Author name code: wiegelmann ADS astronomy entries on 2022-09-14 author:"Wiegelmann, Thomas" ------------------------------------------------------------------------ Title: Mini-filament eruption, QSL reconnection, and reconnection-driven outflows: IRIS and AIA/HMI/SDO observations and modelling Authors: Madjarska, Maria S.; Mackay, Duncan H.; Galsgaard, Klaus; Xie, Haixia; Wiegelmann, Thomas Bibcode: 2022cosp...44.2533M Altcode: We will present unique observations of a mini-filament eruption associated with cancelling magnetic fluxes of a small-scale loop system known as a coronal bright point. The event is uniquely recorded in both the imaging and spectroscopic data taken with the Interface Region Imaging Spectrograph (IRIS). The study aims at providing a better understanding of the physical processes driving these ubiquitous small-scale eruptions. We also analysed images taken in the extreme-ultraviolet channels of the Atmospheric Imaging Assembly (AIA) and line-of-sight magnetic-field data from the Helioseismic Magnetic Imager (HMI) onboard the Solar Dynamics Observatory. As the observations can only give an inkling about the possible physical processes at play, we also employed a non-linear force-free field (NLFFF) relaxation approach based on the HMI magnetogram time series. Furthermore, we computed the squashing factor, Q, in different horizontal planes of the NLFFF model. This allowed us to further investigate the evolution of the magnetic-field structures involved in the eruption process. Title: Effects of Initial Conditions on Magnetic Reconnection in a Solar Transient Authors: Agarwal, Satyam; Bhattacharyya, Ramit; Wiegelmann, Thomas Bibcode: 2022SoPh..297...91A Altcode: Coronal magnetic field extrapolations are necessary to understand the magnetic field morphology of the source region in solar coronal transients. The extrapolation models are broadly classified into nonforce-free and force-free, depending on whether the model allows for a Lorentz force or not. Presently, these models are employed to carry out state-of-the-art data-driven and data-constrained magnetohydrodynamics (MHD) simulations to explore magnetic reconnection (MR)—the underlying cause of the transients. It is then imperative to study the influence of different extrapolation models on simulated evolution. For this purpose, the numerical model EULAG-MHD is employed to carry out simulations with different initial magnetic and velocity fields obtained through nonforce-free and force-free extrapolations. The selected active region is NOAA 11977, hosting a C6.6 class eruptive flare. Both extrapolations are found to be in good agreement with the observed line-of-sight and transverse magnetic fields. Further, a morphological comparison on the global scale and particularly for selected topologies, such as a magnetic null point and a hyperbolic flux tube (HFT), suggests that similar magnetic field line structures are reproducible in both models, although the extent of agreement between the two varies. Astoundingly, generation of a three-dimensional null near the HFT is observed in all the simulations, inferring the evolution to be independent of the particular initial field configuration. Moreover, the magnetic field lines (MFLs) undergoing MRs at the null point and HFT evolve similarly, further confirming the near independence of reconnection details on the chosen initial conditions. Consequently, both the extrapolation techniques can be suitable for initiating data-driven and data-constrained simulations. Title: Active region chromospheric magnetic fields. Observational inference versus magnetohydrostatic modelling Authors: Vissers, G. J. M.; Danilovic, S.; Zhu, X.; Leenaarts, J.; Díaz Baso, C. J.; da Silva Santos, J. M.; de la Cruz Rodríguez, J.; Wiegelmann, T. Bibcode: 2022A&A...662A..88V Altcode: 2021arXiv210902943V Context. A proper estimate of the chromospheric magnetic fields is thought to improve modelling of both active region and coronal mass ejection evolution. However, because the chromospheric field is not regularly obtained for sufficiently large fields of view, estimates thereof are commonly obtained through data-driven models or field extrapolations, based on photospheric boundary conditions alone and involving pre-processing that may reduce details and dynamic range in the magnetograms.
Aims: We investigate the similarity between the chromospheric magnetic field that is directly inferred from observations and the field obtained from a magnetohydrostatic (MHS) extrapolation based on a high-resolution photospheric magnetogram.
Methods: Based on Swedish 1-m Solar Telescope Fe I 6173 Å and Ca II 8542 Å observations of NOAA active region 12723, we employed the spatially regularised weak-field approximation (WFA) to derive the vector magnetic field in the chromosphere from Ca II, as well as non-local thermodynamic equilibrium (non-LTE) inversions of Fe I and Ca II to infer a model atmosphere for selected regions. Milne-Eddington inversions of Fe I serve as photospheric boundary conditions for the MHS model that delivers the three-dimensional field, gas pressure, and density self-consistently.
Results: For the line-of-sight component, the MHS chromospheric field generally agrees with the non-LTE inversions and WFA, but tends to be weaker by 16% on average than these when larger in magnitude than 300 G. The observationally inferred transverse component is systematically stronger, up to an order of magnitude in magnetically weaker regions, but the qualitative distribution with height is similar to the MHS results. For either field component, the MHS chromospheric field lacks the fine structure derived from the inversions. Furthermore, the MHS model does not recover the magnetic imprint from a set of high fibrils connecting the main polarities.
Conclusions: The MHS extrapolation and WFA provide a qualitatively similar chromospheric field, where the azimuth of the former is better aligned with Ca II 8542 Å fibrils than that of the WFA, especially outside strong-field concentrations. The amount of structure as well as the transverse field strengths are, however, underestimated by the MHS extrapolation. This underscores the importance of considering a chromospheric magnetic field constraint in data-driven modelling of active regions, particularly in the context of space weather predictions. Title: Eruptions from coronal bright points: A spectroscopic view by IRIS of a mini-filament eruption, QSL reconnection, and reconnection-driven outflows Authors: Madjarska, Maria S.; Mackay, Duncan H.; Galsgaard, Klaus; Wiegelmann, Thomas; Xie, Haixia Bibcode: 2022A&A...660A..45M Altcode: 2022arXiv220200370M Context. Our study investigates a mini-filament eruption associated with cancelling magnetic fluxes. The eruption originates from a small-scale loop complex commonly known as a coronal bright point (CBP). The event is uniquely recorded in both the imaging and spectroscopic data taken with the Interface Region Imaging Spectrograph (IRIS).
Aims: The investigation aims to gain a better understanding of the physical processes driving these ubiquitous small-scale eruptions.
Methods: We analysed IRIS spectroscopic and slit-jaw imaging observations as well as images taken in the extreme-ultraviolet channels of the Atmospheric Imaging Assembly (AIA) and line-of-sight magnetic-field data from the Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory. As the observations can only indicate the possible physical processes at play, we also employed a non-linear force-free field (NLFFF) relaxation approach based on the HMI magnetogram time series. This allowed us to further investigate the evolution of the magnetic-field structures involved in the eruption process.
Results: We identified a strong small-scale brightening as a micro-flare in a CBP, recorded in emission from chromospheric to flaring plasmas. The mini-eruption is manifested via the ejection of hot (CBP loops) and cool (mini-filament) plasma recorded in both the imaging and spectroscopic data. The micro-flare is preceded by the appearance of an elongated bright feature in the IRIS slit-jaw 1400 Å images, located above the polarity inversion line. The micro-flare starts with an IRIS pixel size brightening and propagates bi-directionally along the elongated feature. We detected, in both the spectral and imaging IRIS data and AIA data, strong flows along and at the edges of the elongated feature; we believe that these represent reconnection outflows. Both edges of the elongated feature that wrap around the edges of the erupting MF evolve into a J-type shape, creating a sigmoid appearance. A quasi-separatrix layer (QSL) is identified in the vicinity of the polarity inversion line by computing the squashing factor, Q, in different horizontal planes of the NLFFF model.
Conclusions: This CBP spectro-imaging study provides further evidence that CBPs represent downscaled active regions and, as such, they may make a significant contribution to the mass and energy balance of the solar atmosphere. They are the sources of all range of typical active-region features, including magnetic reconnection along QSLs, (mini-)filament eruptions, (micro-)flaring, reconnection outflows, etc. The QSL reconnection site has the same spectral appearance as the so-called explosive events identified by strong blue- and red-shifted emission, thus providing an answer to an outstanding question regarding the true nature of this spectral phenomenon.

Movies associated to Figs. A.1 and A.2 are available at https://www.aanda.org Title: Coronal magnetic field evolution over cycle 24 Authors: Chifu, I.; Inhester, B.; Wiegelmann, T. Bibcode: 2022A&A...659A.174C Altcode: 2022arXiv220103853C Context. The photospheric magnetic field vector is continuously derived from measurements, while reconstruction of the three-dimensional (3D) coronal magnetic field requires modelling with photospheric measurements as a boundary condition. For decades, the cycle variation of the magnetic field in the photosphere has been investigated. Until now, there has been no study of the evolution of the coronal magnetic flux in the corona or of the evolution of solar cycle magnetic free energy.
Aims: The aim of this paper is to analyze the temporal variation of the magnetic field and free magnetic energy in the solar corona for solar cycle 24 and the behavior of the magnetic field in the two hemispheres. We want to investigate whether or not we can obtain better estimates of the magnetic field at Earth using the nonlinear force-free field extrapolation method.
Methods: To model the magnetic field over cycle 24 we apply the nonlinear force-free field (NLFFF) optimization method to the entire set of the synoptic vector magnetic maps derived from observations made using the Heliospheric and Magnetic Imager (HMI) on board Solar Dynamic Observatory (SDO).
Results: From our results, we find that during solar cycle 24, the maximum of the Sun's dynamics is different than the sunspot number (SSN) maximum peak. The major contribution to the total unsigned flux is provided by the flux coming from the magnetic field structures other than sunspots (MSOS) within latitudes of −30° and +30°. The magnetic flux variation during solar cycle 24 shows a different evolution in the corona than in the photosphere. We find a correlation value of 0.8 between the derived magnetic energy from our model and the flare energy index derived from observations. On average, cycle 24 had a higher number of sunspots in the northern hemisphere (NH) but stronger flux in the southern hemisphere (SH) which could more effectively reach the higher layers of the atmosphere. The coupling between the hemispheres increases with height. The strongest asymmetries in the unsigned magnetic flux are between the two SSN peaks. Title: Magnetohydrostatic Modeling of the Solar Atmosphere Authors: Zhu, Xiaoshuai; Neukirch, Thomas; Wiegelmann, Thomas Bibcode: 2022arXiv220315356Z Altcode: Understanding structures and evolutions of the magnetic fields and plasma in multiple layers on the Sun is very important. A force-free magnetic field which is an accurate approximation of the solar corona due to the low plasma $\beta$ has been widely studied and used to model the coronal magnetic structure. While the force-freeness assumption is well satisfied in the solar corona, the lower atmosphere is not force-free given the high plasma $\beta$. Therefore, a magnetohydrostatic (MHS) equilibrium which takes into account plasma forces, such as pressure gradient and gravitational force, is considered to be more appropriate to describe the lower atmosphere. This paper reviews both analytical and numerical extrapolation methods based on the MHS assumption for calculating the magnetic fields and plasma in the solar atmosphere from measured magnetograms. Title: Multiwavelength Signatures of Episodic Nullpoint Reconnection in a Quadrupolar Magnetic Configuration and the Cause of Failed Flux Rope Eruption Authors: Mitra, Prabir K.; Joshi, Bhuwan; Veronig, Astrid M.; Wiegelmann, Thomas Bibcode: 2022ApJ...926..143M Altcode: 2021arXiv211214412M In this paper, we present multiwavelength observations of the triggering of a failed-eruptive M-class flare from active region NOAA 11302 and investigate the possible reasons for the associated failed eruption. Photospheric observations and nonlinear force-free field extrapolated coronal magnetic field revealed that the flaring region had a complex quadrupolar configuration with a preexisting coronal nullpoint situated above the core field. Prior to the onset of the M-class flare, we observed multiple periods of small-scale flux enhancements in GOES and RHESSI soft X-ray observations from the location of the nullpoint. The preflare configuration and evolution reported here are similar to the configurations presented in the breakout model, but at much lower coronal heights. The core of the flaring region was characterized by the presence of two flux ropes in a double-decker configuration. During the impulsive phase of the flare, one of the two flux ropes initially started erupting, but resulted in a failed eruption. Calculation of the magnetic decay index revealed a saddle-like profile where the decay index initially increased to the torus-unstable limits within the heights of the flux ropes, but then decreased rapidly and reached negative values, which was most likely responsible for the failed eruption of the initially torus-unstable flux rope. Title: Toward a fast and consistent approach to modeling solar magnetic fields in multiple layers Authors: Zhu, X.; Wiegelmann, T. Bibcode: 2022A&A...658A..37Z Altcode: 2021arXiv210912789Z
Aims: We aim to develop a fast and consistent extrapolation method for modeling multiple layers of the solar atmosphere.
Methods: The new approach combines the magnetohydrostatic (MHS) extrapolation, which models the solar low atmosphere in a flat box, together with the nonlinear force-free field (NLFFF) extrapolation, which models the solar corona with a chromospheric vector magnetogram deduced from the MHS extrapolation. We tested our code with a snapshot of a radiative magnetohydrodynamic simulation of a solar flare and we conducted quantitative comparisons based on several metrics.
