while the latter component to the jets is addressed in this study. Title: Magnetohydrodynamic Seismology of Quiet Solar Active Regions Authors: Anfinogentov, Sergey A.; Nakariakov, V. M. Bibcode: 2019ApJ...884L..40A Altcode: 2019arXiv191003809A The ubiquity of recently discovered low-amplitude decayless kink oscillations of plasma loops allows for the seismological probing of the corona on a regular basis. In particular, in contrast to traditionally applied seismology that is based on the large-amplitude decaying kink oscillations excited by flares and eruptions, decayless oscillations can potentially provide the diagnostics necessary for their forecasting. We analyzed decayless kink oscillations in several distinct loops belonging to active region NOAA 12107 on 2010 July 10 during its quiet time period, when it was observed on the west limb in extreme ultraviolet by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The oscillation periods were estimated with the use of the motion magnification technique. The lengths of the oscillating loops were determined within the assumption of its semicircular shape by measuring the position of their footpoints. The density contrast in the loops was estimated from the observed intensity contrast accounting for the unknown spatial scale of the background plasma. The combination of those measurements allows us to determine the distribution of kink and Alfvén speeds in the active region. Thus, we demonstrate the possibility of obtaining seismological information about coronal active regions during the quiet periods of time. Title: DTCWT based motion magnification v0.5.0 Authors: Anfinogentov, Sergey; Nakariakov, Valery; Kosak, Katie Bibcode: 2019zndo...3368774A Altcode: This is the first release. Title: Formation of quasi-periodic slow magnetoacoustic wave trains by the heating/cooling misbalance Authors: Zavershinskii, D. I.; Kolotkov, D. Y.; Nakariakov, V. M.; Molevich, N. E.; Ryashchikov, D. S. Bibcode: 2019PhPl...26h2113Z Altcode: 2019arXiv190708168Z Slow magnetoacoustic waves are omnipresent in both natural and laboratory plasma systems. The wave-induced misbalance between plasma cooling and heating processes causes the amplification or attenuation, and also dispersion, of slow magnetoacoustic waves. The wave dispersion could be attributed to the presence of characteristic time scales in the system, connected with the plasma heating or cooling due to the competition of the heating and cooling processes in the vicinity of thermal equilibrium. We analyzed linear slow magnetoacoustic waves in a plasma in thermal equilibrium formed by a balance of optically thin radiative losses, field-align thermal conduction, and an unspecified heating process. The dispersion is manifested by the dependence of the effective adiabatic index of the wave on the wave frequency, making the phase and group speeds frequency-dependent. The mutual effect of the wave amplification and dispersion is shown to result in the occurrence of an oscillatory pattern in an initially broadband slow wave, with the characteristic period determined by the thermal misbalance time scales, i.e., by the derivatives of the combined radiation loss and heating function with respect to the density and temperature, evaluated at the equilibrium. This effect is illustrated by estimating the characteristic period of the oscillatory pattern, appearing because of thermal misbalance in the plasma of the solar corona. It is found that by an order of magnitude, the period is about the typical periods of slow magnetoacoustic oscillations detected in the corona. Title: Damping of slow magnetoacoustic oscillations by the misbalance between heating and cooling processes in the solar corona Authors: Kolotkov, D. Y.; Nakariakov, V. M.; Zavershinskii, D. I. Bibcode: 2019A&A...628A.133K Altcode: 2019arXiv190707051K Context. Rapidly decaying slow magnetoacoustic waves are regularly observed in the solar coronal structures, offering a promising tool for a seismological diagnostics of the coronal plasma, including its thermodynamical properties.
Aims: The effect of damping of standing slow magnetoacoustic oscillations in the solar coronal loops is investigated accounting for field-aligned thermal conductivity and a wave-induced misbalance between radiative cooling and some unspecified heating rates.
Methods: The non-adiabatic terms were allowed to be arbitrarily large, corresponding to the observed values. The thermal conductivity was taken in its classical form, and a power-law dependence of the heating function on the density and temperature was assumed. The analysis was conducted in the linear regime and in the infinite magnetic field approximation.
Results: The wave dynamics is found to be highly sensitive to the characteristic timescales of the thermal misbalance. Depending on certain values of the misbalance, timescales three regimes of the wave evolution were identified, namely the regime of a suppressed damping, enhanced damping in which the damping rate drops down to observational values, and acoustic over-stability. The specific regime is determined by the dependences of the radiative cooling and heating functions on thermodynamical parameters of the plasma in the vicinity of the perturbed thermal equilibrium.
Conclusions: The comparison of the observed and theoretically derived decay times and oscillation periods allows us to constrain the coronal heating function. For typical coronal parameters, the observed properties of standing slow magnetoacoustic oscillations could be readily reproduced with a reasonable choice of the heating function. Title: Evidence for Vortex Shedding in the Sun's Hot Corona Authors: Samanta, Tanmoy; Tian, Hui; Nakariakov, Valery M. Bibcode: 2019PhRvL.123c5102S Altcode: 2019arXiv190708930S Vortex shedding is an oscillating flow that is commonly observed in fluids due to the presence of a blunt body in a flowing medium. Numerical simulations have shown that the phenomenon of vortex shedding could also develop in the magnetohydrodynamic (MHD) domain. The dimensionless Strouhal number, the ratio of the blunt body diameter to the product of the period of vortex shedding and the speed of a flowing medium, is a robust indicator for vortex shedding, and, generally of the order of 0.2 for a wide range of Reynolds number. Using an observation from the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory, we report a wavelike or oscillating plasma flow propagating upward against the Sun's gravitational force. A newly formed shrinking loop in the postflare region possibly generates the oscillation of the upflow in the wake of the hot and dense loop through vortex shedding. The computed Strouhal number is consistent with the prediction from previous MHD simulations. Our observation suggests the possibility of vortex shedding in the solar corona. Title: Oscillation of a Small Hα Surge in a Solar Polar Coronal Hole Authors: Cho, Kyung-Suk; Cho, Il-Hyun; Nakariakov, V. M.; Yurchyshyn, Vasyl B.; Yang, Heesu; Kim, Yeon-Han; Kumar, Pankaj; Magara, Tetsuya Bibcode: 2019ApJ...877L...1C Altcode: Hα surges (i.e., cool/dense collimated plasma ejections) may act as a guide for a propagation of magnetohydrodynamic waves. We report a high-resolution observation of a surge observed with 1.6 m Goode Solar Telescope (GST) on 2009 August 26, from 18:20 UT to 18:45 UT. Characteristics of plasma motions in the surge are determined with the normalizing radial gradient filter and the Fourier motion filter. The shape of the surge is found to change from a “C” shape to an inverse “C” shape after a formation of a cusp, a signature of reconnection. There are apparent upflows seen above the cusp top and downflows below it. The upflows show rising and rotational motions in the right-hand direction, with the rotational speed decreasing with height. Near the cusp top, we find a transverse oscillation of the surge, with the period of ∼2 minutes. There is no change of the oscillation phase below the cusp top, but above the top a phase change is identified, giving a vertical phase speed about 86 km s-1. As the height increases, the initial amplitude of the oscillation increases, and the oscillation damping time decreases from 5.13 to 1.18 minutes. We conclude that the oscillation is a propagating kink wave that is possibly excited by the repetitive spontaneous magnetic reconnection. Title: The Physical Nature of Spiral Wave Patterns in Sunspots Authors: Kang, Juhyung; Chae, Jongchul; Nakariakov, Valery M.; Cho, Kyuhyoun; Kwak, Hannah; Lee, Kyeore Bibcode: 2019ApJ...877L...9K Altcode: 2019arXiv190508908K Recently, spiral wave patterns (SWPs) have been detected in 3 minute oscillations of sunspot umbrae, but the nature of this phenomenon has remained elusive. We present a theoretical model that interprets the observed SWPs as the superposition of two different azimuthal modes of slow magnetoacoustic waves driven below the surface in an untwisted and non-rotating magnetic cylinder. We apply this model to SWPs of the line-of-sight (LOS) velocity in a pore observed by the Fast Imaging Solar Spectrograph installed at the 1.6 m Goode Solar Telescope. One- and two-armed SWPs were identified in instantaneous amplitudes of LOS Doppler velocity maps of 3 minute oscillations. The associated oscillation periods are about 160 s, and the durations are about 5 minutes. In our theoretical model, the observed spiral structures are explained by the superposition of non-zero azimuthal modes driven 1600 km below the photosphere in the pore. The one-armed SWP is produced by the slow-body sausage (m = 0) and kink (m = 1) modes, and the two-armed SWP is formed by the slow-body sausage (m = 0) and fluting (m = 2) modes of the magnetic flux tube forming the pore. Title: Scaling laws of quasi-periodic pulsations in solar flares Authors: Pugh, C. E.; Broomhall, A. -M.; Nakariakov, V. M. Bibcode: 2019A&A...624A..65P Altcode: 2019arXiv190209627P Context. Quasi-periodic pulsations (QPPs) are a common feature of solar flares, but there has previously been a lack of observational evidence to support any of the theoretical models that might explain the origin of these QPPs.
Aims: We aimed to determine if there are any relationships between the QPP period and other properties of the flaring region, using a previously assembled sample of flares with QPPs. If any relationships exist, then these can be compared with scaling laws for the theoretical QPP mechanisms.
Methods: To obtain the flaring region properties, we made use of the Atmospheric Imaging Assembly (AIA) 1600 Å and Helioseismic and Magnetic Imager (HMI) data. The flare ribbons are visible in AIA 1600 Å images, and the positive and negative magnetic polarity ribbons can be distinguished and the magnetic properties determined in the HMI magnetograms. The ribbon properties calculated in this study were the ribbon separation distance, area, total unsigned magnetic flux, and average magnetic field strength. Only the flares that occurred within ±60° of the solar disc centre were included, which meant a sample of 20 flares with 22 QPP signals.
Results: Positive correlations were found between the QPP period and the ribbon properties. The strongest correlations were with the separation distance and magnetic flux. Because these ribbon properties also correlate with the flare duration and because the relationship between the QPP period and flare duration may be influenced by observational bias, we also made use of simulated data to determine whether artificial correlations were introduced. These simulations show that although QPPs cannot be detected for certain combinations of QPP period and flare duration, this does not introduce an apparent correlation.
Conclusions: There is evidence of relationships between the QPP period and flare ribbon properties, and in the future, the derived scaling laws between these properties can be compared to equivalent scaling laws for theoretical QPP mechanisms. Title: Catalog of Decaying Kink Oscillations of Coronal Loops in the 24th Solar Cycle Authors: Nechaeva, Alena; Zimovets, Ivan V.; Nakariakov, V. M.; Goddard, C. R. Bibcode: 2019ApJS..241...31N Altcode: A catalog of kink oscillations of solar coronal loops, which spans during almost all of solar cycle 24, is presented. The catalog is based on the observations made in the extreme ultraviolet band at 171 Å with Solar Dynamics Observatory/Atmospheric Imaging Assembly and includes parameters of 223 oscillating loops in 96 oscillation events. The catalog provides the information about the oscillation locations, time, and dates of the events, associated flare, initial displacement, oscillation period, exponential damping time, and apparent amplitude. The vast majority of the oscillation detections, 84%, were made in the loops situated near or off the solar limb. The oscillation periods are found to range from 1 to 28 minutes, with 74% of the events that have the period in the range of 2-10 minutes. About 90% of the oscillations have the apparent amplitude in the range of 1-10 Mm. The oscillating loop lengths are 70-600 Mm. The typical apparent amplitude is about 1% of the loop length. The oscillation period scales linearly with the loop length, and the damping time scales linearly with the period, which confirm previous findings. The oscillation quality factor scales with the amplitude to the power of minus 0.7. No statistically significant evidence of correlation was found between both the oscillation period and the mean sunspot number, and the loop length and mean sunspot number. The catalog provides the research community with the foundation for the further statistical study of kink oscillations and their use for coronal seismology. Title: Fast magnetoacoustic wave trains with time-dependent drivers Authors: Goddard, C. R.; Nakariakov, V. M.; Pascoe, D. J. Bibcode: 2019A&A...624L...4G Altcode: Context. Frequent observations of quasi-periodic rapidly-propagating wave trains in coronal structures have been made in the last decade. The dispersive evolution of fast magnetohydrodynamic waves propagating in coronal waveguides can provide a physical interpretation for many of these observations.
Aims: Previous studies have considered the generation of fast wave trains by impulsive drivers which deposit energy instantaneously. The signatures of dispersively formed wave trains must depend on the temporal nature of the driver. We investigate the effect of varying the temporal width of the driving perturbation.
Methods: 2D magnetohydrodynamic numerical simulations of impulsively generated wave trains in a guiding field-aligned density enhancement were performed with the novel addition of a time-dependant driver.
Results: The final spatial and spectral signatures of the guided wave trains are found to depend strongly on the temporal duration of the initial perturbation. In particular, the wavelength (or frequency) of highest spectral amplitude is found to increase (decrease) with increasing temporal duration, whereas the spectral width decreases. Additionally, the efficiency of generation of fast wave trains is found to decrease strongly with increasing temporal width of the driver, with a cut-off at twice the internal Alfvén crossing time. Title: Properties of Slow Magnetoacoustic Oscillations of Solar Coronal Loops by Multi-instrumental Observations Authors: Nakariakov, V. M.; Kosak, M. K.; Kolotkov, D. Y.; Anfinogentov, S. A.; Kumar, P.; Moon, Y. -J. Bibcode: 2019ApJ...874L...1N Altcode: Rapidly decaying oscillations of the thermal emission detected in the decay phase of solar and stellar flares are usually interpreted as standing or sloshing (reflecting) slow magnetoacoustic oscillations. We determine the scalings of the oscillation periods, damping times, and amplitudes with the temperature, considering both standing and sloshing oscillations detected with different instruments. In addition, the time evolution of different spatial harmonics of a sloshing oscillation is considered. Parameters of slow oscillations observed in the EUV, X-ray, and microwave bands, and published in the literature, are used. The damping time of slow oscillations is found to scale almost linearly with the oscillation period, as the period to 0.87 ± 0.1, giving the average Q-factor determined as the ratio of the damping time to the period, of about 1. The Q-factor is found to scale with the relative amplitude to the power of {0.33}-0.11+0.10 with 95% confidence. The amplitudes of different spatial harmonics forming a sloshing pulse show similar time evolution, suggesting that the period-dependent dissipation is counteracted by another mechanism. The results obtained indicate that the damping of slow oscillations depends on the oscillation amplitude, and that the competition of nonlinear and dissipative effects could allow for the existence of wave pulses of a sustained shape. Title: Seismological Determination of the Alfvén Speed and Plasma Beta in Solar Photospheric Bright Points Authors: Cho, Il-Hyun; Moon, Yong-Jae; Nakariakov, Valery M.; Yu, Dae Jung; Lee, Jin-Yi; Bong, Su-Chan; Kim, Rok-Soon; Cho, Kyung-Suk; Kim, Yeon-Han; Lee, Jae-Ok Bibcode: 2019ApJ...871L..14C Altcode: 2019arXiv190104144C The Alfvén speed and plasma beta in photospheric bright points (BPs) observed by the Broadband Filter Imager (BFI) of the Solar Optical Telescope on board the Hinode satellite are estimated seismologically. The diagnostics is based on the theory of slow magnetoacoustic waves in a non-isothermally stratified photosphere with a uniform vertical magnetic field. We identify and track BPs in a G-band movie by using the 3D region growing method, and align them with blue continuum images to derive their brightness temperatures. From the Fourier power spectra of 118 continuum light curves made in the BPs, we find that light curves of 91 BPs have oscillations with properties that are significantly different from oscillation in quiet regions, with the periods ranging 2.2-16.2 minutes. We find that the model gives a moderate value of the plasma beta when γ lies at around 5/3. The calculated Alfvén speed is 9.68 ± 2.02 km s-1, ranging in 6.3-17.4 km s-1. The plasma beta is estimated to be of 0.93 ± 0.36, ranging in 0.2-1.9. Title: Three-dimensional Oscillations of 21 Halo Coronal Mass Ejections Using Multi-spacecraft Data Authors: Lee, Harim; Moon, Y. -J.; Nakariakov, V. M.; Na, Hyeonock; Cho, Il-Hyun; Park, Eunsu Bibcode: 2018ApJ...868...18L Altcode: We investigate the 3D structure of kinematic oscillations of full halo coronal mass ejections (FHCMEs) using multi-spacecraft coronagraph data from two non-parallel lines of sight. For this, we consider 21 FHCMEs which are simultaneously observed by the Solar and Heliospheric Observatory and the Solar TErrestrial RElations Observatory A or B, from 2010 June to 2012 August when the spacecraft were roughly in quadrature. Using sequences of running difference images, we estimate the instantaneous projected speeds of the FHCMEs at 24 different azimuthal angles in the planes of the sky of those coronagraphs. We find that all these FHCMEs have experienced kinematic oscillations characterized by quasi-periodic variations of the instantaneous projected radial velocity with periods ranging from 24 to 48 min. The oscillations detected in the analyzed events are found to show distinct azimuthal wave modes. Thirteen events (about 62%) are found to oscillate with the azimuthal wave number m = 1. The oscillating directions of the nodes of the m = 1 mode for these FHCMEs are consistent with those of their position angles (or the direction of eruption), with a mean difference of about 23°. The oscillation amplitude is found to correlate well with the projected radial speed of the CME. An estimation of Lorentz accelerations shows that they are dominant over other forces, implying that the magnetic force is responsible for the kinematic oscillations of CMEs. However, we cannot rule out other possibilities: a global layer of enhanced current around the CMEs or the nonlinear nature of its driver, for example the effect of vortex shedding. Title: Sausage oscillations in a plasma cylinder with a surface current Authors: Lim, Daye; Nakariakov, Valery M.; Moon, Yong-Jae Bibcode: 2018JASTP.175...49L Altcode: Linear sausage oscillations of a cylinder embedded in a plasma with an azimuthal magnetic field, created by a current on the surface of the cylinder, are studied. Such a plasma configuration could be applied to modelling flaring loops, and magnetic ropes in coronal mass ejections. The plasma is assumed to be cold everywhere. Dispersion relations demonstrate that the lowest radial harmonic of the sausage mode is in the trapped regime for all values of the parallel wave number. In the long-wavelength limit, phase and group speeds of this mode are equal to the Alfvén speed in the external medium. It makes the oscillation period to be determined by the ratio of the parallel wavelength, e.g. double the length of an oscillating loop, to the external Alfvén speed, allowing for its seismological estimations. The application of the results obtained to the interpretation of long-period (longer than a minute) oscillations of emission intensity detected in solar coronal structures, gives reasonable estimations of the external Alfvén speed. Cutoff values of the parallel wavenumber for higher radial harmonics are determined analytically. Implications of this finding to the observational signatures of fast magnetoacoustic wave trains guided by cylindrical plasma non-uniformities are discussed. Title: Magnetic structure of solar flare regions producing hard X-ray pulsations Authors: Zimovets, I. V.; Wang, R.; Liu, Y. D.; Wang, C.; Kuznetsov, S. A.; Sharykin, I. N.; Struminsky, A. B.; Nakariakov, V. M. Bibcode: 2018JASTP.174...17Z Altcode: 2017arXiv170801869Z We present analysis of the magnetic field in seven solar flare regions accompanied by the pulsations of hard X-ray (HXR) emission. These flares were studied by Kuznetsov et al. (2016) (Paper I), and chosen here because of the availability of the vector magnetograms for their parent active regions (ARs) obtained with the SDO/HMI data. In Paper I, based on the observations only, it was suggested that a magnetic flux rope (MFR) might play an important role in the process of generation of the HXR pulsations. The goal of the present paper is to test this hypothesis by using the extrapolation of magnetic field with the non-linear force-free field (NLFFF) method. Having done this, we found that before each flare indeed there was an MFR elongated along and above a magnetic polarity inversion line (MPIL) on the photosphere. In two flare regions the sources of the HXR pulsations were located at the footpoints of different magnetic field lines wrapping around the central axis, and constituting an MFR by themselves. In five other flares the parent field lines of the HXR pulsations were not a part of an MFR, but surrounded it in the form of an arcade of magnetic loops. These results show that, at least in the analyzed cases, the "single flare loop" models do not satisfy the observations and magnetic field modeling, while are consistent with the concept that the HXR pulsations are a consequence of successive episodes of energy release and electron acceleration in different magnetic flux tubes (loops) of a complex AR. An MFR could generate HXR pulsations by triggering episodes of magnetic reconnection in different loops in the course of its non-uniform evolution along an MPIL. However, since three events studied here were confined flares, actual eruptions may not be required to trigger sequential particle acceleration episodes in the magnetic systems containing an MFR. Title: Oscillations of cometary tails: a vortex shedding phenomenon? Authors: Nisticò, G.; Vladimirov, V.; Nakariakov, V. M.; Battams, K.; Bothmer, V. Bibcode: 2018A&A...615A.143N Altcode: 2018arXiv180400997N Context. During their journey to perihelion, comets may appear in the field of view of space-borne optical instruments, showing in some cases a nicely developed plasma tail extending from their coma and exhibiting an oscillatory behaviour.
Aims: The oscillations of cometary tails may be explained in terms of vortex shedding because of the interaction of the comet with the solar wind streams. Therefore, it is possible to exploit these oscillations in order to infer the value of the Strouhal number S t, which quantifies the vortex shedding phenomenon, and the physical properties of the local medium.
Methods: We used the Heliospheric Imager (HI) data of the Solar TErrestrial Relations Observatory (STEREO) mission to study the oscillations of the tails of comets 2P/Encke and C/2012 S1 (ISON) during their perihelion in Nov 2013. We determined the corresponding Strouhal numbers from the estimates of the halo size, the relative speed of the solar wind flow, and the period of the oscillations.
Results: We found that the estimated Strouhal numbers are very small, and the typical value of S t 0.2 would be extrapolated for size of the halo larger than 106 km.
Conclusions: Although the vortex shedding phenomenon has not been unambiguously revealed, the findings suggest that some kind of magnetohydrodynamic (MHD) instability process is responsible for the observed behaviour of cometary tails, which can be exploited for probing the physical conditions of the near-Sun region.

The movies associated to Figs. 1 and 4 are available at http://www.aanda.org Title: Two-Dimensional Solar Wind Speeds from 6 to 26 Solar Radii in Solar Cycle 24 by Using Fourier Filtering Authors: Cho, Il-Hyun; Moon, Yong-Jae; Nakariakov, Valery M.; Bong, Su-Chan; Lee, Jin-Yi; Song, Donguk; Lee, Harim; Cho, Kyung-Suk Bibcode: 2018PhRvL.121g5101C Altcode: 2018arXiv180608540C Measurement of the solar wind speed near the Sun is important for understanding the acceleration mechanism of the solar wind. In this Letter, we determine 2D solar wind speeds from 6 to 26 solar radii by applying Fourier motion filters to SOHO/LASCO C3 movies observed from 1999 to 2010. Our method successfully reproduces the original flow speeds in the artificially generated data as well as streamer blobs. We measure 2D solar wind speeds from one-day to one-year timescales and their variation in solar cycle 24. We find that the solar wind speeds at timescales longer than a month in the solar maximum period are relatively uniform in the azimuthal direction, while they are clearly bimodal in the minimum period, as expected from the Ulysses observations and interplanetary radio scintillation reconstruction. The bimodal structure appears at around 2006, becomes most distinctive in 2009, and abruptly disappears in 2010. The radial evolution of the solar wind speeds resembles the Parker's solar wind solution. Title: Probing the inner heliosphere with comets Authors: Nisticò, Giuseppe; Vladimirov, Vangelis; Nakariakov, Valery M.; Battams, Karl; Bothmer, Volker Bibcode: 2018shin.confE..41N Altcode: Optical instruments aboard space missions have recently provided us with exciting observations of comets in the vicinity of their perihelion. At this stage, a tail of dust and ions from the comet nucleus is formed, which interacts with the local solar wind flow and exhibits an oscillatory dynamics. The observed phenomenon is attributed to the formation of a Kármán vortex street in the wake of the cometary coma, whose properties depend upon the characteristics of the comet itself and the local medium. We present observations of the comets Encke and ISON detected in 2013 with the Heliospheric Imager aboard the STEREO spacecraft, and discuss the possibility to exploit comets as natural probes of the inner heliosphere, by relating the physical behaviour of cometary tails with the local conditions of the solar wind. Title: Origin of the Modulation of the Radio Emission from the Solar Corona by a Fast Magnetoacoustic Wave Authors: Kolotkov, Dmitrii Y.; Nakariakov, Valery M.; Kontar, Eduard P. Bibcode: 2018ApJ...861...33K Altcode: 2018arXiv180508282K Observational detection of quasi-periodic drifting fine structures in a type III radio burst associated with a solar flare SOL2015-04-16T11:22, with the LOw Frequency ARray (LOFAR), is presented. Although similar modulations of the type III emission have been observed before and were associated with the plasma density fluctuations, the origin of those fluctuations was unknown. Analysis of the striae of the intensity variation in the dynamic spectrum allowed us to reveal two quasi-oscillatory components. The shorter component has an apparent wavelength of ∼2 Mm, phase speed of ∼657 km s-1, which gives an oscillation period of ∼3 s, and a relative amplitude of ∼0.35%. The longer component has a wavelength of ∼12 Mm and relative amplitude of ∼5.1%. The short frequency range of the detection does not allow us to estimate its phase speed. However, the properties of the shorter oscillatory component allowed us to interpret it as a fast magnetoacoustic wave guided by a plasma nonuniformity along the magnetic field outwards from the Sun. The assumption that the intensity of the radio emission is proportional to the amount of plasma in the emitting volume allowed us to show that the superposition of the plasma density modulation by a fast wave and a longer-wavelength oscillation of an unspecified nature could readily reproduce the fine structure of the observed dynamic spectrum. The observed parameters of the fast wave give an absolute value for the magnetic field in the emitting plasma of ∼1.1 G, which is consistent with the radial magnetic field model. Title: Finite amplitude transverse oscillations of a magnetic rope Authors: Kolotkov, Dmitrii Y.; Nisticò, Giuseppe; Rowlands, George; Nakariakov, Valery M. Bibcode: 2018JASTP.172...40K Altcode: 2018arXiv180305195K The effects of finite amplitudes on the transverse oscillations of a quiescent prominence represented by a magnetic rope are investigated in terms of the model proposed by Kolotkov et al. (2016). We consider a weakly nonlinear case governed by a quadratic nonlinearity, and also analyse the fully nonlinear equations of motion. We treat the prominence as a massive line current located above the photosphere and interacting with the magnetised dipped environment via the Lorentz force. In this concept the magnetic dip is produced by two external current sources located at the photosphere. Finite amplitude horizontal and vertical oscillations are found to be strongly coupled between each other. The coupling is more efficient for larger amplitudes and smaller attack angles between the direction of the driver and the horizontal axis. Spatial structure of oscillations is represented by Lissajous-like curves with the limit cycle of a hourglass shape, appearing in the resonant case, when the frequency of the vertical mode is twice the horizontal mode frequency. A metastable equilibrium of the prominence is revealed, which is stable for small amplitude displacements, and becomes horizontally unstable, when the amplitude exceeds a threshold value. The maximum oscillation amplitudes are also analytically derived and analysed. Typical oscillation periods are determined by the oscillation amplitude, prominence current, its mass and position above the photosphere, and the parameters of the magnetic dip. The main new effects of the finite amplitude are the coupling of the horizontally and vertically polarised transverse oscillations (i.e. the lack of a simple, elliptically polarised regime) and the presence of metastable equilibria of prominences. Title: In Situ Generation of Transverse Magnetohydrodynamic Waves from Colliding Flows in the Solar Corona Authors: Antolin, Patrick; Pagano, Paolo; De Moortel, Ineke; Nakariakov, Valery M. Bibcode: 2018ApJ...861L..15A Altcode: 2018arXiv180700395A Transverse magnetohydrodynamic (MHD) waves permeate the solar atmosphere and are a candidate for coronal heating. However, the origin of these waves is still unclear. In this Letter, we analyze coordinated observations from Hinode/Solar Optical Telescope (SOT) and Interface Region Imaging Spectrograph ( IRIS) of a prominence/coronal rain loop-like structure at the limb of the Sun. Cool and dense downflows and upflows are observed along the structure. A collision between a downward and an upward flow with an estimated energy flux of 107-108 erg cm-2 s-1 is observed to generate oscillatory transverse perturbations of the strands with an estimated ≈40 km s-1 total amplitude, and a short-lived brightening event with the plasma temperature increasing to at least 105 K. We interpret this response as sausage and kink transverse MHD waves based on 2D MHD simulations of plasma flow collision. The lengths, density, and velocity differences between the colliding clumps and the strength of the magnetic field are major parameters defining the response to the collision. The presence of asymmetry between the clumps (angle of impact surface and/or offset of flowing axis) is crucial for generating a kink mode. Using the observed values, we successfully reproduce the observed transverse perturbations and brightening, and show adiabatic heating to coronal temperatures. The numerical modeling indicates that the plasma β in this loop-like structure is confined between 0.09 and 0.36. These results suggest that such collisions from counter-streaming flows can be a source of in situ transverse MHD waves, and that for cool and dense prominence conditions such waves could have significant amplitudes. Title: Quasi-periodic Pulsations in a Solar Microflare Authors: Nakariakov, V. M.; Anfinogentov, S.; Storozhenko, A. A.; Kurochkin, E. A.; Bogod, V. M.; Sharykin, I. N.; Kaltman, T. I. Bibcode: 2018ApJ...859..154N Altcode: Irregular time evolution of the radio emission generated in a B2-class microflare (SOL2017-01-25T10:15), occurring on 2017 January 25 in active region 12,628, is studied. The microflare was apparently initiated by an appearance of an s-shaped loop, observed in the EUV band. The radio emission is associated with the nonthermal electrons detected with Ramaty High Energy Solar Spectroscopic Imager, and originates simultaneously from two opposite footpoints of a magnetic fan structure beginning at a sunspot. According to the active region geometry, the footpoints are situated in the meridional direction, and hence are observed by RATAN-600 simultaneously. The radio emission intensity signal, as well as the left-hand and right-hand circular polarization signals in the low-frequency band (3-4 GHz) show good correlation with each other, with the average characteristic time of the variation 1.4 ± 0.3 s. The polarization signal shows a time variation with the characteristic time of about 0.7 ± 0.2 s. The irregular quasi-periodic pulsations of the radio emission are likely to be caused by the superposition of the signals generated at the local electron plasma frequencies by the interaction of nonthermal electrons with the plasma at the footpoints. In this scenario, the precipitation rate of the nonthermal electrons at the opposite footpoints could be modulated by the superposition of fundamental and second harmonic modes of sausage oscillations, resulting in the observed different characteristic times of the intensity and polarization signals. However, other mechanisms, e.g., the oscillatory regime of loop coalescence or magnetic null point oscillation could not be rigorously excluded. Title: Spatiotemporal Analysis of Coronal Loops Using Seismology of Damped Kink Oscillations and Forward Modeling of EUV Intensity Profiles Authors: Pascoe, D. J.; Anfinogentov, S. A.; Goddard, C. R.; Nakariakov, V. M. Bibcode: 2018ApJ...860...31P Altcode: The shape of the damping profile of kink oscillations in coronal loops has recently allowed the transverse density profile of the loop to be estimated. This requires accurate measurement of the damping profile that can distinguish the Gaussian and exponential damping regimes, otherwise there are more unknowns than observables. Forward modeling of the transverse intensity profile may also be used to estimate the width of the inhomogeneous layer of a loop, providing an independent estimate of one of these unknowns. We analyze an oscillating loop for which the seismological determination of the transverse structure is inconclusive except when supplemented by additional spatial information from the transverse intensity profile. Our temporal analysis describes the motion of a coronal loop as a kink oscillation damped by resonant absorption, and our spatial analysis is based on forward modeling the transverse EUV intensity profile of the loop under the isothermal and optically thin approximations. We use Bayesian analysis and Markov chain Monte Carlo sampling to apply our spatial and temporal models both individually and simultaneously to our data and compare the results with numerical simulations. Combining the two methods allows both the inhomogeneous layer width and density contrast to be calculated, which is not possible for the same data when each method is applied individually. We demonstrate that the assumption of an exponential damping profile leads to a significantly larger error in the inferred density contrast ratio compared with a Gaussian damping profile. Title: Quasi-periodic Pulsations in the Most Powerful Solar Flare of Cycle 24 Authors: Kolotkov, Dmitrii Y.; Pugh, Chloe E.; Broomhall, Anne-Marie; Nakariakov, Valery M. Bibcode: 2018ApJ...858L...3K Altcode: 2018arXiv180404955K Quasi-periodic pulsations (QPPs) are common in solar flares and are now regularly observed in stellar flares. We present the detection of two different types of QPP signals in the thermal emission light curves of the X9.3-class solar flare SOL2017-09-06T12:02, which is the most powerful flare of Cycle 24. The period of the shorter-period QPP drifts from about 12 to 25 s during the flare. The observed properties of this QPP are consistent with a sausage oscillation of a plasma loop in the flaring active region. The period of the longer-period QPP is about 4 to 5 minutes. Its properties are compatible with standing slow magnetoacoustic oscillations, which are often detected in coronal loops. For both QPP signals, other mechanisms such as repetitive reconnection cannot be ruled out, however. The studied solar flare has an energy in the realm of observed stellar flares, and the fact that there is evidence of a short-period QPP signal typical of solar flares along with a long-period QPP signal more typical of stellar flares suggests that the different ranges of QPP periods typically observed in solar and stellar flares is likely due to observational constraints, and that similar physical processes may be occurring in solar and stellar flares. Title: Nonlinear waves in the terrestrial quasi-parallel foreshock Authors: Hnat, Bogdan; Kolotkov, Dmitri; O'Connell, Daniel; Nakariakov, Valery; Rowlands, George Bibcode: 2018EGUGA..20.4956H Altcode: Upstream regions of quasiparallel collisionless astrophysical shocks are among the most complex plasma systems. When the magnetic field direction is quasiparallel to the shock normal, a fraction of incoming ions are reflected upstream generating an extended and turbulent foreshock. We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after non harmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrodinger equation, predicted analytically by the use of a pseudo-potential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfven speed. We suggest that the feedback of the large amplitudec fluctuations on background plasma is reflected in the evolution of the pseudo-potential. Title: Detection of the Second Harmonic of Decay-less Kink Oscillations in the Solar Corona Authors: Duckenfield, T.; Anfinogentov, S. A.; Pascoe, D. J.; Nakariakov, V. M. Bibcode: 2018ApJ...854L...5D Altcode: EUV observations of a multi-thermal coronal loop, taken by the Atmospheric Imaging Assembly of the Solar Dynamics Observatory, which exhibits decay-less kink oscillations are presented. The data cube of the quiet-Sun coronal loop was passed through a motion magnification algorithm to accentuate transverse oscillations. Time-distance maps are made from multiple slits evenly spaced along the loop axis and oriented orthogonal to the loop axis. Displacements of the intensity peak are tracked to generate time series of the loop displacement. Fourier analysis on the time series shows the presence of two periods within the loop: {P}1={10.3}-1.7+1.5 minutes and {P}2={7.4}-1.3+1.1 minutes. The longer period component is greatest in amplitude at the apex and remains in phase throughout the loop length. The shorter period component is strongest further down from the apex on both legs and displays an anti-phase behavior between the two loop legs. We interpret these results as the coexistence of the fundamental and second harmonics of the standing kink mode within the loop in the decay-less oscillation regime. An illustration of seismological application using the ratio P 1/2P 2 ∼ 0.7 to estimate the density scale height is presented. The existence of multiple harmonics has implications for understanding the driving and damping mechanisms for decay-less oscillations and adds credence to their interpretation as standing kink mode oscillations. Title: Modelling Quasi-Periodic Pulsations in Solar and Stellar Flares Authors: McLaughlin, J. A.; Nakariakov, V. M.; Dominique, M.; Jelínek, P.; Takasao, S. Bibcode: 2018SSRv..214...45M Altcode: 2018arXiv180204180M Solar flare emission is detected in all EM bands and variations in flux density of solar energetic particles. Often the EM radiation generated in solar and stellar flares shows a pronounced oscillatory pattern, with characteristic periods ranging from a fraction of a second to several minutes. These oscillations are referred to as quasi-periodic pulsations (QPPs), to emphasise that they often contain apparent amplitude and period modulation. We review the current understanding of quasi-periodic pulsations in solar and stellar flares. In particular, we focus on the possible physical mechanisms, with an emphasis on the underlying physics that generates the resultant range of periodicities. These physical mechanisms include MHD oscillations, self-oscillatory mechanisms, oscillatory reconnection/reconnection reversal, wave-driven reconnection, two loop coalescence, MHD flow over-stability, the equivalent LCR-contour mechanism, and thermal-dynamical cycles. We also provide a histogram of all QPP events published in the literature at this time. The occurrence of QPPs puts additional constraints on the interpretation and understanding of the fundamental processes operating in flares, e.g. magnetic energy liberation and particle acceleration. Therefore, a full understanding of QPPs is essential in order to work towards an integrated model of solar and stellar flares. Title: Corrugation Instability of a Coronal Arcade Authors: Klimushkin, D. Y.; Nakariakov, V. M.; Mager, P. N.; Cheremnykh, O. K. Bibcode: 2017SoPh..292..184K Altcode: We analyse the behaviour of linear magnetohydrodynamic perturbations of a coronal arcade modelled by a half-cylinder with an azimuthal magnetic field and non-uniform radial profiles of the plasma pressure, temperature, and the field. Attention is paid to the perturbations with short longitudinal (in the direction along the arcade) wavelengths. The radial structure of the perturbations, either oscillatory or evanescent, is prescribed by the radial profiles of the equilibrium quantities. Conditions for the corrugation instability of the arcade are determined. It is established that the instability growth rate increases with decreases in the longitudinal wavelength and the radial wave number. In the unstable mode, the radial perturbations of the magnetic field are stronger than the longitudinal perturbations, creating an almost circularly corrugated rippling of the arcade in the longitudinal direction. For coronal conditions, the growth time of the instability is shorter than one minute, decreasing with an increase in the temperature. Implications of the developed theory for the dynamics of coronal active regions are discussed. Title: Properties of quasi-periodic pulsations in solar flares from a single active region Authors: Pugh, C. E.; Nakariakov, V. M.; Broomhall, A. -M.; Bogomolov, A. V.; Myagkova, I. N. Bibcode: 2017A&A...608A.101P Altcode: 2017arXiv170909472P Context. Quasi-periodic pulsations (QPPs) are a common feature of solar and stellar flares, and so the nature of these pulsations should be understood in order to fully understand flares.
Aims: We investigate the properties of a set of solar flares originating from a single active region (AR) that exhibit QPPs, and in particular look for any indication of QPP periods relating to AR properties, as might be expected if the characteristic timescale of the pulsations corresponds to a characteristic length scale of the structure from which the pulsations originate. The three AR properties used for this study are the photospheric area, bipole separation distance, and average magnetic field strength at the photosphere. The AR studied, known as NOAA 12172/12192/12209, was unusually long-lived and persisted for over three Carrington rotations between September and November 2014. During this time a total of 181 flares were observed by GOES.
Methods: Data from the GOES/XRS, SDO/EVE/ESP, Fermi/GBM, Vernov/DRGE and Nobeyama Radioheliograph observatories were used to determine if QPPs were present in the flares. For the soft X-ray GOES/XRS and EVE/ESP data, the time derivative of the signal was used so that any variability in the impulsive phase of the flare was emphasised. Periodogram power spectra of the time series data, without any form of detrending, were inspected and flares with a peak above the 95% confidence level in the power spectrum were labelled as having candidate QPPs. The confidence levels were determined taking full account of data uncertainties and the possible presence of red noise. Active region properties were determined using SDO/HMI line of sight magnetogram data.
Results: A total of 37 flares, i.e. 20% of the sample, show good evidence of having stationary or weakly non-stationary QPPs, and some of the pulsations can be seen in data from multiple instruments and in different wavebands. Because the detection method used was rather conservative, this may be a lower bound for the true number of flares with QPPs. The QPP periods were found to show a weak correlation with the flare amplitude and duration, but this is likely due to an observational bias. A stronger correlation was found between the QPP period and duration of the QPP signal, which can be partially but not entirely explained by observational constraints. No correlations were found with the AR area, bipole separation distance, or average magnetic field strength.
Conclusions: The fact that a substantial fraction of the flare sample showed evidence of QPPs, using a strict detection method with minimal processing of the data, demonstrates that these QPPs are a real phenomenon that cannot be explained by the presence of red noise or the superposition of multiple unrelated flares. The lack of correlation between the QPP periods and AR properties implies that the small-scale structure of the AR is important and/or that different QPP mechanisms act in different cases. Title: Effect of Local Thermal Equilibrium Misbalance on Long-wavelength Slow Magnetoacoustic Waves Authors: Nakariakov, V. M.; Afanasyev, A. N.; Kumar, S.; Moon, Y. -J. Bibcode: 2017ApJ...849...62N Altcode: Evolution of slow magnetoacoustic waves guided by a cylindrical magnetic flux tube that represents a coronal loop or plume, is modeled accounting for the effects of finite gas pressure, weak nonlinearity, dissipation by thermal conduction and viscosity, and the misbalance between the cooling by optically thin radiation and unspecified heating of the plasma. An evolutionary equation of the Burgers-Malthus type is derived. It is shown that the cooling/heating misbalance, determined by the derivatives of the combined radiative cooling and heating function, with respect to the density, temperature, and magnetic field at the thermal equilibrium affect the wave rather strongly. This effect may either cause additional damping, or counteract it, or lead to the gradual amplification of the wave. In the latter case, the coronal plasma acts as an active medium for the slow magnetoacoustic waves. The effect of the cooling/heating misbalance could be important for coronal slow waves, and could be responsible for certain discrepancies between theoretical results and observations, in particular, the increased or decreased damping lengths and times, detection of the waves at certain heights only, and excitation of compressive oscillations. The results obtained open up a possibility for the diagnostics of the coronal heating function by slow magnetoacoustic waves. Title: Seismology of contracting and expanding coronal loops using damping of kink oscillations by mode coupling Authors: Pascoe, D. J.; Russell, A. J. B.; Anfinogentov, S. A.; Simões, P. J. A.; Goddard, C. R.; Nakariakov, V. M.; Fletcher, L. Bibcode: 2017A&A...607A...8P Altcode:
Aims: We extend recently developed seismological methods to analyse oscillating loops which feature a large initial shift in the equilibrium position and investigate additional observational signatures related to the loop environment and oscillation driver.
Methods: We model the motion of coronal loops as a kink oscillation damped by mode coupling, accounting for any change in loop length and the possible presence of parallel harmonics in addition to the fundamental mode. We apply our model to a loop which rapidly contracts due to a post-flare implosion (SOL2012-03-09) and a loop with a large lateral displacement (SOL2012-10-20).
Results: The seismological method is used to calculate plasma parameters of the oscillating loops including the transverse density profile, magnetic field strength, and phase mixing timescale. For SOL2012-03-09 the period of oscillation has a linear correlation with the contracting motion and suggests the kink speed remains constant during the oscillation. The implosion excitation mechanism is found to be associated with an absence of additional parallel harmonics.
Conclusions: The improved Bayesian analysis of the coronal loop motion allows for accurate seismology of plasma parameters, and the evolution of the period of oscillation compared with the background trend can be used to distinguish between loop motions in the plane of the loop and those perpendicular to it. The seismologically inferred kink speed and density contrast imply sub-Alfvénic (MA = 0.16 ± 0.03) propagation of the magnetic reconfiguration associated with the implosion, as opposed to triggering by a wave propagating at the Alfvén speed. Title: Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains Authors: Pascoe, D. J.; Goddard, C. R.; Nakariakov, V. M. Bibcode: 2017ApJ...847L..21P Altcode: Quasi-periodic rapidly propagating wave trains are frequently observed in extreme ultraviolet observations of the solar corona, or are inferred by the quasi-periodic modulation of radio emission. The dispersive nature of fast magnetohydrodynamic waves in coronal structures provides a robust mechanism to explain the detected quasi-periodic patterns. We perform 2D numerical simulations of impulsively generated wave trains in coronal plasma slabs and investigate how the behavior of the trapped and leaky components depend on the properties of the initial perturbation. For large amplitude compressive perturbations, the geometrical dispersion associated with the waveguide suppresses the nonlinear steepening for the trapped wave train. The wave train formed by the leaky components does not experience dispersion once it leaves the waveguide and so can steepen and form shocks. The mechanism we consider can lead to the formation of multiple shock fronts by a single, large amplitude, impulsive event and so can account for quasi-periodic features observed in radio spectra. Title: Toward a Next Generation Solar Coronagraph: Development of a Compact Diagnostic Coronagraph on the ISS Authors: Cho, K. -S.; Bong, S. -C.; Choi, S.; Yang, H.; Kim, J.; Baek, J. -H.; Park, J.; Lim, E. -K.; Kim, R. -S.; Kim, S.; Kim, Y. -H.; Park, Y. -D.; Clarke, S. W.; Davila, J. M.; Gopalswamy, N.; Nakariakov, V. M.; Li, B.; Pinto, R. F. Bibcode: 2017JKAS...50..139C Altcode: The Korea Astronomy and Space Science Institute plans to develop a coronagraph in collaboration with National Aeronautics and Space Administration (NASA) and to install it on the International Space Station (ISS). The coronagraph is an externally occulted one-stage coronagraph with a field of view from 3 to 15 solar radii. The observation wavelength is approximately 400 nm, where strong Fraunhofer absorption lines from the photosphere experience thermal broadening and Doppler shift through scattering by coronal electrons. Photometric filter observations around this band enable the estimation of 2D electron temperature and electron velocity distribution in the corona. Together with a high time cadence (<12 min) of corona images used to determine the geometric and kinematic parameters of coronal mass ejections, the coronagraph will yield the spatial distribution of electron density by measuring the polarized brightness. For the purpose of technical demonstration, we intend to observe the total solar eclipse in August 2017 with the filter system and to perform a stratospheric balloon experiment in 2019 with the engineering model of the coronagraph. The coronagraph is planned to be installed on the ISS in 2021 for addressing a number of questions (e.g., coronal heating and solar wind acceleration) that are both fundamental and practically important in the physics of the solar corona and of the heliosphere. Title: A statistical study of the inferred transverse density profile of coronal loop threads observed with SDO/AIA Authors: Goddard, C. R.; Pascoe, D. J.; Anfinogentov, S.; Nakariakov, V. M. Bibcode: 2017A&A...605A..65G Altcode:
Aims: We carry out a statistical study of the inferred coronal loop cross-sectional density profiles using extreme ultraviolet (EUV) imaging data from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO).
Methods: We analysed 233 coronal loops observed during 2015/2016. We consider three models for the density profile; the step function (model S), the linear transition region profile (model L), and a Gaussian profile (model G). Bayesian inference is used to compare the three corresponding forward modelled intensity profiles for each loop. These are constructed by integrating the square of the density from a cylindrical loop cross-section along the line of sight, assuming an isothermal cross-section, and applying the instrumental point spread function.
Results: Calculating the Bayes factors for comparisons between the models, it was found that in 47% of cases there is very strong evidence for model L over model S and in 45% of cases very strong evidence for model G over S. Using multiple permutations of the Bayes factor the favoured density profile for each loop was determined for multiple evidence thresholds. There were a similar number of cases where model L or G are favoured, showing evidence for inhomogeneous layers and constantly varying density cross-sections, subject to our assumptions and simplifications.
Conclusions: For sufficiently well resolved loop threads with no visible substructure it has been shown that using Bayesian inference and the observed intensity profile we can distinguish between the proposed density profiles at a given AIA wavelength and spatial resolution. We have found very strong evidence for inhomogeneous layers, with model L being the most general, and a tendency towards thicker or even continuous layers. Title: Quasi-periodic Radio Bursts Associated with Fast-mode Waves near a Magnetic Null Point Authors: Kumar, Pankaj; Nakariakov, Valery M.; Cho, Kyung-Suk Bibcode: 2017ApJ...844..149K Altcode: 2017arXiv170609988K This paper presents an observation of quasi-periodic rapidly propagating waves observed in the Atmospheric Image Assembly (AIA) 171/193 Å channels during the impulsive phase of an M1.9 flare that occurred on 2012 May 7. The instant period was found to decrease from 240 to 120 s, and the speed of the wavefronts was in the range of ∼664-1416 km s-1. Almost simultaneously, quasi-periodic bursts with similar instant periods, ∼70 and ∼140 s, occur in the microwave emission and in decimetric type IV and type III radio bursts, and in the soft X-ray emission. The magnetic field configuration of the flare site was consistent with a breakout topology, I.e., a quadrupolar field along with a magnetic null point. The quasi-periodic rapidly propagating wavefronts of the EUV emission are interpreted as a fast magnetoacoustic wave train. The observations suggest that the fast-mode waves are generated during the quasi-periodic magnetic reconnection in the cusp region above the flare arcade loops. For the first time, we provide evidence of a tadpole wavelet signature at about 70-140 s in decimetric (245/610 MHz) radio bursts, along with the direct observation of a coronal fast-mode wave train in EUV. In addition, at AIA 131/193 Å we observed quasi-periodic EUV disturbances with periods of 95 and 240 s propagating downward at apparent speeds of 172-273 km s-1. The nature of these downward propagating disturbances is not revealed, but they could be connected to magnetoacoustic waves or periodically shrinking loops. Title: Significance testing for quasi-periodic pulsations in solar and stellar flares Authors: Pugh, C. E.; Broomhall, A. -M.; Nakariakov, V. M. Bibcode: 2017A&A...602A..47P Altcode: 2017arXiv170307294P The robust detection of quasi-periodic pulsations (QPPs) in solar and stellar flares has been the topic of recent debate. In light of this, we have adapted a method described by Vaughan (2005, A&A, 431, 391) to aid with the search for QPPs in flare time series data. The method identifies statistically significant periodic signals in power spectra, and properly accounts for red noise as well as the uncertainties associated with the data. We show how the method can be further developed to be used with rebinned power spectra, allowing us to detect QPPs whose signal is spread over more than one frequency bin. An advantage of these methods is that there is no need to detrend the data prior to creating the power spectrum. Examples are given where the methods have been applied to synthetic data, as well as real flare time series data with candidate QPPs from the Nobeyama Radioheliograph. These show that, despite the transient nature of QPPs, peaks corresponding to the QPPs can be seen at a significant level in the power spectrum without any form of detrending or other processing of the original time series data, providing the background trends are not too steep. Title: Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves Authors: Shestov, S. V.; Nakariakov, V. M.; Ulyanov, A. S.; Reva, A. A.; Kuzin, S. V. Bibcode: 2017ApJ...840...64S Altcode: 2017arXiv170502790S We analyze nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low-β plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform a numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, which constitutes a bulk plasma motion along the magnetic field, the tube wave, and also transverse flows in the radial direction, associated with sausage fast magnetoacoustic modes. In addition, the nonlinear torsional wave steepens and its propagation speed increases. The latter effect leads to the progressive distortion of the torsional wave front, I.e., nonlinear phase mixing. Because of the intrinsic non-uniformity of the torsional wave amplitude across the tube radius, the nonlinear effects are more pronounced in regions with higher wave amplitudes. They are always absent at the axes of the flux tube. In the case of a linear radial profile of the wave amplitude, the nonlinear effects are localized in an annulus region near the tube boundary. Thus, the parallel compressive flows driven by torsional Alfvén waves in the solar and stellar coronae, are essentially non-uniform in the perpendicular direction. The presence of additional sinks for the wave energy reduces the efficiency of the nonlinear parallel cascade in torsional Alfvén waves. Title: Multi-instrument observations of a failed flare eruption associated with MHD waves in a loop bundle Authors: Nisticò, G.; Polito, V.; Nakariakov, V. M.; Del Zanna, G. Bibcode: 2017A&A...600A..37N Altcode: 2016arXiv161202077N Context. We present observations of a B7.9-class flare that occurred on the 24th January, 2015, using the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO), the EUV Imaging Spectrometer (EIS) and the X-Ray Telescope of Hinode. The flare triggers the eruption of a dense cool plasma blob as seen in AIA 171 Å, which is unable to completely break out and remains confined within a local bundle of active region loops. During this process, transverse oscillations of the threads are observed. The cool plasma is then observed to descend back to the chromosphere along each loop strand. At the same time, a larger diffuse co-spatial loop observed in the hot wavebands of SDO/AIA and Hinode/XRT is formed, exhibiting periodic intensity variations along its length.
Aims: The formation and evolution of magnetohydrodynamic (MHD) waves depend upon the values of the local plasma parameters (e.g. density, temperature and magnetic field), which can hence be inferred by coronal seismology. In this study we aim to assess how the observed MHD modes are affected by the variation of density and temperature.
Methods: We combined analysis of EUV/X-ray imaging and spectroscopy using SDO/AIA, Hinode/EIS and XRT.
Results: The transverse oscillations of the cool loop threads are interpreted in terms of vertically polarised kink oscillations. The fitting procedure applied to the loop displacement time series gives a period of 3.5 to 4 min, and an amplitude of 5 Mm. The oscillations are strongly damped showing very low quality factor (1.5-2), which is defined as the ratio of the damping time and the oscillation period. The weak variation of the period of the kink wave, which is estimated from the fitting analysis, is in agreement with the density variations due to the presence of the plasma blob inferred from the intensity light curve at 171 Å. The coexisting intensity oscillations along the hot loop are interpreted as a slow MHD wave with a period of 10 min and phase speed of approximately 436 km s-1. Comparison between the fast and slow modes allows for the determination of the Alfvén speed, and consequently magnetic field values. The plasma-β inferred from the analysis is estimated to be approximately 0.1-0.3.
Conclusions: We show that the evolution of the detected waves is determined by the temporal variations of the local plasma parameters, caused by the flare heating and the consequent cooling. We apply coronal seismology to both waves obtaining estimates of the background plasma parameters.

Movies are available at http://www.aanda.org Title: Coronal loop seismology using damping of standing kink oscillations by mode coupling. II. additional physical effects and Bayesian analysis Authors: Pascoe, D. J.; Anfinogentov, S.; Nisticò, G.; Goddard, C. R.; Nakariakov, V. M. Bibcode: 2017A&A...600A..78P Altcode: Context. The strong damping of kink oscillations of coronal loops can be explained by mode coupling. The damping envelope depends on the transverse density profile of the loop. Observational measurements of the damping envelope have been used to determine the transverse loop structure which is important for understanding other physical processes such as heating.
Aims: The general damping envelope describing the mode coupling of kink waves consists of a Gaussian damping regime followed by an exponential damping regime. Recent observational detection of these damping regimes has been employed as a seismological tool. We extend the description of the damping behaviour to account for additional physical effects, namely a time-dependent period of oscillation, the presence of additional longitudinal harmonics, and the decayless regime of standing kink oscillations.
Methods: We examine four examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We use forward modelling of the loop position and investigate the dependence on the model parameters using Bayesian inference and Markov chain Monte Carlo (MCMC) sampling.
Results: Our improvements to the physical model combined with the use of Bayesian inference and MCMC produce improved estimates of model parameters and their uncertainties. Calculation of the Bayes factor also allows us to compare the suitability of different physical models. We also use a new method based on spline interpolation of the zeroes of the oscillation to accurately describe the background trend of the oscillating loop.
Conclusions: This powerful and robust method allows for accurate seismology of coronal loops, in particular the transverse density profile, and potentially reveals additional physical effects. Title: Coronal loop density profile estimated by forward modelling of EUV intensity Authors: Pascoe, D. J.; Goddard, C. R.; Anfinogentov, S.; Nakariakov, V. M. Bibcode: 2017A&A...600L...7P Altcode:
Aims: The transverse density structuring of coronal loops was recently calculated for the first time using the general damping profile for kink oscillations. This seismological method assumes a density profile with a linear transition region. We consider to what extent this density profile accounts for the observed intensity profile of the loop, and how the transverse intensity profile may be used to complement the seismological technique.
Methods: We use isothermal and optically transparent approximations for which the intensity of extreme ultraviolet (EUV) emission is proportional to the square of the plasma density integrated along the line of sight. We consider four different models for the transverse density profile; the generalised Epstein profile, the step function, the linear transition region profile, and a Gaussian profile. The effect of the point spread function is included and Bayesian analysis is used for comparison of the models.
Results: The two profiles with finite transitions are found to be preferable to the step function profile, which supports the interpretation of kink mode damping as being due to mode coupling. The estimate of the transition layer width using forward modelling is consistent with the seismological estimate.
Conclusions: For wide loops, that is those observed with sufficiently high spatial resolution, this method can provide an independent estimate of density profile parameters for comparison with seismological estimates. In the ill-posed case of only one of the Gaussian or exponential damping regimes being observed, it may provide additional information to allow a seismological inversion to be performed. Alternatively, it may be used to obtain structuring information for loops that do not oscillate. Title: Determination of the Alfvén Speed and Plasma-beta Using the Seismology of Sunspot Umbra Authors: Cho, I. -H.; Cho, K. -S.; Bong, S. -C.; Moon, Y. -J.; Nakariakov, V. M.; Park, J.; Baek, J. -H.; Choi, S.; Kim, Y. -H.; Lee, J. Bibcode: 2017ApJ...837L..11C Altcode: For 478 centrally located sunspots observed in the optical continuum with Solar Dynamics Observatory/Helioseismic Magnetic Imager, we perform seismological diagnostics of the physical parameters of umbral photospheres. The new technique is based on the theory of slow magnetoacoustic waves in a non-isothermally stratified photosphere with a uniform vertical magnetic field. We construct a map of the weighted frequency of three-minute oscillations inside the umbra and use it for the estimation of the Alfvén speed, plasma-beta, and mass density within the umbra. We find the umbral mean Alfvén speed ranges between 10.5 and 7.5 km s-1 and is negatively correlated with magnetic field strength. The umbral mean plasma-beta is found to range approximately between 0.65 and 1.15 and does not vary significantly from pores to mature sunspots. The mean density ranges between (1-6) × 10-4 kg m-3 and shows a strong positive correlation with magnetic field strength. Title: Long-period quasi-periodic oscillations of a small-scale magnetic structure on the Sun Authors: Kolotkov, D. Y.; Smirnova, V. V.; Strekalova, P. V.; Riehokainen, A.; Nakariakov, V. M. Bibcode: 2017A&A...598L...2K Altcode:
Aims: Long-period quasi-periodic variations of the average magnetic field in a small-scale magnetic structure on the Sun are analysed. The structure is situated at the photospheric level and is involved in a facula formation in the chromosphere.
Methods: The observational signal obtained from the SDO/HMI line-of-sight magnetograms of the target structure has a non-stationary behaviour, and is therefore processed with the Hilbert-Huang Transform spectral technique.
Results: The empirical decomposition of the original signal and subsequent testing of the statistical significance of its intrinsic modes reveal the presence of the white and pink noisy components for the periods shorter and longer than 10 min, respectively, and a significant oscillatory mode. The oscillation is found to have a non-stationary period growing from approximately 80 to 230 min and an increasing relative amplitude, while the mean magnetic field in the oscillating structure is seen to decrease. The observed behaviour could be interpreted either by the dynamical interaction of the structure with the boundaries of supergranula cells in the region of interest or in terms of the vortex shedding appearing during the magnetic flux emergence. Title: Observation of a Short Period Quasi-periodic Pulsation in Solar X-Ray, Microwave, and EUV Emissions Authors: Kumar, Pankaj; Nakariakov, Valery M.; Cho, Kyung-Suk Bibcode: 2017ApJ...836..121K Altcode: 2017arXiv170102159K This paper presents the multiwavelength analysis of a 13 s quasi-periodic pulsation (QPP) observed in hard X-ray (12-300 keV) and microwave (4.9-34 GHz) emissions during a C-class flare that occurred on 2015 September 21. Atmospheric Image Assembly (AIA) 304 and 171 Å images show an emerging loop/flux tube (L1) moving radially outward, which interacts with the preexisting structures within the active region (AR). The QPP was observed during the expansion of and rising motion of L1. The Nobeyama Radioheliograph microwave images in 17/34 GHz channels reveal a single radio source that was co-spatial with a neighboring loop (L2). In addition, using AIA 304 Å images, we detected intensity oscillations in the legs of L2 with a period of about 26 s. A similar oscillation period was observed in the GOES soft X-ray flux derivative. This oscillation period seems to increase with time. We suggest that the observed QPP is most likely generated by the interaction between L2 and L3 observed in the AIA hot channels (131 and 94 Å). The merging speed of loops L2 and L3 was ∼35 km s-1. L1 was destroyed possibly by its interaction with preexisting structures in the AR, and produced a cool jet with the speed of ∼106-118 km s-1 associated with a narrow CME (∼770 km s-1). Another mechanism of the QPP in terms of a sausage oscillation of the loop (L2) is also possible. Title: Diagnostics of Coronal Heating in Active-region Loops Authors: Fludra, A.; Hornsey, C.; Nakariakov, V. M. Bibcode: 2017ApJ...834..100F Altcode: Understanding coronal heating remains a central problem in solar physics. Many mechanisms have been proposed to explain how energy is transferred to and deposited in the corona. We summarize past observational studies that attempted to identify the heating mechanism and point out the difficulties in reproducing the observations of the solar corona from the heating models. The aim of this paper is to study whether the observed extreme ultraviolet (EUV) emission in individual coronal loops in solar active regions can provide constraints on the volumetric heating function, and to develop a diagnostic for the heating function for a subset of loops that are found close to static thermal equilibrium. We reconstruct the coronal magnetic field from Solar Dynamics Observatory/HMI data using a nonlinear force-free magnetic field model. We model selected loops using a one-dimensional stationary model, with a heating rate dependent locally on the magnetic field strength along the loop, and we calculate the emission from these loops in various EUV wavelengths for different heating rates. We present a method to measure a power index β defining the dependence of the volumetric heating rate EH on the magnetic field, {E}H\propto {B}β , and controlling also the shape of the heating function: concentrated near the loop top, uniform and concentrated near the footpoints. The diagnostic is based on the dependence of the electron density on the index β. This method is free from the assumptions of the loop filling factor but requires spectroscopic measurements of the density-sensitive lines. The range of applicability for loops of different length and heating distributions is discussed, and the steps to solving the coronal heating problem are outlined. Title: Preface to Topical Issue: Waves in the Solar Corona: From Microphysics to Macrophysics Authors: Nakariakov, V. M.; Pascoe, D. J.; Sych, R.; van Driel-Gesztelyi, L. Bibcode: 2016SoPh..291.3139N Altcode: 2016SoPh..tmp..187N No abstract at ADS Title: Motion Magnification in Coronal Seismology Authors: Anfinogentov, Sergey; Nakariakov, Valery M. Bibcode: 2016SoPh..291.3251A Altcode: 2016SoPh..tmp..180A; 2016arXiv161101790A We introduce a new method for the investigation of low-amplitude transverse oscillations of solar plasma non-uniformities, such as coronal loops, individual strands in coronal arcades, jets, prominence fibrils, polar plumes, and other contrast features that have been observed with imaging instruments. The method is based on the two-dimensional dual-tree complex wavelet transform (DTℂWT). It allows us to magnify transverse, in the plane-of-the-sky, quasi-periodic motions of contrast features in image sequences. The tests performed on the artificial data cubes that imitated exponentially decaying, multi-periodic and frequency-modulated kink oscillations of coronal loops showed the effectiveness, reliability, and robustness of this technique. The algorithm was found to give linear scaling of the magnified amplitudes with the original amplitudes, provided these are sufficiently small. In addition, the magnification is independent of the oscillation period in a broad range of the periods. The application of this technique to SDO/AIA EUV data cubes of a non-flaring active region allowed for the improved detection of low-amplitude decay-less oscillations in the majority of loops. Title: Quasi-periodic Acceleration of Electrons in the Flare on 2012 July 19 Authors: Huang, Jing; Kontar, Eduard P.; Nakariakov, Valery M.; Gao, Guannan Bibcode: 2016ApJ...831..119H Altcode: Quasi-periodic pulsations (QPPs) of nonthermal emission in an M7.7 class flare on 2012 July 19 are investigated with spatially resolved observations at microwave and HXR bands and with spectral observations at decimetric, metric waves. Microwave emission at 17 GHz of two footpoints, HXR emission at 20-50 keV of the north footpoint and loop top, and type III bursts at 0.7-3 GHz show prominent in-phase oscillations at 270 s. The microwave emission of the loop leg has less pulsation but stronger emission. Through the estimation of plasma density around the loop top from EUV observations, we find that the local plasma frequency would be 1.5 GHz or even higher. Thus, type III bursts at 700 MHz originate above the loop top. Quasi-periodic acceleration or injection of energetic electrons is proposed to dominate these in-phase QPPs of nonthermal emission from footpoints, loop top, and above. In the overlying region, drifting pulsations (DPS) at 200-600 MHz oscillate at a distinct period (200 s). Its global structure drifts toward lower frequency, which is closely related to upward plasmoids observed simultaneously from EUV emission. Hence, nonthermal emission from overlying plasmoids and underlying flaring loops show different oscillating periods. Two individual systems of quasi-periodic acceleration of electrons are proposed to coincide in the bi-direction outflows from the reconnection region. Title: Dependence of Occurrence Rates of Solar Flares and Coronal Mass Ejections on the Solar Cycle Phase and the Importance of Large-scale Connectivity Authors: Lee, Kangjin; Moon, Y. -J.; Nakariakov, V. M. Bibcode: 2016ApJ...831..131L Altcode: We investigate the dependence of the occurrence rates of major solar flares (M- and X-class) and front-side halo coronal mass ejections (FHCMEs), observed from 1996 to 2013, on the solar cycle (SC) phase for six active McIntosh sunspot group classes: Fkc, Ekc, Dkc, Fki, Eki, and Dki. We classify SC phases as follows: (1) ascending phase of SC 23 (1996-1999), (2) maximum phase of SC 23 (2000-2002), (3) descending phase of SC 23 (2003-2008), and (4) ascending phase of SC 24 (2009-2013). We find that the occurrence rates of major flares and FHCMEs during the descending phase are noticeably higher than those during the other phases for most sunspot group classes. For the most active sunspot group class, Fkc, the occurrence rate of FHCMEs during the descending phase of SC 23 is three times as high as that during the ascending phase of SC 23. The potential of each McIntosh sunspot group class to produce major flares or FHCMEs is found to depend on the SC phase. The occurrence rates (R) of major flares and FHCMEs are strongly anti-correlated with the annual average latitude of the sunspot groups (L): R∼ {L}-2.07 for major flares and R∼ {L}-2.42 for FHCMEs. This finding indicates the possible role of large-scale coronal connectivity, e.g., trans-equatorial loops, in powerful energy releases. Interestingly, this relationship is very similar to that between the volumetric coronal heating rate and X-ray loop lengths, indicating common energy release mechanisms. Title: Observation of quasi-periodic solar radio bursts associated with propagating fast-mode waves Authors: Goddard, C. R.; Nisticò, G.; Nakariakov, V. M.; Zimovets, I. V.; White, S. M. Bibcode: 2016A&A...594A..96G Altcode: 2016arXiv160804232G
Aims: Radio emission observations from the Learmonth and Bruny Island radio spectrographs are analysed to determine the nature of a train of discrete, periodic radio "sparks" (finite-bandwidth, short-duration isolated radio features) which precede a type II burst. We analyse extreme ultraviolet (EUV) imaging from SDO/AIA at multiple wavelengths and identify a series of quasi-periodic rapidly-propagating enhancements, which we interpret as a fast wave train, and link these to the detected radio features.
Methods: The speeds and positions of the periodic rapidly propagating fast waves and the coronal mass ejection (CME) were recorded using running-difference images and time-distance analysis. From the frequency of the radio sparks the local electron density at the emission location was estimated for each. Using an empirical model for the scaling of density in the corona, the calculated electron density was used to obtain the height above the surface at which the emission occurs, and the propagation velocity of the emission location.
Results: The period of the radio sparks, δtr = 1.78 ± 0.04 min, matches the period of the fast wave train observed at 171 Å, δtEUV = 1.7 ± 0.2 min. The inferred speed of the emission location of the radio sparks, 630 km s-1, is comparable to the measured speed of the CME leading edge, 500 km s-1, and the speeds derived from the drifting of the type II lanes. The calculated height of the radio emission (obtained from the density) matches the observed location of the CME leading edge. From the above evidence we propose that the radio sparks are caused by the quasi-periodic fast waves, and the emission is generated as they catch up and interact with the leading edge of the CME.

The movie associated to Fig. 2 is available at http://www.aanda.org Title: Comparison of Damped Oscillations in Solar and Stellar X-Ray flares Authors: Cho, I. -H.; Cho, K. -S.; Nakariakov, V. M.; Kim, S.; Kumar, P. Bibcode: 2016ApJ...830..110C Altcode: We explore the similarity and difference of the quasi-periodic pulsations (QPPs) observed in the decay phase of solar and stellar flares at X-rays. We identified 42 solar flares with pronounced QPPs, observed with RHESSI, and 36 stellar flares with QPPs, observed with XMM-Newton. The empirical mode decomposition (EMD) method and least-squares fit by a damped sine function were applied to obtain the periods (P) and damping times (τ) of the QPPs. We found that (1) the periods and damping times of the stellar QPPs are 16.21 ± 15.86 minutes and 27.21 ± 28.73 minutes, while those of the solar QPPs are 0.90 ± 0.56 and 1.53 ± 1.10 minutes, respectively; (2) the ratios of the damping times to the periods (τ /P) observed in the stellar QPPs (1.69 ± 0.56) are statistically identical to those of solar QPPs (1.74 ± 0.77) and (3) the scalings of the QPP damping time with the period are well described by the power law in both solar and stellar cases. The power indices of the solar and stellar QPPs are 0.96 ± 0.10 and 0.98+/- 0.05, respectively. This scaling is consistent with the scalings found for standing slow magnetoacoustic and kink modes in solar coronal loops. Thus, we propose that the underlying mechanism responsible for the stellar QPPs is the natural magnetohydrodynamic oscillation in the flaring or adjacent coronal loops, as in the case of solar flares. Title: Spatially resolved observation of the fundamental and second harmonic standing kink modes using SDO/AIA Authors: Pascoe, D. J.; Goddard, C. R.; Nakariakov, V. M. Bibcode: 2016A&A...593A..53P Altcode:
Aims: We consider a coronal loop kink oscillation observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) which demonstrates two strong spectral components. The period of the lower frequency component being approximately twice that of the shorter frequency component suggests the presence of harmonics.
Methods: We examine the presence of two longitudinal harmonics by investigating the spatial dependence of the loop oscillation. The time-dependent displacement of the loop is measured at 15 locations along the loop axis. For each position the displacement is fitted as the sum of two damped sinusoids, having periods P1 and P2, and a damping time τ. The shorter period component exhibits anti-phase oscillations in the loop legs.
Results: We interpret the observation in terms of the first (global or fundamental) and second longitudinal harmonics of the standing kink mode. The strong excitation of the second harmonic appears connected to the preceding coronal mass ejection (CME) which displaced one of the loop legs. The oscillation parameters found are P1 = 5.00±0.62 min, P2 = 2.20±0.23 min, P1/ 2P2 = 1.15±0.22, and τ/P = 3.35 ± 1.45.

A movie associated to Fig. 5 is available in electronic form at http://www.aanda.org Title: Standing sausage modes in curved coronal slabs Authors: Pascoe, D. J.; Nakariakov, V. M. Bibcode: 2016A&A...593A..52P Altcode: Context. Magnetohydrodynamic waveguides such as dense coronal loops can support standing modes. The ratios of the periods of oscillations for different longitudinal harmonics depend on the dispersive nature of the waveguide and so may be used as a seismological tool to determine coronal parameters.
Aims: We extend models of standing sausage modes in low β coronal loops to include the effects of loop curvature. The behaviour of standing sausage modes in this geometry is used to explain the properties of observed oscillations that cannot be accounted for using straight loop models.
Methods: We perform 2D numerical simulations of an oscillating coronal loop, modelled as a dense slab embedded in a potential magnetic field. The loop is field-aligned and so experiences expansion with height in addition to being curved. Standing sausage modes are excited by compressive perturbations of the loop and their properties are studied.
Results: The spatial profiles of standing sausage modes are found to be modified by the expanding loop geometry typical for flaring loops and modelled by a potential magnetic field in our simulations. Longitudinal harmonics of order n > 1 have anti-nodes that are shifted towards the loop apex and the amplitude of anti-nodes near the loop apex is smaller than those near the loop footpoints.
Conclusions: We find that the observation of standing sausage modes by the Nobeyama Radioheliograph in a flaring coronal loop on 12 January 2000 is consistent with interpretation in terms of the global mode (n = 1) and third harmonic (n = 3). This interpretation accounts for the period ratio and spatial structure of the observed oscillations. Title: Empirical mode decomposition analysis of random processes in the solar atmosphere Authors: Kolotkov, D. Y.; Anfinogentov, S. A.; Nakariakov, V. M. Bibcode: 2016A&A...592A.153K Altcode: Context. Coloured noisy components with a power law spectral energy distribution are often shown to appear in solar signals of various types. Such a frequency-dependent noise may indicate the operation of various randomly distributed dynamical processes in the solar atmosphere.
Aims: We develop a recipe for the correct usage of the empirical mode decomposition (EMD) technique in the presence of coloured noise, allowing for clear distinguishing between quasi-periodic oscillatory phenomena in the solar atmosphere and superimposed random background processes. For illustration, we statistically investigate extreme ultraviolet (EUV) emission intensity variations observed with SDO/AIA in the coronal (171 Å), chromospheric (304 Å), and upper photospheric (1600 Å) layers of the solar atmosphere, from a quiet sun and a sunspot umbrae region.
Methods: EMD has been used for analysis because of its adaptive nature and essential applicability to the processing non-stationary and amplitude-modulated time series. For the comparison of the results obtained with EMD, we use the Fourier transform technique as an etalon.
Results: We empirically revealed statistical properties of synthetic coloured noises in EMD, and suggested a scheme that allows for the detection of noisy components among the intrinsic modes obtained with EMD in real signals. Application of the method to the solar EUV signals showed that they indeed behave randomly and could be represented as a combination of different coloured noises characterised by a specific value of the power law indices in their spectral energy distributions. On the other hand, 3-min oscillations in the analysed sunspot were detected to have energies significantly above the corresponding noise level.
Conclusions: The correct accounting for the background frequency-dependent random processes is essential when using EMD for analysis of oscillations in the solar atmosphere. For the quiet sun region the power law index was found to increase with height above the photosphere, indicating that the higher frequency processes are trapped deeper in the quiet sun atmosphere. In contrast, lower levels of the sunspot umbrae were found to be characterised by higher values of the power law index, meaning the domination of lower frequencies deep inside the sunspot atmosphere. Comparison of the EMD results with those obtained with the Fourier transform showed good consistency, justifying the applicability of EMD. Title: Statistically Determined Dispersion Relations of Magnetic Field Fluctuations in the Terrestrial Foreshock Authors: Hnat, B.; O'Connell, D.; Nakariakov, V. M.; Sundberg, T. Bibcode: 2016ApJ...827...91H Altcode: 2016arXiv160108054H We obtain dispersion relations of magnetic field fluctuations for two crossings of the terrestrial foreshock by Cluster spacecraft. These crossings cover plasma conditions that differ significantly in their plasma β and in the density of the reflected ion beam, but not in the properties of the encountered ion population, both showing shell-like distribution function. Dispersion relations are reconstructed using two-point instantaneous wave number estimations from pairs of Cluster spacecraft. The accessible range of wave vectors, limited by the available spacecraft separations, extends to ≈2 × 104 km. Results show multiple branches of dispersion relations, associated with different powers of magnetic field fluctuations. We find that sunward propagating fast magnetosonic waves and beam resonant modes are dominant for the high plasma β interval with a dense beam, while the dispersions of the interval with low beam density include Alfvén and fast magnetosonic modes propagating sunward and anti-sunward. Title: Statistical properties of quasi-periodic pulsations in white-light flares observed with Kepler Authors: Pugh, C. E.; Armstrong, D. J.; Nakariakov, V. M.; Broomhall, A. -M. Bibcode: 2016MNRAS.459.3659P Altcode: 2016arXiv160403018P; 2016MNRAS.tmp..660P We embark on a study of quasi-periodic pulsations (QPPs) in the decay phase of white-light stellar flares observed by Kepler. Out of the 1439 flares on 216 different stars detected in the short-cadence data using an automated search, 56 flares are found to have pronounced QPP-like signatures in the light curve, of which 11 have stable decaying oscillations. No correlation is found between the QPP period and the stellar temperature, radius, rotation period and surface gravity, suggesting that the QPPs are independent of global stellar parameters. Hence they are likely to be the result of processes occurring in the local environment. There is also no significant correlation between the QPP period and flare energy, however there is evidence that the period scales with the QPP decay time for the Gaussian damping scenario, but not to a significant degree for the exponentially damped case. This same scaling has been observed for MHD oscillations on the Sun, suggesting that they could be the cause of the QPPs in those flares. Scaling laws of the flare energy are also investigated, supporting previous reports of a strong correlation between the flare energy and stellar temperature/radius. A negative correlation between the flare energy and stellar surface gravity is also found. Title: Effect of a Sausage Oscillation on Radio Zebra-pattern Structures in a Solar Flare Authors: Yu, Sijie; Nakariakov, V. M.; Yan, Yihua Bibcode: 2016ApJ...826...78Y Altcode: 2016arXiv160804289Y Sausage modes that are axisymmetric fast magnetoacoustic oscillations of solar coronal loops are characterized by variation of the plasma density and magnetic field, and hence cause time variations of the electron plasma frequency and cyclotron frequency. The latter parameters determine the condition for the double plasma resonance (DPR), which is responsible for the appearance of zebra-pattern (ZP) structures in time spectra of solar type IV radio bursts. We perform numerical simulations of standing and propagating sausage oscillations in a coronal loop modeled as a straight, field-aligned plasma slab, and determine the time variation of the DPR layer locations. Instant values of the plasma density and magnetic field at the DPR layers allowed us to construct skeletons of the time variation of ZP stripes in radio spectra. In the presence of a sausage oscillation, the ZP structures are shown to have characteristic wiggles with the time period prescribed by the sausage oscillation. Standing and propagating sausage oscillations are found to have different signatures in ZP patterns. We conclude that ZP wiggles can be used for the detection of short-period sausage oscillations and the exploitation of their seismological potential. Title: Effect of a Radiation Cooling and Heating Function on Standing Longitudinal Oscillations in Coronal Loops Authors: Kumar, S.; Nakariakov, V. M.; Moon, Y. -J. Bibcode: 2016ApJ...824....8K Altcode: 2016arXiv160308335K Standing long-period (with periods longer than several minutes) oscillations in large, hot (with a temperature higher than 3 MK) coronal loops have been observed as the quasi-periodic modulation of the EUV and microwave intensity emission and the Doppler shift of coronal emission lines, and they have been interpreted as standing slow magnetoacoustic (longitudinal) oscillations. Quasi-periodic pulsations of shorter periods, detected in thermal and non-thermal emissions in solar flares could be produced by a similar mechanism. We present theoretical modeling of the standing slow magnetoacoustic mode, showing that this mode of oscillation is highly sensitive to peculiarities of the radiative cooling and heating function. We generalized the theoretical model of standing slow magnetoacoustic oscillations in a hot plasma, including the effects of the radiative losses and accounting for plasma heating. The heating mechanism is not specified and taken empirically to compensate the cooling by radiation and thermal conduction. It is shown that the evolution of the oscillations is described by a generalized Burgers equation. The numerical solution of an initial value problem for the evolutionary equation demonstrates that different dependences of the radiative cooling and plasma heating on the temperature lead to different regimes of the oscillations, including growing, quasi-stationary, and rapidly decaying. Our findings provide a theoretical foundation for probing the coronal heating function and may explain the observations of decayless long-period, quasi-periodic pulsations in flares. The hydrodynamic approach employed in this study should be considered with caution in the modeling of non-thermal emission associated with flares, because it misses potentially important non-hydrodynamic effects. Title: Undamped transverse oscillations of coronal loops as a self-oscillatory process Authors: Nakariakov, V. M.; Anfinogentov, S. A.; Nisticò, G.; Lee, D. -H. Bibcode: 2016A&A...591L...5N Altcode: Context. Standing transverse oscillations of coronal loops are observed to operate in two regimes: rapidly decaying, large amplitude oscillations and undamped small amplitude oscillations. In the latter regime the damping should be compensated by energy supply, which allows the loop to perform almost monochromatic oscillations with almost constant amplitude and phase. Different loops oscillate with different periods. The oscillation amplitude does not show dependence on the loop length or the oscillation period.
Aims: We aim to develop a low-dimensional model explaining the undamped kink oscillations as a self-oscillatory process caused by the effect of negative friction. The source of energy is an external quasi-steady flow, for example, supergranulation motions near the loop footpoints or external flows in the corona.
Methods: We demonstrate that the interaction of a quasi-steady flow with a loop can be described by a Rayleigh oscillator equation that is a non-linear ordinary differential equation, with the damping and resonant terms determined empirically.
Results: Small-amplitude self-oscillatory solutions to the Rayleigh oscillator equation are harmonic signals of constant amplitude, which is consistent with the observed properties of undamped kink oscillations. The period of self-oscillations is determined by the frequency of the kink mode. The damping by dissipation and mode conversion is compensated by the continuous energy deposition at the frequency of the natural oscillation.
Conclusions: We propose that undamped kink oscillations of coronal loops may be caused by the interaction of the loops with quasi-steady flows, and hence are self-oscillations, which is analogous to producing a tune by moving a bow across a violin string. Title: Coronal loop seismology using damping of standing kink oscillations by mode coupling Authors: Pascoe, D. J.; Goddard, C. R.; Nisticò, G.; Anfinogentov, S.; Nakariakov, V. M. Bibcode: 2016A&A...589A.136P Altcode: Context. Kink oscillations of solar coronal loops are frequently observed to be strongly damped. The damping can be explained by mode coupling on the condition that loops have a finite inhomogeneous layer between the higher density core and lower density background. The damping rate depends on the loop density contrast ratio and inhomogeneous layer width.
Aims: The theoretical description for mode coupling of kink waves has been extended to include the initial Gaussian damping regime in addition to the exponential asymptotic state. Observation of these damping regimes would provide information about the structuring of the coronal loop and so provide a seismological tool.
Methods: We consider three examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) for which the general damping profile (Gaussian and exponential regimes) can be fitted. Determining the Gaussian and exponential damping times allows us to perform seismological inversions for the loop density contrast ratio and the inhomogeneous layer width normalised to the loop radius. The layer width and loop minor radius are found separately by comparing the observed loop intensity profile with forward modelling based on our seismological results.
Results: The seismological method which allows the density contrast ratio and inhomogeneous layer width to be simultaneously determined from the kink mode damping profile has been applied to observational data for the first time. This allows the internal and external Alfvén speeds to be calculated, and estimates for the magnetic field strength can be dramatically improved using the given plasma density.
Conclusions: The kink mode damping rate can be used as a powerful diagnostic tool to determine the coronal loop density profile. This information can be used for further calculations such as the magnetic field strength or phase mixing rate. Title: Transverse oscillations and stability of prominences in a magnetic field dip Authors: Kolotkov, D. Y.; Nisticò, G.; Nakariakov, V. M. Bibcode: 2016A&A...590A.120K Altcode:
Aims: We developed an analytical model of the global transverse oscillations and mechanical stability of a quiescent prominence in the magnetised environment with a magnetic field dip that accounts for the mirror current effect.
Methods: The model is based on the interaction of line currents through the Lorentz force. Within this concept the prominence is treated as a straight current-carrying wire, and the magnetic dip is provided by two photospheric current sources.
Results: Properties of both vertical and horizontal oscillations are determined by the value of the prominence current, its density and height above the photosphere, and the parameters of the magnetic dip. The prominence can be stable in both horizontal and vertical directions simultaneously when the prominence current dominates in the system and its height is less than the half-distance between the photospheric sources. Title: Dependence of kink oscillation damping on the amplitude Authors: Goddard, C. R.; Nakariakov, V. M. Bibcode: 2016A&A...590L...5G Altcode: Context. Kink oscillations of coronal loops are one of the most intensively studied oscillatory phenomena in the solar corona. In the large-amplitude rapidly damped regime, these oscillations are observed to have a low quality factor with only a few cycles of oscillation detected before they are damped. The specific mechanism responsible for rapid damping is commonly accepted to be associated with the linear coupling between collective kink oscillations and localised torsional oscillations, the phenomenon of resonant absorption of the kink mode. The role of finite amplitude effects, however, is still not clear.
Aims: We investigated the empirical dependence of the kink oscillation damping time and its quality factor, which is defined as the ratio of damping time to oscillation period, on the oscillation amplitude.
Methods: We analysed decaying kink oscillation events detected previously with TRACE, SDO/AIA and and STEREO/EUVI in the extreme ultraviolet (EUV) 171 Å band.
Results: We found that the ratio of the kink oscillation damping time to the oscillation period systematically decreases with the oscillation amplitude. We approximated the quality factor dependence on the oscillation displacement amplitude via the power-law dependence with the exponent of -1/2, however we stress that this is a by-eye estimate, and a more rigorous estimation of the scaling law requires more accurate measurements and increased statistics. We conclude that damping of kink oscillations of coronal loops depends on the oscillation amplitude, indicating the possible role of non-linear mechanisms for damping. Title: Observation of a Quasiperiodic Pulsation in Hard X-Ray, Radio, and Extreme-ultraviolet Wavelengths Authors: Kumar, Pankaj; Nakariakov, Valery M.; Cho, Kyung-Suk Bibcode: 2016ApJ...822....7K Altcode: 2016arXiv160303121K We present a multiwavelength analysis of a quasiperiodic pulsation (QPP) observed in the hard X-ray (HXR), radio, and extreme-ultraviolet (EUV) channels during an M1.9 flare that occurred on 2011 September 23-24. The nonthermal HXR emission in 25-50 keV observed by RHESSI shows five distinct impulsive peaks of decaying amplitude with a period of about 3 minutes. A similar QPP was observed in the microwave emission recorded by the Nobeyama Radioheliograph and Polarimeter in the 2, 3.75, 9.4, and 17 GHz channels. Interestingly, the 3-minute QPP was also observed in the metric and decimetric radio frequencies (25-180, 245, 610 MHz) as repetitive type III bursts. Multiwavelength observations from the Solar Dynamics Observatory/Atmospheric Image Assembly, Hinode/SOT, and Solar TErrestrial RElations Observatory/SECCHI suggest a fan-spine topology at the eruption site, associated with the formation of a quasi-circular ribbon during the flare. A small filament was observed below the fan loops before the flare onset. The filament rose slowly and interacted with the ambient field. This behavior was followed by an untwisting motion of the filament. Two different structures of the filament showed an approximately 3-minute periodic alternate rotation in the clockwise and counterclockwise directions. The 3-minute QPP was found to highly correlate with 3-minute oscillations in a nearby sunspot. We suggest that the periodic reconnection (modulated either by a sunspot slow-mode wave or by an untwisting filament) at a magnetic null point most likely causes the repetitive particle acceleration, generating the QPP observed in HXR, microwave, and type III radio bursts. Title: Solar Science with the Atacama Large Millimeter/Submillimeter Array—A New View of Our Sun Authors: Wedemeyer, S.; Bastian, T.; Brajša, R.; Hudson, H.; Fleishman, G.; Loukitcheva, M.; Fleck, B.; Kontar, E. P.; De Pontieu, B.; Yagoubov, P.; Tiwari, S. K.; Soler, R.; Black, J. H.; Antolin, P.; Scullion, E.; Gunár, S.; Labrosse, N.; Ludwig, H. -G.; Benz, A. O.; White, S. M.; Hauschildt, P.; Doyle, J. G.; Nakariakov, V. M.; Ayres, T.; Heinzel, P.; Karlicky, M.; Van Doorsselaere, T.; Gary, D.; Alissandrakis, C. E.; Nindos, A.; Solanki, S. K.; Rouppe van der Voort, L.; Shimojo, M.; Kato, Y.; Zaqarashvili, T.; Perez, E.; Selhorst, C. L.; Barta, M. Bibcode: 2016SSRv..200....1W Altcode: 2015SSRv..tmp..118W; 2015arXiv150406887W The Atacama Large Millimeter/submillimeter Array (ALMA) is a new powerful tool for observing the Sun at high spatial, temporal, and spectral resolution. These capabilities can address a broad range of fundamental scientific questions in solar physics. The radiation observed by ALMA originates mostly from the chromosphere—a complex and dynamic region between the photosphere and corona, which plays a crucial role in the transport of energy and matter and, ultimately, the heating of the outer layers of the solar atmosphere. Based on first solar test observations, strategies for regular solar campaigns are currently being developed. State-of-the-art numerical simulations of the solar atmosphere and modeling of instrumental effects can help constrain and optimize future observing modes for ALMA. Here we present a short technical description of ALMA and an overview of past efforts and future possibilities for solar observations at submillimeter and millimeter wavelengths. In addition, selected numerical simulations and observations at other wavelengths demonstrate ALMA's scientific potential for studying the Sun for a large range of science cases. Title: Magnetohydrodynamic Oscillations in the Solar Corona and Earth's Magnetosphere: Towards Consolidated Understanding Authors: Nakariakov, V. M.; Pilipenko, V.; Heilig, B.; Jelínek, P.; Karlický, M.; Klimushkin, D. Y.; Kolotkov, D. Y.; Lee, D. -H.; Nisticò, G.; Van Doorsselaere, T.; Verth, G.; Zimovets, I. V. Bibcode: 2016SSRv..200...75N Altcode: 2016SSRv..tmp....2N Magnetohydrodynamic (MHD) oscillatory processes in different plasma systems, such as the corona of the Sun and the Earth's magnetosphere, show interesting similarities and differences, which so far received little attention and remain under-exploited. The successful commissioning within the past ten years of THEMIS, Hinode, STEREO and SDO spacecraft, in combination with matured analysis of data from earlier spacecraft (Wind, SOHO, ACE, Cluster, TRACE and RHESSI) makes it very timely to survey the breadth of observations giving evidence for MHD oscillatory processes in solar and space plasmas, and state-of-the-art theoretical modelling. The paper reviews several important topics, such as Alfvénic resonances and mode conversion; MHD waveguides, such as the magnetotail, coronal loops, coronal streamers; mechanisms for periodicities produced in energy releases during substorms and solar flares, possibility of Alfvénic resonators along open field lines; possible drivers of MHD waves; diagnostics of plasmas with MHD waves; interaction of MHD waves with partly-ionised boundaries (ionosphere and chromosphere). The review is mainly oriented to specialists in magnetospheric physics and solar physics, but not familiar with specifics of the adjacent research fields. Title: Low-Frequency Waves in Space Plasmas Authors: Keiling, Andreas; Lee, Dong-Hun; Nakariakov, Valery Bibcode: 2016GMS...216.....K Altcode: Low-frequency waves in space plasmas have been studied for several decades, and our knowledge gain has been incremental with several paradigm-changing leaps forward. In our solar system, such waves occur in the ionospheres and magnetospheres of planets, and around our Moon. They occur in the solar wind, and more recently, they have been confirmed in the Sun's atmosphere as well. The goal of wave research is to understand their generation, their propagation, and their interaction with the surrounding plasma. Low-frequency Waves in Space Plasmas presents a concise and authoritative up-to-date look on where wave research stands: What have we learned in the last decade? What are unanswered questions?