Results: Following a number of test runs, we found an optimized configuration for the combination of two extrapolations with a 5.8-Mm-high box for the MHS extrapolation and a magnetogram at a height of 1 Mm for the NLFFF extrapolation. The new approach under this configuration has the capability to reconstruct the magnetic fields in multi-layers accurately and efficiently. Based on figures of merit that are used to assess the performance of different extrapolations (NLFFF extrapolation, MHS extrapolation, and the combined one), we find the combined extrapolation reaches the same level of accuracy as the MHS extrapolation and they are both better than the NLFFF extrapolation. The combined extrapolation is moderately efficient for application to magnetograms with high resolution. Title: Solar force-free magnetic fields Authors: Wiegelmann, Thomas; Sakurai, Takashi Bibcode: 2021LRSP...18....1W Altcode: 2012arXiv1208.4693W The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces such as plasma pressure gradients and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relationship between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently a large area of research, as accurate measurements of the photospheric field are available from ground-based observatories such as the Synoptic Optical Long-term Investigations of the Sun and the Daniel K. Inouye Solar Telescope (DKIST) and space-born, e.g., from Hinode and the Solar Dynamics Observatory. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma. Title: Linking the Sun to the Heliosphere Using Composition Data and Modelling Authors: Parenti, Susanna; Chifu, Iulia; Del Zanna, Giulio; Edmondson, Justin; Giunta, Alessandra; Hansteen, Viggo H.; Higginson, Aleida; Laming, J. Martin; Lepri, Susan T.; Lynch, Benjamin J.; Rivera, Yeimy J.; von Steiger, Rudolf; Wiegelmann, Thomas; Wimmer-Schweingruber, Robert F.; Zambrana Prado, Natalia; Pelouze, Gabriel Bibcode: 2021SSRv..217...78P Altcode: 2021arXiv211006111P Our understanding of the formation and evolution of the corona and the heliosphere is linked to our capability of properly interpret the data from remote sensing and in-situ observations. In this respect, being able to correctly connect in-situ observations with their source regions on the Sun is the key for solving this problem. In this work we aim at testing a diagnostics method for this connectivity. Title: Global coronal and heliospheric magnetic field modelling for Solar Orbiter Authors: Wiegelmann, Thomas; Neukirch, Thomas; Chifu, Iulia; Inhester, Bernd Bibcode: 2021EGUGA..2311005W Altcode: Computing the solar coronal magnetic field and plasmaenvironment is an important research topic on it's own rightand also important for space missions like Solar Orbiter toguide the analysis of remote sensing and in-situ instruments.In the inner solar corona plasma forces can be neglected andthe field is modelled under the assumption of a vanishingLorentz-force. Further outwards (above about two solar radii)plasma forces and the solar wind flow has to be considered.Finally in the heliosphere one has to consider that the Sunis rotating and the well known Parker-spiral forms.We have developed codes based on optimization principlesto solve nonlinear force-free, magneto-hydro-static andstationary MHD-equilibria. In the present work we want toextend these methods by taking the solar rotation into account. Title: Preprocessing of magnetograms for magnetohydrostatic extrapolations Authors: Zhu, Xiaoshuai; Wiegelmann, Thomas; Inhester, Bernd Bibcode: 2021EGUGA..23.1973Z Altcode: Magnetohydrostatic (MHS) extrapolations are developed to model 3D magnetic fields and plasma structures in the solar low atmosphere by using measured vector magnetic fields on the photosphere. However, the photospheric magnetogram may be inconsistent with the MHS assumption. By applying Gauss" theorem to an isolated active region, we obtain a set of surface integrals of the magnetogram as criteria for a MHS system. The integrals are a subset of Aly"s criteria for a force-free field (FFF). Based on the new criteria, we preprocess the magnetogram to make it more consistent with the MHS assumption and, at the same time, close to the original data. As a byproduct, we also find the boundary integral that is used to compute the energy of a FFF usually underestimates the magnetic energy of an active region. Title: An overall view of temperature oscillations in the solar chromosphere with ALMA Authors: Jafarzadeh, S.; Wedemeyer, S.; Fleck, B.; Stangalini, M.; Jess, D. B.; Morton, R. J.; Szydlarski, M.; Henriques, V. M. J.; Zhu, X.; Wiegelmann, T.; Guevara Gómez, J. C.; Grant, S. D. T.; Chen, B.; Reardon, K.; White, S. M. Bibcode: 2021RSPTA.37900174J Altcode: 2021RSTPA.379..174J; 2020arXiv201001918J By direct measurements of the gas temperature, the Atacama Large Millimeter/submillimeter Array (ALMA) has yielded a new diagnostic tool to study the solar chromosphere. Here, we present an overview of the brightness-temperature fluctuations from several high-quality and high-temporal-resolution (i.e. 1 and 2 s cadence) time series of images obtained during the first 2 years of solar observations with ALMA, in Band 3 and Band 6, centred at around 3 mm (100 GHz) and 1.25 mm (239 GHz), respectively. The various datasets represent solar regions with different levels of magnetic flux. We perform fast Fourier and Lomb-Scargle transforms to measure both the spatial structuring of dominant frequencies and the average global frequency distributions of the oscillations (i.e. averaged over the entire field of view). We find that the observed frequencies significantly vary from one dataset to another, which is discussed in terms of the solar regions captured by the observations (i.e. linked to their underlying magnetic topology). While the presence of enhanced power within the frequency range 3-5 mHz is found for the most magnetically quiescent datasets, lower frequencies dominate when there is significant influence from strong underlying magnetic field concentrations (present inside and/or in the immediate vicinity of the observed field of view). We discuss here a number of reasons which could possibly contribute to the power suppression at around 5.5 mHz in the ALMA observations. However, it remains unclear how other chromospheric diagnostics (with an exception of Hα line-core intensity) are unaffected by similar effects, i.e. they show very pronounced 3-min oscillations dominating the dynamics of the chromosphere, whereas only a very small fraction of all the pixels in the 10 ALMA datasets analysed here show peak power near 5.5 mHz.

This article is part of the Theo Murphy meeting issue `High-resolution wave dynamics in the lower solar atmosphere'. Title: Preprocessing of vector magnetograms for magnetohydrostatic extrapolations Authors: Zhu, X.; Wiegelmann, T.; Inhester, B. Bibcode: 2020A&A...644A..57Z Altcode: 2020arXiv201006174Z Context. Understanding the 3D magnetic field as well as the plasma in the chromosphere and transition region is important. One way is to extrapolate the magnetic field and plasma from the routinely measured vector magnetogram on the photosphere based on the assumption of the magnetohydrostatic (MHS) state. However, photospheric data may be inconsistent with the MHS assumption. Therefore, we must study the restriction on the photospheric magnetic field, which is required by the MHS system. Moreover, the data should be transformed accordingly before MHS extrapolations can be applied.
Aims: We aim to obtain a set of surface integrals as criteria for the MHS system and use this set of integrals to preprocess a vector magnetogram.
Methods: By applying Gauss' theorem and assuming an isolated active region on the Sun, we related the magnetic energy and forces in the volume to the surface integral on the photosphere. The same method was applied to obtain restrictions on the photospheric magnetic field as necessary criteria for a MHS system. We used an optimization method to preprocess the data to minimize the deviation from the criteria as well as the measured value.
Results: By applying the virial theorem to the active region, we find the boundary integral that is used to compute the energy of a force-free field usually underestimates the magnetic energy of a large active region. We also find that the MHS assumption only requires the x-, y-component of net Lorentz force and the z-component of net torque to be zero. These zero components are part of Aly's criteria for a force-free field. However, other components of net force and torque can be non-zero values. According to new criteria, we preprocess the magnetogram to make it more consistent with the MHS system and, at the same time close, to the original data. Title: Coordination within the remote sensing payload on the Solar Orbiter mission Authors: Auchère, F.; Andretta, V.; Antonucci, E.; Bach, N.; Battaglia, M.; Bemporad, A.; Berghmans, D.; Buchlin, E.; Caminade, S.; Carlsson, M.; Carlyle, J.; Cerullo, J. J.; Chamberlin, P. C.; Colaninno, R. C.; Davila, J. M.; De Groof, A.; Etesi, L.; Fahmy, S.; Fineschi, S.; Fludra, A.; Gilbert, H. R.; Giunta, A.; Grundy, T.; Haberreiter, M.; Harra, L. K.; Hassler, D. M.; Hirzberger, J.; Howard, R. A.; Hurford, G.; Kleint, L.; Kolleck, M.; Krucker, S.; Lagg, A.; Landini, F.; Long, D. M.; Lefort, J.; Lodiot, S.; Mampaey, B.; Maloney, S.; Marliani, F.; Martinez-Pillet, V.; McMullin, D. R.; Müller, D.; Nicolini, G.; Orozco Suarez, D.; Pacros, A.; Pancrazzi, M.; Parenti, S.; Peter, H.; Philippon, A.; Plunkett, S.; Rich, N.; Rochus, P.; Rouillard, A.; Romoli, M.; Sanchez, L.; Schühle, U.; Sidher, S.; Solanki, S. K.; Spadaro, D.; St Cyr, O. C.; Straus, T.; Tanco, I.; Teriaca, L.; Thompson, W. T.; del Toro Iniesta, J. C.; Verbeeck, C.; Vourlidas, A.; Watson, C.; Wiegelmann, T.; Williams, D.; Woch, J.; Zhukov, A. N.; Zouganelis, I. Bibcode: 2020A&A...642A...6A Altcode: Context. To meet the scientific objectives of the mission, the Solar Orbiter spacecraft carries a suite of in-situ (IS) and remote sensing (RS) instruments designed for joint operations with inter-instrument communication capabilities. Indeed, previous missions have shown that the Sun (imaged by the RS instruments) and the heliosphere (mainly sampled by the IS instruments) should be considered as an integrated system rather than separate entities. Many of the advances expected from Solar Orbiter rely on this synergistic approach between IS and RS measurements.
Aims: Many aspects of hardware development, integration, testing, and operations are common to two or more RS instruments. In this paper, we describe the coordination effort initiated from the early mission phases by the Remote Sensing Working Group. We review the scientific goals and challenges, and give an overview of the technical solutions devised to successfully operate these instruments together.
Methods: A major constraint for the RS instruments is the limited telemetry (TM) bandwidth of the Solar Orbiter deep-space mission compared to missions in Earth orbit. Hence, many of the strategies developed to maximise the scientific return from these instruments revolve around the optimisation of TM usage, relying for example on onboard autonomy for data processing, compression, and selection for downlink. The planning process itself has been optimised to alleviate the dynamic nature of the targets, and an inter-instrument communication scheme has been implemented which can be used to autonomously alter the observing modes. We also outline the plans for in-flight cross-calibration, which will be essential to the joint data reduction and analysis.
Results: The RS instrument package on Solar Orbiter will carry out comprehensive measurements from the solar interior to the inner heliosphere. Thanks to the close coordination between the instrument teams and the European Space Agency, several challenges specific to the RS suite were identified and addressed in a timely manner. Title: Models and data analysis tools for the Solar Orbiter mission Authors: Rouillard, A. P.; Pinto, R. F.; Vourlidas, A.; De Groof, A.; Thompson, W. T.; Bemporad, A.; Dolei, S.; Indurain, M.; Buchlin, E.; Sasso, C.; Spadaro, D.; Dalmasse, K.; Hirzberger, J.; Zouganelis, I.; Strugarek, A.; Brun, A. S.; Alexandre, M.; Berghmans, D.; Raouafi, N. E.; Wiegelmann, T.; Pagano, P.; Arge, C. N.; Nieves-Chinchilla, T.; Lavarra, M.; Poirier, N.; Amari, T.; Aran, A.; Andretta, V.; Antonucci, E.; Anastasiadis, A.; Auchère, F.; Bellot Rubio, L.; Nicula, B.; Bonnin, X.; Bouchemit, M.; Budnik, E.; Caminade, S.; Cecconi, B.; Carlyle, J.; Cernuda, I.; Davila, J. M.; Etesi, L.; Espinosa Lara, F.; Fedorov, A.; Fineschi, S.; Fludra, A.; Génot, V.; Georgoulis, M. K.; Gilbert, H. R.; Giunta, A.; Gomez-Herrero, R.; Guest, S.; Haberreiter, M.; Hassler, D.; Henney, C. J.; Howard, R. A.; Horbury, T. S.; Janvier, M.; Jones, S. I.; Kozarev, K.; Kraaikamp, E.; Kouloumvakos, A.; Krucker, S.; Lagg, A.; Linker, J.; Lavraud, B.; Louarn, P.; Maksimovic, M.; Maloney, S.; Mann, G.; Masson, A.; Müller, D.; Önel, H.; Osuna, P.; Orozco Suarez, D.; Owen, C. J.; Papaioannou, A.; Pérez-Suárez, D.; Rodriguez-Pacheco, J.; Parenti, S.; Pariat, E.; Peter, H.; Plunkett, S.; Pomoell, J.; Raines, J. M.; Riethmüller, T. L.; Rich, N.; Rodriguez, L.; Romoli, M.; Sanchez, L.; Solanki, S. K.; St Cyr, O. C.; Straus, T.; Susino, R.; Teriaca, L.; del Toro Iniesta, J. C.; Ventura, R.; Verbeeck, C.; Vilmer, N.; Warmuth, A.; Walsh, A. P.; Watson, C.; Williams, D.; Wu, Y.; Zhukov, A. N. Bibcode: 2020A&A...642A...2R Altcode: Context. The Solar Orbiter spacecraft will be equipped with a wide range of remote-sensing (RS) and in situ (IS) instruments to record novel and unprecedented measurements of the solar atmosphere and the inner heliosphere. To take full advantage of these new datasets, tools and techniques must be developed to ease multi-instrument and multi-spacecraft studies. In particular the currently inaccessible low solar corona below two solar radii can only be observed remotely. Furthermore techniques must be used to retrieve coronal plasma properties in time and in three dimensional (3D) space. Solar Orbiter will run complex observation campaigns that provide interesting opportunities to maximise the likelihood of linking IS data to their source region near the Sun. Several RS instruments can be directed to specific targets situated on the solar disk just days before data acquisition. To compare IS and RS, data we must improve our understanding of how heliospheric probes magnetically connect to the solar disk.
Aims: The aim of the present paper is to briefly review how the current modelling of the Sun and its atmosphere can support Solar Orbiter science. We describe the results of a community-led effort by European Space Agency's Modelling and Data Analysis Working Group (MADAWG) to develop different models, tools, and techniques deemed necessary to test different theories for the physical processes that may occur in the solar plasma. The focus here is on the large scales and little is described with regards to kinetic processes. To exploit future IS and RS data fully, many techniques have been adapted to model the evolving 3D solar magneto-plasma from the solar interior to the solar wind. A particular focus in the paper is placed on techniques that can estimate how Solar Orbiter will connect magnetically through the complex coronal magnetic fields to various photospheric and coronal features in support of spacecraft operations and future scientific studies.
Methods: Recent missions such as STEREO, provided great opportunities for RS, IS, and multi-spacecraft studies. We summarise the achievements and highlight the challenges faced during these investigations, many of which motivated the Solar Orbiter mission. We present the new tools and techniques developed by the MADAWG to support the science operations and the analysis of the data from the many instruments on Solar Orbiter.
Results: This article reviews current modelling and tool developments that ease the comparison of model results with RS and IS data made available by current and upcoming missions. It also describes the modelling strategy to support the science operations and subsequent exploitation of Solar Orbiter data in order to maximise the scientific output of the mission.