While in the past waves in different astrophysical plasmas have been largely treated in separate books, the unique feature of this monograph is that it covers waves in many plasma regions, including:

Waves in geospace, including ionosphere and magnetosphere

Waves in planetary magnetospheres

Waves at the Moon

Waves in the solar wind

Waves in the solar atmosphere

Because of the breadth of topics covered, this volume should appeal to a broad community of space scientists and students, and it should also be of interest to astronomers/astrophysicists who are studying space plasmas beyond our Solar System. Title: A statistical study of decaying kink oscillations detected using SDO/AIA Authors: Goddard, C. R.; Nisticò, G.; Nakariakov, V. M.; Zimovets, I. V. Bibcode: 2016A&A...585A.137G Altcode: 2015arXiv151103558G Context. Despite intensive studies of kink oscillations of coronal loops in the last decade, a large-scale statistically significant investigation of the oscillation parameters has not been made using data from the Solar Dynamics Observatory (SDO).
Aims: We carry out a statistical study of kink oscillations using extreme ultraviolet imaging data from a previously compiled catalogue.
Methods: We analysed 58 kink oscillation events observed by the Atmospheric Imaging Assembly (AIA) on board SDO during its first four years of operation (2010-2014). Parameters of the oscillations, including the initial apparent amplitude, period, length of the oscillating loop, and damping are studied for 120 individual loop oscillations.
Results: Analysis of the initial loop displacement and oscillation amplitude leads to the conclusion that the initial loop displacement prescribes the initial amplitude of oscillation in general. The period is found to scale with the loop length, and a linear fit of the data cloud gives a kink speed of Ck = (1330 ± 50) km s-1. The main body of the data corresponds to kink speeds in the range Ck = (800-3300) km s-1. Measurements of 52 exponential damping times were made, and it was noted that at least 21 of the damping profiles may be better approximated by a combination of non-exponential and exponential profiles rather than a purely exponential damping envelope. There are nine additional cases where the profile appears to be purely non-exponential and no damping time was measured. A scaling of the exponential damping time with the period is found, following the previously established linear scaling between these two parameters. Title: ALMA Observations of the Sun in Cycle 4 and Beyond Authors: Wedemeyer, S.; Fleck, B.; Battaglia, M.; Labrosse, N.; Fleishman, G.; Hudson, H.; Antolin, P.; Alissandrakis, C.; Ayres, T.; Ballester, J.; Bastian, T.; Black, J.; Benz, A.; Brajsa, R.; Carlsson, M.; Costa, J.; DePontieu, B.; Doyle, G.; Gimenez de Castro, G.; Gunár, S.; Harper, G.; Jafarzadeh, S.; Loukitcheva, M.; Nakariakov, V.; Oliver, R.; Schmieder, B.; Selhorst, C.; Shimojo, M.; Simões, P.; Soler, R.; Temmer, M.; Tiwari, S.; Van Doorsselaere, T.; Veronig, A.; White, S.; Yagoubov, P.; Zaqarashvili, T. Bibcode: 2016arXiv160100587W Altcode: This document was created by the Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) in preparation of the first regular observations of the Sun with the Atacama Large Millimeter/submillimeter Array (ALMA), which are anticipated to start in ALMA Cycle 4 in October 2016. The science cases presented here demonstrate that a large number of scientifically highly interesting observations could be made already with the still limited solar observing modes foreseen for Cycle 4 and that ALMA has the potential to make important contributions to answering long-standing scientific questions in solar physics. With the proposal deadline for ALMA Cycle 4 in April 2016 and the Commissioning and Science Verification campaign in December 2015 in sight, several of the SSALMON Expert Teams composed strategic documents in which they outlined potential solar observations that could be feasible given the anticipated technical capabilities in Cycle 4. These documents have been combined and supplemented with an analysis, resulting in recommendations for solar observing with ALMA in Cycle 4. In addition, the detailed science cases also demonstrate the scientific priorities of the solar physics community and which capabilities are wanted for the next observing cycles. The work on this White Paper effort was coordinated in close cooperation with the two international solar ALMA development studies led by T. Bastian (NRAO, USA) and R. Brajsa, (ESO). This document will be further updated until the beginning of Cycle 4 in October 2016. In particular, we plan to adjust the technical capabilities of the solar observing modes once finally decided and to further demonstrate the feasibility and scientific potential of the included science cases by means of numerical simulations of the solar atmosphere and corresponding simulated ALMA observations. Title: Damping profile of standing kink oscillations observed by SDO/AIA Authors: Pascoe, D. J.; Goddard, C. R.; Nisticò, G.; Anfinogentov, S.; Nakariakov, V. M. Bibcode: 2016A&A...585L...6P Altcode:
Aims: Strongly damped standing and propagating kink oscillations are observed in the solar corona. This can be understood in terms of mode coupling, which causes the wave energy to be converted from the bulk transverse oscillation to localised, unresolved azimuthal motions. The damping rate can provide information about the loop structure, and theory predicts two possible damping profiles.
Methods: We used the recently compiled catalogue of decaying standing kink oscillations of coronal loops to search for examples with high spatial and temporal resolution and sufficient signal quality to allow the damping profile to be examined. The location of the loop axis was tracked, detrended, and fitted with sinusoidal oscillations with Gaussian and exponential damping profiles.
Results: Using the highest quality data currently available, we find that for the majority of our cases a Gaussian profile describes the damping behaviour at least as well as an exponential profile, which is consistent with the recently developed theory for the damping profile due to mode coupling. Title: Solar cycle variations in the powers and damping rates of low-degree solar acoustic oscillations Authors: Broomhall, A. -M.; Pugh, C. E.; Nakariakov, V. M. Bibcode: 2015AdSpR..56.2706B Altcode: Helioseismology uses the Sun's natural resonant oscillations to study the solar interior. The properties of the solar oscillations are sensitive to the Sun'2019;s magnetic activity cycle. Here we examine variations in the powers, damping rates, and energy supply rates of the most prominent acoustic oscillations in unresolved, Sun-as-a-star data, obtained by the Birmingham Solar Oscillations Network (BiSON) during solar cycles 22, 23, and the first half of 24. The variations in the helioseismic parameters are compared to the 10.7 cm flux, a well-known global proxy of solar activity. As expected the oscillations are most heavily damped and the mode powers are at a minimum at solar activity maximum. The 10.7 cm flux was linearly regressed using the fractional variations of damping rates and powers observed during cycle 23. In general, good agreement is found between the damping rates and the 10.7 cm flux. However, the linearly regressed 10.7 cm flux and fractional variation in powers diverge in cycles 22 and 24, indicating that the relationship between the mode powers and the 10.7 cm flux is not consistent from one cycle to the next. The energy supply rate of the oscillations, which is usually approximately constant, also decreases at this time. We have determined that this discrepancy is not because of the first-order bias introduced by an increase in the level of background noise or gaps in the data. Although we cannot categorically rule out an instrumental origin, the divergence observed in cycle 24, when the data were of high quality and the data coverage was over 80%, raises the possibility that the effect may be solar in origin. Title: SSALMON - The Solar Simulations for the Atacama Large Millimeter Observatory Network Authors: Wedemeyer, S.; Bastian, T.; Brajša, R.; Barta, M.; Hudson, H.; Fleishman, G.; Loukitcheva, M.; Fleck, B.; Kontar, E.; De Pontieu, B.; Tiwari, S.; Kato, Y.; Soler, R.; Yagoubov, P.; Black, J. H.; Antolin, P.; Gunár, S.; Labrosse, N.; Benz, A. O.; Nindos, A.; Steffen, M.; Scullion, E.; Doyle, J. G.; Zaqarashvili, T.; Hanslmeier, A.; Nakariakov, V. M.; Heinzel, P.; Ayres, T.; Karlicky, M. Bibcode: 2015AdSpR..56.2679W Altcode: 2015arXiv150205601W The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiated in 2014 in connection with two ALMA development studies. The Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful new tool, which can also observe the Sun at high spatial, temporal, and spectral resolution. The international SSALMONetwork aims at co-ordinating the further development of solar observing modes for ALMA and at promoting scientific opportunities for solar physics with particular focus on numerical simulations, which can provide important constraints for the observing modes and can aid the interpretation of future observations. The radiation detected by ALMA originates mostly in the solar chromosphere - a complex and dynamic layer between the photosphere and corona, which plays an important role in the transport of energy and matter and the heating of the outer layers of the solar atmosphere. Potential targets include active regions, prominences, quiet Sun regions, flares. Here, we give a brief overview over the network and potential science cases for future solar observations with ALMA. Title: Preface: Advances in solar physics Authors: Georgoulis, Manolis K.; Nakariakov, Valery M. Bibcode: 2015AdSpR..56.2677G Altcode: The idea for this special issue of Advances in Space Research (ASR) was formulated during the 14th European Solar Physics Meeting (ESPM-14) that took place in Dublin, Ireland in September 2014. Since ASR does not publish conference proceedings, it was decided to extend a general call to the international solar-physics community for manuscripts pertinent to the following thematic areas:

New and upcoming heliospheric observational and data assimilation facilities. Title: Fast Magnetoacoustic Wave Trains of Sausage Symmetry in Cylindrical Waveguides of the Solar Corona Authors: Shestov, S.; Nakariakov, V. M.; Kuzin, S. Bibcode: 2015ApJ...814..135S Altcode: 2015arXiv151007908S Fast magnetoacoustic waves guided along the magnetic field by plasma non-uniformities, in particular coronal loops, fibrils, and plumes, are known to be highly dispersive, which lead to the formation of quasi-periodic wave trains excited by a broadband impulsive driver, e.g., a solar flare. We investigated the effects of cylindrical geometry on the fast sausage wave train formation. We performed magnetohydrodynamic numerical simulations of fast magnetoacoustic perturbations of a sausage symmetry, propagating from a localized impulsive source along a field-aligned plasma cylinder with a smooth radial profile of the fast speed. The wave trains are found to have pronounced period modulation, with the longer instant period seen in the beginning of the wave train. The wave trains also have a pronounced amplitude modulation. Wavelet spectra of the wave trains have characteristic tadpole features, with the broadband large-amplitude heads preceding low-amplitude quasi-monochromatic tails. The mean period of the wave train is about the transverse fast magnetoacoustic transit time across the cylinder. The mean parallel wavelength is about the diameter of the wave-guiding plasma cylinder. Instant periods are longer than the sausage wave cutoff period. The wave train characteristics depend on the fast magnetoacoustic speed in both the internal and external media, the smoothness of the transverse profile of the equilibrium quantities, and also the spatial size of the initial perturbation. If the initial perturbation is localized at the axis of the cylinder, the wave trains contain higher radial harmonics that have shorter periods. Title: North-south asymmetry in the magnetic deflection of polar coronal hole jets Authors: Nisticò, G.; Zimbardo, G.; Patsourakos, S.; Bothmer, V.; Nakariakov, V. M. Bibcode: 2015A&A...583A.127N Altcode: 2015arXiv150801072N Context. Measurements of the sunspots area, of the magnetic field in the interplanetary medium, and of the heliospheric current sheet (HCS) position, reveal a possible north-south (N-S) asymmetry in the magnetic field of the Sun. This asymmetry could cause the bending of the HCS of the order of 5-10 deg in the southward direction, and it appears to be a recurrent characteristic of the Sun during the minima of solar activity.
Aims: We study the N-S asymmetry as inferred from measurements of the deflection of polar coronal hole jets when they propagate throughout the corona.
Methods: Since the corona is an environment where the magnetic pressure is greater than the kinetic pressure (β ≪ 1), we can assume that the magnetic field controls the dynamics of plasma. On average, jets follow magnetic field lines during their propagation, highlighting their local direction. We measured the position angles at 1 R⊙ and at 2 R⊙ of 79 jets, based on the Solar TErrestrial RElations Observatory (STEREO) ultraviolet and white-light coronagraph observations during the solar minimum period March 2007-April 2008. The average jet deflection is studied both in the plane perpendicular to the line of sight and, for a reduced number of jets, in 3D space. The observed jet deflection is studied in terms of an axisymmetric magnetic field model comprising dipole (g1), quadrupole (g2), and esapole (g3) moments.
Results: We found that the propagation of the jets is not radial, which is in agreement with the deflection due to magnetic field lines. Moreover, the amount of the deflection is different between jets over the north and those from the south pole. A comparison of jet deflections and field line tracing shows that a ratio g2/g1 ≃ -0.5 for the quadrupole and a ratio g3/g1 ≃ 1.6-2.0 for the esapole can describe the field. The presence of a non-negligible quadrupole moment confirms the N-S asymmetry of the solar magnetic field for the considered period.
Conclusions: We find that the magnetic deflection of jets is larger in the north than in the south of the order of 25-40%, with an asymmetry that is consistent with a southward deflection of the heliospheric current sheet of the order of 10 deg, consistent with that inferred from other independent datasets and instruments. Title: A Comparison Between Global Proxies of the Sun's Magnetic Activity Cycle: Inferences from Helioseismology Authors: Broomhall, A. -M.; Nakariakov, V. M. Bibcode: 2015SoPh..290.3095B Altcode: 2015SoPh..tmp...82B; 2015arXiv150702854B The last solar minimum was, by recent standards, unusually deep and long. We are now close to the maximum of the subsequent solar cycle, which is relatively weak. In this article we make comparisons between different global (unresolved) measures of the Sun's magnetic activity to investigate how they are responding to this weak-activity epoch. We focus on helioseismic data, which are sensitive to conditions, including the characteristics of the magnetic field, in the solar interior. Also considered are measures of the magnetic field in the photosphere (sunspot number and sunspot area), the chromosphere and corona (10.7 cm radio flux and 530.3 nm green coronal index), and two measures of the Sun's magnetic activity closer to Earth (the interplanetary magnetic field and the galactic cosmic-ray intensity). Scaled versions of the activity proxies diverge from the helioseismic data around 2000, indicating a change in relationship between the proxies. The degree of divergence varies from proxy to proxy, with sunspot area and 10.7 cm flux showing only small deviations, while sunspot number, coronal index, and the two interplanetary proxies show much larger departures. In Cycle 24 the deviations in the solar proxies and the helioseismic data decrease, raising the possibility that the deviations observed in Cycle 23 are just symptomatic of a 22-year Hale cycle. However, the deviations in the helioseismic data and the interplanetary proxies increase in Cycle 24. Interestingly, the divergence in the solar proxies and the helioseismic data are not reflected in the shorter-term variations (often referred to as quasi-biennial oscillations) observed on top of the dominant 11-year solar cycle. However, despite being highly correlated in Cycle 22, the short-term variations in the interplanetary proxies show very little correlation with the helioseismic data during Cycles 23 and 24. Title: A Multi-period Oscillation in a Stellar Superflare Authors: Pugh, C. E.; Nakariakov, V. M.; Broomhall, A. -M. Bibcode: 2015ApJ...813L...5P Altcode: 2015arXiv151003613P Flares that are orders of magnitude larger than the most energetic solar flares are routinely observed on Sun-like stars, raising the question of whether the same physical processes are responsible for both solar and stellar flares. In this Letter, we present a white-light stellar superflare on the star KIC 9655129, observed by NASA’s Kepler mission, with a rare multi-period quasi-periodic pulsation (QPP) pattern. Two significant periodic processes were detected using the wavelet and autocorrelation techniques, with periods of 78 ± 12 minutes and 32 ± 2 minutes. By comparing the phases and decay times of the two periodicities, the QPP signal was found to most likely be linear, suggesting that the two periodicities are independent, possibly corresponding either to different magnetohydrodynamic (MHD) modes of the flaring region or different spatial harmonics of the same mode. The presence of multiple periodicities is a good indication that the QPPs were caused by MHD oscillations and suggests that the physical processes in operation during stellar flares could be the same as those in solar flares. Title: Decayless low-amplitude kink oscillations: a common phenomenon in the solar corona? Authors: Anfinogentov, S. A.; Nakariakov, V. M.; Nisticò, G. Bibcode: 2015A&A...583A.136A Altcode: 2015arXiv150905519A Context. We investigate the decayless regime of coronal kink oscillations recently discovered in the Solar Dynamics Observatory (SDO)/AIA data. In contrast to decaying kink oscillations that are excited by impulsive dynamical processes, this type of transverse oscillations is not connected to any external impulsive impact, such as a flare or coronal mass ejection, and does not show any significant decay. Moreover the amplitude of these decayless oscillations is typically lower than that of decaying oscillations.
Aims: The aim of this research is to estimate the prevalence of this phenomenon and its characteristic signatures.
Methods: We analysed 21 active regions (NOAA 11637-11657) observed in January 2013 in the 171 Å channel of SDO/AIA. For each active region we inspected six hours of observations, constructing time-distance plots for the slits positioned across pronounced bright loops. The oscillatory patterns in time-distance plots were visually identified and the oscillation periods and amplitudes were measured. We also estimated the length of each oscillating loop.
Results: Low-amplitude decayless kink oscillations are found to be present in the majority of the analysed active regions. The oscillation periods lie in the range from 1.5 to 10 min. In two active regions with insufficient observation conditions we did not identify any oscillation patterns. The oscillation periods are found to increase with the length of the oscillating loop.
Conclusions: The considered type of coronal oscillations is a common phenomenon in the corona. The established dependence of the oscillation period on the loop length is consistent with their interpretation in terms of standing kink waves.

Appendix A is available in electronic form at http://www.aanda.org Title: Cut-off period for slow magnetoacoustic waves in coronal plasma structures Authors: Afanasyev, A. N.; Nakariakov, V. M. Bibcode: 2015A&A...582A..57A Altcode: Context. There is abundant observational evidence of longitudinal compressive waves in plasma structures of the solar corona, which are confidently interpreted in terms of slow magnetoacoustic waves. The uses of coronal slow waves in plasma diagnostics, as well as analysis of their possible contribution to coronal heating and the solar wind acceleration, require detailed theoretical modelling.
Aims: We investigate the effects of obliqueness, magnetic field, and non-uniformity of the medium on the evolution of long-wavelength slow magnetoacoustic waves guided by field-aligned plasma non-uniformities, also called tube waves. Special attention is paid to the cut-off effect due to the gravity stratification of the coronal plasma.
Methods: We study the behaviour of linear tube waves in a vertical untwisted straight field-aligned isothermal plasma cylinder. We apply the thin flux tube approximation, taking into account effects of stratification caused by gravity. The dispersion due to the finite radius of the flux tube is neglected. We analyse the behaviour of the cut-off period for an exponentially divergent magnetic flux tube filled in with a stratified plasma. The results obtained are compared with the known cases of the constant Alfven speed and the pure acoustic wave.
Results: We derive the wave equation for tube waves and reduce it to the form of the Klein-Gordon equation with varying coefficients, which explicitly contains the cut-off frequency. The cut-off period is found to vary with height, decreasing significantly in the low-beta plasma and in the plasma with the beta of the order of unity. The depressions in the cut-off period profiles can affect the propagation of longitudinal waves along coronal plasma structures towards the higher corona and can form coronal resonators. Title: Coexisting fast and slow propagating waves of the extreme-UV intensity in solar coronal plasma structures Authors: Zhang, Yuzong; Zhang, Jun; Wang, Jingxiu; Nakariakov, Valery M. Bibcode: 2015A&A...581A..78Z Altcode: Context. From 06:15 UT to 08:15 UT on 2011 June 2, a toroidal filament located at the joint of two active regions, 11226 and 11227, appeared to perform two eruptions. During this phenomenon, fast and slow magnetoacoustic waves were detected to propagate simultaneously along a funnel coronal loop system of AR 11227.
Aims: We aim to understand the relationship between fast and slow magnetoacoustic waves during their propagations and measure their properties, such as the propagating speed, path, amplitude, and period observed in the extreme ultraviolet (EUV) wavebands.
Methods: We analyse time sequences of EUV images acquired by the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory. By creating time-distance maps along selected directions, we measure the speeds and localisation of EUV intensity waves in different EUV wavebands. We determine the periods of the waves with wavelet analysis.
Results: The fast and slow magnetoacoustic waves, apparently propagating along the same path, are found to have different properties. Their apparent propagation speeds, travel distances, and periods are about 900 km s-1 and 100 km s-1, 145 Mm and 36 Mm, and 2 min and 3 min, respectively.

The movie is available in electronic form at http://www.aanda.org Title: Hilbert-Huang transform analysis of periodicities in the last two solar activity cycles Authors: Kolotkov, D. Y.; Broomhall, A. -M.; Nakariakov, V. M. Bibcode: 2015MNRAS.451.4360K Altcode: We investigated periodicities associated with the last two-and-a-half solar activity cycles with the novel Hilbert-Huang transform (HHT) method. Raw data signals of five different observational proxies: the 10.7 cm radio flux intensity, the helioseismic frequency shift, and the sunspot area signals recorded from the whole solar disc, and separately from the Northern and Southern hemispheres, were expanded into a set of intrinsic modes with the ensemble empirical mode decomposition technique. Instant and mean periods of each empirical mode were obtained with the use of the Hilbert transform applied independently to each separate mode. The periodicities were allocated to three distinct groups: short-term variations (with periods shorter than 0.5 yr), quasi-biennial oscillations (with typical periods from 0.5 yr to 3.9 yr), and longer periodicities, e.g. such as the 11 yr cycle. All periodicities detected in the examined solar cycles 22-24 are consistent with the well-known results found in the earlier solar epochs. We have demonstrated that the HHT method is a good tool for characterizing periodicities in the helioseismic data, which are necessarily relatively limited in terms of their time resolution. Periodicities obtained using the helioseismic data are, nevertheless, consistent with those found in other proxies. Since helioseismic oscillations are sensitive to the solar interior, this indicates that the behaviour of surface and atmospheric magnetic activity reflects that of the Sun's internal magnetic field. All identified intrinsic modes are seen to have clear amplitude modulation highly correlated with the 11 yr cycle. This amplitude modulation is most pronounced in the short-period modes. The short-term periodicities were found to be multiples of the shortest period, of 25 d. This ordering of the short-term periodicities is consistent with the previous findings. Signatures of the north-south asymmetry were detected in the individual hemisphere sunspot area indices. Furthermore, evidence of the last `extended' solar minimum was detected too. Title: Oscillations in stellar superflares Authors: Balona, L. A.; Broomhall, A. -M.; Kosovichev, A.; Nakariakov, V. M.; Pugh, C. E.; Van Doorsselaere, T. Bibcode: 2015MNRAS.450..956B Altcode: 2015arXiv150401491B Two different mechanisms may act to induce quasi-periodic pulsations (QPP) in whole-disc observations of stellar flares. One mechanism may be magnetohydromagnetic forces and other processes acting on flare loops as seen in the Sun. The other mechanism may be forced local acoustic oscillations due to the high-energy particle impulse generated by the flare (known as `sunquakes' in the Sun). We analyse short-cadence Kepler data of 257 flares in 75 stars to search for QPP in the flare decay branch or post-flare oscillations which may be attributed to either of these two mechanisms. About 18 per cent of stellar flares show a distinct bump in the flare decay branch of unknown origin. The bump does not seem to be a highly damped global oscillation because the periods of the bumps derived from wavelet analysis do not correlate with any stellar parameter. We detected damped oscillations covering several cycles (QPP), in seven flares on five stars. The periods of these oscillations also do not correlate with any stellar parameter, suggesting that these may be a due to flare loop oscillations. We searched for forced global oscillations which might result after a strong flare. To this end, we investigated the behaviour of the amplitudes of solar-like oscillations in eight stars before and after a flare. However, no clear amplitude change could be detected. We also analysed the amplitudes of the self-excited pulsations in two δ Scuti stars and one γ Doradus star before and after a flare. Again, no clear amplitude changes were found. Our conclusions are that a new process needs to be found to explain the high incidence of bumps in stellar flare light curves, that flare loop oscillations may have been detected in a few stars and that no conclusive evidence exists as yet for flare induced global acoustic oscillations (starquakes). Title: X-Ray and EUV Observations of Simultaneous Short and Long Period Oscillations in Hot Coronal Arcade Loops Authors: Kumar, Pankaj; Nakariakov, Valery M.; Cho, Kyung-Suk Bibcode: 2015ApJ...804....4K Altcode: 2015arXiv150207117K We report decaying quasi-periodic intensity oscillations in the X-ray (6-12 keV) and extreme-ultraviolet (EUV) channels (131, 94, 1600, 304 Å) observed by the Fermi Gamma-ray Burst Monitor and Solar Dynamics Observatory/Atmospheric Imaging Assembly (AIA), respectively, during a C-class flare. The estimated periods of oscillation and decay time in the X-ray channel (6-12 keV) were about 202 and 154 s, respectively. A similar oscillation period was detected at the footpoint of the arcade loops in the AIA 1600 and 304 Å channels. Simultaneously, AIA hot channels (94 and 131 Å) reveal propagating EUV disturbances bouncing back and forth between the footpoints of the arcade loops. The period of the oscillation and decay time were about 409 and 1121 s, respectively. The characteristic phase speed of the wave is about 560 km s-1 for about 115 Mm of loop length, which is roughly consistent with the sound speed at the temperature about 10-16 MK (480-608 km s-1). These EUV oscillations are consistent with the Solar and Heliospheric Observatory/Solar Ultraviolet Measurement of Emitted Radiation Doppler-shift oscillations interpreted as the global standing slow magnetoacoustic wave excited by a flare. The flare occurred at one of the footpoints of the arcade loops, where the magnetic topology was a 3D fan-spine with a null-point. Repetitive reconnection at this footpoint could have caused the periodic acceleration of non-thermal electrons that propagated to the opposite footpoint along the arcade and that are precipitating there, causing the observed 202 s periodicity. Other possible interpretations, e.g., the second harmonics of the slow mode, are also discussed. Title: Excitation of kink oscillations of coronal loops: statistical study Authors: Zimovets, I. V.; Nakariakov, V. M. Bibcode: 2015A&A...577A...4Z Altcode: Context. Solar flares are often accompanied by kink (transverse) oscillations of coronal loops. Despite intensive study of these oscillations in recent years, the mechanisms that excite them are still not known.
Aims: We aim to clarify the excitation mechanisms for these kink oscillations of coronal loops.
Methods: We analysed 58 kink-oscillation events observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) during its first four years (2010-2014) with the use of the JHelioviewer. Association of these oscillation events with flares, lower coronal (r ≲ 1.4 R⊙) eruptions and plasma ejections, coronal mass ejections (CMEs), and coronal Type-II radio bursts is studied.
Results: We find that 44 of these 58 oscillation events (76%) were associated with CMEs observed in the white light emission. Moreover, 57 events (98%) were accompanied by lower coronal eruptions/ejections (LCEs) observed in the extreme-ultraviolet band in the parental active regions. In the remaining event an LCE was not clearly seen, but it was definitely associated with a CME too. The main observational finding is that the kink oscillations were excited by the deviation of loops from their equilibria by a nearby LCE in 55 events (95%). In three remaining events, it was difficult to reliably determine the cause of the oscillations because of limitations in the observational data. We also found that 53 events (91%) were associated with flares. In five remaining events, the parental active regions were behind the limb and we could not directly see flare sites. It indicates that there is a close relationship between these two kinds of solar activity. However, the estimated speeds of a hypothetical driver of kink oscillations by flares were found to be lower than 500 km s-1 in 80% of the cases. Such low speeds do not favour the association of the oscillation excitation with a shock wave, as usually assumed. That only 23 (40%) of the oscillation events were found to be associated with coronal Type-II radio bursts also goes against the shock wave mechanism for the excitation of kink oscillations.
Conclusions: The statistical analysis shows that the most probable mechanism for exciting the kink oscillations of coronal loops is the deviation of loops from their equilibrium by nearby eruptions or plasma ejections rather than a blast shock wave ignited by a flare.

Table 1 is available in electronic form at http://www.aanda.org Title: Diagnostics of Coronal Heating in Solar Active Regions Authors: Fludra, Andrzej; Hornsey, Christopher; Nakariakov, Valery Bibcode: 2015TESS....120305F Altcode: We aim to develop a diagnostic method for the coronal heating mechanism in active region loops. Observational constraints on coronal heating models have been sought using measurements in the X-ray and EUV wavelengths. Statistical analysis, using EUV emission from many active regions, was done by Fludra and Ireland (2008) who studied power-law relationships between active region integrated magnetic flux and emission line intensities. A subsequent study by Fludra and Warren (2010) for the first time compared fully resolved images in an EUV spectral line of OV 63.0 nm with the photospheric magnetic field, leading to the identification of a dominant, ubiquitous variable component of the transition region EUV emission and a discovery of a steady basal heating, and deriving the dependence of the basal heating rate on the photospheric magnetic flux density. In this study, we compare models of single coronal loops with EUV observations. We assess to what degree observations of individual coronal loops made in the EUV range are capable of providing constraints on the heating mechanism. We model the coronal magnetic field in an active region using an NLFF extrapolation code applied to a photospheric vector magnetogram from SDO/HMI and select several loops that match an SDO/AIA 171 image of the same active region. We then model the plasma in these loops using a 1D hydrostatic code capable of applying an arbitrary heating rate as a function of magnetic field strength along the loop. From the plasma parameters derived from this model, we calculate the EUV emission along the loop in AIA 171 and 335 bands, and in pure spectral lines of Fe IX 17.1 nm and Fe XVI 33.5 nm. We use different spatial distributions of the heating function: concentrated near the loop top, uniform and concentrated near the footpoints, and investigate their effect on the modelled EUV intensities. We find a diagnostics based on the dependence of the total loop intensity on the shape of the heating function and discuss its range of applicability for loops of different length. Title: Solar and Heliospheric Physics with the Square Kilometre Array Authors: Nakariakov, V.; Bisi, M. M.; Browning, P. K.; Maia, D.; Kontar, E. P.; Oberoi, D.; Gallagher, P. T.; Cairns, I. H.; Ratcliffe, H. Bibcode: 2015aska.confE.169N Altcode: 2015PoS...215E.169N; 2015arXiv150700516N The fields of solar radiophysics and solar system radio physics, or radio heliophysics, will benefit immensely from an instrument with the capabilities projected for SKA. Potential applications include interplanetary scintillation (IPS), radio-burst tracking, and solar spectral radio imaging with a superior sensitivity. These will provide breakthrough new insights and results in topics of fundamental importance, such as the physics of impulsive energy releases, magnetohydrodynamic oscillations and turbulence, the dynamics of post-eruptive processes, energetic particle acceleration, the structure of the solar wind and the development and evolution of solar wind transients at distances up to and beyond the orbit of the Earth. The combination of the high spectral, time and spatial resolution and the unprecedented sensitivity of the SKA will radically advance our understanding of basic physical processes operating in solar and heliospheric plasmas and provide a solid foundation for the forecasting of space weather events. Title: Radial and Azimuthal Oscillations in Halo Coronal Mass Ejections Authors: Lee, Harim; Moon, Yong-Jae; Nakariakov, Valery Bibcode: 2015TESS....131002L Altcode: We present the first observational detection of radial and azimuthal oscillations in full halo coronal mass ejections (HCMEs). We analyse nine HCMEs well-observed by the Large Angle and Spectrometric Coronagraph (LASCO) from February to June, 2011. Using the LASCO C3 running difference images, we estimated the instantaneous apparent speeds of the HCMEs in different radial directions from the solar disk centre. We find that the development of all these HCMEs is accompanied with quasi-periodic variations of the instantaneous radial velocity with the periods ranging from 24 to 48 minutes. The amplitudes of the instant speed variations reach about a half of the projected speeds. The amplitudes are found to anti-correlate with the periods and correlate with the HCME speed, indicating the nonlinear nature of the process. The oscillations have a clear azimuthal structure in the heliocentric polar coordinate system. The oscillations in seven events are found to be associated with distinct azimuthal wave modes with the azimuthal wave number m=1 for six events and m=2 for one event. The polarisation of the oscillations in these seven HCMEs is broadly consistent with those of their position angles with the mean difference of 42.5 degree. The oscillations may be connected with natural oscillations of the plasmoids around a dynamical equilibrium, or self-oscillatory processes, e.g. the periodic shedding of Alfvénic vortices. Our results indicate the need for advanced theory of oscillatory processes in CMEs. Title: Radial and Azimuthal Oscillations of Halo Coronal Mass Ejections in the Sun Authors: Lee, Harim; Moon, Y. -J.; Nakariakov, V. M. Bibcode: 2015ApJ...803L...7L Altcode: We present the first observational detection of radial and azimuthal oscillations in full halo coronal mass ejections (HCMEs). We analyze nine HCMEs well-observed by the Large Angle and Spectrometric Coronagraph (LASCO) from 2011 February to June. Using the LASCO C3 running difference images, we estimated the instantaneous apparent speeds of the HCMEs in different radial directions from the solar disk center. We find that the development of all these HCMEs is accompanied by quasi-periodic variations of the instantaneous radial velocity with the periods ranging from 24 to 48 minutes. The amplitudes of the instant speed variations reach about a half of the projected speeds. The amplitudes are found to anti-correlate with the periods and correlate with the HCME speed, indicating the nonlinear nature of the process. The oscillations have a clear azimuthal structure in the heliocentric polar coordinate system. The oscillations in seven events are found to be associated with distinct azimuthal wave modes with the azimuthal wave number m = 1 for six events and m = 2 for one event. The polarization of the oscillations in these seven HCMEs is broadly consistent with those of their position angles with the mean difference of 43°. The oscillations may be connected with natural oscillations of the plasmoids around a dynamical equilibrium, or self-oscillatory processes, e.g., the periodic shedding of Alfvénic vortices. Our results indicate the need for an advanced theory of oscillatory processes in coronal mass ejections. Title: Intensity and Doppler Velocity Oscillations in Pore Atmospheres Authors: Cho, K. -S.; Bong, S. -C.; Nakariakov, V. M.; Lim, E. -K.; Park, Y. -D.; Chae, J. C.; Yang, H. -S.; Park, H. -M.; Yurchyshyn, V. Bibcode: 2015ApJ...802...45C Altcode: We have investigated chromospheric traveling features running across two merged pores from their centers at speeds of about 55 km s-1, in the active region AR 11828. The pores were observed on 2013 August 24 by using high-time, spatial, and spectral resolution data from the Fast Imaging Solar Spectrograph of the 1.6 m New Solar Telescope. We infer a line-of-sight (LOS) velocity by applying the lambdameter method to the Ca ii 8542 Å band and Hα band, and investigate intensity and LOS velocity changes at different wavelengths and different positions at the pores. We find that they have three-minute oscillations, and the intensity oscillation from the line center (0.0 \overset{\circ}A ) is preceded by that from the core (-0.3 \overset{\circ}A ) of the bands. There is no phase difference between the intensity and the LOS velocity oscillations at a given wavelength. The amplitude of LOS velocity from the near core spectra ({Δ }λ =0.10-0.21 \overset{\circ}A ) is greater than that from the far core spectra ({Δ }λ =0.24-0.36 \overset{\circ}A ). These results support the interpretation of the observed wave as a slow magnetoacoustic wave propagating along the magnetic field lines in the pores. The apparent horizontal motion and a sudden decrease of its speed beyond the pores can be explained by the projection effect caused by inclination of the magnetic field with a canopy structure. We conclude that the observed wave properties of the pores are quite similar to those from the sunspot observations. Title: Multi-mode quasi-periodic pulsations in a solar flare Authors: Kolotkov, D. Y.; Nakariakov, V. M.; Kupriyanova, E. G.; Ratcliffe, H.; Shibasaki, K. Bibcode: 2015A&A...574A..53K Altcode: Context. Quasi-periodic pulsations (QPP) of the electromagnetic radiation emitted in solar and stellar flares are often detected in microwave, white light, X-ray, and gamma-ray bands. Mechanisms for QPP are intensively debated in the literature. Previous studies revealed that QPP may manifest non-linear, non-stationary and, perhaps, multi-modal processes operating in flares.
Aims: We study QPP of the microwave emission generated in an X3.2-class solar flare on 14 May, 2013, observed with the Nobeyama Radioheliograph (NoRH), aiming to reveal signatures of the non-linear, non-stationary, and multi-modal processes in the signal.
Methods: The NoRH correlation signal obtained at the 17 GHz intensity has a clear QPP pattern. The signal was analysed with the Hilbert-Huang transform (HHT) that allows one to determine its instant amplitude and frequency, and their time variation.
Results: It was established that the QPP consists of at least three well-defined intrinsic modes, with the mean periods of 15, 45, and 100 s. All the modes have quasi-harmonic behaviour with different modulation patterns. The 100 s intrinsic mode is a decaying oscillation, with the decay time of 250 s. The 15 s intrinsic mode shows a similar behaviour, with the decay time of 90 s. The 45 s mode has a wave-train behaviour.
Conclusions: Dynamical properties of detected intrinsic modes indicate that the 100 s and 15 s modes are likely to be associated with fundamental kink and sausage modes of the flaring loop, respectively. The 100 s oscillation could also be caused by the fundamental longitudinal mode, while this interpretation requires the plasma temperature of about 30 million K and hence is not likely. The 45 s mode could be the second standing harmonics of the kink mode. Title: Evolution of Fast Magnetoacoustic Pulses in Randomly Structured Coronal Plasmas Authors: Yuan, D.; Pascoe, D. J.; Nakariakov, V. M.; Li, B.; Keppens, R. Bibcode: 2015ApJ...799..221Y Altcode: 2014arXiv1411.4152Y We investigate the evolution of fast magnetoacoustic pulses in randomly structured plasmas, in the context of large-scale propagating waves in the solar atmosphere. We perform one-dimensional numerical simulations of fast wave pulses propagating perpendicular to a constant magnetic field in a low-β plasma with a random density profile across the field. Both linear and nonlinear regimes are considered. We study how the evolution of the pulse amplitude and width depends on their initial values and the parameters of the random structuring. Acting as a dispersive medium, a randomly structured plasma causes amplitude attenuation and width broadening of the fast wave pulses. After the passage of the main pulse, secondary propagating and standing fast waves appear. Width evolution of both linear and nonlinear pulses can be well approximated by linear functions; however, narrow pulses may have zero or negative broadening. This arises because narrow pulses are prone to splitting, while broad pulses usually deviate less from their initial Gaussian shape and form ripple structures on top of the main pulse. Linear pulses decay at an almost constant rate, while nonlinear pulses decay exponentially. A pulse interacts most efficiently with a random medium with a correlation length of about half of the initial pulse width. This detailed model of fast wave pulses propagating in highly structured media substantiates the interpretation of EIT waves as fast magnetoacoustic waves. Evolution of a fast pulse provides us with a novel method to diagnose the sub-resolution filamentation of the solar atmosphere. Title: A Combined Analysis of the Observational Aspects of the Quasi-biennial Oscillation in Solar Magnetic Activity Authors: Bazilevskaya, G.; Broomhall, A. -M.; Elsworth, Y.; Nakariakov, V. M. Bibcode: 2015sac..book..359B Altcode: No abstract at ADS Title: Nonlinear slow magnetoacoustic waves in coronal plasma structures Authors: Afanasyev, A. N.; Nakariakov, V. M. Bibcode: 2015A&A...573A..32A Altcode: Context. There is abundant observational evidence of longitudinal waves in the plasma structures of the solar corona. These essentially compressive waves are confidently interpreted as slow magnetoacoustic waves. The use of the slow waves in plasma diagnostics and estimating their possible contribution to plasma heating and acceleration require detailed theoretical modelling.
Aims: We investigate the role of obliqueness and magnetic effects in the evolution of slow magnetoacoustic waves, also called tube waves, in field-aligned plasma structures. Special attention is paid to the wave damping caused by nonlinear steepening.
Methods: We considered an untwisted straight axisymmetric field-aligned plasma cylinder and analysed the behaviour of the slow magnetoacoustic waves that are guided by this plasma structure. We adopted a thin flux tube approximation. We took into account dissipation caused by viscosity, resistivity and thermal conduction, and nonlinearity. Effects of stratification and dispersion caused by the finite radius of the flux tube were neglected.
Results: We derive the Burgers-type evolutionary equation for tube waves in a uniform plasma cylinder. Compared with a plane acoustic wave, the formation of shock fronts in tube waves is found to occur at a larger distance from the source. In addition, tube waves experience stronger damping. These effects are most pronounced in plasmas with the parameter β at about or greater than unity. In a low-β plasma, the evolution of tube waves can satisfactorily be described with the Burgers equation for plane acoustic waves.
Conclusions: Title: Vertical Kink Oscillation of a Magnetic Flux Rope Structure in the Solar Corona Authors: Kim, S.; Nakariakov, V. M.; Cho, K. -S. Bibcode: 2014ApJ...797L..22K Altcode: Vertical transverse oscillations of a coronal magnetic rope, observed simultaneously in the 171 Å and 304 Å bandpasses of the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO), are detected. The oscillation period is about 700 s and the displacement amplitude is about 1 Mm. The oscillation amplitude remains constant during the observation. Simultaneous observation of the rope in the bandpasses corresponding to the coronal and chromospheric temperatures suggests that it has a multi-thermal structure. Oscillatory patterns in 171 Å and 304 Å are coherent, which indicates that the observed kink oscillation is collective, in which the rope moves as a single entity. We interpret the oscillation as a fundamental standing vertically polarized kink mode of the rope, while the interpretation in terms of a perpendicular fast wave could not be entirely ruled out. In addition, the arcade situated above the rope and seen in the 171 Å bandpass shows an oscillatory motion with the period of about 1000 s. Title: A Combined Analysis of the Observational Aspects of the Quasi-biennial Oscillation in Solar Magnetic Activity Authors: Bazilevskaya, G.; Broomhall, A. -M.; Elsworth, Y.; Nakariakov, V. M. Bibcode: 2014SSRv..186..359B Altcode: 2014SSRv..tmp...34B Solar quasi-biennial oscillations (QBOs) with the time scale of 0.6-4 yrs appear to be a basic feature of the Sun's activity. Observational aspects of QBOs are reviewed on the basis of recent publications. Solar QBOs are shown to be ubiquitous and very variable. We demonstrate that many features of QBOs are common to different observations. These features include variable periodicity and intermittence with signs of stochastisity, a presence at all levels of the solar atmosphere and even in the convective zone, independent development in the northern and southern solar hemispheres, most pronounced amplitudes during the maximum phase of the 11-yr cycle and the transition of QBOs into interplanetary space. Temporal weakening of solar activity around the maximum of the 11-yr cycle (Gnevyshev Gap) can be considered an integral part of QBOs. The exact mechanism by which the solar QBO is produced is poorly understood. We describe some of the most plausible theoretical mechanisms and discuss observational features that support/contradict the theory. QBOs have an important meaning as a benchmark of solar activity, not only for investigation of the solar dynamo but also in terms of space weather. Title: Dynamics of a multi-thermal loop in the solar corona Authors: Nisticò, G.; Anfinogentov, S.; Nakariakov, V. M. Bibcode: 2014A&A...570A..84N Altcode: Context. We present an observation of a long-living multi-thermal coronal loop, visible in different extreme ultra-violet wavebands of SDO/AIA in a quiet-Sun region close to the western solar limb.
Aims: Analysis of persistent kink displacements of the loop seen in different bandpasses that correspond to different temperatures of the plasma allows sub-resolution structuring of the loop to be revealed.
Methods: A vertically oriented slit is taken at the loop top, and time-distance maps are made from it. Loop displacements in time-distance maps are automatically tracked with the Gaussian fitting technique and fitted with a sinusoidal function that is "guessed". Wavelet transforms are further used in order to quantify the periodicity variation in time of the kink oscillations.
Results: The loop strands are found to oscillate with the periods ranging between 3 and 15 min. The oscillations are observed in intermittent regime with temporal changes in the period and amplitude. The oscillations are different at three analysed wavelengths.
Conclusions: This finding suggests that the loop-like threads seen at different wavelengths are not co-spatial, hence that the loop consists of several multi-thermal strands. The detected irregularity of the oscillations can be associated with a stochastic driver acting at the footpoints of the loop.