Conclusions: The on-going community effort presented in this paper has provided new models and tools necessary to support mission operations as well as the science exploitation of the Solar Orbiter data. The tools and techniques will no doubt evolve significantly as we refine our procedure and methodology during the first year of operations of this highly promising mission. Title: The Solar Orbiter Science Activity Plan. Translating solar and heliospheric physics questions into action Authors: Zouganelis, I.; De Groof, A.; Walsh, A. P.; Williams, D. R.; Müller, D.; St Cyr, O. C.; Auchère, F.; Berghmans, D.; Fludra, A.; Horbury, T. S.; Howard, R. A.; Krucker, S.; Maksimovic, M.; Owen, C. J.; Rodríguez-Pacheco, J.; Romoli, M.; Solanki, S. K.; Watson, C.; Sanchez, L.; Lefort, J.; Osuna, P.; Gilbert, H. R.; Nieves-Chinchilla, T.; Abbo, L.; Alexandrova, O.; Anastasiadis, A.; Andretta, V.; Antonucci, E.; Appourchaux, T.; Aran, A.; Arge, C. N.; Aulanier, G.; Baker, D.; Bale, S. D.; Battaglia, M.; Bellot Rubio, L.; Bemporad, A.; Berthomier, M.; Bocchialini, K.; Bonnin, X.; Brun, A. S.; Bruno, R.; Buchlin, E.; Büchner, J.; Bucik, R.; Carcaboso, F.; Carr, R.; Carrasco-Blázquez, I.; Cecconi, B.; Cernuda Cangas, I.; Chen, C. H. K.; Chitta, L. P.; Chust, T.; Dalmasse, K.; D'Amicis, R.; Da Deppo, V.; De Marco, R.; Dolei, S.; Dolla, L.; Dudok de Wit, T.; van Driel-Gesztelyi, L.; Eastwood, J. P.; Espinosa Lara, F.; Etesi, L.; Fedorov, A.; Félix-Redondo, F.; Fineschi, S.; Fleck, B.; Fontaine, D.; Fox, N. J.; Gandorfer, A.; Génot, V.; Georgoulis, M. K.; Gissot, S.; Giunta, A.; Gizon, L.; Gómez-Herrero, R.; Gontikakis, C.; Graham, G.; Green, L.; Grundy, T.; Haberreiter, M.; Harra, L. K.; Hassler, D. M.; Hirzberger, J.; Ho, G. C.; Hurford, G.; Innes, D.; Issautier, K.; James, A. W.; Janitzek, N.; Janvier, M.; Jeffrey, N.; Jenkins, J.; Khotyaintsev, Y.; Klein, K. -L.; Kontar, E. P.; Kontogiannis, I.; Krafft, C.; Krasnoselskikh, V.; Kretzschmar, M.; Labrosse, N.; Lagg, A.; Landini, F.; Lavraud, B.; Leon, I.; Lepri, S. T.; Lewis, G. R.; Liewer, P.; Linker, J.; Livi, S.; Long, D. M.; Louarn, P.; Malandraki, O.; Maloney, S.; Martinez-Pillet, V.; Martinovic, M.; Masson, A.; Matthews, S.; Matteini, L.; Meyer-Vernet, N.; Moraitis, K.; Morton, R. J.; Musset, S.; Nicolaou, G.; Nindos, A.; O'Brien, H.; Orozco Suarez, D.; Owens, M.; Pancrazzi, M.; Papaioannou, A.; Parenti, S.; Pariat, E.; Patsourakos, S.; Perrone, D.; Peter, H.; Pinto, R. F.; Plainaki, C.; Plettemeier, D.; Plunkett, S. P.; Raines, J. M.; Raouafi, N.; Reid, H.; Retino, A.; Rezeau, L.; Rochus, P.; Rodriguez, L.; Rodriguez-Garcia, L.; Roth, M.; Rouillard, A. P.; Sahraoui, F.; Sasso, C.; Schou, J.; Schühle, U.; Sorriso-Valvo, L.; Soucek, J.; Spadaro, D.; Stangalini, M.; Stansby, D.; Steller, M.; Strugarek, A.; Štverák, Š.; Susino, R.; Telloni, D.; Terasa, C.; Teriaca, L.; Toledo-Redondo, S.; del Toro Iniesta, J. C.; Tsiropoula, G.; Tsounis, A.; Tziotziou, K.; Valentini, F.; Vaivads, A.; Vecchio, A.; Velli, M.; Verbeeck, C.; Verdini, A.; Verscharen, D.; Vilmer, N.; Vourlidas, A.; Wicks, R.; Wimmer-Schweingruber, R. F.; Wiegelmann, T.; Young, P. R.; Zhukov, A. N. Bibcode: 2020A&A...642A...3Z Altcode: 2020arXiv200910772Z Solar Orbiter is the first space mission observing the solar plasma both in situ and remotely, from a close distance, in and out of the ecliptic. The ultimate goal is to understand how the Sun produces and controls the heliosphere, filling the Solar System and driving the planetary environments. With six remote-sensing and four in-situ instrument suites, the coordination and planning of the operations are essential to address the following four top-level science questions: (1) What drives the solar wind and where does the coronal magnetic field originate?; (2) How do solar transients drive heliospheric variability?; (3) How do solar eruptions produce energetic particle radiation that fills the heliosphere?; (4) How does the solar dynamo work and drive connections between the Sun and the heliosphere? Maximising the mission's science return requires considering the characteristics of each orbit, including the relative position of the spacecraft to Earth (affecting downlink rates), trajectory events (such as gravitational assist manoeuvres), and the phase of the solar activity cycle. Furthermore, since each orbit's science telemetry will be downloaded over the course of the following orbit, science operations must be planned at mission level, rather than at the level of individual orbits. It is important to explore the way in which those science questions are translated into an actual plan of observations that fits into the mission, thus ensuring that no opportunities are missed. First, the overarching goals are broken down into specific, answerable questions along with the required observations and the so-called Science Activity Plan (SAP) is developed to achieve this. The SAP groups objectives that require similar observations into Solar Orbiter Observing Plans, resulting in a strategic, top-level view of the optimal opportunities for science observations during the mission lifetime. This allows for all four mission goals to be addressed. In this paper, we introduce Solar Orbiter's SAP through a series of examples and the strategy being followed. Title: An Optimization Principle for Computing Stationary MHD Equilibria with Solar Wind Flow Authors: Wiegelmann, Thomas; Neukirch, Thomas; Nickeler, Dieter H.; Chifu, Iulia Bibcode: 2020SoPh..295..145W Altcode: 2020arXiv201002945W In this work we describe a numerical optimization method for computing stationary MHD equilibria. The newly developed code is based on a nonlinear force-free optimization principle. We apply our code to model the solar corona using synoptic vector magnetograms as boundary condition. Below about two solar radii the plasma β and Alfvén Mach number MA are small and the magnetic field configuration of stationary MHD is basically identical to a nonlinear force-free field, whereas higher up in the corona (where β and MA are above unity) plasma and flow effects become important and stationary MHD and force-free configuration deviate significantly. The new method allows for the reconstruction of the coronal magnetic field further outwards than with potential field, nonlinear force-free or magnetostatic models. This way the model might help to provide the magnetic connectivity for joint observations of remote sensing and in-situ instruments on Solar Orbiter and Parker Solar Probe. Title: PMI: The Photospheric Magnetic Field Imager Authors: Staub, Jan; Fernandez-Rico, German; Gandorfer, Achim; Gizon, Laurent; Hirzberger, Johann; Kraft, Stefan; Lagg, Andreas; Schou, Jesper; Solanki, Sami K.; del Toro Iniesta, Jose Carlos; Wiegelmann, Thomas; Woch, Joachim Bibcode: 2020JSWSC..10...54S Altcode: We describe the design and the capabilities of the Photospheric Magnetic field Imager (PMI), a compact and lightweight vector magnetograph, which is being developed for ESA's Lagrange mission to the Lagrange L5 point. After listing the design requirements and give a scientific justification for them, we describe the technical implementation and the design solution capable of fulfilling these requirements. This is followed by a description of the hardware architecture as well as the operations principle. An outlook on the expected performance concludes the paper. Title: The Solar Orbiter EUI instrument: The Extreme Ultraviolet Imager Authors: Rochus, P.; Auchère, F.; Berghmans, D.; Harra, L.; Schmutz, W.; Schühle, U.; Addison, P.; Appourchaux, T.; Aznar Cuadrado, R.; Baker, D.; Barbay, J.; Bates, D.; BenMoussa, A.; Bergmann, M.; Beurthe, C.; Borgo, B.; Bonte, K.; Bouzit, M.; Bradley, L.; Büchel, V.; Buchlin, E.; Büchner, J.; Cabé, F.; Cadiergues, L.; Chaigneau, M.; Chares, B.; Choque Cortez, C.; Coker, P.; Condamin, M.; Coumar, S.; Curdt, W.; Cutler, J.; Davies, D.; Davison, G.; Defise, J. -M.; Del Zanna, G.; Delmotte, F.; Delouille, V.; Dolla, L.; Dumesnil, C.; Dürig, F.; Enge, R.; François, S.; Fourmond, J. -J.; Gillis, J. -M.; Giordanengo, B.; Gissot, S.; Green, L. M.; Guerreiro, N.; Guilbaud, A.; Gyo, M.; Haberreiter, M.; Hafiz, A.; Hailey, M.; Halain, J. -P.; Hansotte, J.; Hecquet, C.; Heerlein, K.; Hellin, M. -L.; Hemsley, S.; Hermans, A.; Hervier, V.; Hochedez, J. -F.; Houbrechts, Y.; Ihsan, K.; Jacques, L.; Jérôme, A.; Jones, J.; Kahle, M.; Kennedy, T.; Klaproth, M.; Kolleck, M.; Koller, S.; Kotsialos, E.; Kraaikamp, E.; Langer, P.; Lawrenson, A.; Le Clech', J. -C.; Lenaerts, C.; Liebecq, S.; Linder, D.; Long, D. M.; Mampaey, B.; Markiewicz-Innes, D.; Marquet, B.; Marsch, E.; Matthews, S.; Mazy, E.; Mazzoli, A.; Meining, S.; Meltchakov, E.; Mercier, R.; Meyer, S.; Monecke, M.; Monfort, F.; Morinaud, G.; Moron, F.; Mountney, L.; Müller, R.; Nicula, B.; Parenti, S.; Peter, H.; Pfiffner, D.; Philippon, A.; Phillips, I.; Plesseria, J. -Y.; Pylyser, E.; Rabecki, F.; Ravet-Krill, M. -F.; Rebellato, J.; Renotte, E.; Rodriguez, L.; Roose, S.; Rosin, J.; Rossi, L.; Roth, P.; Rouesnel, F.; Roulliay, M.; Rousseau, A.; Ruane, K.; Scanlan, J.; Schlatter, P.; Seaton, D. B.; Silliman, K.; Smit, S.; Smith, P. J.; Solanki, S. K.; Spescha, M.; Spencer, A.; Stegen, K.; Stockman, Y.; Szwec, N.; Tamiatto, C.; Tandy, J.; Teriaca, L.; Theobald, C.; Tychon, I.; van Driel-Gesztelyi, L.; Verbeeck, C.; Vial, J. -C.; Werner, S.; West, M. J.; Westwood, D.; Wiegelmann, T.; Willis, G.; Winter, B.; Zerr, A.; Zhang, X.; Zhukov, A. N. Bibcode: 2020A&A...642A...8R Altcode: Context. The Extreme Ultraviolet Imager (EUI) is part of the remote sensing instrument package of the ESA/NASA Solar Orbiter mission that will explore the inner heliosphere and observe the Sun from vantage points close to the Sun and out of the ecliptic. Solar Orbiter will advance the "connection science" between solar activity and the heliosphere.
Aims: With EUI we aim to improve our understanding of the structure and dynamics of the solar atmosphere, globally as well as at high resolution, and from high solar latitude perspectives.
Methods: The EUI consists of three telescopes, the Full Sun Imager and two High Resolution Imagers, which are optimised to image in Lyman-α and EUV (17.4 nm, 30.4 nm) to provide a coverage from chromosphere up to corona. The EUI is designed to cope with the strong constraints imposed by the Solar Orbiter mission characteristics. Limited telemetry availability is compensated by state-of-the-art image compression, onboard image processing, and event selection. The imposed power limitations and potentially harsh radiation environment necessitate the use of novel CMOS sensors. As the unobstructed field of view of the telescopes needs to protrude through the spacecraft's heat shield, the apertures have been kept as small as possible, without compromising optical performance. This led to a systematic effort to optimise the throughput of every optical element and the reduction of noise levels in the sensor.
Results: In this paper we review the design of the two elements of the EUI instrument: the Optical Bench System and the Common Electronic Box. Particular attention is also given to the onboard software, the intended operations, the ground software, and the foreseen data products.
Conclusions: The EUI will bring unique science opportunities thanks to its specific design, its viewpoint, and to the planned synergies with the other Solar Orbiter instruments. In particular, we highlight science opportunities brought by the out-of-ecliptic vantage point of the solar poles, the high-resolution imaging of the high chromosphere and corona, and the connection to the outer corona as observed by coronagraphs. Title: Eruptive-Impulsive Homologous M-class Flares Associated with Double-decker Flux Rope Configuration in Minisigmoid of NOAA 12673 Authors: Mitra, Prabir K.; Joshi, Bhuwan; Veronig, Astrid M.; Chandra, Ramesh; Dissauer, K.; Wiegelmann, Thomas Bibcode: 2020ApJ...900...23M Altcode: 2020arXiv200711810M We present a multiwavelength analysis of two homologous, short-lived, impulsive flares of GOES class M1.4 and M7.3 that occurred from a very localized minisigmoid region within the active region NOAA 12673 on 2017 September 7. Both flares were associated with initial jetlike plasma ejection that for a brief amount of time moved toward the east in a collimated manner before drastically changing direction toward the southwest. Nonlinear force-free field extrapolation reveals the presence of a compact double-decker flux rope configuration in the minisigmoid region prior to the flares. A set of open field lines originating near the active region that were most likely responsible for the anomalous dynamics of the erupted plasma gave the earliest indication of an emerging coronal hole near the active region. The horizontal field distribution suggests a rapid decay of the field above the active region, implying high proneness of the flux rope system toward eruption. In view of the low coronal double-decker flux ropes and compact extreme ultraviolet brightening beneath the filament, along with associated photospheric magnetic field changes, our analysis supports the combination of initial tether-cutting reconnection and subsequent torus instability for driving the eruption. Title: Magnetohydrostatic modeling of AR11768 based on a SUNRISE/IMaX vector magnetogram Authors: Zhu, X.; Wiegelmann, T.; Solanki, S. K. Bibcode: 2020A&A...640A.103Z Altcode: 2020arXiv200514332Z Context. High-resolution magnetic field measurements are routinely only done in the solar photosphere. Higher layers, such as the chromosphere and corona, can be modeled by extrapolating these photospheric magnetic field vectors upward. In the solar corona, plasma forces can be neglected and the Lorentz force vanishes. This is not the case in the upper photosphere and chromosphere where magnetic and nonmagnetic forces are equally important. One way to deal with this problem is to compute the plasma and magnetic field self-consistently, in lowest order with a magnetohydrostatic (MHS) model. The non-force-free layer is rather thin and MHS models require high-resolution photospheric magnetic field measurements as the lower boundary condition.
Aims: We aim to derive the magnetic field, plasma pressure, and density of AR11768 by applying the newly developed extrapolation technique to the SUNRISE/IMaX data embedded in SDO/HMI magnetogram.
Methods: We used an optimization method for the MHS modeling. The initial conditions consist of a nonlinear force-free field (NLFFF) and a gravity-stratified atmosphere. During the optimization procedure, the magnetic field, plasma pressure, and density are computed self-consistently.
Results: In the non-force-free layer, which is spatially resolved by the new code, Lorentz forces are effectively balanced by the gas pressure gradient force and gravity force. The pressure and density are depleted in strong field regions, which is consistent with observations. Denser plasma, however, is also observed at some parts of the active region edges. In the chromosphere, the fibril-like plasma structures trace the magnetic field nicely. Bright points in SUNRISE/SuFI 3000 Å images are often accompanied by the plasma pressure and electric current concentrations. In addition, the average of angle between MHS field lines and the selected chromospheric fibrils is 11.8°, which is smaller than those computed from the NLFFF model (15.7°) and linear MHS model (20.9°). This indicates that the MHS solution provides a better representation of the magnetic field in the chromosphere. Title: Magnetohydrostatic modelling of the solar atmosphere: Test and application Authors: Zhu, Xiaoshuai; Wiegelmann, Thomas Bibcode: 2020EGUGA..22.2695Z Altcode: Both magnetic field and plasma play important roles in activities in the solar atmosphere. Unfortunately only the magnetic fields in the photosphere are routinely measured precisely. We aim to extrapolate these photospheric vector magnetograms upwards into the solar atmosphere. In this work we are mainly interested in reconstructing the upper solar photosphere and chromosphere. In these layers magnetic and non-magnetic forces are equally important. Consequently we have to compute an equilibrium of plasma and magnetic forces with a magnetohydrostatic model. A optimization approach which minimize a functional defined by the magnetohydrostatic equations is used in the model. In this talk/poster, I will present a strict test of the new code with a radiative MHD simulation and its first application to a high resolution vector magnetogram measured by SUNRISE/IMaX. Title: Relative magnetic helicity dissipation during the major flares Authors: Wang, Quan; Yang, Shangbin; Zhang, Mei; Wiegelmann, Thomas Bibcode: 2020EGUGA..2218835W Altcode: Magnetic helicity is conserved in ideal magnetic fluid and is still approximately conserved in the process of fast magnetic reconnection when the magnetic Reynolds number is large enough. We can derive the magnetic helicity injecting into corona from the magnetic helicity flux through photoshpere. A statistical research is carried out to investigate the dissipation of magnetic helicity during the major flares. We choose 69M-up flares from 16 major flare-productive active regions in 24th cycle to research the helicity in corona. Among these flares, 19 is X-up flares. We utilize Differential Affine Velocity Estimator for Vector Magnetograms (DAVE4VM) and 12-min successive vector magnetograms from Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) to derive the flux of magnetic helicity through photosphere. At the same time, we extrapolate the vector magnetic field in corona to calculate the relative helicity by the suppose of Non-linear Force Free Field (NLFFF). The calculation window is 12-18 minutes before and after flares. A well correlation is shown between the magnetic free energy and magnetic helicity, the threshold of triggering M-up flare is the change of magnetic helicity above 2×1042Mx2 and the change of magnetic free energy above 3 × 1031erg . Considering one fifth of magnetic helicity injecting into corona, the dissipation of magnetic helicity during the flares is 6-7 %, which is corresponding to the result of previous numerical simulation results, which strongly support that the magnetic helicity is approximate conserved during the major flares. Title: An optimization principle for computing stationary MHD equilibria with solar wind flow Authors: Wiegelmann, Thomas; Neukirch, Thomas; Nickeler, Dieter; Chifu, Iulia Bibcode: 2020EGUGA..22.3029W Altcode: Knowledge about the magnetic field and plasma environment is importantfor almost all physical processes in the solar atmosphere. Precisemeasurements of the magnetic field vector are done routinely only inthe photosphere, e.g. by SDO/HMI. These measurements are used asboundary condition for modelling the solar chromosphere and corona,whereas some model assumptions have to be made. In the low-plasma-betacorona the Lorentz-force vanishes and the magnetic fieldis reconstructed with a nonlinear force-free model. In the mixed-betachromosphere plasma forces have to be taken into account with thehelp of a magnetostatic model. And finally for modelling the globalcorona far beyond the source surface the solar wind flow has tobe incorporated within a stationary MHD model.To do so, we generalize a nonlinear force-free and magneto-static optimizationcode by the inclusion of a field aligned compressible plasma flow.Applications are the implementation of the solar wind onglobal scale. This allows to reconstruct the coronal magnetic field furtheroutwards than with potential field, nonlinear force-free and magneto-static models.This way the model might help in future to provide the magnetic connectivityfor joint observations of remote sensing and in-situ instruments on SolarOrbiter and Parker Solar Probe. Title: The SO/PHI instrument on Solar Orbiter and its data products Authors: Solanki, Sami K.; Hirzberger, Johann; Wiegelmann, Thomas; Gandorfer, Achim; Woch, Joachim; del Toro Iniesta, José Carlos Bibcode: 2020EGUGA..2217904S Altcode: A central instrument of Solar Orbiter is the Polarimetric and Helioseismic Imager, SO/PHI. It is a vector magnetograph that also provides data for helioseismology. SO/PHI is composed of two telescopes, a full-disk telescope (FDT) and a high-resolution telescope (HRT). The HRT will observe at a resolution as high as 200 km on the solar surface, while the FDT will obtain the magnetic field and velocity of the full solar disc whenever it observes. SO/PHI will be the first solar spectro-polarimeter to leave the Sun-Earth line, opening up some unique perspectives, such as the first detailed view of the solar poles. This will allow not just a more precise and exact mapping of the polar magnetic field than possible so far, but will also enable us to follow the dynamics of individual magnetic features at high latitudes and to determine solar surface and sub-surface flows right up to the poles. In addition to its standard data products (vector magnetograms, continuum images and maps of the line-of-sight velocity), SO/PHI will also provide higher-level data products. These will include synoptic charts, local magnetic field extrapolations starting from HRT data and global magnetic field extrapolations (from FDT data) with potential field source-surface (PFSS) models and possibly also non-potential models such as NLFFF (non-linear force-free fields), magnetostatics and MHD. The SO/PHI data products will usefully complement the data taken by other instruments on Solar Orbiter and on Solar Probe, as well as instruments on the ground or in Earth orbit. Combining with observations by Earth-based and near-Earth telescopes will enable new types of investigations, such as stereoscopic polarimetry and stereoscopic helioseismology. Title: Analytical Three-dimensional Magnetohydrostatic Equilibrium Solutions for Magnetic Field Extrapolation Allowing a Transition from Non-force-free to Force-free Magnetic Fields Authors: Neukirch, Thomas; Wiegelmann, Thomas Bibcode: 2019SoPh..294..171N Altcode: 2019arXiv191111084N For the extrapolation of magnetic fields into the solar corona from measurements taken in the photosphere (or chromosphere) force-free magnetic fields are typically used. This does not take into account that the lower layers of the solar atmosphere are not force-free. While some numerical extrapolation methods using magnetohydrostatic magnetic fields have been suggested, a complementary and numerically comparatively cheap method is to use analytical magnetohydrostatic equilibria to extrapolate the magnetic field. In this paper, we present a new family of solutions for a special class of analytical three-dimensional magnetohydrostatic equilibria, which can be of use for such magnetic field extrapolation. The new solutions allow for the more flexible modeling of a transition from non-force-free to (linear) force-free magnetic fields. In particular, the height and width of the region where this transition takes place can be specified by choosing appropriate model parameters. Title: Testing magnetohydrostatic extrapolation with radiative MHD simulation of a solar flare Authors: Zhu, X.; Wiegelmann, T. Bibcode: 2019A&A...631A.162Z Altcode: 2019arXiv191003523Z Context. On the sun, the magnetic field vector is measured routinely solely in the photosphere. By using these photospheric measurements as a boundary condition, we developed magnetohydrostatic (MHS) extrapolation to model the solar atmosphere. The model makes assumptions about the relative importance of magnetic and non-magnetic forces. While the solar corona is force-free, this is not the case with regard to the photosphere and chromosphere.
Aims: The model has previously been tested with an exact equilibria. Here we present a more challenging and more realistic test of our model with the radiative magnetohydrodynamic simulation of a solar flare.
Methods: By using the optimization method, the MHS model computes the magnetic field, plasma pressure and density self-consistently. The nonlinear force-free field (NLFFF) and gravity-stratified atmosphere along the field line are assumed as the initial conditions for optimization.
Results: Compared with the NLFFF, the MHS model provides an improved magnetic field not only in magnitude and direction, but also in magnetic connectivity. In addition, the MHS model is capable of recovering the main structure of plasma in the photosphere and chromosphere. Title: CME-HSS Interaction and Characteristics Tracked from Sun to Earth Authors: Heinemann, Stephan G.; Temmer, Manuela; Farrugia, Charles J.; Dissauer, Karin; Kay, Christina; Wiegelmann, Thomas; Dumbović, Mateja; Veronig, Astrid M.; Podladchikova, Tatiana; Hofmeister, Stefan J.; Lugaz, Noé; Carcaboso, Fernando Bibcode: 2019SoPh..294..121H Altcode: 2019arXiv190810161H In a thorough study, we investigate the origin of a remarkable plasma and magnetic field configuration observed in situ on June 22, 2011, near L1, which appears to be a magnetic ejecta (ME) and a shock signature engulfed by a solar wind high-speed stream (HSS). We identify the signatures as an Earth-directed coronal mass ejection (CME), associated with a C7.7 flare on June 21, 2011, and its interaction with a HSS, which emanates from a coronal hole (CH) close to the launch site of the CME. The results indicate that the major interaction between the CME and the HSS starts at a height of 1.3 R⊙ up to 3 R⊙. Over that distance range, the CME undergoes a strong north-eastward deflection of at least 30∘ due to the open magnetic field configuration of the CH. We perform a comprehensive analysis for the CME-HSS event using multi-viewpoint data (from the Solar TErrestrial RElations Observatories, the Solar and Heliospheric Observatory and the Solar Dynamics Observatory), and combined modeling efforts (nonlinear force-free field modeling, Graduated Cylindrical Shell CME modeling, and the Forecasting a CME's Altered Trajectory - ForeCAT model). We aim at better understanding its early evolution and interaction process as well as its interplanetary propagation and related in situ signatures, and finally the resulting impact on the Earth's magnetosphere. Title: The Magnetic Properties of Heating Events on High-temperature Active-region Loops Authors: Ugarte-Urra, Ignacio; Crump, Nicholas A.; Warren, Harry P.; Wiegelmann, Thomas Bibcode: 2019ApJ...877..129U Altcode: 2019arXiv190411976U Understanding the relationship between the magnetic field and coronal heating is one of the central problems of solar physics. However, studies of the magnetic properties of impulsively heated loops have been rare. We present results from a study of 34 evolving coronal loops observed in the Fe XVIII line component of 94 Å filter images obtained by the Atmospheric Imaging Assembly (AIA)/Solar Dynamics Observatory (SDO) from three active regions with different magnetic conditions. We show that the peak intensity per unit cross section of the loops depends on their individual magnetic and geometric properties. The intensity scales proportionally to the average field strength along the loop (B avg) and inversely with the loop length (L) for a combined dependence of {({B}avg}/L)}0.52+/- 0.13. These loop properties are inferred from magnetic extrapolations of the photospheric Helioseismic and Magnetic Imager (HMI)/SDO line-of-sight and vector magnetic field in three approximations: potential and two nonlinear force-free (NLFF) methods. Through hydrodynamic modeling (enthalpy-based thermal evolution loop (EBTEL) model) we show that this behavior is compatible with impulsively heated loops with a volumetric heating rate that scales as {ɛ }{{H}}∼ {B}avg}0.3+/- 0.2/{L}0.2{+/- 0.10.2}. Title: Linking the Sun to the heliosphere using composition data and modelling: coronal jets as a test case Authors: Wimmer-Schweingruber, Robert F.; Parenti, Susanna; Del Zanna, G.; Edmondson, J.; Giunta, A.; Hansteen, V. H.; Higginson, A.; Lepri, S.; Laming, M.; Lynch, B. J.; von Steiger, R. E.; Wiegelmann, T.; Zambrana Prado, N. Bibcode: 2019shin.confE.231W Altcode: Understanding the formation and evolution of the solar wind is still a priority in the Solar and Heliospheric communities. We expect a significant progress in terms of observations with the upcoming Solar Orbiter mission (launch in 2020), which will provide detailed in-situ measurements of the solar wind and several remote-sensing observations. However, real progress will only be possible if we improve our understanding of the physical link between what measured in-situ and its source regions on the Sun. In this respect, the plasma chemical and charge-state compositions are considered good diagnostic tools. In this paper we present results obtained from an extensive team work aiming at providing solid diagnostics for linking the in-situ and the remote sensing measurements. For our test cases, we selected two periods when a single active region produced, close to its sunspot, jets which had a counterpart signature in the Heliosphere in the form of type-III radio bursts. These jets therefore marked magnetically open regions expanding in the heliosphere. Firstly, we looked for signatures of the open field associated with the active regions in in-situ data from ACE and WIND, finding potential tracers. Secondly, we studied the magnetic topology of the full Sun and Heliosphere with extrapolations of photospheric data and MHD modeling. We found that the open field area is consistent with the source and evolution of the jets, as observed with EUV imagers (SDO/AIA, STEREO/EUVI). Thirdly, we analysed remote sensing EUV spectroscopic observations to measure the plasma conditions (densities, temperatures and chemical composition) whenever available. We then modeled the solar wind and charge state evolution with the solar distance along the open fields to establish a link between the in-situ signatures and the remote sensing observations. We discuss the various difficulties associated with such studies, and highlight how Solar Orbiter measurements can improve them. Title: Nonlinear magnetohydrostatic modeling of an active region based on a SUNRISE/IMaX vector magnetogram Authors: Zhu, Xiaoshuai; Wiegelmann, Thomas Bibcode: 2019EGUGA..21.3986Z Altcode: For modelling the upper solar photosphere and chromosphere, plasma forces are important. Therefore a nonlinear magnetohydrostatic (NLMHS) model is a better approximation of the physical state