A movie associated to Fig. 1 is available in electronic form at http://www.aanda.org Title: Oscillations in a Sunspot with Light Bridges Authors: Yuan, Ding; Nakariakov, Valery M.; Huang, Zhenghua; Li, Bo; Su, Jiangtao; Yan, Yihua; Tan, Baolin Bibcode: 2014ApJ...792...41Y Altcode: 2014arXiv1407.1544Y The Solar Optical Telescope on board Hinode observed a sunspot (AR 11836) with two light bridges (LBs) on 2013 August 31. We analyzed a two-hour Ca II H emission intensity data set and detected strong five-minute oscillation power on both LBs and in the inner penumbra. The time-distance plot reveals that the five-minute oscillation phase does not vary significantly along the thin bridge, indicating that the oscillations are likely to originate from underneath it. The slit taken along the central axis of the wide LB exhibits a standing wave feature. However, at the center of the wide bridge, the five-minute oscillation power is found to be stronger than at its sides. Moreover, the time-distance plot across the wide bridge exhibits a herringbone pattern that indicates a counter-stream of two running waves, which originated at the bridge's sides. Thus, the five-minute oscillations on the wide bridge also resemble the properties of running penumbral waves. The five-minute oscillations are suppressed in the umbra, while the three-minute oscillations occupy all three cores of the sunspot's umbra, separated by the LBs. The three-minute oscillations were found to be in phase at both sides of the LBs. This may indicate that either LBs do not affect umbral oscillations, or that umbral oscillations at different umbral cores share the same source. It also indicates that LBs are rather shallow objects situated in the upper part of the umbra. We found that umbral flashes (UFs) follow the life cycles of umbral oscillations with much larger amplitudes. They cannot propagate across LBs. UFs dominate the three-minute oscillation power within each core; however, they do not disrupt the phase of umbral oscillation. Title: Observation of a high-quality quasi-periodic rapidly propagating wave train using SDO/AIA Authors: Nisticò, G.; Pascoe, D. J.; Nakariakov, V. M. Bibcode: 2014A&A...569A..12N Altcode: Context. We present a new event of quasi-periodic wave trains observed in EUV wavebands that rapidly propagate away from an active region after a flare.
Aims: We measured the parameters of a wave train observed on 7 December 2013 after an M1.2 flare, such as the phase speeds, periods and wavelengths, in relationship to the local coronal environment and the energy sources.
Methods: We compared our observations with a numerical simulation of fast magnetoacoustic waves that undergo dispersive evolution and leakage in a coronal loop embedded in a potential magnetic field.
Results: The wave train is observed to propagate as several arc-shaped intensity disturbances for almost half an hour, with a speed greater than 1000 km s-1 and a period of about 1 min. The wave train followed two different patterns of propagation, in accordance with the magnetic structure of the active region. The oscillatory signal is found to be of high-quality, i.e. there is a large number (10 or more) of subsequent wave fronts observed. The observations are found to be consistent with the numerical simulation of a fast wave train generated by a localised impulsive energy release.
Conclusions: Transverse structuring in the corona can efficiently create and guide high-quality quasi-periodic propagating fast wave trains.

The movies are available in electronic form at http://www.aanda.org Title: Wave dynamics in a sunspot umbra Authors: Sych, R.; Nakariakov, V. M. Bibcode: 2014A&A...569A..72S Altcode: 2014arXiv1409.4530S Context. Sunspot oscillations are one of the most frequently studied wave phenomena in the solar atmosphere. Understanding the basic physical processes responsible for sunspot oscillations requires detailed information about their fine structure.
Aims: We aim to reveal the relationship between the fine horizontal and vertical structure, time evolution, and the fine spectral structure of oscillations in a sunspot umbra.
Methods: The high spatial and time resolution data obtained with SDO/AIA for the sunspot in active region NOAA 11131 on 08 December 2010 were analysed with the time-distance plot technique and the pixelised wavelet filtering method. Different levels of the sunspot atmosphere were studied from the temperature minimum to the corona.
Results: Oscillations in the 3 min band dominate in the umbra. The integrated spectrum of umbral oscillations contains distinct narrowband peaks at 1.9 min, 2.3 min, and 2.8 min. The power significantly varies in time, forming distinct 12-20 min oscillation trains. The oscillation power distribution over the sunspot in the horizontal plane reveals that the enhancements of the oscillation amplitude, or wave fronts, have a distinct structure consisting of an evolving two-armed spiral and a stationary circular patch at the spiral origin, situated near the umbra centre. This structure is seen from the temperature minimum at 1700 Å to the 1.6 MK corona at 193 Å. In time, the spiral rotates anti-clockwise. The wave front spirality is most pronounced during the maximum amplitude phases of the oscillations, and in the bandpasses where umbral oscillations have the highest power, 304 Å and 171 Å. In the low-amplitude phases the spiral breaks into arc-shaped patches. The 2D cross-correlation function shows that the oscillations at higher atmospheric levels occur later than at lower layers. The phase speed is estimated to be about 100 km s-1. The fine spectral analysis shows that the central patch corresponds to the high-frequency oscillations, while the spiral arms highlight the lower-frequency oscillations in the 3 min band.
Conclusions: The vertical and horizontal radial structure of the oscillations is consistent with the model that interprets umbral oscillations as slow magnetoacoustic waves filtered by the atmospheric temperature non-uniformity in the presence of the magnetic field inclination from the vertical. The mechanism for the polar-angle structure of the oscillations, in particular the spirality of the wave fronts, needs to be revealed. Title: Erratum: "Three-minute Oscillations above Sunspot Umbra Observed with the Solar Dynamics Observatory/Atmospheric Imaging Assembly and Nobeyama Radioheliograph" (2012, ApJ, 746, 119) Authors: Reznikova, V. E.; Shibasaki, K.; Sych, R. A.; Nakariakov, V. M. Bibcode: 2014ApJ...792...81R Altcode: No abstract at ADS Title: Fast magnetoacoustic wave trains in coronal holes Authors: Pascoe, D. J.; Nakariakov, V. M.; Kupriyanova, E. G. Bibcode: 2014A&A...568A..20P Altcode: Context. Rapidly propagating coronal EUV disturbances recently discovered in the solar corona are interpreted in terms of guided fast magnetoacoustic waves. Fast magnetoacoustic waves experience geometric dispersion in waveguides, which causes localised, impulsive perturbations to develop into quasi-periodic wave trains.
Aims: We consider the formation of fast wave trains in a super-radially expanding coronal hole modelled by a magnetic funnel with a field-aligned density profile that is rarefied in comparison to the surrounding plasma. This kind of structure is typical of coronal holes, and it forms a fast magnetoacoustic anti-waveguide as a local maximum in the Alfvén speed.
Methods: We performed 2D MHD numerical simulations for impulsively generated perturbations to the system. Both sausage and kink perturbations are considered and the role of the density contrast ratio investigated.
Results: The anti-waveguide funnel geometry refracts wave energy away from the structure. However, in this geometry the quasi-periodic fast wave trains are found to appear, too, and so can be associated with the observed rapidly propagating coronal EUV disturbances. The wave trains propagate along the external edge of the coronal hole. The fast wave trains generated in coronal holes exhibit less dispersive evolution than in the case of a dense waveguide.
Conclusions: We conclude that an impulsive energy release localised in a coronal plasma inhomogeneity develops into a fast wave train for both kink and sausage disturbances and for both waveguide and anti-waveguide transverse plasma profiles. Title: Editorial: solar radiophysics — recent results on observations and theories Authors: Nakariakov, Valery M.; Kashapova, Larisa K.; Yan, Yi-Hua Bibcode: 2014RAA....14....1N Altcode: Solar radiophysics is a rapidly developing branch of solar physics and plasma astrophysics. Solar radiophysics has the goal of analyzing observations of radio emissions from the Sun and understanding basic physical processes operating in quiet and active regions of the solar corona. In the near future, the commissioning of a new generation of solar radio observational facilities, which include the Chinese Spectral Radio Heliograph (CSRH) and the upgrade of the Siberian Solar Radio Telescope (SSRT), and the beginning of solar observations with the Atacama Large Millimeter/submillimeter Array (ALMA), is expected to bring us new breakthrough results of a transformative nature. The Marie-Curie International Research Staff Exchange (MC IRSES) “RadioSun” international network aims to create a solid foundation for the successful exploitation of upcoming solar radio observational facilities, as well as intensive use of the existing observational tools, advanced theoretical modeling of relevant physical processes and observables, and training a new generation of solar radio physicists. The RadioSun network links research teams from China, Czech Republic, Poland, Russia and the UK. This mini-volume presents research papers based on invited reviews and contributed talks at the 1st RadioSun workshop in China. These papers cover a broad range of research topics and include recent observational and theoretical advances in solar radiophysics, MHD seismology of the solar corona, physics of solar flares, generation of radio emission, numerical modeling of MHD and plasma physics processes, charged-particle acceleration and novel instrumentation. Title: Sausage oscillations of coronal plasma slabs Authors: Hornsey, C.; Nakariakov, V. M.; Fludra, A. Bibcode: 2014A&A...567A..24H Altcode: Context. Sausage oscillations are observed in plasma non-uniformities of the solar corona as axisymmetric perturbations of the non-uniformity. Often, these non-uniformities can be modelled as field-aligned slabs of the density enhancement.
Aims: We perform parametric studies of sausage oscillations of plasma slabs, aiming to determine the dependence of the oscillation period on its parameters, and the onset of leaky and trapped regimes of the oscillations.
Methods: Slabs with smooth transverse profiles of the density of a zero-beta plasma are perturbed by an impulsive localised perturbation of the sausage symmetry. In particular, the slab can contain an infinitely thin current sheet in its centre. The initial value problem is then solved numerically. The numerical results are subject to spectral analysis. The results are compared with analytical solutions for a slab with a step-function profile and also with sausage oscillations of a plasma cylinder.
Results: We established that sausage oscillations in slabs generally have the same properties as in plasma cylinders. In the trapped regime, the sausage oscillation period increases with the increase in the longitudinal wavelength. In the leaky regime, the dependence of the period on the wavelength experiences saturation, and the period becomes independent of the wavelength in the long-wavelength limit. In the leaky regime the period is always longer than in the trapped regime. The sausage oscillation period in a slab is always longer than in a cylinder with the same transverse profile. In slabs with steeper transverse profiles, sausage oscillations have longer periods. The leaky regime occurs at shorter wavelengths in slabs with smoother profiles. Title: Temperature Anisotropy in the Presence of Ultra Low Frequency Waves in the Terrestrial Foreshock Authors: Selzer, L. A.; Hnat, B.; Osman, K. T.; Nakariakov, V. M.; Eastwood, J. P.; Burgess, D. Bibcode: 2014ApJ...788L...5S Altcode: We report the first study of the correlation between elevated solar wind core plasma temperatures and temperature anisotropy in the terrestrial foreshock. Plasma temperature is enhanced near the fire hose marginal stability threshold in the presence of ultra low frequency (ULF) large amplitude magnetic perturbations, which are intrinsically right-hand circularly polarized. Direct comparison of contemporaneous anisotropic temperatures in the upstream solar wind and the foreshock suggests that the net heating of plasma is mediated via increase of the parallel temperature in the foreshock region where the ULF waves are present. We consider the possibility that a mechanism based on Landau damping, where solar wind plasma temperature parallel to the background magnetic field is increased by interaction with oblique compressible fast magneto-acoustic ULF waves, influences temperature anisotropy. Title: Fast magnetoacoustic wave trains in magnetic funnels of the solar corona Authors: Pascoe, David; Nakariakov, Valery; Kupriyanova, Elena Bibcode: 2014cosp...40E2453P Altcode: Fast magnetoacoustic waves are highly dispersive in waveguides and so can generate quasi-periodic wave trains if a localised, impulsive driver is applied, such as flaring energy release. Wave trains have been observed propagating in the solar corona and may be of use as a seismological tool since they depend upon the plasma structuring perpendicular to the direction of propagation. We extend existing models of magnetoacoustic waveguides to consider the effects of an expanding magnetic field with a field-aligned density structure, responding to the recent discovery of fast wave trains of EUV intensity. We investigate the dependence of the wave train properties on variables such as the density contrast ratio, density stratification, and the spectral profile of the driver. The funnel geometry leads to novel wave behaviour, such as the formation of additional wave trains that propagate outside but along the density structure due to leakage and refraction. The results of our numerical simulations demonstrate properties similar to those of wave trains observed in the solar corona. Title: Decaying long-period oscillations in flaring coronal loops Authors: Nakariakov, Valery Bibcode: 2014cosp...40E2227N Altcode: Quasi-periodic rapidly-decaying variations of the Doppler shift of the emission lines associated with the hot plasma were detected in solar flares about ten years ago with the SUMER spectrograph operating in EUV. Later, similar field-aligned flows of the hot plasma in flaring loops were found in the data of Yohkoh/BCS. The oscillations characterised by relatively long periods, in the range 10-20 min, and very short decay times, 15-30 min, are known as “SUMER” oscillations. We present observations of SUMER oscillations in the microwave band with the Nobeyama Radioheliograph and SDO/AIA. Analysis of the microwave data, obtained in the 17 GHz channel during an M1.6 flare revealed the presence of 12.6-min oscillations of the emitting plasma density. The oscillations were seen to decay with the characteristic time of about 15 min. Simultaneously, these oscillations were detected in the variation of the EUV emission intensity measured in the 335A channel of SDO/AIA. Our observational findings support the interpretation of SUMER oscillations in terms of impulsively excited standing acoustic oscillations in flaring loops or arcades, based upon numerical radiative MHD simulations. Moreover, very recently a similar dynamical pattern was detected in the light-curve of a megaflare on the dM4.5e star YZ CMi in the white light band. This result indicates striking similarities between dynamical processes in moderate solar flares and stellar megaflares. Title: Spatial Structure of Multimode Oscillations in a Solar Flare on 14 May 2013 in EUV and Radio Bands Authors: Kolotkov, Dmitry; Nakariakov, Valery; Nisticò, Giuseppe; Shibasaki, Kiyoto; Kupriyanova, Elena Bibcode: 2014cosp...40E1558K Altcode: Quasi-periodic pulsations and coronal loop oscillations in an X-class solar flare on 14 May 2013 are considered. Rapidly decaying kink oscillations of coronal loops with periods of several minutes in the flaring active region detected in the EUV band with SDO/AIA after the impulsive phase of the flare. Oscillations of neighbouring loops are excited simultaneously, but get rapidly out of phase. In the impulsive phase, observations in the radio band with the Nobeyama Radioheliograph and Radiopolarimeter show quasi-periodic pulsations that are most pronounced in the 17 GHz band. In the correlation plots and the integrated flux the pulsations have a symmetric triangular shape. The period of pulsations is about 1 min. Analysis of the spatial locations of the radio sources reveal that the triangularity is likely to be caused by superposition of several harmonic modes. Title: Multi-height observations of magnetoacoustic cut-off frequency in a sunspot atmosphere Authors: Yuan, D.; Sych, R.; Reznikova, V. E.; Nakariakov, V. M. Bibcode: 2014A&A...561A..19Y Altcode: 2012arXiv1211.5196Y Context. The cut-off frequency of magnetoacoustic gravity (MAG) waves could be decreased by the inclined magnetic field, and therefore, low-frequency waves could penetrate into the upper atmosphere.
Aims: We observe the distribution of the cut-off frequency of compressive waves at various heights and reconstruct the magnetic field inclination, according to the MAG wave theory in a stratified atmosphere permeated by a uniform magnetic field.
Methods: We analysed the emission intensity oscillations of sunspot AR11131 (08 Dec. 2010) observed at the 1700 Å, 1600 Å, and 304 Å bandpasses of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO), and computed the narrow-band power maps with the pixelised wavelet filtering method. The distribution of the cut-off frequency was defined as the median contour in the azimuthally-averaged oscillation power. The magnetic field inclination was estimated with the local cut-off frequency according to the MAG wave theory in the low-β limit and was compared to the potential field extrapolation.
Results: Shorter period oscillations dominate in the sunspot umbra, while longer period oscillations form an annular shape approximately concentric with the sunspot. Oscillations with longer periods are distributed further away from the sunspot centre. The 5 min oscillations appear to originate at or lower than the photosphere. The magnetic field inclinations determined with the cut-off frequency theory are about 30-40% larger than the values obtained by the potential field extrapolation.
Conclusions: The oscillation power distribution in a sunspot atmosphere reflects its magnetic and thermal structure. The cut-off frequency could be used to probe the magnetic field inclination, however, other factors have to be included to fully understand this phenomenon. The existence of return magnetic flux at the outer penumbra was evidenced by the cut-off frequency distribution. Title: Observations of decay-less low-amplitude kink oscillations of EUV coronal loops Authors: Nisticò, Giuseppe; Nakariakov, Valery; Anfinogentov, Sergey Bibcode: 2014cosp...40E2294N Altcode: The high spatial and temporal resolution observations at Extreme Ultra-Violet (EUV) wavelengths from the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) reveal new features in kink oscillations of coronal loops. We show that, in addition to the well-known rapidly decaying oscillations, a new type of kink waves is present, characterized by low-amplitude and undamped oscillations, that we define as decay-less. Typical periods range from 2.5 to 12 min in both regimes and are different for different loops, increasing with the loop length. Estimates of the loop lengths are supported by three dimensional reconstruction of the loop geometry. The amplitude for the decay-less regime is about 1 Mm, close to the spatial resolution of the AIA instruments. The oscillation phase, measured by the cross-correlation method, is found to be constant along each analysed loop, and the spatial structure of the phase of the oscillations corresponds to the fundamental standing kink mode. We show that the observed behaviours are consistent with the empirical model of a damped linear oscillator excited by a continuous low-amplitude harmonic driver, in addition to an eventual impulsive high-amplitude driver. The observed life-time of the oscillations is likely to be determined by the observational conditions rather than any physical damping. However, the balance between the driving and damping is a necessary ingredient of this model. The properties of this type of transverse oscillations make them interesting object of study in the framework of resonant absorption theory and coronal heating process. Title: Three-dimensional geometry of coronal loops inferred by the Principal Component Analysis Authors: Nisticò, Giuseppe; Nakariakov, Valery Bibcode: 2014cosp...40E2293N Altcode: We propose a new method for the determination of the three dimensional (3D) shape of coronal loops from stereoscopy. The common approach requires to find a 1D geometric curve, as circumference or ellipse, that best-fits the 3D tie-points which sample the loop shape in a given coordinate system. This can be easily achieved by the Principal Component (PC) analysis. It mainly consists in calculating the eigenvalues and eigenvectors of the covariance matrix of the 3D tie-points: the eigenvalues give a measure of the variability of the distribution of the tie-points, and the corresponding eigenvectors define a new cartesian reference frame directly related to the loop. The eigenvector associated with the smallest eigenvalues defines the normal to the loop plane, while the other two determine the directions of the loop axes: the major axis is related to the largest eigenvalue, and the minor axis with the second one. The magnitude of the axes is directly proportional to the square roots of these eigenvalues. The technique is fast and easily implemented in some examples, returning best-fitting estimations of the loop parameters and 3D reconstruction with a reasonable small number of tie-points. The method is suitable for serial reconstruction of coronal loops in active regions, providing a useful tool for comparison between observations and theoretical magnetic field extrapolations from potential or force-free fields. Title: Collective responses of coronal loops and CMEs to the eruptions of a filament Authors: Zhang, Yuzong; Nakariakov, Valery; Wang, Jingxu; Zhang, Jun Bibcode: 2014cosp...40E3810Z Altcode: With the extreme ultraviolet data acquired by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO), we study the dramatic and multiple activities of coronal loops of the active regions (ARs) 11226 and 11227 during the double eruption event of a toroidal filament located at the joint of the two ARs on 2011 June 2. It is found that 11 of 21 identified coronal loop systems demonstrated collective responses in five different ways, i.e., 1) shrinkage; 2) oscillation; 3) expansion; 4) eruption; 5) sideward motion, observed in six coronal wavebands of AIA. Moreover, an EUV wave triggered by the first filament eruption was seen to reflect back and also contributed to the shrinkage of the coronal loop systems in the two ARs. The different responding ways are closely related to the relative positions and the directions of the filament eruptions and the driven EUV wave propagation. Also, for the first time, both fast and slow magnetoacoustic waves are observed to propagate simultaneously along the same loop systems, with the speeds of ∼1,000 and tens of km s-1 , respectively. The slow mode waves were found to be unaffected by the fast ones. Furthermore, we shift to a more global scale to discuss the waves and some of the responses of the loops in conjunction with the CMEs. Title: Fast magnetoacoustic wave trains in magnetic funnels of the solar corona Authors: Pascoe, D. J.; Nakariakov, V. M.; Kupriyanova, E. G. Bibcode: 2013A&A...560A..97P Altcode: Context. Fast magneto-acoustic waves are highly dispersive in waveguides, so they can generate quasi-periodic wave trains if a localised, impulsive driver is applied. Such wave trains have been observed in the solar corona and may be of use as a seismological tool since they depend upon the plasma structuring perpendicular to the direction of propagation.
Aims: We extend existing models of magnetoacoustic waveguides to consider the effects of an expanding magnetic field. The funnel geometry employed includes a field-aligned density structure.
Methods: We performed 2D numerical simulations of impulsively generated fast magneto-acoustic perturbations. The effects of the density contrast ratio, density stratification, and spectral profile of the driver upon the excited wave trains were investigated.
Results: The density structure acts as a dispersive waveguide for fast magneto-acoustic waves and generates a quasi-periodic wave train similar to previous models. The funnel geometry leads to generating additional wave trains that propagate outside the density structure. These newly discovered wave trains are formed by the leakage of transverse perturbations, but they propagate upwards owing to the refraction caused by the magnetic funnel.
Conclusions: The results of our funnel model may be applicable to wave trains observed propagating in the solar corona. They demonstrate similar properties to those found in our simulations. Title: Long-Period Oscillations of Sunspots by NoRH and SSRT Observations Authors: Bakunina, Irina A.; Abramov-maximov, Vladimir E.; Nakariakov, Valery M.; Lesovoy, Sergei V.; Soloviev, Alexander A.; Tikhomirov, Yurii V.; Melnikov, Victor F.; Shibasaki, Kiyoto; Nagovitsyn, Yurii A.; Averina, Elena L. Bibcode: 2013PASJ...65S..13B Altcode: Long-term oscillations of microwave emission generated in sunspot magnetospheres are detected with the Nobeyama Radioheliograph (NoRH) at a frequency of 17 GHz, and the Siberian Solar Radio Telescope (SSRT) at 5.7 GHz. Significant periodicities in the range of 22-170 min are found in the variation of the emission intensity, polarisation and the degree of circular polarisation. Periods of the oscillations are not stable: they are different in different sunspots and in the same sunspot on different days. A cross-correlation analysis shows the presence of common significant periods in both NoRH and SSRT data. The cross-correlation coefficients are typically lower than 0.5, which can be attributed to the different heights of the emission formation, and different mechanisms for the emission generation (gyroresonance and thermal bremstrahlung at 17 GHz, and pure gyroresonance at 5.7 GHz). The observational results are consistent with the global sunspot oscillation model. Title: Decay-less kink oscillations in coronal loops Authors: Anfinogentov, S.; Nisticò, G.; Nakariakov, V. M. Bibcode: 2013A&A...560A.107A Altcode: Context. Kink oscillations of coronal loops in an off-limb active region are detected with the Imaging Assembly Array (AIA) instruments of the Solar Dynamics Observatory (SDO) at 171 Å.
Aims: We aim to measure periods and amplitudes of kink oscillations of different loops and to determinate the evolution of the oscillation phase along the oscillating loop.
Methods: Oscillating coronal loops were visually identified in the field of view of SDO/AIA and STEREO/EUVI-A: the loop length was derived by three-dimensional analysis. Several slits were taken along the loops to assemble time-distance maps. We identified oscillatory patterns and retrieved periods and amplitudes of the oscillations. We applied the cross-correlation technique to estimate the phase shift between oscillations at different segments of oscillating loops.
Results: We found that all analysed loops show low-amplitude undamped transverse oscillations. Oscillation periods of loops in the same active region range from 2.5 to 11 min, and are different for different loops. The displacement amplitude is lower than 1 Mm. The oscillation phase is constant along each analysed loop. The spatial structure of the phase of the oscillations corresponds to the fundamental standing kink mode. We conclude that the observed behaviour is consistent with the empirical model in terms of a damped harmonic resonator affected by a non-resonant continuously operating external force.

A movie is available in electronic form at http://www.aanda.org Title: Quasi-periodic Wiggles of Microwave Zebra Structures in a Solar Flare Authors: Yu, Sijie; Nakariakov, V. M.; Selzer, L. A.; Tan, Baolin; Yan, Yihua Bibcode: 2013ApJ...777..159Y Altcode: 2013arXiv1309.5777Y Quasi-periodic wiggles of microwave zebra pattern (ZP) structures with periods ranging from about 0.5 s to 1.5 s are found in an X-class solar flare on 2006 December 13 at the 2.6-3.8 GHz with the Chinese Solar Broadband Radio Spectrometer (SBRS/Huairou). Periodogram and correlation analysis show that the wiggles have two to three significant periodicities and are almost in phase between stripes at different frequencies. The Alfvén speed estimated from the ZP structures is about 700 km s-1. We find the spatial size of the wave-guiding plasma structure to be about 1 Mm with a detected period of about 1 s. This suggests that the ZP wiggles can be associated with the fast magnetoacoustic oscillations in the flaring active region. The lack of a significant phase shift between wiggles of different stripes suggests that the ZP wiggles are caused by a standing sausage oscillation. Title: 3D Reconstruction of Coronal Loops by the Principal Component Analysis Authors: Nisticò, Giuseppe; Verwichte, Erwin; Nakariakov, Valery Bibcode: 2013Entrp..15.4520N Altcode: Knowing the three dimensional structure of plasma filaments in the uppermost part of the solar atmosphere, known as coronal loops, and especially their length, is an important parameter in the wave-based diagnostics of this part of the Sun. The combination of observations of the Sun from different points of observations in space, thanks to the most recent missions, including the Solar Dynamics Observatory (SDO) and the Solar TErrestrial RElations Observatory (STEREO), allows us to infer information about the geometrical shape of coronal loops in 3D space. Here, we propose a new method to reconstruct the loop shape starting from stereoscopically determined 3D points, which sample the loop length, by principal component analysis. This method is shown to retrieve in an easy way the main parameters that define the loop, e.g., the minor and major axes, the loop plane, the azimuthal and inclination angles, for the special case of a coplanar loop. Title: The Decaying Long-period Oscillation of a Stellar Megaflare Authors: Anfinogentov, S.; Nakariakov, V. M.; Mathioudakis, M.; Van Doorsselaere, T.; Kowalski, A. F. Bibcode: 2013ApJ...773..156A Altcode: We analyze and interpret the oscillatory signal in the decay phase of the U-band light curve of a stellar megaflare observed on 2009 January 16 on the dM4.5e star YZ CMi. The oscillation is well approximated by an exponentially decaying harmonic function. The period of the oscillation is found to be 32 minutes, the decay time about 46 minutes, and the relative amplitude 15%. As this observational signature is typical of the longitudinal oscillations observed in solar flares at extreme ultraviolet and radio wavelengths, associated with standing slow magnetoacoustic waves, we suggest that this megaflare may be of a similar nature. In this scenario, macroscopic variations of the plasma parameters in the oscillations modulate the ejection of non-thermal electrons. The phase speed of the longitudinal (slow magnetoacoustic) waves in the flaring loop or arcade, the tube speed, of about 230 km s-1 would require a loop length of about 200 Mm. Other mechanisms, such as standing kink oscillations, are also considered. Title: Distinct propagating fast wave trains associated with flaring energy releases Authors: Yuan, D.; Shen, Y.; Liu, Y.; Nakariakov, V. M.; Tan, B.; Huang, J. Bibcode: 2013A&A...554A.144Y Altcode: Context. Large-scale fast waves with perturbation of the EUV emission intensity are well resolved in both temporal and spatial scale by SDO/AIA. These waves are prone to propagate along the magnetic field line.
Aims: We aim to probe the link between propagating fast wave trains and flaring energy releases. By measuring the wave parameters, we reveal their nature and investigate the potential to diagnose the energy source and waveguide.
Methods: The spatial and temporal evolution of the wave amplitude and propagating speed are studied. The correlation of individual wave trains with flare-generated radio bursts is tested.
Results: The propagating wave pattern comprises distinct wave trains with varying periods and wavelengths. This characteristic signature is consistent with the patterns formed by waveguide dispersion, when different spectral components propagate at different phase and group speeds. The wave train releases are found to be highly correlated in start time with the radio bursts emitted by the non-thermal electrons that were accelerated in bursty energy releases. The wave amplitude is seen to reach the maximum midway during its course. This can be caused by a combined effect of the waveguide spread in the transverse direction and density stratification. The transverse amplitude distribution perpendicular to the wave vector is found to follow approximately a Gaussian profile. The spatial structure is consistent with the kink mode that is polarised along the line-of-sight. The propagating speed is subject to deceleration from ~735-845 km s-1 to ~600 km s-1. This could be caused by the decrease in the local Alfvén speed and/or the projection effect. Title: Decaying and decayless transverse oscillations of a coronal loop Authors: Nisticò, G.; Nakariakov, V. M.; Verwichte, E. Bibcode: 2013A&A...552A..57N Altcode:
Aims: We investigate kink oscillations of loops observed in an active region with the Atmospheric Imaging Assembly (AIA) instrument on board the Solar Dynamics Observatory (SDO) spacecraft before and after a flare.
Methods: The oscillations were depicted and analysed with time-distance maps, extracted from the cuts taken parallel or perpendicular to the loop axis. Moving loops were followed in time with steadily moving slits. The period of oscillations and its time variation were determined by best-fitting harmonic functions.
Results: We show that before and well after the occurrence of the flare, the loops experience low-amplitude decayless oscillations. The flare and the coronal mass ejection associated to it trigger large-amplitude oscillations that decay exponentially in time. The periods of the kink oscillations in both regimes (about 240 s) are similar. An empirical model of the phenomenon in terms of a damped linear oscillator excited by a continuous low-amplitude harmonic driver and by an impulsive high-amplitude driver is found to be consistent with the observations.