in these layers than a nonlinear force-free (NLFF) model. The latter one is only valid in the low plasma-beta corona. The magnetohydrostatic model computes self-consistently the magnetic field and plasma distribution. We intensively tested the new code with exact equilibria (Zhu & Wiegelmann, 2018, ApJ, 866, 130) and the NLMHS code has been able to meaningfully recover the plasma density, pressure and magnetic field. Here we present a first application of our new code to an active region (AR 11768), which was observed by IMaX during the second flight of the balloon-borne SUNRISE solar observatory in 2013. The high spatial resolution IMaX vector magnetogram was embedded in SDO/HMI data to cover the entire active region. We were able to model the non-force-free layer in the lower atmosphere. Our model shows strongly localized electric currents and Lorentz forces and self-consistently the corresponding plasma distribution. Such features require the use of a NLMHS model and cannot be reconstructed with linear MHS or NLFFF models. Title: Global coronal magnetic field modelling for Solar Orbiter Authors: Wiegelmann, Thomas; Inhester, Bernd; Chifu, Iulia Bibcode: 2019EGUGA..21.3311W Altcode: Modelling the solar coronal magnetic field in 3D is an interesting research topic on its own right. But field models are also important for combining the analysis of data from remote sensing and in-situ instrument on Solar Orbiter by providing the magnetic connectivity. A well tested and frequently applied method is to use photospheric field measurements, e.g. synoptic vector magnetograms from SDO/HMI, and extrapolate them into the solar corona under the assumption that the field is force-free. We do this by a nonlinear force-free code, based on minimizing a functional. The method is very flexible and allows to incorporate loop shapes from coronal images. Ongoing projects are to go beyond the force-free approximation, which is necessary in the outer solar corona beyond the source surface. A first step are magneto-static extrapolations (including plasma pressure gradient and gravity force). In a second step we compute stationary MHD-equilibria which additionally consider the solar wind flow. Title: Reconstructing nonlinear force-free fields by a constrained optimization Authors: Nasiri, S.; Wiegelmann, T. Bibcode: 2019JASTP.182..181N Altcode: It seems that the potential and linear force-free magnetic fields are inadequate to represent the observed magnetic events occurring in different regions of the solar corona. To reconstruct the nonlinear force-free fields from the solar surface magnetograms, various analytical and numerical methods have already been examined by different authors. Here, using the Lagrange multiplier technique, a constrained optimization approach for reconstructing force-free magnetic fields is proposed. In the optimization procedure the solenoidal property is considered as a constraint on the initial non-force-free field. In the Wheatland et al. (2000) method as an unconstrained optimization, both solenoidal and force-free conditions are fulfilled approximately. In contrast, the constrained optimization method, up to numerical precision, leads us to a nearly force-free magnetic field with exactly zero divergence. The solutions are obtained and tested by the Low and Lou (1990) semi-analytic solution. Title: On the extrapolation of magneto-hydro-static equilibria on the sun: model and tests Authors: Zhu, Xiaoshuai; Wiegelmann, Thomas Bibcode: 2018csc..confE.133Z Altcode: Modeling the interface region between solar photosphere and corona is challenging, because the relative importance of magnetic and plasma forces change by several orders of magnitude. While the solar corona can be modeled by the force-free assumption, we need to take care about plasma forces (pressure gradient and gravity) in photosphere and chromosphere, here within the magneto-hydro-static (MHS) model. We solve the MHS equations with the help of an optimization principle and use vector magnetogram as boundary condition. Positive pressure and density are ensured by replacing them with two new basic variables. The Lorentz force during optimization is used to update the plasma pressure on the bottom boundary, which makes the new extrapolation works even without pressure measurement on the photosphere. Our code is tested by using a linear MHS model as reference. From the detailed analyses, we find that the newly developed MHS extrapolation not only recovers the plasma distribution at high accuracy. but also gives the better fit magnetic field than the nonlinear force-free extrapolation. Title: Observations of solar chromospheric heating at sub-arcsec spatial resolution Authors: Smitha, H. N.; Chitta, L. P.; Wiegelmann, T.; Solanki, S. K. Bibcode: 2018A&A...617A.128S Altcode: 2018arXiv180701078S A wide variety of phenomena such as gentle but persistent brightening, dynamic slender features (∼100 km), and compact (∼1″) ultraviolet (UV) bursts are associated with the heating of the solar chromosphere. High spatio-temporal resolution is required to capture the finer details of the likely magnetic reconnection-driven, rapidly evolving bursts. Such observations are also needed to reveal their similarities to large-scale flares, which are also thought to be reconnection driven, and more generally their role in chromospheric heating. Here we report observations of chromospheric heating in the form of a UV burst obtained with the balloon-borne observatory SUNRISE. The observed burst displayed a spatial morphology similar to that of a large-scale solar flare with a circular ribbon. While the co-temporal UV observations at 1.5″ spatial resolution and 24 s cadence from the Solar Dynamics Observatory showed a compact brightening, the SUNRISE observations at diffraction-limited spatial resolution of 0.1″ at 7 s cadence revealed a dynamic substructure of the burst that it is composed of an extended ribbon-like feature and a rapidly evolving arcade of thin (∼0.1″) magnetic loop-like features, similar to post-flare loops. Such a dynamic substructure reveals the small-scale nature of chromospheric heating in these bursts. Furthermore, based on magnetic field extrapolations, this heating event is associated with a complex fan-spine magnetic topology. Our observations strongly hint at a unified picture of magnetic heating in the solar atmosphere from some large-scale flares to small-scale bursts, all associated with such a magnetic topology.

The movie associated to Fig. 2 is available at https://www.aanda.org/ Title: On the Extrapolation of Magnetohydrostatic Equilibria on the Sun Authors: Zhu, Xiaoshuai; Wiegelmann, Thomas Bibcode: 2018ApJ...866..130Z Altcode: 2018arXiv180902168Z Modeling the interface region between the solar photosphere and corona is challenging because the relative importance of magnetic and plasma forces change by several orders of magnitude. While the solar corona can be modeled by the force-free assumption, we need to take plasma forces into account (pressure gradient and gravity) in photosphere and chromosphere, here within the magnetohydrostatic (MHS) model. We solve the MHS equations with the help of an optimization principle and use vector magnetogram as the boundary condition. Positive pressure and density are ensured by replacing them with two new basic variables. The Lorentz force during optimization is used to update the plasma pressure on the bottom boundary, which makes the new extrapolation work even without pressure measurements on the photosphere. Our code is tested using a linear MHS model as reference. From the detailed analyses, we find that the newly developed MHS extrapolation recovers the reference model at high accuracy. The MHS extrapolation is, however, numerically more expensive than the nonlinear force-free field extrapolation and consequently one should limit their application to regions where plasma forces become important, e.g., in a layer of about 2 Mm above the photosphere. Title: Global Non-Potential Magnetic Models of the Solar Corona During the March 2015 Eclipse Authors: Yeates, Anthony R.; Amari, Tahar; Contopoulos, Ioannis; Feng, Xueshang; Mackay, Duncan H.; Mikić, Zoran; Wiegelmann, Thomas; Hutton, Joseph; Lowder, Christopher A.; Morgan, Huw; Petrie, Gordon; Rachmeler, Laurel A.; Upton, Lisa A.; Canou, Aurelien; Chopin, Pierre; Downs, Cooper; Druckmüller, Miloslav; Linker, Jon A.; Seaton, Daniel B.; Török, Tibor Bibcode: 2018SSRv..214...99Y Altcode: 2018arXiv180800785Y Seven different models are applied to the same problem of simulating the Sun's coronal magnetic field during the solar eclipse on 2015 March 20. All of the models are non-potential, allowing for free magnetic energy, but the associated electric currents are developed in significantly different ways. This is not a direct comparison of the coronal modelling techniques, in that the different models also use different photospheric boundary conditions, reflecting the range of approaches currently used in the community. Despite the significant differences, the results show broad agreement in the overall magnetic topology. Among those models with significant volume currents in much of the corona, there is general agreement that the ratio of total to potential magnetic energy should be approximately 1.4. However, there are significant differences in the electric current distributions; while static extrapolations are best able to reproduce active regions, they are unable to recover sheared magnetic fields in filament channels using currently available vector magnetogram data. By contrast, time-evolving simulations can recover the filament channel fields at the expense of not matching the observed vector magnetic fields within active regions. We suggest that, at present, the best approach may be a hybrid model using static extrapolations but with additional energization informed by simplified evolution models. This is demonstrated by one of the models. Title: Toward a Quantitative Comparison of Magnetic Field Extrapolations and Observed Coronal Loops Authors: Warren, Harry P.; Crump, Nicholas A.; Ugarte-Urra, Ignacio; Sun, Xudong; Aschwanden, Markus J.; Wiegelmann, Thomas Bibcode: 2018ApJ...860...46W Altcode: 2018arXiv180500281W It is widely believed that loops observed in the solar atmosphere trace out magnetic field lines. However, the degree to which magnetic field extrapolations yield field lines that actually do follow loops has yet to be studied systematically. In this paper, we apply three different extrapolation techniques—a simple potential model, a nonlinear force-free (NLFF) model based on photospheric vector data, and an NLFF model based on forward fitting magnetic sources with vertical currents—to 15 active regions that span a wide range of magnetic conditions. We use a distance metric to assess how well each of these models is able to match field lines to the 12202 loops traced in coronal images. These distances are typically 1″-2″. We also compute the misalignment angle between each traced loop and the local magnetic field vector, and find values of 5°-12°. We find that the NLFF models generally outperform the potential extrapolation on these metrics, although the differences between the different extrapolations are relatively small. The methodology that we employ for this study suggests a number of ways that both the extrapolations and loop identification can be improved. Title: Global non-potential coronal magnetic field models Authors: Wiegelmann, Thomas Bibcode: 2018EGUGA..20.1787W Altcode: Knowledge of the Sun's large scale magnetic field is an important research topic on its own right, but also important to guide future space missions like Parker Solar Probe and Solar Orbiter. To combine remote sensing and in-situ measurements from these mission, information regarding the magnetic connectivity is essential. Within an international collaboration we compared several static and evolutionary corona models: non-linear force-free, magneto-static, evolutionary magneto- frictional, full MHD and zero-beta MHD. The models agree on the amount of open flux, streamer location and broad magnetic topology. They disagree on the shape of helmet streamers and electric currents. Static models are better in active regions, evolutionary models better to model filaments. Our advice is to combine static extrapolations with energisation from evolutionary models. Title: Magnetic Braids in Eruptions of a Spiral Structure in the Solar Atmosphere Authors: Huang, Zhenghua; Xia, Lidong; Nelson, Chris J.; Liu, Jiajia; Wiegelmann, Thomas; Tian, Hui; Klimchuk, James A.; Chen, Yao; Li, Bo Bibcode: 2018ApJ...854...80H Altcode: 2018arXiv180105967H We report on high-resolution imaging and spectral observations of eruptions of a spiral structure in the transition region, which were taken with the Interface Region Imaging Spectrograph, and the Atmospheric Imaging Assembly (AIA) and the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). The eruption coincided with the appearance of two series of jets, with velocities comparable to the Alfvén speeds in their footpoints. Several pieces of evidence of magnetic braiding in the eruption are revealed, including localized bright knots, multiple well-separated jet threads, transition region explosive events, and the fact that all three of these are falling into the same locations within the eruptive structures. Through analysis of the extrapolated 3D magnetic field in the region, we found that the eruptive spiral structure corresponded well to locations of twisted magnetic flux tubes with varying curl values along their lengths. The eruption occurred where strong parallel currents, high squashing factors, and large twist numbers were obtained. The electron number density of the eruptive structure is found to be ∼3 × 1012 cm-3, indicating that a significant amount of mass could be pumped into the corona by the jets. Following the eruption, the extrapolations revealed a set of seemingly relaxed loops, which were visible in the AIA 94 Å channel, indicating temperatures of around 6.3 MK. With these observations, we suggest that magnetic braiding could be part of the mechanisms explaining the formation of solar eruption and the mass and energy supplement to the corona. Title: Coronal Magnetic Field Models Authors: Wiegelmann, Thomas; Petrie, Gordon J. D.; Riley, Pete Bibcode: 2018smf..book..249W Altcode: No abstract at ADS Title: Magnetic topological analysis of coronal bright points Authors: Galsgaard, K.; Madjarska, M. S.; Moreno-Insertis, F.; Huang, Z.; Wiegelmann, T. Bibcode: 2017A&A...606A..46G Altcode: 2017arXiv170704174G Context. We report on the first of a series of studies on coronal bright points which investigate the physical mechanism that generates these phenomena.
Aims: The aim of this paper is to understand the magnetic-field structure that hosts the bright points.
Methods: We use longitudinal magnetograms taken by the Solar Optical Telescope with the Narrowband Filter Imager. For a single case, magnetograms from the Helioseismic and Magnetic Imager were added to the analysis. The longitudinal magnetic field component is used to derive the potential magnetic fields of the large regions around the bright points. A magneto-static field extrapolation method is tested to verify the accuracy of the potential field modelling. The three dimensional magnetic fields are investigated for the presence of magnetic null points and their influence on the local magnetic domain.
Results: In nine out of ten cases the bright point resides in areas where the coronal magnetic field contains an opposite polarity intrusion defining a magnetic null point above it. We find that X-ray bright points reside, in these nine cases, in a limited part of the projected fan-dome area, either fully inside the dome or expanding over a limited area below which typically a dominant flux concentration resides. The tenth bright point is located in a bipolar loop system without an overlying null point.
Conclusions: All bright points in coronal holes and two out of three bright points in quiet Sun regions are seen to reside in regions containing a magnetic null point. An as yet unidentified process(es) generates the brigh points in specific regions of the fan-dome structure.

The movies are available at http://www.aanda.org Title: Coronal Magnetic Field Models Authors: Wiegelmann, Thomas; Petrie, Gordon J. D.; Riley, Pete Bibcode: 2017SSRv..210..249W Altcode: 2015SSRv..tmp...75W Coronal magnetic field models use photospheric field measurements as boundary condition to model the solar corona. We review in this paper the most common model assumptions, starting from MHD-models, magnetohydrostatics, force-free and finally potential field models. Each model in this list is somewhat less complex than the previous one and makes more restrictive assumptions by neglecting physical effects. The magnetohydrostatic approach neglects time-dependent phenomena and plasma flows, the force-free approach neglects additionally the gradient of the plasma pressure and the gravity force. This leads to the assumption of a vanishing Lorentz force and electric currents are parallel (or anti-parallel) to the magnetic field lines. Finally, the potential field approach neglects also these currents. We outline the main assumptions, benefits and limitations of these models both from a theoretical (how realistic are the models?) and a practical viewpoint (which computer resources to we need?). Finally we address the important problem of noisy and inconsistent photospheric boundary conditions and the possibility of using chromospheric and coronal observations to improve the models. Title: The Plasma Parameters and Geometry of Cool and Warm Active Region Loops Authors: Xie, Haixia; Madjarska, Maria S.; Li, Bo; Huang, Zhenghua; Xia, Lidong; Wiegelmann, Thomas; Fu, Hui; Mou, Chaozhou Bibcode: 2017ApJ...842...38X Altcode: 2017arXiv170502564X How the solar corona is heated to high temperatures remains an unsolved mystery in solar physics. In the present study we analyze observations of 50 whole active region loops taken with the Extreme-ultraviolet Imaging Spectrometer on board the Hinode satellite. Eleven loops were classified as cool loops (<1 MK) and 39 as warm loops (1-2 MK). We study their plasma parameters, such as densities, temperatures, filling factors, nonthermal velocities, and Doppler velocities. We combine spectroscopic analysis with linear force-free magnetic field extrapolation to derive the 3D structure and positioning of the loops, their lengths and heights, and the magnetic field strength along the loops. We use density-sensitive line pairs from Fe xii, Fe xiii, Si x, and Mg vii ions to obtain electron densities by taking special care of intensity background subtraction. The emission measure loci method is used to obtain the loop temperatures. We find that the loops are nearly isothermal along the line of sight. Their filling factors are between 8% and 89%. We also compare the observed parameters with the theoretical Rosner-Tucker-Vaiana (RTV) scaling law. We find that most of the loops are in an overpressure state relative to the RTV predictions. In a follow-up study, we will report a heating model of a parallel-cascade-based mechanism and will compare the model parameters with the loop plasma and structural parameters derived here. Title: Coronal magnetic field extrapolation Authors: Wiegelmann, Thomas Bibcode: 2017EGUGA..19.2788W Altcode: The solar corona is structured by the solar magnetic field and to understand physical processes in the solar corona it is key to get information about the coronal magnetic field. Due to the low plasma beta of the coronal plasma, the magnetic forces dominate and other plasma forces can be neglected in lowest order. In this approach the Lorentz-force vanishes and the magnetic field is force-free. Unfortunately we do not have routine direct measurements of the magnetic field in the solar corona, but in the photosphere, e.g. from SDO/HMI. These photospheric magnetic field measurements are then extrapolated into the higher layers of the solar atmosphere. Because of the high conductivity of the coronal plasma, EUV-images, e.g. from SDO/AIA or STEREO/SECCHI, outline the magnetic field lines and these coronal images are used to validate and improve coronal magnetic field models. The models provide the 3D-magnetic field structure and can be used to compute the free magnetic energy and helicity. Both quantities are important to understand the onset of coronal eruptions. Title: Slender Ca II H Fibrils Mapping Magnetic Fields in the Low Solar Chromosphere Authors: Jafarzadeh, S.; Rutten, R. J.; Solanki, S. K.; Wiegelmann, T.; Riethmüller, T. L.; van Noort, M.; Szydlarski, M.; Blanco Rodríguez, J.; Barthol, P.; del Toro Iniesta, J. C.; Gandorfer, A.; Gizon, L.; Hirzberger, J.; Knölker, M.; Martínez Pillet, V.; Orozco Suárez, D.; Schmidt, W. Bibcode: 2017ApJS..229...11J Altcode: 2016arXiv161003104J A dense forest of slender bright fibrils near a small solar active region is seen in high-quality narrowband Ca II H images from the SuFI instrument onboard the Sunrise balloon-borne solar observatory. The orientation of these slender Ca II H fibrils (SCF) overlaps with the magnetic field configuration in the low solar chromosphere derived by magnetostatic extrapolation of the photospheric field observed with Sunrise/IMaX and SDO/HMI. In addition, many observed SCFs are qualitatively aligned with small-scale loops computed from a novel inversion approach based on best-fit numerical MHD simulation. Such loops are organized in canopy-like arches over quiet areas that differ in height depending on the field strength near their roots. Title: Magneto-static Modeling from Sunrise/IMaX: Application to an Active Region Observed with Sunrise II Authors: Wiegelmann, T.; Neukirch, T.; Nickeler, D. H.; Solanki, S. K.; Barthol, P.; Gandorfer, A.; Gizon, L.; Hirzberger, J.; Riethmüller, T. L.; van Noort, M.; Blanco Rodríguez, J.; Del Toro Iniesta, J. C.; Orozco Suárez, D.; Schmidt, W.; Martínez Pillet, V.; Knölker, M. Bibcode: 2017ApJS..229...18W Altcode: 2017arXiv170101458N; 2017arXiv170101458W Magneto-static models may overcome some of the issues facing force-free magnetic field extrapolations. So far they have seen limited use and have faced problems when applied to quiet-Sun data. Here we present a first application to an active region. We use solar vector magnetic field measurements gathered by the IMaX polarimeter during the flight of the Sunrise balloon-borne solar observatory in 2013 June as boundary conditions for a magneto-static model of the higher solar atmosphere above an active region. The IMaX data are embedded in active region vector magnetograms observed with SDO/HMI. This work continues our magneto-static extrapolation approach, which was applied earlier to a quiet-Sun region observed with Sunrise I. In an active region the signal-to-noise-ratio in the measured Stokes parameters is considerably higher than in the quiet-Sun and consequently the IMaX measurements of the horizontal photospheric magnetic field allow us to specify the free parameters of the model in a special class of linear magneto-static equilibria. The high spatial resolution of IMaX (110-130 km, pixel size 40 km) enables us to model the non-force-free layer between the photosphere and the mid-chromosphere vertically by about 50 grid points. In our approach we can incorporate some aspects of the mixed beta layer of photosphere and chromosphere, e.g., taking a finite Lorentz force into account, which was not possible with lower-resolution photospheric measurements in the past. The linear model does not, however, permit us to model intrinsic nonlinear structures like strongly localized electric currents. Title: Electric Current Filamentation Induced by 3D Plasma Flows in the Solar Corona Authors: Nickeler, Dieter H.; Wiegelmann, Thomas; Karlický, Marian; Kraus, Michaela Bibcode: 2017ApJ...837..104N Altcode: 2017arXiv170203986N Many magnetic structures in the solar atmosphere evolve rather slowly, so they can be assumed as (quasi-)static or (quasi-)stationary and represented via magnetohydrostatic (MHS) or stationary magnetohydrodynamic (MHD) equilibria, respectively. While exact 3D solutions would be desired, they are extremely difficult to find in stationary MHD. We construct solutions with magnetic and flow vector fields that have three components depending on all three coordinates. We show that the noncanonical transformation method produces quasi-3D solutions of stationary MHD by mapping 2D or 2.5D MHS equilibria to corresponding stationary MHD states, that is, states that display the same field-line structure as the original MHS equilibria. These stationary MHD states exist on magnetic flux surfaces of the original 2D MHS states. Although the flux surfaces and therefore also the equilibria have a 2D character, these stationary MHD states depend on all three coordinates and display highly complex currents. The existence of geometrically complex 3D currents within symmetric field-line structures provides the basis for efficient dissipation of the magnetic energy in the solar corona by ohmic heating. We also discuss the possibility of maintaining an important subset of nonlinear MHS states, namely force-free fields, by stationary flows. We find that force-free fields with nonlinear flows only arise under severe restrictions of the field-line geometry and of the magnetic flux density distribution. Title: Nonlinear Force-free Coronal Magnetic Stereoscopy Authors: Chifu, Iulia; Wiegelmann, Thomas; Inhester, Bernd Bibcode: 2017ApJ...837...10C Altcode: 2017arXiv170904177C Insights into the 3D structure of the solar coronal magnetic field have been obtained in the past by two completely different approaches. The first approach are nonlinear force-free field (NLFFF) extrapolations, which use photospheric vector magnetograms as boundary condition. The second approach uses stereoscopy of coronal magnetic loops observed in EUV coronal images from different vantage points. Both approaches have their strengths and weaknesses. Extrapolation methods are sensitive to noise and inconsistencies in the boundary data, and the accuracy of stereoscopy is affected by the ability of identifying the same structure in different images and by the separation angle between the view directions. As a consequence, for the same observational data, the 3D coronal magnetic fields computed with the two methods do not necessarily coincide. In an earlier work (Paper I) we extended our NLFFF optimization code by including stereoscopic constrains. The method was successfully tested with synthetic data, and within this work, we apply the newly developed code to a combined data set from SDO/HMI, SDO/AIA, and the two STEREO spacecraft. The extended method (called S-NLFFF) contains an additional term that monitors and minimizes the angle between the local magnetic field direction and the orientation of the 3D coronal loops reconstructed by stereoscopy. We find that when we prescribe the shape of the 3D stereoscopically reconstructed loops, the S-NLFFF method leads to a much better agreement between the modeled field and the stereoscopically reconstructed loops. We also find an appreciable decrease by a factor of two in the angle between the current and the magnetic field. This indicates the improved quality of the force-free solution obtained by S-NLFFF. Title: Sources of the Slow Solar Wind During the Solar Cycle 23/24 Minimum Authors: Kilpua, E. K. J.; Madjarska, M. S.; Karna, N.; Wiegelmann, T.; Farrugia, C.; Yu, W.; Andreeova, K. Bibcode: 2016SoPh..291.2441K Altcode: 2016arXiv160605142K; 2016SoPh..tmp..149K We investigate the characteristics and the sources of the slow (<450 kms−1) solar wind during the four years (2006 - 2009) of low solar activity between Solar Cycles 23 and 24. We used a comprehensive set of in-situ observations in the near-Earth solar wind (Wind and ACE) and removed the periods when large-scale interplanetary coronal mass ejections were present. The investigated period features significant variations in the global coronal structure, including the frequent presence of low-latitude active regions in 2006 - 2007, long-lived low- and mid-latitude coronal holes in 2006 - mid-2008 and mostly the quiet Sun in 2009. We examined Carrington rotation averages of selected solar plasma, charge state, and compositional parameters and distributions of these parameters related to the quiet Sun, active region Sun, and the coronal hole Sun. While some of the investigated parameters (e.g. speed, the C+6/C+4 and He/H ratios) show clear variations over our study period and with solar wind source type, some (Fe/O) exhibit very little changes. Our results highlight the difficulty of distinguishing between the slow solar wind sources based on the inspection of solar wind conditions. Title: Comparison of CME/Shock Propagation Models with Heliospheric Imaging and In Situ Observations Authors: Zhao, Xinhua; Liu, Ying D.; Inhester, Bernd; Feng, Xueshang; Wiegelmann, Thomas; Lu, Lei Bibcode: 2016ApJ...830...48Z Altcode: 2016arXiv160705533Z The prediction of the arrival time for fast coronal mass ejections (CMEs) and their associated shocks is highly desirable in space weather studies. In this paper, we use two shock propagation models, I.e., Data Guided Shock Time Of Arrival (DGSTOA) and Data Guided Shock Propagation Model (DGSPM), to predict the kinematical evolution of interplanetary shocks associated with fast CMEs. DGSTOA is based on the similarity theory of shock waves in the solar wind reference frame, and DGSPM is based on the non-similarity theory in the stationary reference frame. The inputs are the kinematics of the CME front at the maximum speed moment obtained from the geometric triangulation method applied to STEREO imaging observations together with the Harmonic Mean approximation. The outputs provide the subsequent propagation of the associated shock. We apply these models to the CMEs on 2012 January 19, January 23, and March 7. We find that the shock models predict reasonably well the shock’s propagation after the impulsive acceleration. The shock’s arrival time and local propagation speed at Earth predicted by these models are consistent with in situ measurements of WIND. We also employ the Drag-Based Model (DBM) as a comparison, and find that it predicts a steeper deceleration than the