Two movies are available in electronic form at http://www.aanda.org Title: Sausage Oscillations of Coronal Plasma Structures Authors: Nakariakov, V. M.; Hornsey, C.; Melnikov, V. F. Bibcode: 2012ApJ...761..134N Altcode: The dependence of the period of sausage oscillations of coronal loops on length together with the depth and steepness of the radial profile are determined. We performed a parametric study of linear axisymmetric fast magnetoacoustic (sausage) oscillations of coronal loops modeled as a field-aligned low-β plasma cylinder with a smooth inhomogeneity of the plasma density in the radial direction. The density decreases smoothly in the radial direction. Sausage oscillations are impulsively excited by a perturbation of the radial velocity, localized at the cylinder axis and with a harmonic dependence on the longitudinal coordinate. The initial perturbation results in either a leaky or a trapped sausage oscillation, depending upon whether the longitudinal wavenumber is smaller or greater than a cutoff value, respectively. The period of the sausage oscillations was found to always increase with increasing longitudinal wavelength, with the dependence saturating in the long-wavelength limit. Deeper and steeper radial profiles of the Alfvén speed correspond to more efficient trapping of sausage modes: the cutoff value of the wavelength increases with the steepness and the density (or Alfvén speed) contrast ratio. In the leaky regime, the period is always longer than the period of a trapped mode of a shorter wavelength in the same cylinder. For shallow density profiles and shorter wavelengths, the period increases with wavelength. In the long-wavelength limit, the period becomes independent of the wavelength and increases with the depth and steepness of the radial profile of the Alfvén speed. Title: Preface Authors: Nakariakov, V. M.; Georgoulis, M. K.; Poedts, S.; van Driel-Gesztelyi, L.; Mandrini, C. H.; Leibacher, J. Bibcode: 2012SoPh..280..295N Altcode: 2012SoPh..tmp..226N No abstract at ADS Title: Slow Magnetoacoustic Oscillations in the Microwave Emission of Solar Flares Authors: Kim, S.; Nakariakov, V. M.; Shibasaki, K. Bibcode: 2012ApJ...756L..36K Altcode: 2013arXiv1310.2796K Analysis of the microwave data, obtained in the 17 GHz channel of the Nobeyama Radioheliograph during the M1.6 flare on 2010 November 4, revealed the presence of 12.6 minute oscillations of the emitting plasma density. The oscillations decayed with the characteristic time of about 15 minutes. Similar oscillations with the period of about 13.8 minutes and the decay time of 25 minutes are also detected in the variation of EUV emission intensity measured in the 335 Å channel of the Solar Dynamics Observatory/Atmospheric Imaging Assembly. The observed properties of the oscillations are consistent with the oscillations of hot loops observed by the Solar and Heliospheric Observatory/Solar Ultraviolet Measurement of Emitted Radiation (SUMER) in the EUV spectra in the form of periodic Doppler shift. Our analysis presents the first direct observations of the slow magnetoacoustic oscillations in the microwave emission of a solar flare, complementing accepted interpretations of SUMER hot loop oscillations as standing slow magnetoacoustic waves. Title: Nonlinear evolution of torsional Alfvén waves Authors: Vasheghani Farahani, S.; Nakariakov, V. M.; Verwichte, E.; Van Doorsselaere, T. Bibcode: 2012A&A...544A.127V Altcode:
Aims: We study the efficiency of the energy transfer to shorter scales in the field-aligned direction - the parallel nonlinear cascade - that accompanies the propagation of torsional Alfvén waves along open magnetic fields in the solar and stellar coronae, and compare it with the same effects for the shear Alfvén wave. The evolution of the torsional Alfvén wave is caused by the back reaction of nonlinearly induced compressive perturbations on the Alfvén wave.
Methods: The evolution of upwardly propagating torsional Alfvén waves is considered in terms of the second-order thin flux-tube approximation in a straight untwisted and non-rotating magnetic flux-tube. The Cohen-Kulsrud equation for weakly nonlinear torsional waves is derived. In the model, the effect of the cubic nonlinearity on the propagation of long-wavelength axisymmetric torsional waves is compared with the similar effect that accompanies the propagation of plane linearly-polarised (shear) Alfvén waves of small amplitude.
Results: The solution to the Cohen-Kulsrud type equation for torsional waves shows that their evolution is independent of the plasma-β, which is in contrast to the shear Alfvén wave. In a finite-β plasma, the nonlinear evolution of torsional Alfvén waves is slower and the parallel nonlinear cascade is less efficient than those of shear Alfvén waves. These results have important implications for the analysis of possible heating of the plasma and its acceleration in the upper layers of solar and stellar coronae. In particular, one-dimensional models of coronal heating and wave acceleration, which use shear Alfvén waves instead of torsional Alfvén waves, over-estimate the efficiency of these processes. Title: Magnetohydrodynamic vortices in the solar corona Authors: Nakariakov, Valery Bibcode: 2012cosp...39.1329N Altcode: 2012cosp.meet.1329N Interaction of coronal mass ejections with the plasma of the solar corona is accompanied with the generation of sharp shear flows that cause the induction of Alfvenic vortices. Numerical simulations revealed that for a broad range of parameters, the vortices are essentially compressible, with the perturbations of the density and the absolute value of the magnetic field in the vortex arms reaching 50% of the background density. The typical size of the vortex is about the size of the obstacle. The frequency of the vortex shedding is controlled by a dimensionless parameter known as the Strouhal number. We found that in collisionless low-beta plasma this number is about 0.2. Recent imaging observations with SDO/AIA revealed the generation of Alfvenic vortices at the flanks of emerging plasmoids. The vortices introduce a frictionless aerodynamic drag force, applied to the interacting plasmas. Implication of these findings for the excitation of kink oscillations of coronal loops and CME kinematics is discussed. Title: Intensity variations associated with fast sausage modes Authors: Gruszecki, M.; Nakariakov, V. M.; Van Doorsselaere, T. Bibcode: 2012A&A...543A..12G Altcode:
Aims: We determine the dependence of the observed properties of fast magnetoacoustic axisymmetric oscillations (the sausage mode) of a thick and dense flaring coronal loop, modelled by a magnetic cylinder, on the parameters of the equilibrium plasma configuration. The plasma inside and outside the cylinder is of low-beta, and penetrated by a straight magnetic field. The plasma density has a smooth profile across the magnetic field.
Methods: We use three-dimensional ideal magnetohydrodynamic equations to model numerically the development of the perturbations of the cylindrical equilibrium, considering both leaky and trapped regimes.
Results: Short-period sausage oscillations, trapped by the cylinder, are qualitatively consistent with the analytical results obtained in the models of a plasma slab or a cylinder with a step-function transverse profile. The period of trapped sausage oscillations is determined by the ratio of the phase speed, with the value between the internal and external Alfvén speeds, to the wavelength. Longer-period sausage oscillations are leaky, and their decay times are longer for higher density contrasts between the internal and external media. Leaky sausage oscillations have longer periods than trapped sausage oscillations of the same cylinder. In the coronal conditions, sausage oscillations are essentially compressible and transverse, hence produce modulation of the thermal optically thin emission intensity and periodic Doppler broadening of emission lines. However, if the oscillating plasma non-uniformity is poorly spatially resolved, the variation in the emission intensity is weak and proportional to the actual amplitude of the oscillation squared. The latter variation property is connected with the transverse nature of the oscillation, causing the conservation of mass in the transverse cross-section of the oscillating plasma structure. Title: Slow magnetoacoustic waves in the solar corona Authors: Nakariakov, Valery Bibcode: 2012cosp...39.1330N Altcode: 2012cosp.meet.1330N Quasi-monochromatic propagating disturbances of EUV intensity emission are often detected in fan-like structures and in polar plumes of the solar corona. We demonstrate that the observed characteristics of these propagating disturbances, including the apparent blue-wind asymmetry of the emission line, are consistent with their interpretation in terms of slow magnetoacoustic waves. The propagating waves are well-described by a one-dimensional evolutionary equation that accounts for the effects of thermal conduction and stratification. Moreover, the waves are shown to be a genuine counterpart of 3-min oscillations in the chromospheric slow-magnetoacoustic resonator. It is also found that the leaky slow magnetoacoustic waves provide a link between oscillations in sunspots and quasi-periodic pulsations in a solar flare occurring nearby, suggesting that the waves can play a role of external triggering of the energy release. Title: Measuring the apparent phase speed of propagating EUV disturbances Authors: Yuan, D.; Nakariakov, V. M. Bibcode: 2012A&A...543A...9Y Altcode: Context. Propagating disturbances of the EUV emission intensity are commonly observed over a variety of coronal structures. Parameters of these disturbances, particularly the observed apparent (image-plane projected) propagation speed, are important tools for MHD coronal seismology.
Aims: We design and test tools to reliably measure the apparent phase speed of propagating disturbances in imaging data sets.
Methods: We designed cross-fitting technique (CFT), 2D coupled fitting (DCF) and best similarity match (BSM) to measure the apparent phase speed of propagating EUV disturbances in the running differences of time-distance plots (R) and background-removed and normalised time-distance plots (D).
Results: The methods were applied to the analysis of quasi-periodic EUV disturbances propagating at a coronal fan-structure of active region NOAA11330 on 27 Oct. 2011, observed with the Atmospheric Imaging Assembly (AIA) on SDO in the 171 Å bandpass. The noise propagation in the AIA image processing was estimated, resulting in the preliminary estimation of the uncertainties in the AIA image flux. This information was used in measuring the apparent phase speed of the propagating disturbances with the CFT, DCF and BSM methods, which gave consistent results. The average projected speed is measured at 47.6 ± 0.6 km s-1 and 49.0 ± 0.7 km s-1 for R and D, with the corresponding periods at 179.7 ± 0.2 s and 179.7 ± 0.3 s, respectively. We analysed the effects of the lag time and the detrending time in the running difference processing and the background-removed plot, on the measurement of the speed, and found that they are fairly weak.
Conclusions: The CFT, DCF and BSM methods are found to be reliable techniques for measuring the apparent (projected) phase speed. The samples of larger effective spatial length are more suitable for these methods. Time-distance plots with background removal and normalisation allow for more robust measurements, with little effect of the choice of the detrending time. Cross-fitting technique provides reliable measurements on good samples (e.g. samples with large effective detection length and recurring features). 2D coupled-fitting is found to be sensitive to the initial guess for parameters of the 2D fitting function. Thus DCF is only optimised in measuring one of the parameters (the phase speed in our application), while the period is poorly measured. Best similarity measure is robust for all types of samples and very tolerant to image pre-processing and regularisation (smoothing). Title: Nonlinear long-wavelength torsional Alfven waves Authors: Nakariakov, Valery Bibcode: 2012cosp...39.1331N Altcode: 2012cosp.meet.1331N Long-wavelength torsional (Alfven) waves in solar and stellar coronal structures experience geometrical amplification with height and hence are subject to nonlinear effects. We analyse this regime in frames the second order thin flux-tube approximation of Zhugzhda, which describes axisymmetric (sausage) magnetohydrodynamic perturbations of a straight untwisted and non-rotating magnetic flux-tube, representing e.g. a polar plume or a jet, or a coronal loop or a prominence filament. Attention is paid to the compressible motions nonlinearly induced by long-wavelength torsional waves of small, but finite amplitude. We obtained that propagating torsional waves induce compressible perturbations oscillating with double the frequency of the torsional waves. In contrast with plane shear Alfven waves, the amplitude of compressible perturbations is independent of the plasma-beta. Moreover, nonlinear evolution of torsional waves is not affected by the singularity appearing at the height when the local Alfven speed is equal to the sound speed. This result significantly reduces the efficiency of nonlinear cascade, and hence suggests that the present theories of the solar and stellar wind heating and acceleration by Alfven waves, based upon the plane wave theory, require modification. Title: Magnetohydrodynamic waves and coronal seismology: an overview of recent results Authors: De Moortel, I.; Nakariakov, V. M. Bibcode: 2012RSPTA.370.3193D Altcode: 2012arXiv1202.1944D Recent observations have revealed that MHD waves and oscillations are ubiquitous in the solar atmosphere, with a wide range of periods. We give a brief review of some aspects of MHD waves and coronal seismology which have recently been the focus of intense debate or are newly emerging. In particular, we focus on four topics: (i) the current controversy surrounding propagating intensity perturbations along coronal loops, (ii) the interpretation of propagating transverse loop oscillations, (iii) the ongoing search for coronal (torsional) Alfven waves and (iv) the rapidly developing topic of quasi-periodic pulsations (QPP) in solar flares. Title: Solar Particle Acceleration Radiation and Kinetics (SPARK). A mission to understand the nature of particle acceleration Authors: Matthews, Sarah A.; Williams, David R.; Klein, Karl-Ludwig; Kontar, Eduard P.; Smith, David M.; Lagg, Andreas; Krucker, Sam; Hurford, Gordon J.; Vilmer, Nicole; MacKinnon, Alexander L.; Zharkova, Valentina V.; Fletcher, Lyndsay; Hannah, Iain G.; Browning, Philippa K.; Innes, Davina E.; Trottet, Gerard; Foullon, Clare; Nakariakov, Valery M.; Green, Lucie M.; Lamoureux, Herve; Forsyth, Colin; Walton, David M.; Mathioudakis, Mihalis; Gandorfer, Achim; Martinez-Pillet, Valentin; Limousin, Olivier; Verwichte, Erwin; Dalla, Silvia; Mann, Gottfried; Aurass, Henri; Neukirch, Thomas Bibcode: 2012ExA....33..237M Altcode: 2011ExA...tmp..124M Energetic particles are critical components of plasma populations found throughout the universe. In many cases particles are accelerated to relativistic energies and represent a substantial fraction of the total energy of the system, thus requiring extremely efficient acceleration processes. The production of accelerated particles also appears coupled to magnetic field evolution in astrophysical plasmas through the turbulent magnetic fields produced by diffusive shock acceleration. Particle acceleration is thus a key component in helping to understand the origin and evolution of magnetic structures in, e.g. galaxies. The proximity of the Sun and the range of high-resolution diagnostics available within the solar atmosphere offers unique opportunities to study the processes involved in particle acceleration through the use of a combination of remote sensing observations of the radiative signatures of accelerated particles, and of their plasma and magnetic environment. The SPARK concept targets the broad range of energy, spatial and temporal scales over which particle acceleration occurs in the solar atmosphere, in order to determine how and where energetic particles are accelerated. SPARK combines highly complementary imaging and spectroscopic observations of radiation from energetic electrons, protons and ions set in their plasma and magnetic context. The payload comprises focusing-optics X-ray imaging covering the range from 1 to 60 keV; indirect HXR imaging and spectroscopy from 5 to 200 keV, γ-ray spectroscopic imaging with high-resolution LaBr3 scintillators, and photometry and source localisation at far-infrared wavelengths. The plasma environment of the regions of acceleration and interaction will be probed using soft X-ray imaging of the corona and vector magnetography of the photosphere and chromosphere. SPARK is designed for solar research. However, in addition it will be able to provide exciting new insights into the origin of particle acceleration in other regimes, including terrestrial gamma-ray flashes (TGF), the origin of γ-ray bursts, and the possible existence of axions. Title: Coronal Seismology: Waves and Oscillations in Stellar Coronae Flare Plasma Authors: Stepanov, Alexander V.; Zaitsev, Valery V.; Nakariakov, Valery M. Bibcode: 2012cswo.book.....S Altcode: This concise and systematic account of the current state of this new branch of astrophysics presents the theoretical foundations of plasma astrophysics, magneto-hydrodynamics and coronal magnetic structures, taking into account the full range of available observation techniques -- from radio to gamma.

The book discusses stellar loops during flare energy releases, MHD waves and oscillations, plasma instabilities and heating and charged particle acceleration. Current trends and developments in MHD seismology of solar and stellar coronal plasma systems are also covered, while recent progress is presented in the observational study of quasi-periodic pulsations in solar and stellar flares with radio, optical, X and gamma rays. In addition, the authors investigate the origin of coherent radio emission from stellar loops, paying special attention to their fine structure.

For advanced students and specialists in astronomy, as well as theoretical and plasma physics. Title: Frequency drifts of 3-min oscillations in microwave and EUV emission above sunspots Authors: Sych, R.; Zaqarashvili, T. V.; Nakariakov, V. M.; Anfinogentov, S. A.; Shibasaki, K.; Yan, Y. Bibcode: 2012A&A...539A..23S Altcode: 2011arXiv1110.2556S
Aims: We analysed 3-min oscillations of microwave and extreme ultraviolet (EUV) emission generated at different heights of a sunspot atmosphere, studied the amplitude and frequency modulation of the oscillations, and its relationship with the variation of the spatial structure of the oscillations.
Methods: High-resolution data obtained with the Nobeyama Radioheliograph, TRACE and SDO/AIA were analysed with pixelised wavelet filtering (PWF) and wavelet skeleton techniques.
Results: Three-minute oscillations in sunspots appear in the form of recurring trains of 8-20 min duration (13 min in average). The typical interval between the trains is 30-50 min. The oscillation trains are transient in frequency and power. The relative amplitude of 3-min oscillations was about 3-8% and sometimes reached 17%. Recurring frequency drifts of 3-min oscillations were detected during the development of individual trains, with the period varying in the range 90-240 s. A wavelet analysis showed that there are three types of oscillation trains: with positive drifts (to high frequencies), negative drifts, and without a drift. Negative drifts, i.e., when the 3-min oscillation period gradually increases, were found to occur more often. The start and end of the drifts coincides with the start time and end of the train. Sometimes two drifts co-exist, i.e. during the end of the previous drift, a new drift appears near 160 s, when the frequency is in the low-frequency part of the 3-min spectrum, near 200 s. This behaviour is seen at all levels of the sunspot atmosphere. The speed of the drift is 4-5 mHz/h in the photosphere, 5-8 mHz/h in the chromosphere, and 11-13 mHz/h in the corona. There were also low-frequency peaks in the spectrum, corresponding to the periods of 10-20 min, and 30-60 min. The comparative study of the spatial structure of 3-min oscillations in microwave and EUV shows the appearance of new sources of the sunspot oscillations during the development of the trains.
Conclusions: These structures can be interpreted as waveguides that channel upward propagating waves, which in turn are responsible for the 3-min oscillations. A possible explanation of the observed properties are two simultaneously operating factors: dispersive evolution of the upward propagating wave pulses and the non-uniformity of the oscillation power distribution over the sunspot umbra with different wave sources that correspond to different magnetic flux tubes with different physical conditions and line-of-sight angles. Title: Three-minute Oscillations above Sunspot Umbra Observed with the Solar Dynamics Observatory/Atmospheric Imaging Assembly and Nobeyama Radioheliograph Authors: Reznikova, V. E.; Shibasaki, K.; Sych, R. A.; Nakariakov, V. M. Bibcode: 2012ApJ...746..119R Altcode: 2011arXiv1109.5434R Three-minute oscillations over a sunspot's umbra in AR 11131 were observed simultaneously in UV/EUV emission by the Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) and in radio emission by the Nobeyama Radioheliograph (NoRH). We use 24 hr series of SDO and 8 hr series of NoRH observations to study spectral, spatial, and temporal variations of pulsations in the 5-9 mHz frequency range at different layers of the solar atmosphere. High spatial and temporal resolution of SDO/AIA in combination with long-duration observations allowed us to trace the variations of the cutoff frequency and spectrum of oscillations across the umbra. We found that higher frequency oscillations are more pronounced closer to the umbra's center, while the lower frequencies concentrate on the peripheral parts. We interpreted this discovery as a manifestation of variation of the magnetic field inclination across the umbra at the level of temperature minimum. Possible implications of this interpretation for the diagnostics of sunspot atmospheres are discussed. Title: Slow magnetacoustic waves in magnetic arcades Authors: Gruszecki, M.; Nakariakov, V. M. Bibcode: 2011A&A...536A..68G Altcode:
Aims: We investigate two-dimensional effects on the evolution of impulsively-generated slow magnetoacoustic waves in magnetic arcades of the solar corona.
Methods: We used a two-dimensional box model of a coronal arcade, neglecting the effects of gravity and magnetic curvature. Ideal finite-β magnetohydrodynamic equations were employed. The plasma was taken to be uniform, penetrated by a straight and uniform magnetic field. We applied line-tying boundary conditions at the magnetic footpoints.
Results: Running and standing slow magnetoacoustic waves develop across the magnetic field due to the reflection from the footpoints in the arcade. The perpendicular group speed is lower than both sound and Alfvén speeds. The speed grows with the increase in plasma-β, which is consistent with analytical theory. Slow magnetoacoustic pulse perturbs the magnetic field and current density; this effect is stronger for higher amplitudes. Standing waves spread across the field, forming a characteristic phase-mixing pattern of anti-parallel flows. The two-dimensional effects are more pronounced for higher β. Our results confirm the plausibility of the interpretation of the observed evolution of two-ribbon flares in terms of slow magnetoacoustic waves in magnetic arcades. Title: Entropy mode at a magnetic null point as a possible tool for indirect observation of nanoflares in the solar corona Authors: Murawski, K.; Zaqarashvili, T. V.; Nakariakov, V. M. Bibcode: 2011A&A...533A..18M Altcode:
Aims: We aim to explore the dynamics of the entropy mode perturbation excited by an energy release in the vicinity of a magnetic null point that is embedded in a gravitationally stratified solar corona.
Methods: We solve two-dimensional, time-dependent magnetohydrodynamic equations numerically to find spatial and temporal signatures of the entropy mode that is triggered impulsively by a spatially localized pulse of the gas pressure.
Results: We find that the properties of the entropy mode are determined by the sign of the initial pressure pulse. The initial increase in the gas pressure creates, together with the magnetoacoustic-gravity waves, a stationary void of the rarefied plasma at the launching place, associated with the entropy mode. In contrast, an initial decrease in the gas pressure, which corresponds to a rapid (or catastrophic) cooling, forms a blob of the dense plasma at the launching place.
Conclusions: The cool, dense blobs at magnetic null points may be observed in transition region and chromospheric spectral lines at coronal heights off the solar limb and may be associated with the places of nanoflare occurrence. Therefore, extensions of entropy mode studies may produce a diagnostic tool for indirect observations of nanoflares. The dense cool blobs may be affected by the gravity or carried by downflows, hence may initiate a coronal rain. Title: Leakage of long-period oscillations from the chromosphere to the corona Authors: Yuan, D.; Nakariakov, V. M.; Chorley, N.; Foullon, C. Bibcode: 2011A&A...533A.116Y Altcode: Long-period oscillations in a coronal diffuse structure are detected with the Transition Region And Coronal Explorer (TRACE). The EUV images of the NOAA active region 8253 are available in 171 Å and 195 Å bandpasses from 30 June to 4 July 1998. The average intensity variation is found to be connected with the CCD temperature, which varies with the orbital motion of the spacecraft. Hence, oscillations with the orbital period and its higher harmonics appear as artifacts in the light curves. After the exclusion of the orbital effects, we identified several long-period oscillations in the diffuse fan-like structure of the active region. Similar periodicities were detected in the radio emission from the chromospheric part of that active region, observed with the ground-based Nobeyama Radioheliograph (NoRH) in the 17 GHz channel. It was found that 0.221, 0.312 and 0.573 mHz oscillations were present in both EUV emission lines in the corona and the radio signal from the sunspot in the chromosphere, just beneath the active region. From the frequency values, the 1st and 3rd detected oscillations could be associated with the l = 2, n = -3 or l = 3, n = -5 and l = 1 gravity-driven solar interior modes, respectively. The appearance of these oscillations in the coronal part of the active region can be connected with the wave leakage or the evanescence of chromospheric oscillations. Title: Magnetoacoustic shock formation near a magnetic null point Authors: Gruszecki, M.; Vasheghani Farahani, S.; Nakariakov, V. M.; Arber, T. D. Bibcode: 2011A&A...531A..63G Altcode:
Aims: We investigate the interaction of nonlinear fast magnetoacoustic waves with a magnetic null point in connection with the triggering of solar flares.
Methods: We model the propagation of fast, initially axisymmetric waves towards a two-dimensional isothermal magnetic null point in terms of ideal magnetohydrodynamic equations. The numerical simulations are carried out with the Lagrangian remap code Lare2D.
Results: Dynamics of initially axisymmetric fast pulses of small amplitude is found to be consistent with a linear analytical solution proposed earlier. The increase in the amplitude leads to the nonlinear acceleration of the compression pulse and deceleration of the rarefaction pulse and hence the distortion of the wave front. The pulse experiences nonlinear steepening in the radial direction either on the leading or the back slopes for the compression and rarefaction pulses, respectively. This effect is most pronounced in the directions perpendicular to the field. Hence, the nonlinear evolution of the fast pulse depends on the polar angle. The nonlinear steepening generates the sharp spikes of the electric current density. As in the uniform medium, the position of the shock formation also depends on the initial width of the pulse. Only sufficiently smooth and low-amplitude initial pulses can reach the vicinity of the null point, create there current density spikes, and initiate magnetic reconnection by seeding anomalous electrical resistivity. Steeper and higher amplitude initial pulses overturn at larger distance from the null point, and cannot trigger reconnection. Title: Damped large amplitude transverse oscillations in an EUV solar prominence, triggered by large-scale transient coronal waves Authors: Hershaw, J.; Foullon, C.; Nakariakov, V. M.; Verwichte, E. Bibcode: 2011A&A...531A..53H Altcode:
Aims: We investigate two successive trains of large amplitude transverse oscillations in an arched EUV prominence, observed with SoHO/EIT on the north-east solar limb on 30 July 2005. The oscillatory trains are triggered by two large scale coronal waves, associated with an X-class and a C-class flare occurring in the same remote active region.
Methods: The oscillations are tracked within rectangular slits parallel to the solar limb at different heights, which are taken to move with the apparent height profile of the prominence to account for solar rotation. Time series for the two prominence arch legs are extracted using Gaussian fitting on the 195 Å absorption features, and fitted to a damped cosine curve to determine the oscillatory parameters.
Results: Differing energies of the two triggering flares and associated waves are found to agree with the velocity amplitudes, of 50.6 ± 3.2 and 15.9 ± 8.0 km s-1 at the apex, for the first and second oscillatory trains respectively, as estimated in the transverse direction. The period of oscillation is similar for both trains, with an average of 99 ± 11 min, indicating a characteristic frequency as predicted by magnetohydrodynamics. Increasing velocity amplitude with height during the first oscillatory train, and in-phase starting motions of the two legs regardless of height, for each train, demonstrate that the prominence exhibits a global kink mode to a first approximation. However, discrepancies between the oscillatory characteristics of the two legs and an apparent dependence of period upon height, suggest that the prominence actually oscillates as a collection of separate but interacting threads. Damping times of around two to three cycles are observed. Combining our results with those of previously analysed loop oscillations, we find an approximately linear dependence of damping time upon period for kink oscillations, supporting resonant absorption as the damping mechanism despite limitations in testing this theory. Title: Instrumental oscillations in RHESSI count rates during solar flares Authors: Inglis, A. R.; Zimovets, I. V.; Dennis, B. R.; Kontar, E. P.; Nakariakov, V. M.; Struminsky, A. B.; Tolbert, A. K. Bibcode: 2011A&A...530A..47I Altcode: 2011arXiv1102.5349I
Aims: We seek to illustrate the analysis problems posed by RHESSI spacecraft motion by studying persistent instrumental oscillations found in the lightcurves measured by RHESSI's X-ray detectors in the 6-12 keV and 12-25 keV energy range during the decay phase of the flares of 2004 November 4 and 6.
Methods: The various motions of the RHESSI spacecraft which may contribute to the manifestation of oscillations are studied. The response of each detector in turn is also investigated.
Results: We find that on 2004 November 6 the observed oscillations correspond to the nutation period of the RHESSI instrument. These oscillations are of greatest amplitude for detector 5, while in the lightcurves of many other detectors the oscillations are small or undetectable. We also find that the variation in detector pointing is much larger during this flare than the counterexample of 2004 November 4.
Conclusions: Sufficiently large nutation motions of the RHESSI spacecraft lead to clearly observable oscillations in count rates, posing a significant hazard for data analysis. This issue is particularly problematic for detector 5 due to its design characteristics. Dynamic correction of the RHESSI counts, accounting for the livetime, data gaps, and the transmission of the bi-grid collimator of each detector, is required to overcome this issue. These corrections should be applied to all future oscillation studies. Title: Period persistence of long period oscillations in sunspots Authors: Chorley, N.; Foullon, C.; Hnat, B.; Nakariakov, V. M.; Shibasaki, K. Bibcode: 2011A&A...529A.123C Altcode: Long period oscillations in the microwave radiation intensity generated over the sunspot of NOAA AR 10330 are studied with the Nobeyama Radioheliograph as the sunspot passes over the solar disk, over the course of 9 days (06-15 April 2003). Periodogram, Fourier and global wavelet analyses reveal the presence of a significant oscillatory component in the range P ≈ 50-120 min over the course of the observations. The spectral amplitudes of five significant Fourier components in the range P = 50-150 min are also seen to be stable over the observations, when the data are not affected by changes in magnetic configuration in the region. The ground-based nature of the instrument naturally introduces long data gaps in such long duration observations and the presence of the gaps does not allow any conclusion as to the stability of the phases of the oscillations. As a model to explain the persistence of the dominant long periods, a simple oscillator with a nonlinear driving term is proposed. The spectral difference between distinct peaks within, e.g. the 3 min spectral band, is expected to be able to resonate with the long period one hour oscillations. Title: Slow Magnetoacoustic Waves in Two-ribbon Flares Authors: Nakariakov, V. M.; Zimovets, I. V. Bibcode: 2011ApJ...730L..27N Altcode: We demonstrate that disturbances observed to propagate along the axis of the arcade in two-ribbon solar flares at the speed of a few tens of km s-1, well below the Alfvén and sound speeds, can be interpreted in terms of slow magnetoacoustic waves. The waves can propagate across the magnetic field, parallel to the magnetic neutral line, because of the wave-guiding effect due to the reflection from the footpoints. The perpendicular group speed of the perturbation is found to be a fraction of the sound speed, which is consistent with observations. The highest value of the group speed grows with the increase in the ratio of the sound and Alfvén speeds. For a broad range of parameters, the highest value of the group speed corresponds to the propagation angle of 25°-28° to the magnetic field. This effect can explain the temporal and spatial structure of quasi-periodic pulsations observed in two-ribbon flares. Title: Magnetic Kelvin-Helmholtz Instability at the Sun Authors: Foullon, Claire; Verwichte, Erwin; Nakariakov, Valery M.; Nykyri, Katariina; Farrugia, Charles J. Bibcode: 2011ApJ...729L...8F Altcode: Flows and instabilities play a major role in the dynamics of magnetized plasmas including the solar corona, magnetospheric and heliospheric boundaries, cometary tails, and astrophysical jets. The nonlinear effects, multi-scale and microphysical interactions inherent to the flow-driven instabilities, are believed to play a role, e.g., in plasma entry across a discontinuity, generation of turbulence, and enhanced drag. However, in order to clarify the efficiency of macroscopic instabilities in these processes, we lack proper knowledge of their overall morphological features. Here we show the first observations of the temporally and spatially resolved evolution of the magnetic Kelvin-Helmholtz instability in the solar corona. Unprecedented high-resolution imaging observations of vortices developing at the surface of a fast coronal mass ejecta are taken by the new Solar Dynamics Observatory, validating theories of the nonlinear dynamics involved. The new findings are a cornerstone for developing a unifying theory on flow-driven instabilities in rarefied magnetized plasmas, which is important for understanding the fundamental processes at work in key regions of the Sun-Earth system. Title: Nonlinear long-wavelength torsional Alfvén waves Authors: Vasheghani Farahani, S.; Nakariakov, V. M.; van Doorsselaere, T.; Verwichte, E. Bibcode: 2011A&A...526A..80V Altcode:
Aims: We investigate the nonlinear phenomena accompanying long-wavelength torsional waves in solar and stellar coronae.
Methods: The second order thin flux-tube approximation is used to determine perturbations of a straight untwisted and non-rotating magnetic flux-tube, nonlinearly induced by long-wavelength axisymmetric magnetohydrodynamic waves of small, but finite amplitude.
Results: Propagating torsional waves induce compressible perturbations oscillating with double the frequency of the torsional waves. In contrast with plane shear Alfvén waves, the amplitude of compressible perturbations is independent of the plasma-β and is proportional to the torsional wave amplitude squared. Standing torsional waves induce compressible perturbations of two kinds, that grow with the characteristic time inversely proportional to the sound speed, and that oscillate at double the frequency of the inducing torsional wave. The growing density perturbation saturates at the level, inversely proportional to the sound speed. Title: Chromospheric Resonances above Sunspot Umbrae Authors: Botha, G. J. J.; Arber, T. D.; Nakariakov, V. M.; Zhugzhda, Y. D. Bibcode: 2011ApJ...728...84B Altcode: Three-minute oscillations are observed in the chromosphere above sunspot umbrae. One of the models used to explain these oscillations is that of a chromospheric acoustic resonator, where the cavity between the photosphere and transition region partially reflects slow magnetoacoustic waves to form resonances in the lower sunspot atmosphere. We present a phenomenological study that compares simulation results with observations. The ideal magnetohydrodynamic equations are used with a uniform vertical magnetic field and a temperature profile that models sunspot atmospheres above umbrae. The simulations are initialized with a single broadband pulse in the vertical velocity inside the convection zone underneath the photosphere. The frequencies in the spectrum of the broadband pulse that lie below the acoustic cutoff frequency are filtered out so that frequencies equal and above the acoustic cutoff frequency resonate inside the chromospheric cavity. The chromospheric cavity resonates with approximately three-minute oscillations and is a leaky resonator, so that these oscillations generate traveling waves that propagate upward into the corona. Thus, there is no requirement that a narrowband three-minute signal is present in the photosphere to explain the narrowband three-minute oscillations in the chromosphere and corona. The oscillations in the chromospheric cavity have larger relative amplitudes (normalized to the local sound speed) than those in the corona and reproduce the intensity fluctuations of observations. Different umbral temperature profiles lead to different peaks in the spectrum of the resonating chromospheric cavity, which can explain the frequency shift in sunspot oscillations over the solar cycle. Title: The First Measurement of the Adiabatic Index in the Solar Corona Using Time-dependent Spectroscopy of Hinode/EIS Observations Authors: Van Doorsselaere, Tom; Wardle, Nick; Del Zanna, Giulio; Jansari, Kishan; Verwichte, Erwin; Nakariakov, Valery M. Bibcode: 2011ApJ...727L..32V Altcode: We use observations of a slow magnetohydrodynamic wave in the corona to determine for the first time the value of the effective adiabatic index, using data from the Extreme-ultraviolet Imaging Spectrometer on board Hinode. We detect oscillations in the electron density, using the CHIANTI atomic database to perform spectroscopy. From the time-dependent wave signals from multiple spectral lines the relationship between relative density and temperature perturbations is determined, which allows in turn to measure the effective adiabatic index to be γeff = 1.10 ± 0.02. This confirms that the thermal conduction along the magnetic field is very efficient in the solar corona. The thermal conduction coefficient is measured from the phase lag between the temperature and density, and is shown to be compatible with Spitzer conductivity. Title: Height distribution of the power of 3-min oscillations over sunspots Authors: Kobanov, N. I.; Kolobov, D. Y.; Chupin, S. A.; Nakariakov, V. M. Bibcode: 2011A&A...525A..41K Altcode: 2011arXiv1111.6676K Context. The height structure of 3-min oscillations over sunspots is studied in the context of the recently discovered effect of height inversion: over the umbra, the spatial location of the maximum of chromospheric 3-min oscillation power corresponds to the relative decrease in the power of photospheric oscillations.
Aims: We investigate whether the height inversion of the power of 3-min oscillations is a common feature of the spatial structure of the oscillations for the majority of sunspots.
Methods: Spectrogram sequences of Hα 6563 Å and Fe i 6569 Å over sunspots, acquired with very high cadency (about 2 s or better) are obtained. The distribution of the oscillation power of the line-of-sight velocity signal is studied by using methods of wavelet frequency filtration and Fourier analysis.
Results: The effect of the height inversion is found in 9 of 11 analyzed active regions. The interpretation of this effect is possibly connected to both the decrease in the level of photosphere in sunspot umbrae and the magnetic field topology. Title: Transient induced MHD oscillations: a tool to probe the solar active regions Authors: Srivastava, Abhishek K.; Nakariakov, V. M.; Dwivedi, B. N.; Kumar, Pankaj Bibcode: 2011ASInC...2..271S Altcode: 2011arXiv1110.0705S Solar transients and eruptive phenomena which are ubiquitous in the solar atmosphere, can shed new light to the understanding of the outstanding problems like coronal heating and the solar wind acceleration. Observations in the entire electromagnetic spectrum of such dynamical processes of large and small-scale transient/eruptive events, with highly dynamic magnetic field configuration, and energetic particles, provide crucial information about the plasma processes at mega-Kelvin temperature embedded in a complex magnetic field, and also energy build-up/energy-release processes, taking place in such events. One of the most important phenomenological aspects of solar eruptive phenomena is the induced magnetohydrodynamic (MHD) waves generated during these energetic processes, which carry a potential signature to probing the solar active regions. In this paper, we briefly review the recent trends of the transient (e.g., flares) induced quasi-periodic oscillations in the solar atmosphere and discuss their implications in diagnosing the solar active regions, providing the clue to understanding local plasma dynamics and heating. Title: Oscillatory processes in solar flares Authors: Nakariakov, V. M.; Inglis, A. R.; Zimovets, I. V.; Foullon, C.; Verwichte, E.; Sych, R.; Myagkova, I. N. Bibcode: 2010PPCF...52l4009N Altcode: 2010arXiv1010.0063N Electromagnetic (radio, visible-light, UV, EUV, x-ray and gamma-ray) emission generated by solar and stellar flares often contains pronounced quasi-periodic pulsations (QPPs). Physical mechanisms responsible for the generation of long-period QPP (with periods longer than 1 s) are likely to be associated with MHD processes. The observed modulation depths, periods and anharmonicity of QPP suggest that they can be linked with some kind of MHD auto-oscillations, e.g. an oscillatory regime of magnetic reconnection. Such regimes, of both spontaneous and induced nature, have been observed in resistive-MHD numerical simulations. The oscillations are essentially nonlinear and non-stationary. We demonstrate that a promising novel method for their analysis is the empirical mode decomposition technique. Title: Types of Microwave Quasi-Periodic Pulsations in Single Flaring Loops Authors: Kupriyanova, E. G.; Melnikov, V. F.; Nakariakov, V. M.; Shibasaki, K. Bibcode: 2010SoPh..267..329K Altcode: 2010SoPh..tmp..179K Quasi-periodic pulsations (QPP) of microwave emission generated in single flaring loops observed with the Nobeyama Radioheliograph (NoRH) and Nobeyama Radio Polarimeters (NoRP) are studied. Specific features of the time profiles, i.e. the visible presence or absence of QPPs, are not accounted for in the selection. The time evolution of the periods of the QPPs is examined using wavelet and correlation analyses. In ten out of twelve considered events, at least one or more significant spectral components with periods from 5 - 60 s have been found. The quality of the oscillations is rather low: Q=πN, where N is the number of cycles, mostly varies in the range 12 to 40, with an average of 25. We suggest that the detected QPPs can be classified into four types: i) those with stable mean periods (e.g. of 15 - 20 s or 8 - 9 s, the prevailing type); ii) those with spectral drift to shorter periods (mostly in the rise phase of the microwave emission); iii) those with drift to longer periods (mostly in the decay phase); iv) those with multiple periods showing an X-shaped drift (e.g. in the range from 20 - 40 s in the rise phase). Title: Periodic Spectral Line Asymmetries in Solar Coronal Structures from Slow Magnetoacoustic Waves Authors: Verwichte, E.; Marsh, M.; Foullon, C.; Van Doorsselaere, T.; De Moortel, I.; Hood, A. W.; Nakariakov, V. M. Bibcode: 2010ApJ...724L.194V Altcode: Recent spectral observations of upward moving quasi-periodic intensity perturbations in solar coronal structures have shown evidence of periodic line asymmetries near their footpoints. These observations challenge the established interpretation of the intensity perturbations in terms of propagating slow magnetoacoustic waves. We show that slow waves inherently have a bias toward enhancement of emission in the blue wing of the emission line due to in-phase behavior of velocity and density perturbations. We demonstrate that slow waves cause line asymmetries when the emission line is averaged over an oscillation period or when a quasi-static plasma component in the line of sight is included. Therefore, we conclude that slow magnetoacoustic waves remain a valid explanation for the observed quasi-periodic intensity perturbations. Title: Web-Based Data Processing System for Automated Detection of Oscillations with Applications to the Solar Atmosphere Authors: Sych, R. A.; Nakariakov, V. M.; Anfinogentov, S. A.; Ofman, L. Bibcode: 2010SoPh..266..349S Altcode: 2010SoPh..tmp..154S; 2010arXiv1005.3591S A web-based, interactive system for the remote processing of imaging data sets (i.e., EUV, X-ray, and microwave) and the automated interactive detection of wave and oscillatory phenomena in the solar atmosphere is presented. The system targets localized, but spatially resolved, phenomena such as kink, sausage, and longitudinal propagating and standing waves. The system implements the methods of Periodmapping for pre-analysis, and Pixelized Wavelet Filtering for detailed analysis of the imaging data cubes. The system is implemented on the dedicated data-processing server http://pwf.iszf.irk.ru, which is situated at the Institute of Solar-Terrestrial Physics, Irkutsk, Russia. Input data in the .sav, .fits, or .txt formats can be submitted via the local and/or global network (the Internet). The output data can be in the png, jpeg, and binary formats, on the user's request. The output data are periodmaps; narrowband amplitude, power, phase and correlation maps of the wave's sources at significant harmonics and in the chosen spectral intervals, and mpeg movies of their evolution. The system was tested by the analysis of the EUV and microwave emission from the active region NOAA 10756 on 4 May 2005 observed with TRACE and the Nobeyama Radioheliograph. The similarity of the spatial localization of three-minute propagating waves, near the footpoint of locally open magnetic-field lines determined by the potential-field extrapolation, in both the transition region and the corona was established. In the transition region the growth of the three-minute amplitude was found to be accompanied by the decrease in the line-of-sight angle to the wave-propagation direction. Title: From Large-scale Loops to the Sites of Dense Flaring Loops: Preferential Conditions for Long-period Pulsations in Solar Flares Authors: Foullon, C.; Fletcher, L.; Hannah, I. G.; Verwichte, E.; Cecconi, B.; Nakariakov, V. M.; Phillips, K. J. H.; Tan, B. L. Bibcode: 2010ApJ...719..151F Altcode: Long-period quasi-periodic pulsations (QPPs) of solar flares are a class apart from shorter period events. By involving an external resonator, the mechanism they call upon differs from traditional QPP models, but has wider applications. We present a multi-wavelength analysis of spatially resolved QPPs, with periods around 10 minutes, observed in the X-ray spectrum primarily at energies between 3 and 25 keV. Complementary observations obtained in Hα and radio emission in the kHz to GHz frequency range, together with an analysis of the X-ray plasma properties provide a comprehensive picture that is consistent with a dense flaring loop subject to periodic energization and thermalization. The QPPs obtained in Hα and type III radio bursts, with similar periods as the QPPs in soft X-rays, have the longest periods ever reported for those types of data sets. We also report 1-2 GHz radio emission, concurrent with but unrestricted to the QPP time intervals, which is multi-structured at regularly separated narrowband frequencies and modulated with ~18 minute periods. This radio emission can be attributed to the presence of multiple "quiet" large-scale loops in the background corona. Large scale but shorter inner loops below may act as preferential resonators for the QPPs. The observations support interpretations consistent with both inner and outer loops subject to fast kink magnetohydrodynamic waves. Finally, X-ray imaging indicates the presence of double coronal sources in the flaring sites, which could be the particular signatures of the magnetically linked inner loops. We discuss the preferential conditions and the driving mechanisms causing the repeated flaring. Title: Phenomenon of Alfvénic Vortex Shedding Authors: Gruszecki, M.; Nakariakov, V. M.; van Doorsselaere, T.; Arber, T. D. Bibcode: 2010PhRvL.105e5004G Altcode: Generation of Alfvénic (magnetohydrodynamic) vortices by the interaction of compressible plasma flows with magnetic-field-aligned blunt obstacles is modeled in terms of magnetohydrodynamics. It is found that periodic shedding of vortices with opposite vorticity is a robust feature of the interaction in a broad range of plasma parameters: for plasma beta from 0.025 to 0.5, and for the flow speeds from 0.1 to 0.99 of the fast magnetoacoustic speed. The Strouhal number is the dimensionless ratio of the blunt body diameter to the product of the period of vortex shedding and the inflow speed. It is found to be consistently in the range 0.15-0.25 in the whole range of parameters. The induced Alfvénic vortices are compressible and contain spiral-armed perturbations of the magnetic field strength and plasma mass density up to 50%-60% of the background values. The generated electric current also has the spiral-armed structuring. Title: Long-wavelength torsional modes of solar coronal plasma structures Authors: Vasheghani Farahani, S.; Nakariakov, V. M.; van Doorsselaere, T. Bibcode: 2010A&A...517A..29V Altcode:
Aims: We consider the effects of the magnetic twist and plasma rotation on the propagation of torsional m = 0 perturbations of cylindrical plasma structures (straight magnetic flux tubes) in the case when the wavelength is much longer than the cylinder diameter.
Methods: The second order thin flux tube approximation is used to derive dispersion relations and phase relations in linear long-wavelength axisymmetric magnetohydrodynamic waves in uniformly twisted and rotating plasma structures.
Results: Asymptotic dispersion relations linking phase speeds with the plasma parameters are derived. When twist and rotation are both present, the phase speed of torsional waves depends upon the direction of the wave propagation, and also the waves are compressible. The phase relations show that in a torsional wave the density and azimuthal magnetic field perturbations are in phase with the axial magnetic field perturbations and anti-phase with tube cross-section perturbations. In a zero-β non-rotating plasma cylinder confined by the equilibrium twist, the density perturbation is found to be about 66 percent of the amplitude of the twist perturbation in torsional waves. Title: Independent Signals from the Influence of Internal Magnetic Layers on the Frequencies of Solar p-modes Authors: Foullon, C.; Nakariakov, V. M. Bibcode: 2010ApJ...714L..68F Altcode: The discovery that p-mode frequencies of low degree do not follow changes of solar surface activity during the recent solar minimum offers the possibility of a new diagnostic signature of the responsible pressure perturbation in the wave guiding medium, potentially rich of information regarding the structure of the Sun and the cause of the unusually long solar minimum. Magnetic fields, as well as temperature changes, introduce equilibrium pressure deviations that modify the resonant frequencies of p-mode oscillations. Assuming the perturbation to be caused by a horizontal layer of magnetic field located in a plane-stratified model of the Sun, we compile analytical frequency shifts and process them to allow direct comparison with observations. The effect of magnetism itself on the central p-mode frequencies can be neglected in comparison with the thermal effect of a perturbative layer buried in the solar interior. A parametric study shows that a layer as thin as 2100 km at subsurface depths is able to reproduce reported mean anomalous frequency shifts (not correlated with the surface activity), while a layer of size around 4200 km increasing by a small amount at depths near 0.08 R sun can explain individual low-degree shifts. It is also possible to obtain the mean shifts via the upward motion through depths near 0.03 R sun of a rising perturbative layer of thickness around 7000 km. Hence, the anomalous frequency shifts are best explained by thermal effects in the upper regions of the convection zone. The effects of latitudinal distribution are not treated here. Title: Quasi-Periodic Pulsations in the Gamma-Ray Emission of a Solar Flare Authors: Nakariakov, V. M.; Foullon, C.; Myagkova, I. N.; Inglis, A. R. Bibcode: 2010EGUGA..12.8615N Altcode: Quasi-periodic pulsations (QPPs) of gamma-ray emission with a period of about 40 s are found in a single loop X-class solar flare on 2005 January 1 at photon energies up to 2-6 MeV with the SOlar Neutrons and Gamma-rays (SONG) experiment aboard the CORONAS-F mission. The oscillations are also found to be present in the microwave emission detected with the Nobeyama Radioheliograph, and in the hard X-ray and low energy gamma-ray channels of RHESSI. Periodogram and correlation analysis shows that the 40 s QPPs of microwave, hard X-ray, and gamma-ray emission are almost synchronous in all observation bands. Analysis of the spatial structure of hard X-ray and low energy (80-225 keV) gamma-ray QPP with RHESSI reveals synchronous while asymmetric QPP at both footpoints of the flaring loop. The difference between the averaged hard X-ray fluxes coming from the two footpoint sources is found to oscillate with a period of about 13 s for five cycles in the highest emission stage of the flare. The proposed mechanism generating the 40 s QPP is a triggering of magnetic reconnection by a kink oscillation in a nearby loop. The 13 s periodicity could be produced by the second harmonics of the sausage mode of the flaring loop. Title: Long period oscillations in sunspots Authors: Chorley, N.; Hnat, B.; Nakariakov, V. M.; Inglis, A. R.; Bakunina, I. A. Bibcode: 2010A&A...513A..27C Altcode: Long period oscillations of the gyroresonant emission from sunspot atmospheres are studied. Time series data generated from the sequences of images obtained by the Nobeyama Radioheliograph operating at a frequency of 17 GHz for three sunspots have been analysed and are found to contain significant periods in the range of several tens of minutes. Wavelet analysis shows that these periods are persistent throughout the observation periods. The presence of the oscillations is confirmed by several methods (periodogram, wavelets, Fisher randomisation and empirical mode decomposition). Spatial analysis using the techniques of period, power, correlation and time lag mapping reveals regions of enhanced oscillatory power in the umbral regions. Also seen are two regions of coherent oscillation of about 25 pixels in size, that oscillate in anti-phase with each other. Possible interpretation of the observed periodicities is discussed, in terms of the shallow sunspot model and the leakage of the solar g-modes. Title: Spatially-resolved X-ray observations of the global sausage mode oscillations in a coronal loop Authors: Zimovets, Ivan; Nakariakov, Valery Bibcode: 2010cosp...38.1813Z Altcode: 2010cosp.meet.1813Z We present the first identification of the global (or fundamental) fast magnetoacoustic sausage mode of a coronal loop in the X-ray band, based upon the detailed analysis of multi-wavelength spatially-resolving observations of the M9.3 solar flare on 6 November 2004 by RHESSI. High quality harmonic oscillations with the time period of about 78 s and Q=240 have been detected in the thermal X-ray (with energies lower than 25 keV) emission flux in the decay phase of the flare. Similar quasi-periodic pulsations were also observed in the decimetric-centimetric radio emission flux (as pulsations of type IV radio burst). In the non-thermal hard X-ray emission (higher than 25 keV) the oscillations were less pronounced. It is found that the area of the quasi-stationary and cooling soft X-ray source (lower than 15 keV), which was situated near the top of the flaring loop, varied in anti-phase with the oscillating flux of its radiation. The oscillation period remained constant during all the oscillations. The observed properties of the oscillations coincide with the theoretically predicted properties of standing sausage modes. Cooling of heated plasma during the oscillations is explained mainly by the conductive losses. Title: Quasi-Periodic Pulsations in the Gamma-Ray Emission of a Solar Flare Authors: Nakariakov, V. M.; Foullon, C.; Myagkova, I. N.; Inglis, A. R. Bibcode: 2010ApJ...708L..47N Altcode: Quasi-periodic pulsations (QPPs) of gamma-ray emission with a period of about 40 s are found in a single loop X-class solar flare on 2005 January 1 at photon energies up to 2-6 MeV with the SOlar Neutrons and Gamma-rays (SONG) experiment aboard the CORONAS-F mission. The oscillations are also found to be present in the microwave emission detected with the Nobeyama Radioheliograph, and in the hard X-ray and low energy gamma-ray channels of RHESSI. Periodogram and correlation analysis shows that the 40 s QPPs of microwave, hard X-ray, and gamma-ray emission are almost synchronous in all observation bands. Analysis of the spatial structure of hard X-ray and low energy (80-225 keV) gamma-ray QPP with RHESSI reveals synchronous while asymmetric QPP at both footpoints of the flaring loop. The difference between the averaged hard X-ray fluxes coming from the two footpoint sources is found to oscillate with a period of about 13 s for five cycles in the highest emission stage of the flare. The proposed mechanism generating the 40 s QPP is a triggering of magnetic reconnection by a kink oscillation in a nearby loop. The 13 s periodicity could be produced by the second harmonics of the sausage mode of the flaring loop. Title: Foreword Authors: Nakariakov, V. M.; Erdélyi, R. Bibcode: 2009SSRv..149....1N Altcode: No abstract at ADS Title: Quasi-Periodic Pulsations in Solar Flares Authors: Nakariakov, V. M.; Melnikov, V. F. Bibcode: 2009SSRv..149..119N Altcode: Quasi-periodic pulsations (QPP) are a common feature of flaring energy releases in the solar atmosphere, observed in all bands, from radio to hard X-ray. In this review we concentrate on QPP with the periods longer than one second. Physical mechanisms responsible for the generation of long QPP split into two groups: “load/unload” mechanisms and MHD oscillations. Load/unload mechanisms are repetitive regimes of flaring energy releases by magnetic reconnection or by other means. MHD oscillations can affect all elements of the flaring emission generation: triggering of reconnection and modulation of its rate, acceleration and dynamics of non-thermal electrons, and physical conditions in the emitting plasmas. In the case of MHD oscillations, the periodicity of QPP is determined either by the presence of some resonances, e.g. standing modes of plasma structures, or by wave dispersion. Periods and other parameters of QPP are linked with properties of flaring plasmas and their morphology. Observational investigation of the QPP generation mechanisms based upon the use of spatial information, broadband spectral coverage and multi-periodicity is discussed. Title: Relationship between wave processes in sunspots and quasi-periodic pulsations in active region flares Authors: Sych, R.; Nakariakov, V. M.; Karlicky, M.; Anfinogentov, S. Bibcode: 2009A&A...505..791S Altcode: 2010arXiv1005.3594S A phenomenological relationship between oscillations in a sunspot and quasi-periodic pulsations (QPP) in flaring energy releases at an active region (AR) above the sunspot is established. The analysis of the microwave emission recorded by the Nobeyama Radioheliograph at 17 GHz shows a gradual increase in the power of the 3-min oscillation train in the sunspot associated with AR 10756 before flares in this AR. The flaring light curves are found to be bursty with a period of 3 min. Our analysis of the spatial distribution of the 3-min oscillation power implies that the oscillations follow from sunspots along coronal loops towards the flaring site. It is proposed that QPP in the flaring energy releases can be triggered by 3-min slow magnetoacoustic waves leaking from sunspots. Title: Ultra-long-period Oscillations in EUV Filaments Near to Eruption: Two-wavelength Correlation and Seismology Authors: Foullon, C.; Verwichte, E.; Nakariakov, V. M. Bibcode: 2009ApJ...700.1658F Altcode: We investigate whether or not ultra-long-period oscillations in EUV filaments can be related to their eruption. We report new observations of long-period (~10-30 hr) oscillatory motions in an apparently quiescent filament, as it crosses the solar disk in a 12 minute cadence SOHO/Extreme-Ultraviolet Imaging Telescope (EIT) 195 Å uninterrupted data set. This data set is chosen to explore characteristics of the filament oscillations depending on its eruptive behavior, which is observed while the filament is still on the disk. The periods are found to increase in a near-stable regime prior to eruption. For the two sequences reported so far, we compare and link the EUV filament oscillations with pulsations in full-disk solar EUV irradiance from SOHO/CELIAS/SEM 304 Å flux measurements. In intervals with stationary periods, we find that the 304 Å pulsations and the 195 Å filament oscillations have similar periodicities, but are phase-shifted by about a quarter of period. The two-wavelength correlation serves to show that, when the filament is the dominant dynamical feature but can no longer be tracked on the disk, the full-disk irradiance may provide a mean to identify the period increase prior to the filament eruption. We use the periods thus obtained to estimate the height increase of filaments' suspending coronal magnetic field lines, based on a magnetohydrodynamic (MHD) wave interpretation of the oscillations. The results are consistent with changes in prominence heights detected off-limb and thus support the seismological tool employed. Other interpretations connected with thermal overstability or MHD piston effect are possible. These theoretical predictions however do not explain the quarter-period shift between the two EUV-wavelength signals. In any case, the detected variations may provide a powerful diagnostic tool for the forecasting of prominence eruptions. Title: Characteristics of magnetoacoustic sausage modes Authors: Inglis, A. R.; van Doorsselaere, T.; Brady, C. S.; Nakariakov, V. M. Bibcode: 2009A&A...503..569I Altcode: 2013arXiv1303.6301I Aims: We perform an advanced study of the fast magnetoacoustic sausage oscillations of coronal loops in the context of MHD coronal seismology to establish the dependence of the sausage mode period and cut-off wavenumber on the plasma-β of the loop-filling plasma. A parametric study of the ratios for different harmonics of the mode is also carried out.
Methods: Full magnetohydrodynamic numerical simulations were performed using Lare2d, simulating hot, dense loops in a magnetic slab environment. The symmetric Epstein profile and a simple step-function profile were both used to model the density structure of the simulated loops. Analytical expressions for the cut-off wavenumber and the harmonic ratio between the second longitudinal harmonic and the fundamental were also examined.
Results: It was established that the period of the global sausage mode is only very weakly dependent on the value of the plasma-β inside a coronal loop, which justifies the application of this model to hot flaring loops. The cut-off wavenumber kc for the global mode was found to be dependent on both internal and external values of the plasma-β, again only weakly. By far the most important factor in this case was the value of the density contrast ratio between the loop and the surroundings. Finally, the deviation of the harmonic ratio P_1/2P2 from the ideal non-dispersive case was shown to be considerable at low k, again strongly dependent on plasma density. Quantifying the behaviour of the cut-off wavenumber and the harmonic ratio has significant applications to the field of coronal seismology. Title: The possible role of vortex shedding in the excitation of kink-mode oscillations in the solar corona Authors: Nakariakov, V. M.; Aschwanden, M. J.; van Doorsselaere, T. Bibcode: 2009A&A...502..661N Altcode: We propose a model for the excitation of horizontally polarised transverse (kink) magnetoacoustic oscillations of solar coronal loops by upflows associated with coronal mass ejections. If the magnetic field in the plasma that is dragged in the vertical direction by the flow is parallel to the loop, the phenomenon of vortex shedding causes the appearance of a quasi-periodic horizontal force that is applied to alternating sides of the loop. The period of the force is determined by the flow speed and the loop's minor radius. The oscillations are excited the most effectively when the force is in resonance with the natural frequency of the kink oscillations. This model can explain the selectivity of the excitation of the oscillations and the initial growth of the oscillation amplitude. Title: Seismology of a Large Solar Coronal Loop from EUVI/STEREO Observations of its Transverse Oscillation Authors: Verwichte, E.; Aschwanden, M. J.; Van Doorsselaere, T.; Foullon, C.; Nakariakov, V. M. Bibcode: 2009ApJ...698..397V Altcode: The first analysis of a transverse loop oscillation observed by both Solar TErrestrial RElations Observatories (STEREO) spacecraft is presented, for an event on the 2007 June 27 as seen by the Extreme Ultraviolet Imager (EUVI). The three-dimensional loop geometry is determined using a three-dimensional reconstruction with a semicircular loop model, which allows for an accurate measurement of the loop length. The plane of wave polarization is found from comparison with a simulated loop model and shows that the oscillation is a fundamental horizontally polarized fast magnetoacoustic kink mode. The oscillation is characterized using an automated method and the results from both spacecraft are found to match closely. The oscillation period is 630 ± 30 s and the damping time is 1000 ± 300 s. Also, clear intensity variations associated with the transverse loop oscillations are reported for the first time. They are shown to be caused by the effect of line-of-sight integration. The Alfvén speed and coronal magnetic field derived using coronal seismology are discussed. This study shows that EUVI/STEREO observations achieve an adequate accuracy for studying long-period, large-amplitude transverse loop oscillations. Title: Propagating transverse waves in soft X-ray coronal jets Authors: Vasheghani Farahani, S.; Van Doorsselaere, T.; Verwichte, E.; Nakariakov, V. M. Bibcode: 2009A&A...498L..29V Altcode: Aims: The theoretical model for magnetohydrodynamic (MHD) modes guided by a field-aligned plasma cylinder with a steady flow is adapted to interpret transverse waves observed in solar coronal hot jets, discovered with Hinode/XRT in terms of fast magnetoacoustic kink modes.
Methods: Dispersion relations for linear magnetoacoustic perturbations of a plasma jet of constant cross-section surrounded by static magnetised plasma are used to determine the phase and group speeds of guided transverse waves and their relationship with the physical parameters of the jet and the background plasma. The structure of the perturbations in the macroscopic parameters of the plasma inside and outside the jet, and the phase relations between them are also established.
Results: We obtained a convenient expansion for the long wave-length limit of the phase and group speeds and have shown that transverse waves observed in soft-X-ray solar coronal jets are adequately described in terms of fast magnetoacoustic kink modes by a magnetic cylinder model, which includes the effect of a steady flow. In the observationally determined range of parameters, the waves are not found to be subject to either the Kelvin-Helmholtz instability or the negative energy wave instability, and hence they are likely to be excited at the source of the jet. Title: Sausage oscillations in loops with a non-uniform cross-section Authors: Pascoe, D. J.; Nakariakov, V. M.; Arber, T. D.; Murawski, K. Bibcode: 2009A&A...494.1119P Altcode: Context: Flaring coronal loops are often observed in microwave and sometimes in soft X-rays, as extended structures of variable cross-section or width. The quasi-periodic pulsations associated with flaring coronal loops have been interpreted in terms of standing, fast sausage magnetoacoustic modes and suggested for the diagnostics of the magnetic field outside the oscillating loop.
Aims: We investigate the effects of a non-uniform cross-section on a coronal loop with respect to the standing sausage modes it supports.
Methods: Numerical simulations of standing sausage modes are performed for a straight, zero-β coronal loop with a varying cross-section. The global sausage mode and higher harmonics are considered, and simulations were performed for a range of density contrast ratios and loop divergence parameter. We consider modifications of the period of oscillation and the spatial profile of the standing modes.
Results: As the loop divergence parameter increases, the period of the standing modes decreases. The fractional change period is independent of the density contrast ratio. The spatial profiles of the standing modes are modified by the cross-section inhomogeneity, but this effect is too weak to be observable by modern instruments. For the global sausage mode, the cross-section radius divergence by a factor of 2 is found to cause the decrease in the period of about 5%. Title: A multi-periodic oscillatory event in a solar flare Authors: Inglis, A. R.; Nakariakov, V. M. Bibcode: 2009A&A...493..259I Altcode: Aims: Ratios of different significant periods found in the light curves of a solar flare exhibiting quasi-periodic pulsations (QPP) are used to distinguish between the possible physical mechanisms responsible for such periodic behaviour.
Methods: Time series data of the flaring event of 2002 July 3, observed via the Nobeyama Radioheliograph, Nobeyama Radiopolarimeters, and the RHESSI satellite, are investigated with the use of the Lomb-Scargle periodogram technique. Images of the event are also recovered via the RHESSI, SOHO, and Nobeyama Radioheliograph instruments.
Results: Statistical analysis of the Lomb-Scargle periodogram results indicates three distinct periods above the 99% confidence level in Nobeyama Radioheliograph and Radiopolarimeter data, at 28 s, 18 s, and 12 s, respectively. The two longest of these periods were also observed in the RHESSI data at the same confidence level. Wavelet analysis demonstrated that multiple periods occurred simultaneously without any significant frequency shift over time. Reconstructed images of the event reveal a very compact flare structure unsuitable for spatially resolved analysis. Consideration of the period ratios leads to the conclusion that the cause of this multi-periodic event is likely to be a kink mode periodically triggering magnetic reconnection. Title: Seismological demonstration of perpendicular density structuring in the solar corona Authors: Van Doorsselaere, T.; Brady, C. S.; Verwichte, E.; Nakariakov, V. M. Bibcode: 2008A&A...491L...9V Altcode: The peculiarities of the propagating transverse waves observed in the solar corona with the Coronal Multi-channel Polarimeter (CoMP) indicate the existence of fine field structuring in the coronal density. We present results of numerical simulations studying the evolution of a localised transverse magneto-hydrodynamic wave in a uniform magnetic field. We consider two initial low plasma-beta equilibria: one with a homogeneous density, and one with a field-aligned dense structure (such as a loop or a plume). The perpendicular localisation of the wave strongly determines the angular distribution of the energy propagation. If the perpendicular scale of the wave is significantly smaller than the parallel scale (e.g. wavelength), as established by CoMP, the wave develops as an oblique fast magneto-acoustic wave. In an unstructured medium, the energy of such a wave is transferred mainly across the magnetic field. However, it is possible to channel the energy of the transverse wave along the magnetic field in the presence of a field-aligned density enhancement. We conclude that the CoMP results provide an independent seismological proof that the corona is structured in density in the perpendicular direction. Title: Magnetohydrodynamic seismology of solar and stellar coronae Authors: Nakariakov, V. M. Bibcode: 2008JPhCS.118a2038N Altcode: The review presents the study of long period (longer than a few seconds) wave and oscillation phenomena in the corona of the Sun in radio, VL, EUV and X-ray bands, interpreted in terms of MHD theory. This study provides us with the observational foundation for the remote diagnostics of solar and stellar coronae with MHD waves. Kink and sausage magnetoacoustic modes and longitudinal (or acoustic) modes of coronal loops have already been confidently identified in the data. At present, the main research emphasis is put on the determination of parametric relations in the wave and oscillatory phenomena, the study of multi-modal events, and on the identification of MHD modes in quasi-periodic pulsations of solar and stellar flares. Title: Forward Modeling of EIS Spectroscopic Data Emitted by a Vertically Oscillating Loop Authors: Doorsselaere, T. V.; Nakariakov, V. M. Bibcode: 2008ASPC..397...58D Altcode: This paper focuses on forward modeling of spectroscopic data, as would be emitted by a coronal loop oscillating in the vertical fast kink mode. The Doppler shift, broadening and deformation of the observed spectral lines are investigated. It is concluded that the vertical kink mode causes strong line broadening, either inside the loop or at the edges of the loop, depending on the time integration and the oscillatory phase observed. Title: Detection of Waves in the Solar Corona: Kink or Alfvén? Authors: van Doorsselaere, T.; Nakariakov, V. M.; Verwichte, E.; Young, P. R. Bibcode: 2008ESPM...12.2.81V Altcode: Last year, Tomczyk et al. (2007) have conclusively proven that low amplitude (1km/s) waves are ubiquitously present in the corona. A few months later, this was followed up with the discovery that chromospheric spicules carry tremendous wave power (De Pontieu et al., 2007). These new developments form a basis for coronal seismological magnetic field mapping of the corona and chromosphere. However, this must be based upon a confident identification of the observed wave mode.