shock models after the rapid deceleration phase. The predictions of DBM at 1 au agree with the following ICME or sheath structure, not the preceding shock. These results demonstrate the applicability of the shock models used here for future arrival time prediction of interplanetary shocks associated with fast CMEs. Title: Erratum: “Evolution of Magnetic Field and Energy in A Major Eruptive Active Region Based on SDO/HMI Observation” (2012, ApJ, 748, 77) Authors: Sun, Xudong; Hoeksema, J. Todd; Liu, Yang; Wiegelmann, Thomas; Hayashi, Keiji; Chen, Qingrong; Thalmann, Julia Bibcode: 2016ApJ...828...65S Altcode: No abstract at ADS Title: Relationship Between Sunspot Rotation and a Major Solar Eruption on 12 July 2012 Authors: Wang, Rui; Liu, Ying D.; Wiegelmann, Thomas; Cheng, Xin; Hu, Huidong; Yang, Zhongwei Bibcode: 2016SoPh..291.1159W Altcode: 2016SoPh..tmp...49W We present an analysis of Solar Dynamics Observatory (SDO) observations of an X1.4 class flare on 12 July 2012 (SOL2012-07-12T15:37L082C105), which was associated with a pronounced sunspot rotation in the associated active region. Based on the magnetograms taken with the Helioseismic and Magnetic Imager (HMI) on the SDO, we measured the rotational speed of the sunspot. We also used a technique, called the differential affine velocity estimator for vector magnetograms (DAVE4VM), to determine the horizontal velocities and the magnetic helicity flux transport. The helicity flux rate due to shearing motion changed sign after the onset of the eruption. A high correlation between the sunspot rotation speed and the change in the total accumulated helicity was found. We also calculated the net fluxes of the respective magnetic polarities and the net vertical currents. The net current in the region of interest showed a synchronous change with the sunspot rotation rate. The magnetic configurations of the sigmoid filament in the active region and the associated possible interaction between different structures were further investigated by means of a nonlinear force-free field extrapolation. We identified a possible magnetic reconnection region from the three-dimensional magnetic fields and its association with EUV structures. These results suggest that the major eruption of this active region was connected with the sunspot rotation. Title: Structure, Stability, and Evolution of Magnetic Flux Ropes from the Perspective of Magnetic Twist Authors: Liu, Rui; Kliem, Bernhard; Titov, Viacheslav S.; Chen, Jun; Wang, Yuming; Wang, Haimin; Liu, Chang; Xu, Yan; Wiegelmann, Thomas Bibcode: 2016ApJ...818..148L Altcode: 2015arXiv151202338L We investigate the evolution of NOAA Active Region (AR) 11817 during 2013 August 10-12, when it developed a complex field configuration and produced four confined, followed by two eruptive, flares. These C-and-above flares are all associated with a magnetic flux rope (MFR) located along the major polarity inversion line, where shearing and converging photospheric flows are present. Aided by the nonlinear force-free field modeling, we identify the MFR through mapping magnetic connectivities and computing the twist number {{ T }}w for each individual field line. The MFR is moderately twisted (| {{ T }}w| \lt 2) and has a well-defined boundary of high squashing factor Q. We found that the field line with the extremum | {{ T }}w| is a reliable proxy of the rope axis, and that the MFR's peak | {{ T }}w| temporarily increases within half an hour before each flare while it decreases after the flare peak for both confined and eruptive flares. This pre-flare increase in | {{ T }}w| has little effect on the AR's free magnetic energy or any other parameters derived for the whole region, due to its moderate amount and the MFR's relatively small volume, while its decrease after flares is clearly associated with the stepwise decrease in the whole region's free magnetic energy due to the flare. We suggest that {{ T }}w may serve as a useful parameter in forewarning the onset of eruption, and therefore, the consequent space weather effects. The helical kink instability is identified as the prime candidate onset mechanism for the considered flares. Title: Structure, Stability and Evolution of a Magnetic Flux Rope Authors: Liu, R.; Kliem, B.; Titov, V. S.; Chen, J.; Wang, Y.; Wang, H.; Liu, C.; Xu, Y.; Wiegelmann, T. Bibcode: 2015AGUFMSH13D2457L Altcode: We investigate the evolution of NOAA Active Region 11817 during 2013 August 10--12, when it developed a complex field configuration and produced four confined, followed by two eruptive, flares. These C-and-above flares are all associated with a magnetic flux rope (MFR) located along the major polarity inversion line, where shearing and converging photospheric flows are present. With the aid of nonlinear force-free field modeling, we identify the MFR through mapping magnetic connectivities and computing the twist number Tw for each individual field line. The MFR is moderately twisted (Tw < 2) and has a well-defined boundary of high squashing factor Q. Its axis coincides with the field line with the peak Tw in the rope. We find that the MFR's peak Tw temporarily increases within half an hour before each flare while it decreases after the flare peak for both confined and eruptive flares. This pre-flare increase in Tw has little effect on the active region's free magnetic energy or any other parameters derived for the whole region, due to its moderate amount and the MFR's relatively small volume, while its decrease after flares is clearly associated with the stepwise decrease in free magnetic energy due to the flare. We suggest that Tw may serve as a useful parameter in prewarning the onset of eruption, and therefore, the consequent space weather effects. The helical kink instability is identified as the prime candidate onset mechanism for the considered flares. Title: Magneto-static Modeling of the Mixed Plasma Beta Solar Atmosphere Based on Sunrise/IMaX Data Authors: Wiegelmann, T.; Neukirch, T.; Nickeler, D. H.; Solanki, S. K.; Martínez Pillet, V.; Borrero, J. M. Bibcode: 2015ApJ...815...10W Altcode: 2015arXiv151105568W Our aim is to model the three-dimensional magnetic field structure of the upper solar atmosphere, including regions of non-negligible plasma beta. We use high-resolution photospheric magnetic field measurements from SUNRISE/IMaX as the boundary condition for a magneto-static magnetic field model. The high resolution of IMaX allows us to resolve the interface region between the photosphere and corona, but modeling this region is challenging for the following reasons. While the coronal magnetic field is thought to be force-free (the Lorentz force vanishes), this is not the case in the mixed plasma β environment in the photosphere and lower chromosphere. In our model, pressure gradients and gravity forces are self-consistently taken into account and compensate for the non-vanishing Lorentz force. Above a certain height (about 2 Mm) the non-magnetic forces become very weak and consequently the magnetic field becomes almost force-free. Here, we apply a linear approach where the electric current density consists of a superposition of a field-line parallel current and a current perpendicular to the Sun's gravity field. We illustrate the prospects and limitations of this approach and give an outlook for an extension toward a nonlinear model. Title: The Influence of Spatial resolution on Nonlinear Force-free Modeling Authors: DeRosa, M. L.; Wheatland, M. S.; Leka, K. D.; Barnes, G.; Amari, T.; Canou, A.; Gilchrist, S. A.; Thalmann, J. K.; Valori, G.; Wiegelmann, T.; Schrijver, C. J.; Malanushenko, A.; Sun, X.; Régnier, S. Bibcode: 2015ApJ...811..107D Altcode: 2015arXiv150805455D The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric boundary data. We investigate the sensitivity of the modeling to the spatial resolution of the boundary data, by applying multiple codes that numerically solve the NLFFF model to a sequence of vector magnetogram data at different resolutions, prepared from a single Hinode/Solar Optical Telescope Spectro-Polarimeter scan of NOAA Active Region 10978 on 2007 December 13. We analyze the resulting energies and relative magnetic helicities, employ a Helmholtz decomposition to characterize divergence errors, and quantify changes made by the codes to the vector magnetogram boundary data in order to be compatible with the force-free model. This study shows that NLFFF modeling results depend quantitatively on the spatial resolution of the input boundary data, and that using more highly resolved boundary data yields more self-consistent results. The free energies of the resulting solutions generally trend higher with increasing resolution, while relative magnetic helicity values vary significantly between resolutions for all methods. All methods require changing the horizontal components, and for some methods also the vertical components, of the vector magnetogram boundary field in excess of nominal uncertainties in the data. The solutions produced by the various methods are significantly different at each resolution level. We continue to recommend verifying agreement between the modeled field lines and corresponding coronal loop images before any NLFFF model is used in a scientific setting. Title: A Circular-ribbon Solar Flare Following an Asymmetric Filament Eruption Authors: Liu, Chang; Deng, Na; Liu, Rui; Lee, Jeongwoo; Pariat, Étienne; Wiegelmann, Thomas; Liu, Yang; Kleint, Lucia; Wang, Haimin Bibcode: 2015ApJ...812L..19L Altcode: 2015arXiv150908414L The dynamic properties of flare ribbons and the often associated filament eruptions can provide crucial information on the flaring coronal magnetic field. This Letter analyzes the GOES-class X1.0 flare on 2014 March 29 (SOL2014-03-29T17:48), in which we found an asymmetric eruption of a sigmoidal filament and an ensuing circular flare ribbon. Initially both EUV images and a preflare nonlinear force-free field model show that the filament is embedded in magnetic fields with a fan-spine-like structure. In the first phase, which is defined by a weak but still increasing X-ray emission, the western portion of the sigmoidal filament arches upward and then remains quasi-static for about five minutes. The western fan-like and the outer spine-like fields display an ascending motion, and several associated ribbons begin to brighten. Also found is a bright EUV flow that streams down along the eastern fan-like field. In the second phase that includes the main peak of hard X-ray (HXR) emission, the filament erupts, leaving behind two major HXR sources formed around its central dip portion and a circular ribbon brightened sequentially. The expanding western fan-like field interacts intensively with the outer spine-like field, as clearly seen in running difference EUV images. We discuss these observations in favor of a scenario where the asymmetric eruption of the sigmoidal filament is initiated due to an MHD instability and further facilitated by reconnection at a quasi-null in corona; the latter is in turn enhanced by the filament eruption and subsequently produces the circular flare ribbon. Title: Comparison between the eruptive X2.2 flare on 2011 February 15 and confined X3.1 flare on 2014 October 24 Authors: Jing, Ju; Xu, Yan; Lee, Jeongwoo; Nitta, Nariaki V.; Liu, Chang; Park, Sung-Hong; Wiegelmann, Thomas; Wang, Haimin Bibcode: 2015RAA....15.1537J Altcode: We compare two contrasting X-class flares in terms of magnetic free energy, relative magnetic helicity and decay index of the active regions (ARs) in which they occurred. The events in question are the eruptive X2.2 flare from AR 11158 accompanied by a halo coronal mass ejection (CME) and the confined X3.1 flare from AR 12192 with no associated CME. These two flares exhibit similar behavior of free magnetic energy and helicity buildup for a few days preceding them. A major difference between the two flares is found to lie in the time-dependent change of magnetic helicity of the ARs that hosted them. AR 11158 shows a significant decrease in magnetic helicity starting ∼4 hours prior to the flare, but no apparent decrease in helicity is observed in AR 12192. By examining the magnetic helicity injection rates in terms of sign, we confirmed that the drastic decrease in magnetic helicity before the eruptive X2.2 flare was not caused by the injection of reversed helicity through the photosphere but rather the CME-related change in the coronal magnetic field. Another major difference we find is that AR 11158 had a significantly larger decay index and therefore weaker overlying field than AR 12192. These results suggest that the coronal magnetic helicity and the decay index of the overlying field can provide a clue about the occurrence of CMEs. Title: Coronal magnetic field modeling using stereoscopy constraints Authors: Chifu, I.; Inhester, B.; Wiegelmann, T. Bibcode: 2015A&A...577A.123C Altcode:
Aims: Nonlinear force-free field (NLFFF) extrapolation has been used extensively in the past to extrapolate solar surface magnetograms to stationary coronal field models. In theoretical tests with known boundary conditions, the nonlinear boundary value problem can be solved reliably. However, if the magnetogram is measured with errors, the extrapolation often yields field lines that disagree with the shapes of simultaneously observed and stereoscopically reconstructed coronal loops. We here propose an extension to an NLFFF extrapolation scheme that remedies this deficiency in that it incorporates the loop information in the extrapolation procedure.
Methods: We extended the variational formulation of the NLFFF optimization code by an additional term that monitors and minimizes the difference of the local magnetic field direction and the orientation of 3D plasma loops. We tested the performance of the new code with a previously reported semi-analytical force-free solution.
Results: We demonstrate that there is a range of force-free and divergence-free solutions that comply with the boundary measurements within some error bound. With our new approach we can obtain the solution out of this set the coronal fields which is well aligned with given loops.