Using basic MHD wave theory, we demonstrate that the only way to interpret the observed wave motions is in terms of fast magnetoacoustic kink waves. We prove that the interpretation in terms of Alfven waves, as was put forward in the original articles, does not explain the observed phenomenology, while the fast magnetoacoustic kink waves reproduce the required observational constraints.

To underline the potential of magnetic field mapping, we discuss a recent observation of coronal loop kink oscillations observed with Hinode/EIS. Because of its spectroscopic and imaging capabilities, we are able to measure the loop density, simultaneously with the loop length. This allows us to determine the magnetic field with unprecedented accuracy. Title: Multi-wavelength spatially resolved analysis of quasi-periodic pulsations in a solar flare Authors: Inglis, A. R.; Nakariakov, V. M.; Melnikov, V. F. Bibcode: 2008A&A...487.1147I Altcode: Aims: We aim to perform a spatially resolved analysis of a quasi-periodic pulsation event from 8th May 1998 using microwave data from the Nobeyama Radioheliograph and Radiopolarimeter, and X-ray data from the Yohkoh satellite.
Methods: Time spectra of the signals integrated over the emission source are constructed with the use of the Lomb-Scargle periodogram method, revealing the presence of a pronounced 16 s periodicity. The Pixon image reconstruction algorithm and Hanaoka algorithm are used to reconstruct images from the hard X-ray data from Yohkoh/HXT and Nobeyama Radioheliograph respectively. The phase relationship of the microwave emission was analysed with the use of cross-correlation techniques.
Results: The flaring loop was resolved in the microwave band. The hard X-ray sources are found to be located near the footpoint and at the loop apex determined by the soft X-ray image. The apex source is much fainter than footpoint one. In microwave, all parts of the loop are seen to oscillate with the same period and almost in phase. It was not possible to determine the spatial structure of the oscillation in the hard X-ray band. The period and the coherent spatial structure of the oscillation are indicative of the presence of either an MHD sausage mode or a periodic regime of magnetic reconnection. Title: Coronal magnetic field measurement using loop oscillations observed by Hinode/EIS Authors: Van Doorsselaere, T.; Nakariakov, V. M.; Young, P. R.; Verwichte, E. Bibcode: 2008A&A...487L..17V Altcode: We report the first spectroscopic detection of a kink MHD oscillation of a solar coronal structure by the Extreme-Ultraviolet Imaging Spectrometer (EIS) on the Japanese Hinode satellite. The detected oscillation has an amplitude of 1 km s-1 in the Doppler shift of the FeXII 195 Å spectral line (1.3~MK), and a period of 296~s. The unique combination of EIS's spectroscopic and imaging abilities enables us to measure simultaneously the mass density and length of the oscillating loop. This enables us to measure directly the magnitude of the local magnetic field, the fundamental coronal plasma parameter, as 39 ± 8~G, with unprecedented accuracy. This proof of concept makes EIS an exclusive instrument for the full scale implementation of the MHD coronal seismological technique. Title: Coronal loop seismology using multiple transverse loop oscillation harmonics Authors: Van Doorsselaere, T.; Nakariakov, V. M.; Verwichte, E. Bibcode: 2008IAUS..247..140V Altcode: 2007IAUS..247..140V TRACE observations (23/11/1998 06:35:57-06:48:43UT) in the 171 Å bandpass of an active region are studied. Coronal loop oscillations are observed after a violent disruption of the equilibrium. The oscillation properties are studied to give seismological estimates of physical quantities, such as the density scale height. A loop segment is traced during the oscillation, and the resulting time series is analysed for periodicities. In the loop segment displacement, two periods are found: 435.6±4.5 s and 242.7±6.4 s, consistent with the periods of the fundamental and 2nd harmonic fast kink oscillation. The small uncertainties allow us to estimate the density scale height in the loop to be 109 Mm, which is about double the estimated hydrostatical value of 50 Mm. The eigenfunction is used to do spatial coronal seismology, but that method does not give any conclusive results. Title: The Pixelised Wavelet Filtering Method to Study Waves and Oscillations in Time Sequences of Solar Atmospheric Images Authors: Sych, R. A.; Nakariakov, V. M. Bibcode: 2008SoPh..248..395S Altcode: Pixelised wavelet filtering (PWF) for the determination of the spatial, temporal, and phase structure of oscillation sources in temporal sequences of 2D images, based upon the continuous wavelet transform, has been designed and tested. The PWF method allows us to obtain information about the presence of propagating and nonpropagating waves in the data and localise them precisely in time and in space. The method is tested on the data sets obtained in microwaves with the Nobeyama Radioheliograph and in the EUV with TRACE. The method reveals fine spatial structuring of the sources of 3-, 5-, and 15-minute periodicities in the microwave and EUV emission generated in sunspot atmospheres. In addition, the PWF method provides us with unique information about the temporal variability of the power, amplitude, and phase narrowband maps of the observed oscillations and waves. The applicability of the method to the analysis of coronal wave phenomena is discussed. Title: Detection of Waves in the Solar Corona: Kink or Alfvén? Authors: Van Doorsselaere, T.; Nakariakov, V. M.; Verwichte, E. Bibcode: 2008ApJ...676L..73V Altcode: Recently, the omnipresence of waves has been discovered in the corona using the CoMP instrument. We demonstrate that the observational findings can be explained in terms of guided kink magnetoacoustic modes. The interpretation of the observations in terms of Alfvén waves is shown to be inconsistent with MHD wave theory. The implications of the interpretation in terms of kink waves are discussed. Title: Interactive remote data processing using Pixelize Wavelet Filtration (PWF-method) and PeriodMap analysis Authors: Sych, Robert; Nakariakov, Valery; Anfinogentov, Sergey Bibcode: 2008cosp...37.3106S Altcode: 2008cosp.meet.3106S Wavelet analysis is suitable for investigating waves and oscillating in solar atmosphere, which are limited in both time and frequency. We have developed an algorithms to detect this waves by use the Pixelize Wavelet Filtration (PWF-method). This method allows to obtain information about the presence of propagating and non-propagating waves in the data observation (cube images), and localize them precisely in time as well in space. We tested the algorithm and found that the results of coronal waves detection are consistent with those obtained by visual inspection. For fast exploration of the data cube, in addition, we applied early-developed Period- Map analysis. This method based on the Fast Fourier Transform and allows on initial stage quickly to look for "hot" regions with the peak harmonic oscillations and determine spatial distribution at the significant harmonics. We propose the detection procedure of coronal waves separate on two parts: at the first part, we apply the PeriodMap analysis (fast preparation) and than, at the second part, use information about spatial distribution of oscillation sources to apply the PWF-method (slow preparation). There are two possible algorithms working with the data: in automatic and hands-on operation mode. Firstly we use multiply PWF analysis as a preparation narrowband maps at frequency subbands multiply two and/or harmonic PWF analysis for separate harmonics in a spectrum. Secondly we manually select necessary spectral subband and temporal interval and than construct narrowband maps. For practical implementation of the proposed methods, we have developed the remote data processing system at Institute of Solar-Terrestrial Physics, Irkutsk. The system based on the data processing server - http://pwf.iszf.irk.ru. The main aim of this resource is calculation in remote access through the local and/or global network (Internet) narrowband maps of wave's sources both in whole spectral band and at significant harmonics. In addition, we can obtain temporal dynamics (mpeg- files) of the main oscillation characteristics: amplitude, power and phase as a spatial-temporal coordinates. For periodogram mapping of data cubes as a method for the pre-analysis, we developed preparation of the color maps where the pixel's colour corresponds to the frequency of the power spectrum maximum. The computer system based on applications ION-scripts, algorithmic languages IDL and PHP, and Apache WEB server. The IDL ION-scripts use for preparation and configuration of network requests at the central data server with subsequent connection to IDL run-unit software and graphic output on FTP-server and screen. Web page is constructed using PHP language. Title: Sausage Oscillations in Multishell Coronal Structures Authors: Pascoe, D. J.; Nakariakov, V. M.; Arber, T. D. Bibcode: 2007SoPh..246..165P Altcode: The effect of fine multilayered structuring on the resonant periods of global sausage (m=0), fast magnetoacoustic oscillations of coronal loops is studied for the straight magnetic slab model filled with a zero-β plasma. The slab is considered to have a one-dimensional inhomogeneity of the Alfvén speed in the direction perpendicular to the axis of the slab, which coincides with the equilibrium, straight, magnetic field. This magnetic configuration models an oscillating coronal loop that is formed by a bundle of field-aligned, smooth, concentric, circular shells of variable density and width. The number of the layers (or shells), along with their density, width, and radial steepness, are randomly distributed. It is shown that the resonant properties of long-wavelength sausage standing modes of the slab are not sensitive to the details of fine structuring. It is concluded that the coronal seismological technique for the determination of the magnetic field strength by the period of global sausage oscillations is not sensitive to the fine multilayered or multishell structuring. Title: Preface: A Topical Issue in Honor of Professor Bernard Roberts Authors: Ballester, J. L.; Erdélyi, R.; Hood, A. W.; Leibacher, J. W.; Nakariakov, V. M. Bibcode: 2007SoPh..246....1B Altcode: No abstract at ADS Title: Coronal loop seismology using multiple transverse loop oscillation harmonics Authors: Van Doorsselaere, T.; Nakariakov, V. M.; Verwichte, E. Bibcode: 2007A&A...473..959V Altcode: Context: TRACE observations (23/11/1998 06:35:57-06:48:43 UT) in the 171 Å bandpass of an active region are studied. Coronal loop oscillations are observed after a violent disruption of the equilibrium.
Aims: The oscillation properties are studied to give seismological estimates of physical quantities, such as the density scale height.
Methods: A loop segment is traced during the oscillation, and the resulting time series is analysed for periodicities.
Results: In the loop segment displacement, two periods are found: 435.6 ± 4.5~s and 242.7 ± 6.4~s, consistent with the periods of the fundamental and 2nd harmonic fast kink oscillation. The small uncertainties allow us to estimate the density scale height in the loop to be 109~Mm, which is about double the estimated hydrostatical value of 50~Mm. Because a loop segment is traced, the amplitude dependence along the loop is found for each of these oscillations. The obtained spatial information is used as a seismological tool to give details about the geometry of the observed loop. Title: Solar-B as a Tool for Coronal Wave Studies Authors: Nakariakov, V. M. Bibcode: 2007ASPC..369..221N Altcode: Direct observational evidence of wave and oscillatory activity of the solar corona is abundant in all observational bands and includes recent discoveries of propagating compressible waves in polar plumes and near loop footpoints, flare-generated transverse oscillations of loops, and longitudinal and sausage standing oscillations within loops. These phenomena are successfully interpreted in terms of magnetohydrodynamic (MHD) waves. This observational breakthrough gave rise to the rapid development of a new method for the remote diagnostics of the coronal plasma, MHD coronal seismology, allowing for estimation of the absolute value of the magnetic field in coronal loops, Alfvén speeds, transport coefficients, fine structuring, heating function and other important coronal parameters. EIS and XRT instruments are excellent tools for the further development of coronal wave studies and especially flare generated oscillations and waves. We present the recent findings, theoretical estimations of the observability of different MHD modes with Solar-B instruments, theory-based observational and data analysis strategies and some ideas about the utilisation of the results for coronal seismology. The expected results are of particular interest for the revealing of coronal heating mechanisms. Title: Coronal dynamics Authors: Nakariakov, V. M. Bibcode: 2007AIPC..919..214N Altcode: The lectures present the foundation of solar coronal physics with the main emphasis on the MHD theory and on wave and oscillatory phenomena. We discuss major challenges of the modern coronal physics; the main plasma structures observed in the corona and the conditions for their equilibrium; phenomenology of large scale long period oscillatory coronal phenomena and their theoretical modelling as MHD waves. The possibility of the remote diagnostics of coronal plasmas with the use of MHD oscillations is demonstrated. Title: Quasi-periodic oscillations associated with solar flares Authors: Nakariakov, V. M. Bibcode: 2007AGUSMSH22A..06N Altcode: Mechanisms for the generation of quasi-periodic pulsations (QPP) in microwave, X-ray and visible light emission generated by solar and stellar flares, based upon magnetohydrodynamic (MHD) oscillations, are discussed. QPP can be produced by internal MHD oscillations of flaring magnetic structures, in particular by kink, sausage and longitudinal modes. Different modes have different observational signatures in different emission bands, allowing for the correct identification of the mode. Another mechanism is based upon periodic triggering of flaring energy releases by oscillations in a non-flaring loop situated nearby the flaring region. The use of observable parameters of QPP for remote diagnostics of coronal plasmas, in particular of the magnetic field in the flaring regions is demonstrated. Title: Coronal Periodmaps Authors: Nakariakov, V. M.; King, D. B. Bibcode: 2007SoPh..241..397N Altcode: The search for signatures of wave and oscillatory processes in the solar corona in the data obtained with imaging instruments can be automated by using the periodmap method. The method reduces a three-dimensional data cube to a two-dimensional map of the analysed field of view. The map reveals the presence and distribution of the most pronounced frequencies in the power spectrum of the time signal recorded at spatial pixels. We demonstrate the applicability of this method as a pre-analysis tool with the use of TRACE EUV coronal data, which contain examples of transverse and longitudinal oscillations of coronal loops. The main advantage of using periodmaps over other possible (more sophisticated) pre-analysis tools, such as wavelet analysis, is their robustness and efficiency (both in speed and computational power). The method can be implemented in the Hinode/XRT and SDO/AIA data pre-analysis. Title: Sausage oscillations of coronal loops Authors: Pascoe, D. J.; Nakariakov, V. M.; Arber, T. D. Bibcode: 2007A&A...461.1149P Altcode: Aims:Analytical theory predicts the existence of trapped global (or fundamental) sausage fast magnetoacoustic modes in thick and dense coronal loops only, with the periods estimated as the ratio of double the loop length and the Alfvén speed outside the loop. We extend this study to the leaking regime, considering global sausage modes of long loops with small density contrasts.
Methods: Anti-symmetric fast magnetoacoustic perturbations (sausage, or m=0 modes) of a low β plasma slab with the symmetric Epstein profile of plasma density are modelled numerically.
Results: It was found that long loops with sufficiently small density contrast can support global sausage leaky modes of detectable quality. The periods of the leaky modes are found to be approximately determined by the loop length and the external Alfvén speed. If the loop length can be estimated from imaging observations, the observed period of this mode provides us with the information about the Alfvén speed outside the loop. For typical flaring coronal loops, the estimated periods of the global sausage modes are about 5-60 s. Title: A Magnetometer For The Solar Orbiter Mission Authors: Carr, C. M.; Horbury, T. S.; Balogh, A.; Baumjohann, W.; Bavassano, B.; Breen, A.; Burgess, D.; Cargill, P. J.; Brooker, N.; Erdõs, G.; Fletcher, L.; Forsyth, R. J.; Giacalone, J.; Glassmeier, K. -H.; Hoeksema, J. T.; Goldstein, M. L.; Lockwood, M.; Magnes, W.; Masimovic, M.; Marsch, G.; Matthaeus, W. H.; Murphy, N.; Nakariakov, V. M.; Pacheco, J. R.; Pincon, J. -L.; Riley, P.; Russell, C. T.; Schwartz, S. J.; Szabo, A.; Thompson, M.; Vainio, R.; Velli, M.; Vennerstrom, S.; Walsh, R.; Wimmer-Schweingruber, R.; Zank, G. Bibcode: 2007ESASP.641E..41C Altcode: The magnetometer is a key instrument to the Solar Orbiter mission. The magnetic field is a fundamental parameter in any plasma: a precise and accurate measurement of the field is essential for understanding almost all aspects of plasma dynamics such as shocks and stream-stream interactions. Many of Solar Orbiter's mission goals are focussed around the links between the Sun and space. A combination of in situ measurements by the magnetometer, remote measurements of solar magnetic fields and global modelling is required to determine this link and hence how the Sun affects interplanetary space. The magnetic field is typically one of the most precisely measured plasma parameters and is therefore the most commonly used measurement for studies of waves, turbulence and other small scale phenomena. It is also related to the coronal magnetic field which cannot be measured directly. Accurate knowledge of the magnetic field is essential for the calculation of fundamental plasma parameters such as the plasma beta, Alfvén speed and gyroperiod. We describe here the objectives and context of magnetic field measurements on Solar Orbiter and an instrument that fulfils those objectives as defined by the scientific requirements for the mission. Title: Quasi-periodic Pulsations as a Diagnostic Tool for Coronal Plasma Parameters Authors: Nakariakov, V. M.; Stepanov, A. V. Bibcode: 2007LNP...725..221N Altcode: Quasi-periodic pulsations of radio emission generated in solar and stellar flares are interpreted in terms of MHD oscillations of coronal loops and in the frame of equivalent electric circuit approach, and compared with coronal wave and oscillatory phenomena recently discovered in the EUV, X-ray and visible light bands. Various methods of remote diagnostics of the coronal plasma, based upon the use of observationally detectable properties of quasi-periodic pulsations - their period, amplitude and quality - are discussed. The applicability of these methods to the diagnostics of stellar coronae is demonstrated. Title: MHD oscillations in solar and stellar coronae: Current results and perspectives Authors: Nakariakov, Valery M. Bibcode: 2007AdSpR..39.1804N Altcode: Wave and oscillatory activity is observed with modern imaging and spectral instruments in the visible light, EUV, X-ray and radio bands in all parts of the solar corona. Magnetohydrodynamic (MHD) wave theory gives satisfactory interpretation of these phenomena in terms of MHD modes of coronal structures. The paper reviews the current trends in the observational study of coronal oscillations, recent development of theoretical modelling of MHD wave interaction with plasma structures, and implementation of the theoretical results for the mode identification. Also the use of MHD waves for remote diagnostics of coronal plasmas is discussed. In particular, the applicability of this method to the estimation of the coronal magnetic field is demonstrated. Title: MHD-Oscillation Modes of a Flaring Loop Using Microwave Observations With High Spatial Resolution Authors: Reznikova, Veronika E.; Melnikov, Victor F.; Nakariakov, Valery M.; Shibasaki, Kiyoto Bibcode: 2006AIPC..848..133R Altcode: Study of an oscillating loop observed with high spatial resolution (NoRH) shows the presence of two Fourier spectral peaks: P1 = 14-17 s, which is more pronounced at the loop apex and P2 = 8-11 s, that is stronger at the loop legs. We found the phase shift, P2/4, between the pulsations at the northern leg and at the loop top for the P2 spectral component and a lack of the phase shift between different parts of the flare loop for the P1 component. The computed phase speeds and periods of MHD modes of a coronal loop confirm identification of the first periodicity P1 as the global (fundamental) sausage mode. The second periodicity can be associated with several modes: the second and the third longitudinal harmonics of the kink mode, the third harmonics of the sausage mode and the second harmonics of ballooning mode. Title: Quasi-periodic modulation of solar and stellar flaring emission by magnetohydrodynamic oscillations in a nearby loop Authors: Nakariakov, V. M.; Foullon, C.; Verwichte, E.; Young, N. P. Bibcode: 2006A&A...452..343N Altcode: We propose a new model for quasi-periodic modulation of solar and stellar flaring emission. Fast magnetoacoustic oscillations of a non-flaring loop can interact with a nearby flaring active region. This interaction occurs when part of the oscillation situated outside the loop reaches the regions of steep gradients in magnetic field within an active region and produces periodic variations of electric current density. The modulation depth of these variations is a few orders of magnitude greater than the amplitude of the driving oscillation. The variations of the current can induce current-driven plasma micro-instabilities and thus anomalous resistivity. This can periodically trigger magnetic reconnection, and hence acceleration of charged particles, producing quasi-periodic pulsations of X-ray, optical and radio emission at the arcade footpoints. Title: Seismology of curved coronal loops with vertically polarised transverse oscillations Authors: Verwichte, E.; Foullon, C.; Nakariakov, V. M. Bibcode: 2006A&A...452..615V Altcode: Aims.Using a model of vertically polarised fast magnetoacoustic waves in curved coronal loops, the method of coronal seismology is applied to observations of transverse loop oscillations.
Methods: . A coronal loop is modeled as a curved magnetic slab in the zero plasma-β limit. For an arbitrary piece-wise continuous power law equilibrium density profile, the dispersion relation governing linear vertically polarised fast magnetoacoustic kink waves is derived. The ways in which this model can be used for coronal seismology are explored and applied to two observational examples.
Results: . The Alfvén speed and equilibrium density profile are determined from observations. It is shown that the mechanism of lateral leakage of fast magnetoacoustic kink oscillations described in this model is efficient. In fact, the damping is so efficient that in order to match predicted values with observational ones, either the loop needs to be highly contrasted or the transverse Alfvén speed profile needs to be close to linear. Possible improvements to make the modeling of lateral wave leakage in loops more realistic, allowing a lower damping efficiency, are discussed.
Title: Fast magnetoacoustic waves in curved coronal loops. II. Tunneling modes Authors: Verwichte, E.; Foullon, C.; Nakariakov, V. M. Bibcode: 2006A&A...449..769V Altcode: Aims. Fast magnetoacoustic waves in curved coronal loops are investigated and the role of lateral leakage in wave damping, which includes the mechanism of wave tunneling, is explored. Methods. A coronal loop is modeled as a curved, magnetic slab in the zero plasma-β limit. In this model and for an arbitrary piece-wise continuous power law equilibrium density profile, the wave equation governing linear vertically polarised fast magnetoacoustic waves is solved analytically. An associated dispersion relation is derived and the frequencies and eigenfunctions of the wave modes are characterised. Results. For some equilibria, the waves are shown to be all damped due to lateral leakage. It is demonstrated that waves either leak straight out into the external medium or have to overcome an evanescent barrier, which is linked to wave tunneling. The wave solutions consist of alternating vertically polarised kink and sausage branches. Fast kink oscillations may have a non-zero density perturbation when averaged across the loop. The calculated damping rate of fast magnetoacoustic kink oscillations is shown to be consistent with related numerical simulations and show that lateral leakage may explain the observed damping of (vertically polarised) fast magnetoacoustic kink oscillations. Title: Modulation of gyrosynchrotron emission in solar and stellar flares by slow magnetoacoustic oscillations Authors: Nakariakov, V. M.; Melnikov, V. F. Bibcode: 2006A&A...446.1151N Altcode: Gyrosynchrotron emission generated by non-thermal electrons in solar and stellar coronal flares can be efficiently modulated by slow magnetoacoustic oscillations in the flaring loops. The modulation mechanism is based upon perturbation of the efficiency in the Razin suppression of optically thin gyrosynchrotron emission. Modulation of the emission is in anti-phase with the density perturbation in the slow wave. The observed emission modulation depth can be up to an order of magnitude higher than the slow wave amplitude. This effect is more pronounced at lower frequencies. Observations with spatial resolution, together with analysis of the modulation frequency, are shown to be sufficient for providing the information needed to identify the mode. Title: Magnetohydrodynamic waves in coronal polar plumes Authors: Nakariakov, Valery M. Bibcode: 2006RSPTA.364..473N Altcode: No abstract at ADS Title: Hydromagnetic surface waves on a tangential discontinuity Authors: Joarder, P. S.; Nakariakov, V. M. Bibcode: 2006GApFD.100...59J Altcode: Propagation of hydromagnetic surface waves on an MHD tangential discontinuity, separating two uniform magnetic plasmas, across which the magnetic field changes both its direction and field-strength, is examined. The study is arbitrarily confined to discontinuities one side of which has a plasma-ß value larger than unity. A classification scheme to identify the ‘fast’ and the ‘slow’ surface waves is employed thus enabling us to find new features in the modal structure of these waves. In the case of sufficiently small values for the density ratio between the higher and the lower Alfvén speed regions on opposite sides of the interface, this study reveals the presence of a ‘forbidden region’ for propagation of fast surface waves with values of their propagation angle being smaller than a certain critical value. The study also reveals the existence of two distinct slow surface waves with angles of propagation larger than a certain critical value but for two different ranges of values for the angle between magnetic field vectors across the interface. While revealing such new structures of the surface modes for intermediate parameter values, the present investigation also confirms earlier results regarding the asymptotic behaviour of the modes in the incompressible limit. Title: Fast magnetoacoustic waves in curved coronal loops Authors: Verwichte, E.; Foullon, C.; Nakariakov, V. M. Bibcode: 2006A&A...446.1139V Altcode: A study of vertically polarised fast magnetoacoustic waves in a curved coronal loop is presented. The loop is modeled as a semi-circular magnetic slab in the zero plasma-β limit. The governing equations for linear waves are derived. We show that the wave mode behaviour depends on the slope of the equilibrium density profile, which is modeled as a piece-wise continuous power law curve of index α. For all profiles, except for α=-4, wave modes are not trapped in the loop and leak out into the external medium through wave tunneling. The particular case of α=-4, which corresponds to a linearly increasing Alfvén speed profile, is examined in more detail as this is the only model that can support trapped wave modes. We compare the results with a straight slab model and find similar behaviour. Coupling between sausage and kink wave modes has not been found in the model. Title: A parametric study of the effect of pressure anisotropy on slow nonlinear acoustic waves in high-beta plasmas Authors: Simon, B.; Nakariakov, V.; Rowlands, G.; Chapman, S.; Dendy, R. Bibcode: 2006cosp...36.1041S Altcode: 2006cosp.meet.1041S Solitary wave solutions arise naturally from one dimensional Hall-Magnetohydrodynamic MHD equations These solutions have been recently identified as models for slow-mode solitary structures observed in the magnetosheath and other magnetospheric boundary layers and as a model for magnetic holes MH which are localized depressions of magnetic field observed in the solar wind We extend the analysis of the model of Stasiewicz which is based on one dimesional Hall-MHD with an explicit pressure anisotropy Applying the methods of the Sagdeev potential and direct numerical modelling we performed parametric studies of highly oblique magnetoacoustic nonlinear waves in a high- beta ratio of kinetic to magnetic pressures plasmas We found that anisotropy is crucial for the existence of solitary structures in this model Furthermore if the perpendicular pressure is greater than the parallel pressure there can be both field enhancing bright and field depleting dark solitary structures whereas increased parallel pressure compared to perpendicular pressure only allows for dark solitary structures Combinations of the plasma parameters corresponding to the different regimes are determined Title: Coronal waves and oscillations Authors: Nakariakov, Valery M. Bibcode: 2006IAUS..233..464N Altcode: Wave and oscillatory activity of the solar corona is confidently observed with modern imaging and spectral instruments in the visible light, EUV, X-ray and radio bands, and interpreted in terms of magnetohydrodynamic (MHD) wave theory. The review reflects the current trends in the observational study of coronal waves and oscillations, theoretical modelling of interaction of MHD waves with plasma structures, and implementation of the theoretical results for the mode identification. Also the use of MHD waves for remote diagnostics of coronal plasma - MHD coronal seismology - is discussed. Title: Current results and perspectives of coronal wave investigations Authors: Nakariakov, V. M. Bibcode: 2006cosp...36..794N Altcode: 2006cosp.meet..794N Wave and oscillatory activity is observed with modern imaging and spectral instruments in the visible light EUV X-ray and radio bands in all parts of the solar corona in particular in active regions and polar plumes Magnetohydrodynamic MHD wave theory gives satisfactory interpretation of these phenomena in terms of MHD modes of coronal structures The talk reviews the current trends in the observational study of coronal waves and oscillations with spaceborne and ground-based facilities with the main emphasis on the standing kink and sausage modes and propagating fast wave recent development of theoretical modelling of interaction of MHD waves with plasma structures and implementation of the theoretical results for the mode identification The use of MHD waves for remote diagnostics of coronal plasma is discussed and the applicability of this method for the estimation of coronal magnetic field and fine structuring is demonstrated Title: Diagnostics of Mhd-Oscillation Modes of a Flaring Loop Using Microwave Observations with High Spatial Resolution Authors: Reznikova, V. E.; Nakariakov, V. M.; Melnikov, V. F.; Shibasaki, K. Bibcode: 2005ESASP.600E.140R Altcode: 2005ESPM...11..140R; 2005dysu.confE.140R No abstract at ADS Title: Transverse Waves in a Post-Flare Supra-Arcade Authors: Verwichte, E.; Nakariakov, V. M.; Cooper, F. C. Bibcode: 2005ESASP.600E.101V Altcode: 2005dysu.confE.101V; 2005ESPM...11..101V No abstract at ADS Title: X-Ray Quasi-Periodic Pulsations in Solar Flares as Magnetohydrodynamic Oscillations Authors: Foullon, C.; Verwichte, E.; Nakariakov, V. M.; Fletcher, L. Bibcode: 2005ESASP.600E..33F Altcode: 2005ESPM...11...33F; 2005dysu.confE..33F No abstract at ADS Title: Magnetoacoustic Solitons in High-β Plasmas Authors: Simon, B.; Nakariakov, V. M.; Chapman, S. C.; Dendy, R. O. Bibcode: 2005AGUFMSH53A1238S Altcode: Solitary wave solutions arise naturally from one dimensional Hall-Magnetohydrodynamic equations. These solutions have been recently identified as models for slow-mode solitary structures observed in the magnetosheath and other magnetospheric boundary layers, and as a model for magnetic holes (MH), which are localized depressions of magnetic field observed in the solar wind. We perform a parametric study of highly oblique magnetoacoustic solitons in frames of Stasiewicz's analytical model [1], taking plasma pressure anisotropy into account. We study the stability of these structures using a 1.5D hybrid code. In particular, we focus on magnetic structures in a high-β (ratio of kinetic to magnetic pressures) plasmas. These plasma conditions are typical in the region around MHs, and the study of stability is vital in verifying the theory that MHs are manifestations of such solitons. Our simulations are aimed at studying linear magnetic holes, where there is almost no variation in direction of the ambient magnetic field direction. The majority of MHs discovered in space plasmas fall into this category. [1] Stasiewicz,K., Phys. Rev. Lett., 93, 125004, 2004 Title: Transverse Waves in a Post-Flare Supra-Arcade Authors: Verwichte, E.; Nakariakov, V. M.; Cooper, F. C. Bibcode: 2005ESASP.596E..38V Altcode: 2005ccmf.confE..38V No abstract at ADS Title: Short Quasi-Periodic MHD Waves in Coronal Structures Authors: Nakariakov, V. M.; Pascoe, D. J.; Arber, T. D. Bibcode: 2005SSRv..121..115N Altcode: The possibility of remote diagnostics of coronal structures with impulsively-generated short-period fast magnetoacoustic wave trains is demonstrated. An initially broad-band, aperiodic fast magnetoacoustic perturbation guided by a 1D plasma inhomogeneity develops into a quasi-periodic wave train with a well-pronounced frequency and amplitude modulation. The quasi-periodicity results from the geometrical dispersion of the modes, determined by the transverse profile of the loop, and hence contains information about the profile. Wavelet images of the wave train demonstrate that their typical spectral signature is of a “crazy tadpole’’ shape: a narrow spectrum tail precedes a broad-band head. The instantaneous period of the oscillations in the wave train decreases gradually with time, with a mean value of several seconds for typical coronal values. The period and the spectral amplitude evolution are determined by the steepness of the transverse density profile and the density contrast ratio in the loop, which offers a tool for estimation of the sub-resolution structuring of the corona. Title: X-Ray Quasi-Periodic Pulsations in Solar Flares as Magnetohydrodynamic Oscillations Authors: Foullon, C.; Verwichte, E.; Nakariakov, V. M.; Fletcher, L. Bibcode: 2005ESASP.596E..46F Altcode: 2005ccmf.confE..46F No abstract at ADS Title: X-ray quasi-periodic pulsations in solar flares as magnetohydrodynamic oscillations Authors: Foullon, C.; Verwichte, E.; Nakariakov, V. M.; Fletcher, L. Bibcode: 2005A&A...440L..59F Altcode: We report the first observation at high spatial resolution of long-period quasi-periodic pulsations (QPP) of X-ray radiation during solar flares, made possible with the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), supported by complementary data at other wavelengths from space-based and ground-based telescopes. Evidence for the presence of a transequatorial loop possibly responsible for the detected periodicity connected with its kink mode is found. Our findings suggest that QPP can be interpreted as a periodic pumping of electrons in a compact flaring loop, modulated by oscillations in a magnetically linked and larger loop acting as a long-period magnetohydrodynamic resonator. Title: High-frequency Alfvén waves in multi-ion coronal plasma: Observational implications Authors: Ofman, L.; Davila, J. M.; Nakariakov, V. M.; ViñAs, A. -F. Bibcode: 2005JGRA..110.9102O Altcode: 2005JGRA..11009102O We investigate the effects of high-frequency (of order ion gyrofrequency) Alfvén and ion-cyclotron waves on ion emission lines by studying the dispersion of these waves in a multi-ion coronal plasma. For this purpose we solve the dispersion relation of the linearized multifluid and Vlasov equations in a magnetized multi-ion plasma with coronal abundances of heavy ions. We also calculate the dispersion relation using nonlinear one-dimensional hybrid kinetic simulations of the multi-ion plasma. When heavy ions are present the dispersion relation of parallel propagating Alfvén cyclotron waves exhibits the following branches (in the positive Ω - k quadrant): right-hand polarized nonresonant and left-hand polarized resonant branch for protons and each ion. We calculate the ratio of ion to proton velocities perpendicular to the direction of the magnetic field for each wave modes for typical coronal parameters and find strong enhancement of the heavy ion perpendicular fluid velocity compared with proton perpendicular fluid velocity. The linear multifluid cold plasma results agree with linear warm plasma Vlasov results and with the nonlinear hybrid simulation model results. In view of our findings we discuss how the observed nonthermal line broadening of minor ions in coronal holes may relate to the high-frequency wave motions. Title: Spatially resolved microwave pulsations of a flare loop Authors: Melnikov, V. F.; Reznikova, V. E.; Shibasaki, K.; Nakariakov, V. M. Bibcode: 2005A&A...439..727M Altcode: A microwave burst with quasi-periodic pulsations was studied with high spatial resolution using observations with the Nobeyama Radioheliograph (NoRH). We found that the time profiles of the microwave emission at 17 and 34 GHz exhibit quasi-periodic (with two well defined periods P_1= 14-17 s and P_2= 8-11 s) variations of the intensity at different parts of an observed flaring loop. Detailed Fourier analysis shows the P1 spectral component to be dominant at the top, while the P2 one near the feet of the loop. The 14-17 s pulsations are synchronous at the top and in both legs of the loop. The 8-11 s pulsations at the legs are well correlated with each other but the correlation is not so obvious with the pulsations at the loop top. For this P2 spectral component, a definite phase shift, P_2/4≈ 2.2~s, between pulsations in the northern leg and loop top parts of the loop have been found. The length of the flaring loop is estimated as L = 25 Mm (≈ 34 arcsec) and its average width at half intensity at 34 GHz as about 6 Mm (≈ 8 arcsec). Microwave diagnostics shows the loop to be filled with a dense plasma with the number density n0 ≈ 1011 cm-3, penetrated by the magnetic field changing from B0 ≈ 100 G near the loop top up to B0 ≈ 200 G near the north footpoint. A comparative analysis of different MHD modes of the loop demonstrates the possibility of the simultaneous existence of two modes of oscillations in the loop: the global sausage mode, with the period P_1= 14-17 s and the nodes at the footpoints, and a higher harmonics mode (possibly with the radial wave number l>1), with P_2= 8-11 s. Title: Acoustic Oscillations in Solar and Stellar Flaring Loops Authors: Kelly, A.; Nakariakov, V. M.; Arber, T. D. Bibcode: 2005PADEU..15..125K Altcode: Observations of flaring loops in radio, visible and x-ray bands show quasi-periodic pulsations with periods from a few seconds to several minutes. Recent numerical studies have shown that some of these oscillations can be interpreted as standing slow magnetoacoustic waves. Energy deposition from the flare excites the second standing harmonic, with a period determined by the temperature and loop length. The excited longitudinal oscillations can be practically dissipationless and can, possibly, be considered MHD autowaves. Numerical simulations with a wide range of flare durations and choices of heat deposition location show that the second harmonic is a common feature of flaring loops. Title: Coronal Waves and Oscillations Authors: Nakariakov, Valery M.; Verwichte, Erwin Bibcode: 2005LRSP....2....3N Altcode: Wave and oscillatory activity of the solar corona is confidently observed with modern imaging and spectral instruments in the visible light, EUV, X-ray and radio bands, and interpreted in terms of magnetohydrodynamic (MHD) wave theory. The review reflects the current trends in the observational study of coronal waves and oscillations (standing kink, sausage and longitudinal modes, propagating slow waves and fast wave trains, the search for torsional waves), theoretical modelling of interaction of MHD waves with plasma structures, and implementation of the theoretical results for the mode identification. Also the use of MHD waves for remote diagnostics of coronal plasma — MHD coronal seismology — is discussed and the applicability of this method for the estimation of coronal magnetic field, transport coefficients, fine structuring and heating function is demonstrated. Title: Transverse waves in a post-flare supra-arcade Authors: Verwichte, E.; Nakariakov, V. M.; Cooper, F. C. Bibcode: 2005A&A...430L..65V Altcode: Observations of propagating transverse waves in an open magnetic field structure with the Transition Region And Coronal Explorer (TRACE) are presented. Waves associated with dark tadpole-like sunward moving structures in the post-flare supra-arcade of NOAA active region 9906 on the 21st of April 2002 are analysed. They are seen as quasi-periodic transverse displacements of the dark tadpole tails, with periods in the range of 90-220 s. Their phase speeds and displacement amplitudes decrease as they propagate sunwards. At heights of 90 and 60 Mm above the post-flare loop footpoints the phase speeds are in the ranges 200-700 km s-1 and 90-200 km s-1 respectively. Furthermore, for consecutive tadpoles the phase speeds decrease and periods increase as a function of time. The waves are interpreted as propagating fast magnetoacoustic kink waves guided by a vertical, evolving, open structure. Title: Detection of Ultra-Long Oscillations in an EUV Filament Authors: Foullon, C.; Verwichte, E.; Nakariakov, V. M. Bibcode: 2004ESASP.575..394F Altcode: 2004soho...15..394F No abstract at ADS Title: Transverse Oscillations in a Coronal Loop Arcade Authors: Verwichte, E.; Nakariakov, V. M.; Ofman, L.; Deluca, E. E. Bibcode: 2004ESASP.575..460V Altcode: 2004soho...15..460V No abstract at ADS Title: Coronal Waves: Coronal Heating and Coronal Seismology Authors: Nakariakov, V. M. Bibcode: 2004ASPC..325..253N Altcode: SOHO and TRACE missions have demonstrated that wave phenomena are abundant in the corona and provided us with an observational basis for MHD coronal seismology. This review covers the recent observational finding of coronal wave phenomena and their theoretical models. The relevance of these observational and theoretical efforts to the coronal heating is discussed. Possible observability of these phenomena with EIS and XRT instruments is discussed. Title: Transverse Waves in a Post-Flare Supra-Arcade Authors: Verwichte, E.; Nakariakov, V. M.; Cooper, F. C. Bibcode: 2004ESASP.575..126V Altcode: 2004soho...15..126V No abstract at ADS Title: The Nature and Excitation Mechanisms of Acoustic Oscillations in Solar and Stellar Coronal Loops Authors: Tsiklauri, D.; Nakariakov, V. M.; Arber, T. D.; Aschwanden, M. J. Bibcode: 2004ESASP.575..114T Altcode: 2004soho...15..114T; 2004astro.ph..9556T In the recent work of Nakariakov et al. (2004), it has been shown that the time dependences of density and velocity in a flaring loop contain pronounced quasi-harmonic oscillations associated with the 2nd harmonic of a standing slow magnetoacoustic wave. That model used a symmetric heating function (heat deposition was strictly at the apex). This left outstanding questions: A) is the generation of the 2nd harmonic a consequence of the fact that the heating function was symmetric? B) Would the generation of these oscillations occur if we break symmetry? C) What is the spectrum of these oscillations? Is it consistent with a 2nd spatial harmonic? The present work (and partly Tsiklauri et al. (2004b)) attempts to answer these important outstanding questions. Namely, we investigate the physical nature of these oscillations in greater detail: we study their spectrum (using periodogram technique) and how heat positioning affects the mode excitation. We found that excitation of such oscillations is practically independent of location of the heat deposition in the loop. Because of the change of the background temperature and density, the phase shift between the density and velocity perturbations is not exactly a quarter of the period, it varies along the loop and is time dependent, especially in the case of one footpoint (asymmetric) heating. We also were able to model successfully SUMER oscillations observed in hot coronal loops. Title: Detection of ultra-long-period oscillations in an EUV filament Authors: Foullon, C.; Verwichte, E.; Nakariakov, V. M. Bibcode: 2004A&A...427L...5F Altcode: We report the first detection of long-period (8-27 h) oscillatory intensity variations in a coronal filament. The filament is observed continuously as it crosses the solar disk in a 12-min-cadence SoHO/EIT 195 Å, uninterrupted data set. Cyclic intensity variations are found to be correlated along the filament, while the most pronounced oscillations are detected at its southern end for nearly 6 days. The dominant period of these oscillations is 12.1 h and the amplitude of the intensity variations reaches approximately 10% of the background intensity. The ultra-long-period oscillations may be interpreted in terms of slow string MHD modes or may be connected with thermal over-stability associated with peculiarities of the cooling/heating function and with the effect of neutrals. These theoretical predictions however do not explain the spatial structure of the oscillations along the filament. Title: Meeting report: Waves in solar and magnetospheric plasmas Authors: Nakariakov, V. M.; Roberts, B.; Wright, A. N. Bibcode: 2004A&G....45e..32N Altcode: This RAS discussion meeting was arranged with the idea of bringing together solar physicists and magnetospheric physicists, so as to understand better how the two disciplines approach waves, and ultimately to learn from each other. V M Nakariakov, B Roberts and A N Wright report. Title: CDS wide slit time-series of EUV coronal bright points Authors: Ugarte-Urra, I.; Doyle, J. G.; Nakariakov, V. M.; Foley, C. R. Bibcode: 2004A&A...425.1083U Altcode: Wide slit (90''×240'') movies of four Extreme Ultraviolet coronal bright points (BPs) obtained with the Coronal Diagnostic Spectrometer (CDS) on board the Solar and Heliospheric Observatory (SoHO) have been inspected. The wavelet analysis of the He I 584.34 Å, O V 629.73 Å and Mg VII/IX 368 Å time-series confirms the oscillating nature of the BPs, with periods ranging between 600 and 1100 s. In one case we detect periods as short as 236 s. We suggest that these oscillations are the same as those seen in the chromospheric network and that a fraction of the network bright points are most likely the cool footpoints of the loops comprising coronal bright points. These oscillations are interpreted in terms of global acoustic modes of the closed magnetic structures associated with BPs. Title: Characteristics of transverse oscillations in a coronal loop arcade Authors: Verwichte, E.; Nakariakov, V. M.; Ofman, L.; Deluca, E. E. Bibcode: 2004SoPh..223...77V Altcode: TRACE observations from 15 April 2001 of transverse oscillations in coronal loops of a post-flare loop arcade are investigated. They are considered to be standing fast kink oscillations. Oscillation signatures such as displacement amplitude, period, phase and damping time are deduced from 9 loops as a function of distance along the loop length. Multiple oscillation modes are found with different amplitude profile along the loop length, suggesting the presence of a second harmonic. The damping times are consistent with the hypothesis of phase mixing and resonant absorption, although there is a clear bias towards longer damping times compared with previous studies. The coronal magnetic field strength and coronal shear viscosity in the loop arcade are derived. Title: Coronal seismology: Seismology of the corona of the Sun Authors: Nakariakov, V. M.; Verwichte, E. Bibcode: 2004A&G....45d..26N Altcode: Seismology now includes study of the Sun's corona, a promising research target both in its own right and for its role in the relationship between the Sun and the Earth and its links to the solar magnetic field. In addition, the corona, as a natural plasma, is itself an objective for fundamental physics. Observations using spacecraft such as SOHO and TRACE highlight the interrelationship between the magnetic field and corona. Title: Astrophysical Implications of Magnetoacoustic Autowaves in Thermally Unstable Plasmas Authors: Kelly, A.; Nakariakov, V. M. Bibcode: 2004plph.confE...1K Altcode: The formation and evolution of magnetoacoustic autowaves in thermally unstable plasmas is discussed, with particular reference to solar and stellar flares. The competition of thermal overstability, thermal conductivity and radiative losses leads to self-organisation of weakly nonlinear magnetoacoustic perturbations into dissipative structures with the parameters independent of the initial perturbation. This evolution is modelled in terms of the extended Burgers equation. The properties of the autowaves are expressed through the plasma parameters such as the magnetic field, plasma temperature and density. The autowaves are saw-tooth shaped waves, with an eventual amplitude that depends upon the balance between the amplification due to radiative losses and decay due to thermal conductivity. Increased dissipation due to thermal conductivity or stronger non-linearity leads to a lower amplitude, while stronger thermal instability leads to a higher final amplitude. X-ray, white light and radio band observations and numerical simulations of flaring loops show quasi-periodic pulsations during the flares. These pulsations are standing acoustic waves (primarily the second harmonic) and show little decay over a number of periods despite the large theoretically predicted damping due to thermal conductivity. It is suggested that these waves are magnetoacoustic autowaves. Title: Flare-generated acoustic oscillations in solar and stellar coronal loops Authors: Tsiklauri, D.; Nakariakov, V. M.; Arber, T. D.; Aschwanden, M. J. Bibcode: 2004A&A...422..351T Altcode: 2004astro.ph..2261T Long period longitudinal oscillations of a flaring coronal loop are studied numerically. In the recent work of Nakariakov et al. (2004) it has been shown that the time dependence of density and velocity in a flaring loop contain pronounced quasi-harmonic oscillations associated with the 2nd harmonic of a standing slow magnetoacoustic wave. In this work we investigate the physical nature of these oscillations in greater detail, namely, their spectrum (using the periodogram technique) and how heat positioning affects mode excitation. We found that excitation of such oscillations is practically independent of the location of the heat deposition in the loop. Because of the change of the background temperature and density, the phase shift between the density and velocity perturbations is not exactly a quarter of the period; it varies along the loop and is time dependent, especially in the case of one footpoint (asymmetric) heating. Title: Radiative hydrodynamic modeling of the Bastille-Day flare (14 July, 2000). I. Numerical simulations Authors: Tsiklauri, D.; Aschwanden, M. J.; Nakariakov, V. M.; Arber, T. D. Bibcode: 2004A&A...419.1149T Altcode: 2004astro.ph..2260T A 1D loop radiative hydrodynamic model that incorporates the effects of gravitational stratification, heat conduction, radiative losses, external heat input, presence of helium, and Braginskii viscosity is used to simulate elementary flare loops. The physical parameters for the input are taken from observations of the Bastille-Day flare of 2000 July 14. The present analysis shows that: a) the obtained maximum values of the electron density can be considerably higher (4.2 × 1011 cm-3 or more) in the case of footpoint heating than in the case of apex heating (2.5 × 1011 cm-3); b) the average cooling time after the flare peak takes less time in the case of footpoint heating than in the case of apex heating; c) the peak apex temperatures are significantly lower (by about 10 MK) for the case of footpoint heating than for apex heating (for the same average loop temperature of about 30 MK). This characteristic would allow to discriminate between different heating positioning; d) in both cases (of apex and footpoint heating), the maximum obtained apex temperature Tmax is practically independent of the heating duration σt, but scales directly with the heating rate EH0; e) the maximum obtained densities at the loop apex, nemax, increase with the heating rate EH0 and heating duration σt for both footpoint and apex heating. In Paper II we will use the outputs of these hydrodynamic simulations, which cover a wide range of the parameter space of heating rates and durations, as an input for forward-fitting of the multi-loop arcade of the Bastille-day flare. Title: Time signatures of impulsively generated coronal fast wave trains Authors: Nakariakov, V. M.; Arber, T. D.; Ault, C. E.; Katsiyannis, A. C.; Williams, D. R.; Keenan, F. P. Bibcode: 2004MNRAS.349..705N Altcode: Impulsively generated short-period fast magneto-acoustic wave trains, guided by solar and stellar coronal loops, are numerically modelled. In the developed stage of the evolution, the wave trains have a characteristic quasi-periodic signature. The quasi-periodicity results from the geometrical dispersion of the guided fast modes, determined by the transverse profile of the loop. A typical feature of the signature is a tadpole wavelet spectrum: a narrow-spectrum tail precedes a broad-band head. The instantaneous period of the oscillations in the wave train decreases gradually with time. The period and the spectral amplitude evolution are shown to be determined by the steepness of the transverse density profile and the density contrast ratio in the loop. The propagating wave trains recently discovered with the Solar Eclipse Coronal Imaging System (SECIS) instrument are noted to have similar wavelet spectral features, which strengthens the interpretation of SECIS results as guided fast wave trains. Title: Theoretical Aspects of MHD Coronal Seismology Authors: Nakariakov, V. M. Bibcode: 2004ESASP.547..407N Altcode: 2004soho...13..407N The revolutionary breakthrough in observational detection of propagating and standing quasi-periodic disturbances of coronal plasma parameters, made in the EUV band with SOHO and TRACE mission instruments, toin terms of magnetohydrodynamic (MHD) waves, has given rise to MHD coronal seismology. This review presents the theoretical background of these studies and reflects current trends in the development of the theory. Title: Global Sausage Magnetoacoustic Modes of Coronal Loops Authors: Nakariakov, V. M.; Melnikov, V. F.; Reznikova, V. E. Bibcode: 2004IAUS..223..653N Altcode: 2005IAUS..223..653N A sufficiently thick and dense flaring magnetic loop is shown to be able to support global sausage magnetoacoustic modes. The oscillation period of this mode, calculated in the straight cylinder approximation, is determined by the length of the loop, not by its diameter, as it has previously been assumed. For the existence of this mode, the ratio of the loop length to its diameter is to be less than about a half of the square root of the density contrast ratio. This mode has a maximum of the magnetic field perturbation at the loop apex and nodes at the footpoints. We demonstrate that the 14-17 sec quasi-periodical pulsations of microwave emission, oscillating in phase at a loop apex and at its legs, as observed with the Nobeyama Radioheliograph, are interpreted in terms of the global sausage mode. Title: Coronal Seismology by MHD Autowaves Authors: Kelly, A.; Nakariakov, V. M. Bibcode: 2004ESASP.547..483K Altcode: 2004soho...13..483K Slow magnetoacoustic waves are routinely observed in solar coronal structures. These waves can be strongly affected by non-adiabatic effects leading to self-organising compressible propagating disturbances -- magnetoacoustic autowaves. Autowaves are propagating disturbances which have parameters independent of the excitation that are determined by the parameters of the medium only and, consequently, are potentially an ideal tool for coronal seismology. The influence of non-adiabatic effects is studied and magnetoacoustic autowaves are modelled with the extended Burgers equation. A numerical code is developed to study the evolution of such waves and a parametric study is carried out. Observable parameters of coronal magnetoacoustic autowaves could provide a tool for the determination of heat deposition mechanisms in the corona. Title: Acoustic Oscillations in Solar and Stellar Flaring Loops Authors: Tsiklauri, D.; Nakariakov, V. M.; Kelly, A.; Aschwanden, M. J.; Arber, T. D. Bibcode: 2004ESASP.547..473T Altcode: 2004soho...13..473T No abstract at ADS Title: Acoustic oscillations in solar and stellar flaring loops Authors: Nakariakov, V. M.; Tsiklauri, D.; Kelly, A.; Arber, T. D.; Aschwanden, M. J. Bibcode: 2004A&A...414L..25N Altcode: 2004astro.ph..2223N Evolution of a coronal loop in response to an impulsive energy release is numerically modelled. It is shown that the loop density evolution curves exhibit quasi-periodic perturbations with the periods given approximately by the ratio of the loop length to the average sound speed, associated with the second standing harmonics of an acoustic wave. The density perturbations have a maximum near the loop apex. The corresponding field-aligned flows have a node near the apex. We suggest that the quasi-periodic pulsations with periods in the range 10-300 s, frequently observed in flaring coronal loops in the radio, visible light and X-ray bands, may be produced by the second standing harmonic of the acoustic mode. Title: Magnetohydrodynamic Sausage-Mode Oscillations in Coronal Loops Authors: Aschwanden, Markus J.; Nakariakov, Valery M.; Melnikov, Victor F. Bibcode: 2004ApJ...600..458A Altcode: 2003astro.ph..9493A A recent study by Nakariakov and coworkers pointed out that the dispersion relation of MHD sausage-mode oscillations has been incorrectly applied to coronal loops, neglecting the highly dispersive nature of the phase speed and the long-wavelength cutoff of the wavenumber. In the light of these new insights, we revisit previous observations that have been interpreted in terms of MHD sausage-mode oscillations in coronal loops and come to the following conclusions: (1) fast sausage MHD-mode oscillations require such a high electron density imposed by the wavenumber cutoff that they can only occur in flare loops, and (2) in the previously reported radio observations (ν~100 MHz to 1 GHz) with periods of P~0.5-5 s, the fast sausage MHD-mode oscillation is likely to be confined to a small segment (corresponding to a high harmonic node) near the apex of the loop, rather than involving a global oscillation over the entire loop length. The recent microwave and soft X-ray observations of fast periods (P~6-17 s) by Asai and coworkers and Melnikov and coworkers, however, are consistent with fast sausage MHD oscillations at the fundamental harmonic. Title: 3D Numerical Simulations of Impulsively Generated MHD Waves in Solar Coronal Loops Authors: Selwa, M.; Murawski, K.; Kowal, G.; Nakariakov, V.; Aschwanden, M.; Oliver, R.; Ballester, J. L. Bibcode: 2004ESASP.547..495S Altcode: 2004soho...13..495S Impulsively generated magnetohydrodynamic waves in a typical EUV solar coronal loop are studied numerically with a use of the three-dimensional FLASH code. Our results reveal several 3D effects such as distinctive time signatures which are collected at a detection point inside the loop. A slow magnetosonic wave generates a significant variation in a mass density profile with a time-scale of the order of s. A fast kink wave affects a mass density too but its magnitude is much lower than in the case of a slow wave. Time-scales which are associated with the fast kink wave are generally lower than in the case of a slow wave; they are in the range of a dozen or so seconds. Temporal signatures of a fast sausage wave reveal s oscillations in the quasi-periodic phase. Impulses which are launched outside the loop excite few seconds oscillations in the mass density. Time-signatures depend on a position of the detection point; they are usually more complex further out from the exciter. Title: Observations of sausage mode oscillations in a flaring loop Authors: Melnikov, V. F.; Reznikova, V. E.; Shibasaki, K.; Nakariakov, V. M. Bibcode: 2004IAUS..223..647M Altcode: 2005IAUS..223..647M We provide an observational proof of the existence of the global sausage mode oscillations in a flaring loop studying a microwave burst with quasi-periodical pulsations observed with the Nobeyama Radioheliograph (NoRH). Title: The possible back-rotation of sunspots Authors: Williams, D. R.; van Driel-Gesztelyi, L.; Nakariakov, V. M. Bibcode: 2004cosp...35.4391W Altcode: 2004cosp.meet.4391W The curious case of sunspot rotation in two senses, presented by Kucera (1982), provided an interesting challenge to the idea of sunspot rotation being due simply to the differential rotation of the Sun above the tachocline. As the rotation rate and direction, in that case, are seen to vary as a damped sinusoid, this presents the possibility that such motion is the result of torsional waves trapped in the sunspot's sub-photospheric flux tube. We therefore analyse the rotation of a number of sunspots using SoHO/MDI and track their rotation, presenting evidence of 'back-rotation' -- rotational motion which reverses -- in a several of these spots. Intuitively, this raises the possibility of extending the field of 'Coronal Seismology' back down to beneath the photosphere (where helioseismology already exists). Title: Alfvén Waves in Multi-ion Coronal Plasma: Observational Implications Authors: Ofman, L.; Nakariakov, V. M.; Davila, J. M. Bibcode: 2003AGUFMSH11D1129O Altcode: We investigate low-frequency Alfvén waves in a multi-ion coronal plasma by deriving the dispersion relation of the linearized three-fluid equations in magnetized plasma with coronal parameters. We study the effect of collisions on the velocity amplitude of minor ions due to the Alfvén waves compared to the proton wave amplitude. We find that in the collisionless plasma the minor ion velocity is reduced by the factor Z/A compared to protons, where Z is the ion charge, and A is mass in units of proton mass. When the collision frequency is much larger then the Alfvén wave frequency the velocity amplitude of the minor ions is equal to the proton velocity amplitude. We show the effects of minor ions and collisions on the dispersion relation of Alfvén waves in the three fluid plasma. In view of our results we show how the observed nonthermal line broadening of minor ions relates to the wave motions of protons as a function of heliocentric distance, and the plasma physical parameters. Title: Global sausage modes of coronal loops Authors: Nakariakov, V. M.; Melnikov, V. F.; Reznikova, V. E. Bibcode: 2003A&A...412L...7N Altcode: Sufficiently thick and dense coronal loops can support global sausage magnetoacoustic modes. We demonstrate that the oscillation period of this mode, calculated in the straight cylinder approximation, is determined by the length of the loop, not by its diameter, as it was previously assumed. The existence condition for this mode is the ratio of the loop length to its diameter to be less than about a half of the square root of the density contrast ratio. This mode has a maximum of the magnetic field perturbation at the loop apex and nodes at the footpoints. We demonstrate that the 14-17 s quasi-periodic pulsations, oscillating in phase at a loop apex and at its legs, observed with the Nobeyama Radioheliograph, are interpreted in terms of the global sausage mode. Title: Statistical characterisation of full-disk EUV/XUV solar irradiance and correlation with solar activity Authors: Greenhough, J.; Chapman, S. C.; Dendy, R. O.; Nakariakov, V. M.; Rowlands, G. Bibcode: 2003A&A...409L..17G Altcode: 2003astro.ph..2277G We investigate the distribution of fluctuations in solar irradiance when integrated over the full disk, obtained using extreme ultraviolet/soft X-ray observations from the SOHO CELIAS/SEM instrument. This time series sums over both the contributions of single distinguishable flares, and of many other processes. By detrending we select events with timescales of less than a few hours such as waves, slow flows, and CMEs. The statistics generated by this range of phenomena can be characterised by power-law-tailed distributions. We show that (i) during the high activity period 2000 Jan.-June the tail exponent aT=1.5+/-0.1; (ii) during the low activity period 1996 Jan.-June aT=3.0+/-0.2; and (iii) in general aT decreases with increasing activity. Title: Short period fast waves in solar coronal loops Authors: Cooper, F. C.; Nakariakov, V. M.; Williams, D. R. Bibcode: 2003A&A...409..325C Altcode: Short period fast magnetoacoustic waves propagating along solar coronal loops, perturbing the loop boundary along the line of sight (LOS), may be observed by imaging telescopes. The relationship between the difference in emission intensity, the angle between the LOS and the direction of propagation and the wave amplitude and wavelength, is explored for kink and sausage fast waves. It is shown that the compressibility of the plasma in the loop significantly affects the observability of the waves. For both wave types there is an optimal observation angle which is determined by the ratio of the wave length and the loop radius. The change of the observational conditions because of the loop curvature predicts a significant, up to an order of magnitude, change in the observed wave amplitude. This prediction is confirmed by the analysis of the evolution of the fast wave train amplitude, observed with the SECIS instrument. The wave train amplitude experiences a sharp increase and then a decrease along the loop. The observational results are in a good agreement with the theory. Title: A Three Dimensional Magnetohydrodynamic Pulse in a Transversely Inhomogeneous Medium Authors: Tsiklauri, D.; Nakariakov, V. M. Bibcode: 2003AIPC..679..570T Altcode: Interaction of impulsively generated MHD waves with a one-dimensional plasma inhomogeneity, transverse to the magnetic field, is considered in the three-dimensional regime. Because of the transverse inhomogeneity, MHD fluctuations, even if they do not include initially any density perturbation, evolve toward states where the compressible components tend to become predominant. The propagating MHD pulse asymptotically reaches a quasi-steady state with the final levels of density perturbation weakly depending on the degree of non-planeness of the pulse in the homogeneous transverse direction and somewhat stronger depending on plasma β. Our study demonstrates the necessity of incorporation of compressible and 3D effects in theory of Alfvén wave phase mixing. However, as far as the dynamics of weakly non-plane Alfvén waves is concerned it can still be qualitatively understood in terms of the previous 2.5D models. Title: Propagating EUV disturbances in the Solar corona: Two-wavelength observations Authors: King, D. B.; Nakariakov, V. M.; Deluca, E. E.; Golub, L.; McClements, K. G. Bibcode: 2003A&A...404L...1K Altcode: Quasi-periodic EUV disturbances simultaneously observed in 171 Å and 195 Å TRACE bandpasses propagating outwardly in a fan-like magnetic structure of a coronal active region are analysed. Time series of disturbances observed in the different bandpasses have a relatively high correlation coefficient (up to about 0.7). The correlation has a tendency to decrease with distance along the structure: this is consistent with an interpretation of the disturbances in terms of parallel-propagating slow magnetoacoustic waves. The wavelet analysis does not show a significant difference between waves observed in different bandpasses. Periodic patterns of two distinct periods: 2-3 min and 5-8 min are detected in both bandpasses, existing simultaneously and at the same distance along the loop, suggesting the nonlinear generation of the second harmonics. Title: Coronal `Tadpoles' Observed by TRACE Authors: Seaton, D. B.; Deluca, E. E.; Cooper, F. C.; Nakariakov, V. M. Bibcode: 2003SPD....34.1618S Altcode: 2003BAAS...35..836S The X1.5 flare event observed by TRACE in 195 Å on 21 April 2002, showed dark, downward-propagating features over the flare arcade which we call `coronal tadpoles.' We analyzed these features and determined their distinguishing characteristics. Estimating plasma densities inside the features, we determined that they are of very low density and possibly >10 million K. We propose that the coronal tadpoles my be interpreted in terms of kink modes of the flaring current sheet filled by hot, rarefied plasma. Title: Nonlinear Multi-Scale Processes in the Heliosphere in the IHY Authors: Chapman, S. C.; Nakariakov, V. M.; Arber, T. D. Bibcode: 2003EAEJA....10486C Altcode: University of Warwick's Space and Astrophysics Group have undertaken an intensive research programme in magnetospheric, heliospheric and solar physics, including analytical theory, large scale numerical simulation, advanced visualization techniques and theory led data analysis. The unifying theme is that these are nonlinear multiscale processes, which control the energy release and conversion processes, turbulence and self-organisation. The coordinated studies of solar, heliospheric and magnetospheric processes proposed in frames of the IHY provide a unique opportunity to unify knowledge that is presently fragmented. For example, remote sensing of physical processes in the solar corona with the use of ground-based and space-borne facilities (potentially, including the multiple vantage point observations with STEREO), remote (e.g. IPS) and in-situ (e.g. WIND, CLUSTER) studies of the development of these processes in the solar wind and the coupling to the dynamic Earth magnetosphere (as indicated by scaling in geomagnetic indices and POLAR UVI images of dynamic auroras) and ionosphere, will allow us to understand the chain of solar-terrestrial connections and, in particular, the nonlinear processes governing these connections. Title: Phase mixing of a three dimensional magnetohydrodynamic pulse Authors: Tsiklauri, D.; Nakariakov, V. M.; Rowlands, G. Bibcode: 2003A&A...400.1051T Altcode: 2002astro.ph.10117T Phase mixing of a three dimensional magnetohydrodynamic (MHD) pulse is studied in the compressive, three-dimensional (without an ignorable coordinate) regime. It is shown that the efficiency of decay of an Alfvénic part of a compressible MHD pulse is related linearly to the degree of localization of the pulse in the homogeneous transverse direction. In the developed stage of phase mixing (for large times), coupling to its compressive part does not alter the power-law decay of an Alfvénic part of a compressible MHD pulse. The same applies to the dependence upon the resistivity of the Alfvénic part of the pulse. All this implies that the dynamics of Alfvén waves can still be qualitatively understood in terms of the previous 2.5D models. Thus, the phase mixing remains a relevant paradigm for the coronal heating applications in the realistic 3D geometry and compressive plasma. Title: Quasi-periodic behaviour of a flare ribbon system Authors: Ludmány, A.; Major, B.; Nakariakov, V. M. Bibcode: 2003PADEU..13..139L Altcode: A series of quasi-periodic pulsations have been detected in the flare of 19th July 1999. The total area occupied by the flare ribbons exhibited temporary increases in the declining phase of the flare at certain moments, the period of the pulses was about 20-30 minutes. The phenomenon has been recognized in the center, as well as at 0.5 and 1.0 Å wings on both sides of the H-alpha line. Title: Coronal oscillations Authors: Nakariakov, V. M. Bibcode: 2003dysu.book..314N Altcode: The detection of coronal waves provides us with a new tool for the determination of the unknown parameters of the corona - MHD seismology of the corona. The method is similar to helioseismology. But MHD coronal seismology is much richer as it is based upon three different wave modes - Alfvén, slow and fast magnetoacoustic modes. These MHD modes have quite different dispersive, polarization and propagation properties, which make this approach even more powerful. The delicate interplay of MHD wave theory and the observations of coronal waves and oscillations are presented, illustrating it with several examples. Title: Line-of-sight effects on observability of kink and sausage modes in coronal structures with imaging telescopes Authors: Cooper, F. C.; Nakariakov, V. M.; Tsiklauri, D. Bibcode: 2003A&A...397..765C Altcode: 2002astro.ph..7167C Kink modes of solar coronal structures, perturbing the loop in the direction along the line-of-sight (LOS), can be observed as emission intensity disturbances propagating along the loop provided the angle between the LOS and the structure is not ninety degrees. The effect is based upon the change of the column depth of the loop (along the LOS) by the wave. The observed amplitude of the emission intensity variations can be larger than the actual amplitude of the wave by a factor of two and there is an optimal angle maximizing the observed amplitude. For other angles this effect can also attenuate the observed wave amplitude. The observed amplitude depends upon the ratio of the wave length of kink perturbations to the width of the structure and on the angle between the LOS and the axis of the structure. Sausage modes are always affected negatively from the observational point of view, as the observed amplitude is always less than the actual one. This effect should be taken into account in the interpretation of wave phenomena observed in the corona with space-borne and ground-based imaging telescopes. Title: Book Review: Current theoretical models and high resolution solar observations / Astronomical Society of the Pacific, 2003 Authors: Nakariakov, Valery Bibcode: 2003Obs...123..391N Altcode: No abstract at ADS Title: Phase mixing of a three dimensional magnetohydrodynamic pulse Authors: Tsiklauri, D.; Nakariakov, V. M. Bibcode: 2002ESASP.506...67T Altcode: 2002ESPM...10...67T; 2002svco.conf...67T Phase mixing of a three dimensional magnetohydrodynamic (MHD) pulse is studied in the compressive three-dimensional (without an ignorable coordinate) regime. It is shown that the coupling to the compressive modes dramatically enhances the efficiency of decay of an Alfvénic part of a compressible MHD pulse. However, the dynamics of weakly non-plane Alfvén waves can still be qualitatively understood in terms of the previous 2.5D models. Title: Line-of-sight effects on observability of kink modes in coronal structures with imaging telescopes Authors: Cooper, F. C.; Nakariakov, V. M.; Tsiklauri, D. Bibcode: 2002ESASP.506..577C Altcode: 2002svco.conf..577C; 2002ESPM...10..577C Kink modes of solar coronal structures, perturbing the loop in the direction along the line-of-sight (LOS), can be observed as emission intensity disturbances propagating along the loop provided the angle between the LOS and the structure is not ninety degrees. The phenomenon is based upon the change of the column depth of the loop (along the LOS) by the wave. The observed amplitude of the emission intensity variations can be larger than the actual amplitude of the wave by a factor of two and there is an optimal angle maximizing the observed amplitude. The observed amplitude depends upon the ratio of the wavelength of kink perturbations to the width of the structure and on the angle between the LOS and the axis of the structure. This phenomenon should be taken into account in the interpretation of wave phenomena observed in the corona with space-borne and ground-based imaging telescopes. Title: Slow magnetoacoustic waves in coronal loops Authors: Nakariakov, V. M.; King, D. B.; Tsiklauri, D. Bibcode: 2002ESASP.506..705N Altcode: 2002ESPM...10..705N; 2002svco.conf..705N Propagating disturbances of EUV emission, recently discovered in coronal loops with SOHO/EIT and TRACE, are interpreted as slow magnetoacoustic waves. This interpretation is based upon several observational findings: (a) the disturbances seem to propagate along the magnetic field (b) at a constant speed which is below the estimated sound speed, (c) the perturbations are compressible, (d) the periods are shorter than the acoustic cut-off period in the corona. A theoretical model describing the wave evolution and incorporating effects of dissipation, stratification and weak nonlinearity is created. In particular, the model explains why only the upwardly propagating waves are observed. The interpretation suggested is in a good agreement with obervational findings. It is shown that wide spectrum slow magnetoacoustic waves, consistent with currently available observations in the low frequency part of the spectrum, can provide the rate of heat deposition sufficient to heat the loop. In this scenario, the heat would be deposited near the loop footpoints which also agrees with the current observational data. The analysis of simultaneous observations of propagating EUV disturbances in 171 Å and 195 Å bandpasses of TRACE telescope shows high correlation which systematically decreases with the distance along the loop. Title: Kink oscillations of coronal loops as a tool for the determination of coronal magnetic field Authors: Nakariakov, Valery; Ofman, Leon Bibcode: 2002ESASP.506..461N Altcode: 2002svco.conf..461N; 2002ESPM...10..461N We develop a new method for the determination of the absolute value of the magnetic field strength in coronal closed magnetic structures, based on the analysis of flare-generated oscillations of coronal loops. Interpretation of the quasi-harmonic oscillations observed in terms of global standing kink waves allows to connect the period of the oscillations and the loops length with the magnetic field strength in the loops. Improved diagnostic of the loop length, the oscillation period, and the plasma density in the loop will significantly improve the method's precision. Title: A strongly nonlinear Alfvénic pulse in a transversely inhomogeneous medium Authors: Tsiklauri, D.; Nakariakov, V. M.; Arber, T. D. Bibcode: 2002A&A...395..285T Altcode: 2002astro.ph.10625T We investigate the interaction of a plane, linearly polarized, Alfvénic pulse with a one-dimensional, perpendicular to the magnetic field, plasma density inhomogeneity in the strongly nonlinear regime. Our numerical study of the full MHD equations shows that: (i) Plasma density inhomogeneity substantially enhances (by about a factor of 2) the generation of longitudinal compressive waves. (ii) Attained maximal values of the generated transverse compressive perturbations are insensitive to the strength of the plasma density inhomogeneity, plasma beta and the initial amplitude of the Alfvén wave. Typically, they reach about 40% of the initial Alfvén wave amplitude. (iii) Attained maximal values of the generated relative density perturbations are within 20-40% for 0.5 <= beta <= 2.0. They depend upon plasma beta strongly; and scale almost linearly with the initial Alfvén wave amplitude. Title: A three dimensional magnetohydrodynamic pulse in a transversely inhomogeneous medium Authors: Tsiklauri, D.; Nakariakov, V. M. Bibcode: 2002A&A...393..321T Altcode: 2002astro.ph..2489T Interaction of impulsively generated MHD waves with a one-dimensional plasma inhomogeneity, transverse to the magnetic field, is considered in the three-dimensional regime. Because of the transverse inhomogeneity, MHD fluctuations, even if they do not include initially any density perturbation, evolve toward states where the compressible components tend to become predominant. The propagating MHD pulse asymptotically reaches a quasi-steady state with the final levels of density perturbation weakly depending on the degree of non-planeness of the pulse in the homogeneous transverse direction and somewhat stronger depending on plasma beta . Our study demonstrates the necessity of incorporation of compressible and 3D effects in theory of Alfvén wave phase mixing. However, as far as the dynamics of weakly non-plane Alfvén waves is concerned it can still be qualitatively understood in terms of the previous 2.5D models. Title: Nonlinear MHD waves in the solar wind plasma structures Authors: Tsiklauri, D.; Nakariakov, V. M.; Arber, T. D. Bibcode: 2002ESASP.477..381T Altcode: 2002scsw.conf..381T; 2001astro.ph.10494T We investigate the interaction of magnetohydrodnamic waves with plasma density inhomogeneities. Our numerical study of the full MHD equations shows that: (A) Plasma density inhomogeneities are a source of non-linear generation of transverse compressive waves by a plane Alfvén wave, and substantially enhance (by about a factor of 2) the generation of the longitudinal compressive waves. (B) Attained maximal values of the generated transverse compressive waves are insensitive to the strength of the plasma density inhomogeneity and the initial amplitude of the Alfvén wave. (C) Efficiency of the generation depends weakly upon the plasma β parameter. The maximum generated amplitude of transverse compressive wave, up to 32% of the initial Alfvén wave amplitude, is reached for about β = 0.5. The results obtained demonstrate that plasma inhomogeneities enhance the efficiency of the non-linear wave coupling. Title: Wide-spectrum slow magnetoacoustic waves in coronal loops Authors: Tsiklauri, D.; Nakariakov, V. M. Bibcode: 2001A&A...379.1106T Altcode: 2001astro.ph..7579T A model interpreting variations of EUV brightness upward propagating in solar coronal loops as slow magnetoacoustic waves is developed. A loop is considered to have a non-zero plane inclination angle and offset of the circular loop centre from the baseline. The model also incorporates effects of dissipation and gravitational stratification. A linear evolutionary equation is derived and applied to investigations of slow wave dynamics. Both the non-zero plane inclination and the offset decrease the growth of the wave amplitude due to stratification. It is shown that wide-spectrum slow magnetoacoustic waves, consistent with currently available observations in the low frequency part of the spectrum, can provide a rate of heat deposition sufficient to heat the loop. In this scenario, the heat would be deposited near the loop footpoints, which agrees with the current observational data. Title: A weakly nonlinear Alfvénic pulse in a transversely inhomogeneous medium Authors: Tsiklauri, D.; Arber, T. D.; Nakariakov, V. M. Bibcode: 2001A&A...379.1098T Altcode: 2001astro.ph..7580T The interaction of a weakly nonlinear Alfvénic pulse with an Alfvén speed inhomogeneity in the direction perpendicular to the magnetic field is investigated. Identical to the phase mixing experienced by a harmonic Alfvén wave, sharp transverse gradients are generated in the pulse by the inhomogeneity. In the initial stage of the evolution of an initially plane Alfvénic pulse, the transverse gradients efficiently generate transversely propagating fast magnetoacoustic waves. However, high resolution full MHD numerical simulations of the developed stage of the pulse evolution show that the generation saturates due to destructive wave interference. It is shown that the weakly non-linear description of the generated fast magnetoacoustic wave is well described by the driven wave equation proposed in Nakariakov et al. (\cite{Nakariakov97}), and a simple numerical code (2D MacCromack), which solves it with minimal CPU resources, produces identical results to those obtained from the full MHD code (Lare2d, Arber et al. \cite{Arber01}). A parametric study of the phenomenon is undertaken, showing that, contrary to one's expectations, steeper inhomogeneities of the Alfvén speed do not produce higher saturation levels of the fast wave generation. There is a certain optimal gradient of the inhomogeneity that ensures the maximal efficiency of the fast wave generation. Title: Non-resonant nonlinear coupling of magnetohydrodynamic waves in inhomogeneous media Authors: Nakariakov, V. M.; Tsiklauri, D.; Arber, T. D. Bibcode: 2001astro.ph.10493N Altcode: A new mechanism for the enhanced generation of compressible fluctuations by Alfven waves is presented. A strongly nonlinear regime of Alfven wave phase-mixing is numerically simulated in a one-dimensionally inhomogeneous plasma of finite temperature. It is found that the inhomogeneity of the medium determines the efficiency of nonlinear excitation of magnetoacoustic waves. The level of the compressible fluctuations is found to be higher (up to the factor of two) in inhomogeneous regions. The amplitude of the generated magnetoacoustic wave can reach up to 30% of the source Alfven wave amplitude, and this value is practically independent of the Alfven wave amplitude and the steepness of Alfven speed profile. The highest amplitudes of compressible disturbances are reached in plasmas with beta of about 0.5. The further growth of the amplitude of compressible fluctuations is depressed by saturation. Title: Nonlinear magneto-acoustic waves in the solar atmosphere Authors: Mendoza-Briceño, César A.; Ibáñez, Miguel H.; Nakariakov, Valery M. Bibcode: 2001DyAtO..34..399M Altcode: The weakly nonlinear evolution of quasi-isentropic magnetoacoustic waves in the solar atmosphere is analyzed. The plasma is assumed to be initially homogeneous, in thermal equilibrium and with a straight and homogeneous magnetic field frozen in. Additionally, the plasma is assumed to be cooled by the standard cooling function in the range of 10 4 K<T<10 7 K and heated by a mechanism which is proportional to the density and temperature. The range of temperature where the plasma is isentropically unstable, the e-folding time for thermal instability and the corresponding time and length-scale for wave breaking are found. Title: Slow magneto-acoustic waves in coronal loops Authors: Verwichte, E.; Nakariakov, V. M.; Berghmans, D.; Hochedez, J. -F. Bibcode: 2001ESASP.493..395V Altcode: 2001sefs.work..395V No abstract at ADS Title: Determination of the coronal magnetic field by coronal loop oscillations Authors: Nakariakov, V. M.; Ofman, L. Bibcode: 2001A&A...372L..53N Altcode: We develop a new method for the determination of the absolute value of the magnetic field strength in coronal closed magnetic structures, based on the analysis of flare-generated oscillations of coronal loops. Interpretation of the oscillations observed in terms of global standing kink waves allows to connect the period of the oscillations and the loops length with the magnetic field strength in the loops. For loop oscillations observed with TRACE on 14th July 1998 and 4th July 1999, we estimate the magnetic field strength as 4-30 G. Using TRACE 171 Å and 195 Å images of the loop, taken on 4th July 1999 to determine the plasma density, we estimate the magnetic field in the loop as 13+/- 9 G. Improved diagnostic of the loop length, the oscillation period, and the plasma density in the loop will significantly improve the method's precision. Title: Slow magnetoacoustic waves in coronal loops: EIT and TRACE Authors: Robbrecht, E.; Verwichte, E.; Berghmans, D.; Hochedez, J. F.; Poedts, S.; Nakariakov, V. M. Bibcode: 2001A&A...370..591R Altcode: On May 13, 1998 the EIT (Extreme ultraviolet Imaging Telescope) on board of SoHO (Solar and Heliospheric Observatory) and TRACE (Transition Region And Coronal Explorer) instruments produced simultaneous high cadence image sequences of the same active region (AR 8218). TRACE achieved a 25 s cadence in the Fe Ix (171 Å) bandpass while EIT achieved a 15 s cadence (operating in ``shutterless mode'', SoHO JOP 80) in the Fe Xii (195 Å) bandpass. These high cadence observations in two complementary wavelengths have revealed the existence of weak transient disturbances in an extended coronal loop system. These propagating disturbances (PDs) seem to be a common phenomenon in this part of the active region. The disturbances originate from small scale brightenings at the footpoints of the loops and propagate along the loops. The projected propagation speeds roughly vary between 65 and 150 km s-1 for both instruments which is close to and below the expected sound speed in the coronal loops. The measured slow magnetoacoustic propagation speeds seem to suggest that the transients are sound (or slow) wave disturbances. This work differs from previous studies in the sense that it is based on a multi-wavelength observation of an entire loop bundle at high cadence by two EUV imagers. The observation of sound waves along the same path shows that they propagate along the same loop, suggesting that loops contain sharp temperature gradients and consist of either concentric shells or thin loop threads, at different temperatures. Title: Fast magnetoacoustic waves in a randomly structured solar corona Authors: Murawski, K.; Nakariakov, V. M.; Pelinovsky, E. N. Bibcode: 2001A&A...366..306M Altcode: The propagation of fast magnetoacoustic waves in a randomly structured solar corona is considered in the linear and cold plasma limits. The random field is assumed to be static and associated with plasma density inhomogeneities only. A transcendental dispersion relation for the fast magnetoacoustic waves which propagate perpendicularly to the magnetic field is derived in the weak random field approximation. It is shown analytically that the fast magnetosonic waves experience acceleration, attenuation, and dispersion in comparison to the homogeneous case. These analytical findings are essentially confirmed by numerical simulations for a wide-spectrum pulse, except that the waves were found decelerated. It is concluded that the coronal Moreton waves can be applied to MHD seismology of the solar corona. Title: MHD Seismology of the Solar Cornoa with SOHO and TRACE Authors: Nakariakov, V. M. Bibcode: 2001IAUS..203..353N Altcode: Recent discoveries of MHD wave motions in the solar corona (slow magnetoacoustic waves in polar plumes and long loops, oscillations of coronal loops, coronal Moreton waves) done with EUV imaging telescopes onboard SOHO and TRACE provide an observational basis for the MHD seismology of the corona. Measuring the properties of MHD waves and oscillations (periods, wavelengths, amplitudes, temporal and spatial signatures), combined with theoretical modelling of the wave phenomena, allow us to determine values of the mean parameters of the corona (the magnetic field strength, transport coefficients, etc.). As an example, we consider post-flare decaying oscillations of loops, observed with TRACE (14th July 1998 at 12:55 UT). An analysis of the oscillations shows that they are quasi-harmonic, with a period of about 265 s, and quickly decaying with the decay time of about 14.5 min. We interpret these oscillations as a standing kink global modes of the loops. The period of oscillations allows us to determine the Alfvén speed in the oscillating loop about 770 km/s. This value can be used for deduction of the value of the magnetic field in the loop (giving 15-25 G). The decay time, together with the assumption that the decay is caused by viscous (or resistive) dissipation, gives us the Reynolds number of 105.3-6.1 (or the Lundquist number of 105.0-5.8). Other possible means for the oscillation decay, such as wave leakage and linear and nonlinear wave coupling are estimated. Title: A developed stage of Alfvén wave phase mixing Authors: Botha, G. J. J.; Arber, T. D.; Nakariakov, V. M.; Keenan, F. P. Bibcode: 2000A&A...363.1186B Altcode: Alfvén wave phase mixing is an extensively studied mechanism for dissipating wave energy in an inhomogeneous medium. It is common in the vast majority of phase mixing papers to assume that even though short scale lengths and steep gradients develop as a result of phase mixing, nonlinear wave coupling does not occur. However, weakly nonlinear studies have shown that phase mixing generates magnetoacoustic modes. Numerical results are presented which show the nonlinear generation of magnetosonic waves by Alfvén wave phase mixing. The efficiency of the effect is determined by the wave amplitude, the frequency of the Alfvén waves and the gradient in the background Alfvén speed. Weakly nonlinear theory has shown that the amplitude of the fast magnetosonic wave grows linearly in time. The simulations presented in this paper extend this result to later times and show saturation of the fast magnetosonic component at amplitudes much lower than that of the Alfvén wave. For the case where Alfvén waves are driven at the boundary, simulating photospheric footpoint motion, a clear modulation of the saturated amplitude is observed. All the results in this paper are for a low amplitude (<= 0.1), single frequency Alfvén wave and a uniform background magnetic field in a two dimensional domain. For this simplified geometry, and with a monochromatic driver, we concluded that the nonlinear generation of fast modes has little effect on classical phase mixing. Title: Slow magnetoacoustic waves in coronal loops Authors: Nakariakov, V. M.; Verwichte, E.; Berghmans, D.; Robbrecht, E. Bibcode: 2000A&A...362.1151N Altcode: A theoretical model interpreting propagating disturbances of EUV emission intensity, recently observed in coronal loops, is constructed in terms of slow magnetoacoustic waves. The model is one-dimensional and incorporates effects of nonlinearity, dissipation due to finite viscosity and thermal conduction, and gravitational stratification of plasma in the loop. It has been found that, for the observationally detected parameters of the waves, the main factors influencing the wave evolution are dissipation and stratification. The upwardly propagating waves of observed periods (5-20 min) are found to decay significantly in the vicinity of the loop apex, explaining the rarity of observational detection of downwardly propagating waves. The model provides a theoretical basis for development of MHD seismology of the coronal loops. Title: Flare-generated coronal loop oscillations: A tool for MHD coronal seismology Authors: Nakariakov, Valery M. Bibcode: 2000AIPC..537..264N Altcode: 2000wdss.conf..264N Quasi-periodical oscillations of positions of coronal loops were observed in the extreme-ultraviolet band (171A, FeIX) with the imaging telescope onboard the TRACE spacecraft. Oscillating transversal displacements (swinging) of a long (~130 Mm) thin (diameter ~2 Mm) bright loop, were detected. The oscillations were excited by a flare (14th July 1998 at about 12:55 UT) at distance of about 60 Mm from the loop. The frequency of the oscillations was about 4 mHz (the period about 265 s) and was determined by the wavelet analysis. Neighboring perpendicular slits show synphase temporal behavior, suggesting that the oscillations are produced by a kink global fast magnetoacoustic mode of the loop. With this interpretation, we determine the kink speed in the loop as 1040 km/s, which gives the Alfvén speed of about 770+/-40 km/s. The detection and analysis of post-flare oscillations of coronal loops provides us with an efficient tool for indirect determination of coronal parameters, e.g. the magnetic field found to be of about 20 G. . Title: Propagational Aspects of Sunquake Waves Authors: Medrek, M.; Murawski, K.; Nakariakov, V. Bibcode: 2000AcA....50..405M Altcode: We present the results of numerical simulations of impulsively generated seismic waves excited by a spatially localized impulse source which is connected with a nearby solar flare. The solar atmosphere is modeled as a two layer medium with constant temperature over the photosphere and linearly growing temperature below the photosphere. Effects of magnetic fields are neglected. Only two dimensional effects are considered. The source is localized slightly below the photosphere. The numerical results show that the initial pulse of enhanced pressure, which can be connected with the thermal energy release by interaction of flare-generated particles with the sub-photospheric medium in the flare-loop footpoint, generates an acoustic (seismic) wave. Interaction of the wave with the solar surface produces perturbations registered as sunquakes. Typical observationally registered features of the sunquakes, such as characteristic wave signatures and acceleration of the wave with the distance from the epicenter, are well reproduced with the model developed. It is found that the seismic waves are essentially dispersive and non-linear. The proposed model provides us with a theoretical basis for sunquake seismology of the solar interior. Title: Dissipation of Slow Magnetosonic Waves in Coronal Plumes Authors: Ofman, L.; Nakariakov, V. M.; Sehgal, N. Bibcode: 2000ApJ...533.1071O Altcode: Recently, slow magnetosonic waves were identified in polar plumes, at heights up to about 1.2 Rsolar using the Extreme Ultraviolet Imaging Telescope (EIT) observations of quasi-periodic EUV intensity fluctuations, and higher in the corona using the Ultraviolet Coronagraph Spectrometer (UVCS) white-light channel. First, we derive the linear dispersion relation for the slow waves in the viscous plasma. Next, we derive and solve an evolutionary equation of the Burgers type for the slow waves, incorporating the effects of radial stratification, quadratic nonlinearity, and viscosity. Finally, we model the propagation and dissipation of slow magnetosonic waves in polar plumes using one-dimensional and two-dimensional MHD codes in spherical geometry. The waves are launched at the base of the corona with a monochromatic source. We find that the slow waves nonlinearly steepen as they propagate away from the Sun into the solar wind. The nonlinear steepening of the waves leads to enhanced dissipation owing to compressive viscosity at the wave fronts. The efficient dissipation of the slow wave by compressive viscosity leads to damping of the waves within the first solar radii above the surface. We investigate the parametric dependence of the wave properties. Title: Nonlinear dissipative spherical Alfvén waves in solar coronal holes Authors: Nakariakov, V. M.; Ofman, L.; Arber, T. D. Bibcode: 2000A&A...353..741N Altcode: The weakly nonlinear dynamics of linearly polarized, spherical Alfvén waves in coronal holes is investigated. An evolutionary equation, combining the effects of spherical stratification, nonlinear steepening and dissipation due to shear viscosity is derived. The equation is a spherical analog of the scalar Cohen-Kulsrud-Burgers equation. Three main stages of the wave evolution are distinguished: geometrical amplification, wave breaking and enhanced dissipation. The wave dissipation is dramatically increased by the nonlinear transfer of energy to smaller scales. The scenario of the nonlinear dissipation is practically independent of viscosity. The dissipation rate is stronger for highest amplitudes, and depends weakly on the wave period and the temperature of the atmosphere. Waves with periods less than 300 s and initial amplitudes about 2-3% of the Alfvén speed at the base of the corona are subject to the nonlinear steepening and dissipation in less than 10 solar radii. For the Alfvén waves with amplitudes less than 25 km s-1 at the base of the corona, the maximum amplitude of up to 200 km s-1 is reached at several solar radii. The nonlinear distortion of the wave shape is accompanied by the generation of longitudinal motions and density perturbations. Title: Magnetoacoustic Waves of Small Amplitude in Optically Thin Quasi-isentropic Plasmas Authors: Nakariakov, Valery M.; Mendoza-Briceño, César A.; Ibáñez S., Miguel H. Bibcode: 2000ApJ...528..767N Altcode: 1999astro.ph..9318N The evolution of quasi-isentropic magnetohydrodynamic waves of small but finite amplitude in an optically thin plasma is analyzed. The plasma is assumed to be initially homogeneous, in thermal equilibrium and with a straight and homogeneous magnetic field frozen in. Depending on the particular form of the heating/cooling function, the plasma may act as a dissipative or active medium for magnetoacoustic waves, while Alfvén waves are not affected directly. An evolutionary equation for fast and slow magnetoacoustic waves in the single wave limit has been derived and solved that allows us to analyze the wave modification by competition of weakly nonlinear and quasi-isentropic effects. It was shown that the sign of the quasi-isentropic term determines the scenario of the evolution, either dissipative or active. In the dissipative case, when the plasma is first-order isentropically stable, the magnetoacoustic waves are damped and the time for shock wave formation is delayed. However, in the active case when the plasma is isentropically overstable, the wave amplitude grows, the strength of the shock increases, and the breaking time decreases. The magnitude of the above effects depends on the angle between the wavevector and the magnetic field. For hot (T>104 K) atomic plasmas with solar abundances either in the interstellar medium or in the solar atmosphere, as well as for the cold (T<103 K) ISM molecular gas, the range of temperatures in which the plasma is isentropically unstable and the corresponding timescale and length scale for wave breaking have been found. Title: Slow Magnetoacoustic Waves in Coronal Loops? Authors: Robbrecht, E.; Berghmans, D.; Nakariakov, V.; Poedts, S. Bibcode: 1999ESASP.446..575R Altcode: 1999soho....8..575R On May 13, 1998 the EIT and TRACE instruments produced simultaneous high cadence image sequences of the same active region (AR 8218). TRACE achieved a 25 sec cadence in the 171 deg passband while EIT achieved a 15 sec cadence (operating in 'shutterless mode', SOHO JOP 80) in the 195 deg passband. These high cadence observations in two complementary wavelengths have revealed the existence of weak disturbances in an extended coronal loop system. The disturbances originate from small scale brightenings at the footpoints of the loops and propagate along the loops at an apparant speed of the order of 150 km/s which is close to the expected sound speed. To conclude whether these propagating disturbances should be interpreted as slow magnetoacoustic waves or as mass motions ('microflows'), we compare our observational findings with theoretical models. Our results suggest that the recent discovery of DeForest and Gurman (1998) of slow MHD waves in polar plumes, are in fact not typical of polar plumes but occur also in extended coronal structures elsewhere. Title: MHD Waves in Open Magnetic Structures Authors: Nakariakov, V. M.; Roberts, B.; Murawski, K. Bibcode: 1999ASPC..184..243N Altcode: The dynamics of Alfvén and magnetoacoustic waves of finite amplitude in open magnetic structures is considered. A transversal inhomogeneity in the magnetic structure in the density and/or in a field-aligned steady flow gives rise to Alfvén wave phase mixing, which, in the almost collisionless and dissipationless plasma of the corona, nonlinearly generates obliquely propagating fast magnetoacoustic waves. The generated fast waves are more effectively damped than the Alfvén waves and so the process of heating by phase mixing is enhanced. This "indirect" heating leads to the spreading of the heated plasma across the magnetic field. We point out also that an inhomogeneous flow gives rise to the secular generation of longitudinal motions through Alfvén wave phase mixing, accelerating the plasma along the field. Title: TRACE observation of damped coronal loop oscillations: Implications for coronal heating Authors: Nakariakov, V. M.; Ofman, L.; Deluca, E. E.; Roberts, B.; Davila, J. M. Bibcode: 1999Sci...285..862N Altcode: The imaging telescope on board the Transition Region and Coronal Explorer (TRACE) spacecraft observed the decaying transversal oscillations of a long [(130 ± 6) × 106 meters], thin [diameter (2.0 ± 0.36) × 106 meters], bright coronal loop in the 171 angstrom FeIX emission line. The oscillations were excited by a solar flare in the adjacent active region. The decay time of the oscillations is 14.5 ± 2.7 minutes for an oscillation with a frequency 3.90 ± 0.13 millihertz. The coronal dissipation coefficient is estimated to be eight to nine orders of magnitude larger than the theoretically predicted classical value. The larger dissipation coefficient may solve existing difficulties with wave heating and reconnection theories. Title: Determination of the Reynolds number from TRACE Observation of Damped Coronal Loop Oscillations Induced by a Flare Authors: Ofman, L.; Nakariakov, V. M.; Deluca, E.; Roberts, B.; Davila, J. M. Bibcode: 1999AAS...194.7909O Altcode: 1999BAAS...31..964O The Transition Region and Coronal Expolorer (TRACE) observes the solar corona with unprecedented spatial and temporal resolution. We analyzed active region loop observation in the 171 Angstroms Fe IX emission line, and report the direct observations of damped transverse oscillations of a long (130+/-6 Mm) thin (diameter 2+/-0.36 Mm) bright active region loop. The oscillations were detected following a flare in the adjacent active region. We determined the oscillation frequency and the decay time by the least-square fit of an exponentially decaying sinusoidal function. Using the dispersion relation for the transverse oscillations, and the observed loop geometry we estimated the Alfven crossing time in the loop. The Alfven time can be used to determine the magnetic field strength in the loop if the density is known. All parts of the loop were observed to oscillate transversly in-phase, implying that the ocillation is a global mode of the loop. Using dissipative MHD model for resonant absorption of global mode oscillations for the coronal loop we determined the Reynolds number that produces the observed damping rate of the observed global mode. The value of the Reynolds number is in the 10(5-10^6) range, which is eight to nine orders of magnitude smaller than the classical coronal value. We discuss the important implication of the small Reynolds number on coronal heating theories. Title: Slow Magnetosonic Waves in Coronal Plumes Authors: Ofman, L.; Nakariakov, V. M.; DeForest, C. E. Bibcode: 1999ApJ...514..441O Altcode: Recent observations of polar plumes in the southern solar coronal hole by the Extreme-Ultraviolet Imaging Telescope (EIT) on board the SOHO spacecraft show signatures of quasi-periodic compressional waves with periods of 10-15 minutes. The relative wave amplitude was found to increase with height in the plumes up to about 1.2 Rsolar. Using a one-dimensional linear wave equation for the magnetosonic wave, we show that the waves are propagating and that their amplitude increases with height. The observed propagation velocity agrees well with the expected sound velocity inside the plumes. We present the results of the first nonlinear, two-dimensional, magnetohydrodynamic (MHD) simulation of the magnetosonic waves in plumes for typical coronal conditions consistent with observations and gravitationally stratified solar corona. We find numerically that outward-propagating slow magnetosonic waves are trapped, and nonlinearly steepen in the polar plumes. The nonlinear steepening of the magnetosonic waves may contribute significantly to the heating of the lower corona by compressive dissipation. Title: Excitation of magnetospheric waveguide modes by magnetosheath flows Authors: Mann, Ian R.; Wright, Andrew N.; Mills, Katharine J.; Nakariakov, Valery M. Bibcode: 1999JGR...104..333M Altcode: Standard models of the Earth's outer magnetospheric waveguide assume that a perfectly reflecting magnetopause can trap energy inside the waveguide. In contrast, we show that the near-noon magnetopause often acts as a leaky boundary, wave trapping only being possible for large magnetosheath flow speeds. Moreover, for sufficiently fast flow speeds, we show how waveguide modes may be energized by magnetosheath flows via the overreflection mechanism. Unbounded simulations of the growth of surface waves via the development of a Kelvin-Helmholtz instability (KHI) vortex sheet show growth rates which increase without limit proportional to wavenumber (ky), until the assumption of a thin boundary is no longer valid. For a bounded magnetosphere, however, overreflected body type waveguide modes can introduce wavenumber selection, that is, generate modes with maximum linear growth rates at finite ky. A necessary condition is that the wave is propagating in the magnetosphere, that is, the wave's turning point lies inside the magnetosphere. By developing a new description of both KHI and waveguide mode growth in terms of overreflection and the propagation of negative energy waves, we show how the maximum growth rate can be understood in terms of the reflection coefficient of waves incident upon the magnetopause. Our model can also explain the observed local time dependence of Pc5 field line resonance wave power, and can explain the observed correlation between high solar wind speeds and Pc5 wave power. Finally, we show how a waveguide with a free magnetopause boundary supports quarter-wavelength modes. These modes have lower frequencies than the standard (magnetopause velocity node) half-wavelength modes, perhaps generating the millihertz waveguide mode eigenfrequencies which appear to drive field line resonances in HF radar data. Title: Alfvén wave phase mixing in two-dimensional open magnetic configurations. Authors: Ruderman, M. S.; Nakariakov, V. M.; Roberts, B. Bibcode: 1999joso.proc..143R Altcode: The phase mixing of Alfvén waves in planar two-dimensional open magnetic configurations is considered. It is assumed that the characteristic vertical spatial scale of the configuration is much larger than the horizontal scale, and that the latter is of the order of a wavelength. The WKB method is used to derive the governing equation for the wave amplitude, which in appropriate coordinates is the diffusion equation with the diffusion coefficient being spatially dependent. The dependency of the energy flux on the vertical coordinate is obtained for monochromatic waves, and illustrated for three particular cases. The theory is applied to Alfvén wave damping in coronal holes. Title: Alfven wave phase mixing in two-dimensional open magnetic configurations. Authors: Ruderman, Michael S.; Nakariakov, Valery M.; Roberts, Bernard Bibcode: 1998A&A...338.1118R Altcode: The phase mixing of Alfven waves in planar two-dimensional open magnetic plasma configurations is considered. It is assumed that the characteristic vertical spatial scale of the configuration is much larger than the horizontal scale, and that the latter is of the order of a wavelength. The WKB method is used to derive the governing equation for the wave amplitude, which in appropriate coordinates is the diffusion equation with the diffusion coefficient being spatially dependent. The dependency of the energy flux on the vertical coordinate is obtained for monochromatic waves, and illustrated for three particular cases. In all three cases, at low heights phase-mixed Alfven waves damp at the same rate as in a one-dimensional configuration. However, in the first and third cases phase mixing operates only at low and intermediate heights and practically stops at heights larger than a few characteristic vertical length scales. Only a part of the energy flux is damped due to phase mixing. In the second case the situation is reversed: the damping of the energy flux with height is much faster that in one-dimensional configurations. The rate of damping of the energy flux with height due to phase mixing in two-dimensional configurations thus depends strongly on the particular form of the configuration. The theory is applied to Alfven wave damping in coronal holes. Title: Nonlinear coupling of MHD waves in inhomogeneous steady flows Authors: Nakariakov, V. M.; Roberts, B.; Murawski, K. Bibcode: 1998A&A...332..795N Altcode: The nonlinear coupling of MHD waves in a cold (beta =3D 0) compressible plasma with a smoothly inhomogeneous low-speed steady flow directed along the magnetic field is considered. The effect is similar to Alfven wave phase mixing in a static, inhomogeneous medium and leads to the production of steep transversal gradients in the plasma parameters, which increases dissipation. Transversal gradients in the total pressure, produced by phase mixing, lead to the secular generation of obliquely propagating fast magnetosonic waves, at double the frequency and the wavenumber of the source Alfven waves. The efficiency of the generation is defined by the Alfven wave amplitude and the transversal spatial scale of the flow inhomogeneity. The secular growth of density perturbations, connected with fast waves, takes place for flow speeds that are considerably below the thresholds of the Kelvin - Helmholtz and negative energy wave instabilities. The initial stage of the nonlinear generation of the fast waves is considered analytically and illustrated by numerical simulations. Title: Nonlinear Waves in Force-Free Fibrils Authors: Zhugzhda, Y. D.; Nakariakov, V. M. Bibcode: 1998ASPC..150..151Z Altcode: 1998npsp.conf..151Z; 1998IAUCo.167..151Z No abstract at ADS Title: A Manifestation of Negative Energy Waves in the Solar Atmosphere Authors: Joarder, P. S.; Nakariakov, V. M.; Roberts, B. Bibcode: 1997SoPh..176..285J Altcode: Magnetosonic modes of magnetic structures of the solar atmosphere in the presence of inhomogeneous steady flows are considered. It is shown that, when the speed of the steady flow exceeds the phase speed of one of the modes, the mode has negative energy, and can be subject to an over-stability due to the negative energy wave instabilities. It is shown that registered steady flows in the solar atmosphere, with speeds below the threshold of the Kelvin-Helmholtz instability, can provide the existence of the magnetosonic negative energy wave phenomena. In particular, in isolated photospheric magnetic flux tubes, there are kink surface modes with negative energy, produced by the external granulation downflows. Dissipative instability of these modes due to finite thermal conductivity and explosive instability due to nonlinear coupling of these modes with Alfvén waves are discussed. For coronal loops, it is found that only very high-speed flows (>300 km s-1) can produce negative energy slow body modes. In solar wind flow structures, both slow and fast body modes have negative energy and are unstable. Title: Latent Heating of Coronal Loops Authors: Zhugzhda, Y. D.; Nakariakov, V. M. Bibcode: 1997SoPh..175..107Z Altcode: The theory of weakly nonlinear slow magnetosonic waves in thin flux tubes is developed. A Korteweg-de Vries equation is derived for slow body waves. The analysis of solitary and periodic solutions shows that the nonlinear waves produce running narrowings of the tube. The similarity of the shallow-water theory and the thin-flux-tube approximation helps to outline the peaking and breaking of the nonlinear slow body waves. It appears that the running narrowing of the tube works as the de Laval nozzle in generating a cool supersonic jet and a subsequent shock that heats the plasma. The presented theory of nonlinear slow body waves suggests a mechanism of coronal loop heating, which meets many of the observational constraints. Title: Alfvén Wave Phase Mixing as a Source of Fast Magnetosonic Waves Authors: Nakariakov, V. M.; Roberts, B.; Murawski, K. Bibcode: 1997SoPh..175...93N Altcode: The nonlinear excitation of fast magnetosonic waves by phase mixing Alfvén waves in a cold plasma with a smooth inhomogeneity of density across a uniform magnetic field is considered. If initially fast waves are absent from the system, then nonlinearity leads to their excitation by transversal gradients in the Alfvén wave. The efficiency of the nonlinear Alfvén-fast magnetosonic wave coupling is strongly increased by the inhomogeneity of the medium. The fast waves, permanently generated by Alfvén wave phase mixing, are refracted from the region with transversal gradients of the Alfvén speed. This nonlinear process suggests a mechanism of indirect plasma heating by phase mixing through the excitation of obliquely propagating fast waves. Title: Oscillations in Prominence Fine-Structures Authors: Joarder, P. S.; Nakariakov, V. M.; Roberts, B. Bibcode: 1997SoPh..173...81J Altcode: Oscillatory spectra of solar quiescent prominences highlight the importance of incorporating the effect of prominence fine-structure in the theory of prominence oscillations. We determine the magnetohydrodynamic modes of oscillation of an elementary, zero-β model of a prominence fibril, arguing that the fast body kink modes, namely, the string and the internal magnetic Love modes, produce the observed short periodicities in prominence fine-structures. Estimates for the periods of these modes are presented: the modes are subject to testing in future high-resolution observations. Title: On nonlinear dynamics of twisted magnetic flux tubes. Authors: Zhugzhda, Yu. D.; Nakariakov, V. M. Bibcode: 1997joso.proc...95Z Altcode: No abstract at ADS Title: Negative energy wave instabilities in magnetic flux tubes. Authors: Nakariakov, V. M.; Roberts, B.; Joarder, P. S. Bibcode: 1997joso.proc...64N Altcode: No abstract at ADS Title: Nonlinearly Selected Frequencies in Coronal Loops Authors: Nakariakov, V. M.; Roberts, B. Bibcode: 1996SoPh..168..273N Altcode: A nonlinear process for the resonant generation of low-frequency fast magnetosonic kink waves in coronal loops is discussed. The efficiency of the process is strongly enhanced due to the existence of a nonlinearly selected frequency produced by a constant frequency difference in the dispersion curves in the short wavelength limit. The kink wave with the selected frequency interacts with high-frequency kink and sausage waves. The efficiency of such interaction does not require coherence in the interactive waves. In a loop of width 2 × 103 km, field strength 50 G and number density 5 × 1015 m−3, the nonlinearly selected frequency is of order 46 mHz (period 21.8 s), but this may range through 11 mHz to 184 mHz (periods 86.5 s to 5.4 s) for typical coronal conditions. Title: On the interaction of longitudinal and transversal waves in thin magnetic flux tubes. Authors: Nakariakov, V. M.; Zhugzhda, Y. D.; Ulmschneider, P. Bibcode: 1996A&A...312..691N Altcode: An analytical investigation of the nonlinear interaction of longitudinal and transversal waves in thin magnetic flux tubes is presented and the nonlinear terms which give rise to wave generation of other modes and to shock formation are isolated. The nonlinear resonant three-wave interaction of longitudinal and transversal waves is studied together with the growth and decay behaviour of these waves. This analytical study clarifies our previous numerical computations of nonlinear wave generation and of the steepening of longitudinal as well as transversal wave profiles. Title: MHD modes of solar wind flow tubes. Authors: Nakariakov, V. M.; Roberts, B.; Mann, G. Bibcode: 1996A&A...311..311N Altcode: The properties of linear magnetosonic waves trapped within solar wind flow tubes are considered. The trapping is due to reflection of the waves from the tube boundary, which may correspond to either a jump in plasma density or magnetic field, or a jump in the steady flow velocity. The structure of the waves transverse to the magnetic field is defined by the boundary conditions. The phase and group speeds of the waves depend upon the wave frequency and wavelength. For realistic conditions in a flow tube, corresponding to a "spaghetti structure", there are two types of trapped waves propagating away from the Sun, fast and slow waves. These waves are "backward", in the sense that they would propagate towards the Sun in the absence of any difference in the steady flow velocity inside and outside the tube. The "forward" magnetosonic waves are not trapped under solar wind conditions. Both slow and fast backward waves have phase velocities that are sub-Alfvenic. There are no MHD waves propagating towards the Sun. Title: Resonant interactions of modes in coronal magnetic flux tubes Authors: Nakariakov, V. M.; Oraevsky, V. N. Bibcode: 1995SoPh..160..289N Altcode: Nonlinear resonant interactions of different kinds of fast magnetosonic (FMS) waves trapped in the inhomogeneity of a low-β plasma density, stretched along a magnetic field (as, for example, in coronal loops) are investigated. A set of equations describing the amplitudes of interactive modes is derived for an arbitrary density profile. The quantitative characteristics of such interactions are found. The decay instability of the wave with highest frequency is possible in the system. If amplitudes of interactive modes have close values, the long-period temporal and spatial oscillations are in the system. Title: Effects of plasma temperature anisotropy on the Kelvin-Helmholtz instability of the heliopause Authors: Kruznetsov, V. D.; Nakaryakov, V. M.; Tsyganov, P. V. Bibcode: 1995AstL...21..710K Altcode: 1995PAZh...21..793K No abstract at ADS Title: Magnetosonic Waves in Structured Atmospheres with Steady Flows, I Authors: Nakariakov, V. M.; Roberts, B. Bibcode: 1995SoPh..159..213N Altcode: The magnetosonic modes of magnetic plasma structures in the solar atmosphere are considered taking into account steady flows of plasma in the internal and external media and using a slab geometry. The investigation brings nearer the theory of magnetosonic waveguides, in such structures as coronal loops and photospheric flux tubes, to realistic conditions of the solar atmosphere. The general dispersion relation for the magnetosonic modes of a magnetic slab in magnetic surroundings is derived, allowing for field-aligned steady flows in either region. It is shown that flows change both qualitatively and quantitatively the characteristics of magnetosonic modes. The flow may lead to the appearance of a new type of trapped mode, namelybackward waves. These waves are the usual slab modes propagating in the direction opposite to the internal flow, but advected with the flow. The disappearance of some modes due to the flow is also demonstrated. Title: On Fast Magnetosonic Coronal Pulsations Authors: Nakariakov, V. M.; Roberts, B. Bibcode: 1995SoPh..159..399N Altcode: The linear properties of the fast magnetosonic modes of a coronal loop modelled as a smooth density inhomogeneity in a uniform magnetic field are compared with the case of a step function slab. It is shown that the group velocityCgof the modes, important in determining the structure of impulsively excited wave packets, possesses a minimum for a wide class of profile including the slab, with the exception of the Epstein profile for which the minimum inCgmoves out to infinity. Results for the simple step profile are thus of wider validity, and likely to be applicable to coronal loops. Title: Waves in Cosmic Magnetic Structures Taking into Account the Anisotropic Plasma Pressure Authors: Nakariakov, V. M.; Oraevsky, V. N. Bibcode: 1995SoPh..158...29N Altcode: This paper provides an analysis of magneto-sonic eigenwaves travelling in magnetic plasma structures based on the Chew-Goldberger-Low approximation, for which the plasma kinetic pressure is different along and across the magnetic field. The anisotropy does not lead to the emergence of new modes. The dependence of phase velocities of the waves, trapped by a single magnetic surface, on the pressure anisotropy is investigated. For a magnetic slab with field-free surroundings, the dispersion relations for the eigenwaves are obtained. The pressure anisotropy may change dispersion relations of such modes significantly. In particular, backward waves are possible in the case of strong anisotropy. The dependences of the thresholds for the mirror and hose instabilities on the system parameters are obtained. In particular, hose and mirror instabilities of such waves are absent for some wave number regions. The results are used to obtain the eigenwave characteristics in coronal loops and chromospheric flux tubes. Title: Superreflection of fast magnetosonic waves from a tangential discontinuity of velocity Authors: Nakaryakov, V. M.; Stepanyants, Yu. A. Bibcode: 1994AstL...20..763N Altcode: 1994PAZh...20..873N No abstract at ADS Title: Parametric modulation of magnetoacoustic waves in a magnetic field tube by an external wave Authors: Nakaryakov, V. M.; Petrukhin, N. S. Bibcode: 1994AstL...20..365N Altcode: 1994PAZh...20..431N No abstract at ADS Title: Effect of pressure anisotropy on the magnetosonic wave propagation in a plasma sheet Authors: Gromov, E. M.; Nakariakov, V. M.; Oraevskii, V. N. Bibcode: 1992SvAL...18..341G Altcode: 1992PAZh...18..841G The propagation of magnetosonic waves localized within a sheet of magnetized plasma is studied, with the anisotropy of plasma kinetic pressure in the magnetic field taken into account. Dispersion dependences of wave phase velocities on the ratio of the sheet size to the wavelength are derived for various plasma parameters within and outside the sheet. The thresholds of the appearance of mirror and hose instabilities are investigated. The ranges of the parameters of the system under consideration for which anisotropy must be taken into account are indicated. Changes due to anisotropy are estimated for various magnetic structures in the solar atmosphere. Title: Generation of Low-Frequency Pulsations in Magnetic Waveguides in the Sun's Atmosphere Authors: Nakaryakov, V. M.; Petrukhin, N. S.; Fainshtein, S. M. Bibcode: 1991SvAL...17..423N Altcode: No abstract at ADS Title: Generation of low-frequency pulsations in magnetic waveguides in the solar atmosphere Authors: Nakariakov, V. M.; Petrukhin, N. S.; Feinstein, S. M. Bibcode: 1991PAZh...17.1008N Altcode: An analytical conclusion is presented of Schroedinger's nonlinear equation describing the nonlinear dynamics of the envelope of the eigenmodes of the magnetic flux tube in the solar atmosphere within the framework of the ideal magnetic layer approximation. The generation of LF pulsations arising as a result of the instability of the packets of captured modes is investigated, and estimates of the period of LF pulsations for photospheric magnetic tubes are made. Title: Generation of the Alfven-wave second harmonic in a plane plasma waveguide Authors: Nakariakov, V. N.; Fainshtein, S. M. Bibcode: 1991RaF....34..211N Altcode: 1991R&QE...34..211N The interaction and self-defocusing of different types of waves in unbounded media are studied. A plane waveguide filled with 'cold' plasma with a constant magnetic field guided along the waveguide walls is considered. It is shown that efficient excitation of the Alfven wave harmonic is possible in this plasma system.