Conclusions: We conclude that the shape of coronal loops reconstructed by stereoscopy may lead to an important stabilization of coronal NLFFF field solutions when, as is typically the case, magnetic surface measurements with limited precision do not allow determining the solution solely from photospheric field measurements. Title: Multiwavelength Observations of a Partially Eruptive Filament on 2011 September 8 Authors: Zhang, Q. M.; Ning, Z. J.; Guo, Y.; Zhou, T. H.; Cheng, X.; Ji, H. S.; Feng, L.; Wiegelmann, T. Bibcode: 2015ApJ...805....4Z Altcode: 2015arXiv150302933Z In this paper, we report our multiwavelength observations of a partial filament eruption event in NOAA active region (AR) 11283 on 8 September 2011. A magnetic null point and the corresponding spine and separatrix surface are found in the AR. Beneath the null point, a sheared arcade supports the filament along the highly complex and fragmented polarity inversion line. After being activated, the sigmoidal filament erupted and split into two parts. The major part rose at speeds of 90-150 km s-1 before reaching the maximum apparent height of ∼115 Mm. Afterward, it returned to the solar surface in a bumpy way at speeds of 20-80 km s-1. The rising and falling motions were clearly observed in the extreme-ultraviolet, UV, and Hα wavelengths. The failed eruption of the main part was associated with an M6.7 flare with a single hard X-ray source. The runaway part of the filament, however, separated from and rotated around the major part for ∼1 turn at the eastern leg before escaping from the corona, probably along large-scale open magnetic field lines. The ejection of the runaway part resulted in a very faint coronal mass ejection that propagated at an apparent speed of 214 km s-1 in the outer corona. The filament eruption also triggered a transverse kink-mode oscillation of the adjacent coronal loops in the same AR. The amplitude and period of the oscillation were 1.6 Mm and 225 s. Our results are important for understanding the mechanisms of partial filament eruptions, and provide new constraints to theoretical models. The multiwavelength observations also shed light on space weather prediction. Title: Effect of the Size of the Computational Domain on Spherical Nonlinear Force-Free Modeling of a Coronal Magnetic Field Using SDO/HMI Data Authors: Tadesse, Tilaye; Wiegelmann, T.; MacNeice, P. J. Bibcode: 2015SoPh..290.1159T Altcode: 2014arXiv1409.1775T; 2015SoPh..tmp...23T The solar coronal magnetic field produces solar activity, including extremely energetic solar flares and coronal mass ejections (CMEs). Knowledge of the structure and evolution of the magnetic field of the solar corona is important for investigating and understanding the origins of space weather. Although the coronal field remains difficult to measure directly, there is considerable interest in accurate modeling of magnetic fields in and around sunspot regions on the Sun using photospheric vector magnetograms as boundary data. In this work, we investigate effects of the size of the domain chosen for coronal magnetic field modeling on resulting model solutions. We applied a spherical nonlinear force-free optimization procedure to vector magnetogram data of the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). We selected a particular observation in which there were four active regions observed on 9 March 2012 at 20:55 UT. The results imply that quantities such as magnetic flux density, electric current density, and free magnetic energy density of active regions of interest are significantly different from the corresponding quantities obtained in the same region with a larger computational domain. The difference is even more pronounced in the regions that are connected to the outside of the domain. Title: Effect of Size of the Computational Domain on Nonlinear Force-Free Modeling of Coronal Magnetic Field Using SDO/HMI Data Authors: Asfaw, T. T.; Wiegelmann, T.; MacNeice, P. J. Bibcode: 2014AGUFMSH21A4083A Altcode: The solar coronal magnetic field produces solar activity, including extremely energetic solar flares and coronal mass ejections (CMEs). Knowledge of the structure and evolution of the magnetic field of the solar corona is important for investigating and understanding the origins of space weather. Although the coronal field remains difficult to measure directly, there is considerable interest in accurate modeling of magnetic fields in and around sunspot regions on the Sun using photospheric vector magnetograms as boundary data. In this work, we investigate effects of the size of the domain chosen for coronal magnetic field modeling on resulting model solution. We apply spherical Optimization procedure to vector magnetogram data of Helioseismic and Magnetic Imager (HMI) onboardSolar Dynamics Observatory (SDO) with four Active Region observed on 09 March 2012 at 20:55UT. The results imply that quantities like magnetic flux density, electric current density and free magnetic energy density of ARs of interest are significantly different from the corresponding quantities obtained in the same region within the wider field of view. The difference is even more pronounced in the regions where there are connections to outside the domain. Title: The magnetic field in the solar atmosphere Authors: Wiegelmann, Thomas; Thalmann, Julia K.; Solanki, Sami K. Bibcode: 2014A&ARv..22...78W Altcode: 2014arXiv1410.4214W This publication provides an overview of magnetic fields in the solar atmosphere with the focus lying on the corona. The solar magnetic field couples the solar interior with the visible surface of the Sun and with its atmosphere. It is also responsible for all solar activity in its numerous manifestations. Thus, dynamic phenomena such as coronal mass ejections and flares are magnetically driven. In addition, the field also plays a crucial role in heating the solar chromosphere and corona as well as in accelerating the solar wind. Our main emphasis is the magnetic field in the upper solar atmosphere so that photospheric and chromospheric magnetic structures are mainly discussed where relevant for higher solar layers. Also, the discussion of the solar atmosphere and activity is limited to those topics of direct relevance to the magnetic field. After giving a brief overview about the solar magnetic field in general and its global structure, we discuss in more detail the magnetic field in active regions, the quiet Sun and coronal holes. Title: Global Solar Free Magnetic Energy and Electric Current Density Distribution of Carrington Rotation 2124 Authors: Tadesse, Tilaye; Pevtsov, Alexei A.; Wiegelmann, T.; MacNeice, P. J.; Gosain, S. Bibcode: 2014SoPh..289.4031T Altcode: 2013arXiv1310.5790T Solar eruptive phenomena, like flares and coronal mass ejections (CMEs), are governed by magnetic fields. To describe the structure of these phenomena one needs information on the magnetic flux density and the electric current density vector components in three dimensions throughout the atmosphere. However, current spectro-polarimetric measurements typically limit the determination of the vector magnetic field to only the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field for global solar atmosphere using nonlinear force-free field (NLFFF) extrapolation codes implemented to a synoptic maps of photospheric vector magnetic field synthesized from the Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) as boundary condition. Using the resulting three-dimensional magnetic field, we calculate the three-dimensional electric current density and magnetic energy throughout the solar atmosphere for Carrington rotation 2124 using our global extrapolation code. We found that spatially, the low-lying, current-carrying core field demonstrates a strong concentration of free energy in the active-region core, from the photosphere to the lower corona (about 70 Mm). The free energy density appears largely co-spatial with the electric current distribution. Title: Three-dimensional Magnetic Restructuring in Two Homologous Solar Flares in the Seismically Active NOAA AR 11283 Authors: Liu, Chang; Deng, Na; Lee, Jeongwoo; Wiegelmann, Thomas; Jiang, Chaowei; Dennis, Brian R.; Su, Yang; Donea, Alina; Wang, Haimin Bibcode: 2014ApJ...795..128L Altcode: 2014arXiv1409.6391L We carry out a comprehensive investigation comparing the three-dimensional magnetic field restructuring, flare energy release, and the helioseismic response of two homologous flares, the 2011 September 6 X2.1 (FL1) and September 7 X1.8 (FL2) flares in NOAA AR 11283. In our analysis, (1) a twisted flux rope (FR) collapses onto the surface at a speed of 1.5 km s-1 after a partial eruption in FL1. The FR then gradually grows to reach a higher altitude and collapses again at 3 km s-1 after a fuller eruption in FL2. Also, FL2 shows a larger decrease of the flux-weighted centroid separation of opposite magnetic polarities and a greater change of the horizontal field on the surface. These imply a more violent coronal implosion with corresponding more intense surface signatures in FL2. (2) The FR is inclined northward and together with the ambient fields, it undergoes a southward turning after both events. This agrees with the asymmetric decay of the penumbra observed in the peripheral regions. (3) The amounts of free magnetic energy and nonthermal electron energy released during FL1 are comparable to those of FL2 within the uncertainties of the measurements. (4) No sunquake was detected in FL1; in contrast, FL2 produced two seismic emission sources S1 and S2 both lying in the penumbral regions. Interestingly, S1 and S2 are connected by magnetic loops, and the stronger source S2 has a weaker vertical magnetic field. We discuss these results in relation to the implosion process in the low corona and the sunquake generation. Title: MHD flows at astropauses and in astrotails Authors: Nickeler, D. H.; Wiegelmann, T.; Karlický, M.; Kraus, M. Bibcode: 2014ASTRP...1...51N Altcode: 2015arXiv150105122N The geometrical shapes and the physical properties of stellar wind - interstellar medium interaction regions form an important stage for studying stellar winds and their embedded magnetic fields as well as cosmic ray modulation. Our goal is to provide a proper representation and classification of counter-flow configurations and counter-flow interfaces in the frame of fluid theory. In addition we calculate flows and large-scale electromagnetic fields based on which the large-scale dynamics and its role as possible background for particle acceleration, e.g., in the form of anomalous cosmic rays, can be studied. We find that for the definition of the boundaries, which are determining the astropause shape, the number and location of magnetic null points and stagnation points is essential. Multiple separatrices can exist, forming a highly complex environment for the interstellar and stellar plasma. Furthermore, the formation of extended tail structures occur naturally, and their stretched field and streamlines provide surroundings and mechanisms for the acceleration of particles by field-aligned electric fields. Title: Quasi-static Three-dimensional Magnetic Field Evolution in Solar Active Region NOAA 11166 Associated with an X1.5 Flare Authors: Vemareddy, P.; Wiegelmann, T. Bibcode: 2014ApJ...792...40V Altcode: 2014arXiv1406.7823V We study the quasi-static evolution of coronal magnetic fields constructed from the non-linear force-free field (NLFFF) approximation aiming to understand the relation between the magnetic field topology and ribbon emission during an X1.5 flare in active region (AR) NOAA 11166. The flare with a quasi-elliptical and two remote ribbons occurred on 2011 March 9 at 23:13 UT over a positive flux region surrounded by negative flux at the center of the bipolar AR. Our analysis of the coronal magnetic structure with potential and NLFFF solutions unveiled the existence of a single magnetic null point associated with a fan-spine topology and is co-spatial with the hard X-ray source. The footpoints of the fan separatrix surface agree with the inner edge of the quasi-elliptical ribbon and the outer spine is linked to one of the remote ribbons. During the evolution, the slow footpoint motions stressed the field lines along the polarity inversion line and caused electric current layers in the corona around the fan separatrix surface. These current layers trigger magnetic reconnection as a consequence of dissipating currents, which are visible as cusp-shaped structures at lower heights. The reconnection process reorganized the magnetic field topology whose signatures are observed at the separatrices/quasi-separatrix layer structure in both the photosphere and the corona during the pre-to-post flare evolution. In agreement with previous numerical studies, our results suggest that the line-tied footpoint motions perturb the fan-spine system and cause null point reconnection, which eventually causes the flare emission at the footpoints of the field lines. Title: Self-consistent stationary MHD shear flows in the solar atmosphere as electric field generators Authors: Nickeler, D. H.; Karlický, M.; Wiegelmann, T.; Kraus, M. Bibcode: 2014A&A...569A..44N Altcode: 2014arXiv1407.3227N Context. Magnetic fields and flows in coronal structures, for example, in gradual phases in flares, can be described by 2D and 3D magnetohydrostatic (MHS) and steady magnetohydrodynamic (MHD) equilibria.
Aims: Within a physically simplified, but exact mathematical model, we study the electric currents and corresponding electric fields generated by shear flows.
Methods: Starting from exact and analytically calculated magnetic potential fields, we solved the nonlinear MHD equations self-consistently. By applying a magnetic shear flow and assuming a nonideal MHD environment, we calculated an electric field via Faraday's law. The formal solution for the electromagnetic field allowed us to compute an expression of an effective resistivity similar to the collisionless Speiser resistivity.
Results: We find that the electric field can be highly spatially structured, or in other words, filamented. The electric field component parallel to the magnetic field is the dominant component and is high where the resistivity has a maximum. The electric field is a potential field, therefore, the highest energy gain of the particles can be directly derived from the corresponding voltage. In our example of a coronal post-flare scenario we obtain electron energies of tens of keV, which are on the same order of magnitude as found observationally. This energy serves as a source for heating and acceleration of particles. Title: Well-observed Dynamics of Flaring and Peripheral Coronal Magnetic Loops during an M-class Limb Flare Authors: Shen, Jinhua; Zhou, Tuanhui; Ji, Haisheng; Wiegelmann, Thomas; Inhester, Bernd; Feng, Li Bibcode: 2014ApJ...791...83S Altcode: In this paper, we present a variety of well-observed dynamic behaviors for the flaring and peripheral magnetic loops of the M6.6 class extreme limb flare that occurred on 2011 February 24 (SOL2011-02-24T07:20) from EUV observations by the Atmospheric Imaging Assembly on the Solar Dynamics Observatory and X-ray observations by RHESSI. The flaring loop motion confirms the earlier contraction-expansion picture. We find that the U-shaped trajectory delineated by the X-ray corona source of the flare roughly follows the direction of a filament eruption associated with the flare. Different temperature structures of the coronal source during the contraction and expansion phases strongly suggest different kinds of magnetic reconnection processes. For some peripheral loops, we discover that their dynamics are closely correlated with the filament eruption. During the slow rising to abrupt, fast rising of the filament, overlying peripheral magnetic loops display different responses. Two magnetic loops on the elbow of the active region had a slow descending motion followed by an abrupt successive fast contraction, while magnetic loops on the top of the filament were pushed outward, slowly being inflated for a while and then erupting as a moving front. We show that the filament activation and eruption play a dominant role in determining the dynamics of the overlying peripheral coronal magnetic loops. Title: Statistical Study of Free Magnetic Energy and Flare Productivity of Solar Active Regions Authors: Su, J. T.; Jing, J.; Wang, S.; Wiegelmann, T.; Wang, H. M. Bibcode: 2014ApJ...788..150S Altcode: 2014arXiv1405.2131S Photospheric vector magnetograms from the Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory are utilized as the boundary conditions to extrapolate both nonlinear force-free and potential magnetic fields in solar corona. Based on the extrapolations, we are able to determine the free magnetic energy (FME) stored in active regions (ARs). Over 3000 vector magnetograms in 61 ARs were analyzed. We compare FME with the ARs' flare index (FI) and find that there is a weak correlation (<60%) between FME and FI. FME shows slightly improved flare predictability relative to the total unsigned magnetic flux of ARs in the following two aspects: (1) the flare productivity predicted by FME is higher than that predicted by magnetic flux and (2) the correlation between FI and FME is higher than that between FI and magnetic flux. However, this improvement is not significant enough to make a substantial difference in time-accumulated FI, rather than individual flare, predictions. Title: Temporal Evolution of the Magnetic Topology of the NOAA Active Region 11158 Authors: Zhao, Jie; Li, Hui; Pariat, Etienne; Schmieder, Brigitte; Guo, Yang; Wiegelmann, Thomas Bibcode: 2014ApJ...787...88Z Altcode: 2014arXiv1404.5004Z We studied the temporal evolution of the magnetic topology of the active region (AR) 11158 based on the reconstructed three-dimensional magnetic fields in the corona. The non-linear force-free field extrapolation method was applied to the 12 minute cadence data obtained with the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory during 5 days. By calculating the squashing degree factor Q in the volume, the derived quasi-separatrix layers (QSLs) show that this AR has an overall topology, resulting from a magnetic quadrupole, including a hyperbolic flux tube (HFT) configuration that is relatively stable at the timescale of the flare (~1-2 hr). A strong QSL, which corresponds to some highly sheared arcades that might be related to the formation of a flux rope, is prominent just before the M6.6 and X2.2 flares, respectively. These facts indicate the close relationship between the strong QSL and the high flare productivity of AR 11158. In addition, with a close inspection of the topology, we found a small-scale HFT that has an inverse tear-drop structure above the aforementioned QSL before the X2.2 flare. It indicates the existence of magnetic flux rope at this place. Even though a global configuration (HFT) is recognized in this AR, it turns out that the large-scale HFT only plays a secondary role during the eruption. In conclusion, we dismiss a trigger based on the breakout model and highlight the central role of the flux rope in the related eruption. Title: A Comparison Between Nonlinear Force-Free Field and Potential Field Models Using Full-Disk SDO/HMI Magnetogram Authors: Tadesse, Tilaye; Wiegelmann, T.; MacNeice, P. J.; Inhester, B.; Olson, K.; Pevtsov, A. Bibcode: 2014SoPh..289..831T Altcode: 2012arXiv1212.5639T Measurements of magnetic fields and electric currents in the pre-eruptive corona are crucial to the study of solar eruptive phenomena, like flares and coronal mass ejections (CMEs). However, spectro-polarimetric measurements of certain photospheric lines permit a determination of the vector magnetic field only at the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field above multiple active regions with the help of a potential field and a nonlinear force-free field (NLFFF) extrapolation code over the full solar disk using Helioseismic and Magnetic Imager (SDO/HMI) data as boundary conditions. We compare projections of the resulting magnetic field lines with full-disk coronal images from the Atmospheric Imaging Assembly (SDO/AIA) for both models. This study has found that the NLFFF model reconstructs the magnetic configuration closer to observation than the potential field model for full-disk magnetic field extrapolation. We conclude that many of the trans-equatorial loops connecting the two solar hemispheres are current-free. Title: Evolution of a Magnetic Flux Rope and its Overlying Arcade Based on Nonlinear Force-free Field Extrapolations Authors: Jing, Ju; Liu, Chang; Lee, Jeongwoo; Wang, Shuo; Wiegelmann, Thomas; Xu, Yan; Wang, Haimin Bibcode: 2014ApJ...784L..13J Altcode: Dynamic phenomena indicative of slipping reconnection and magnetic implosion were found in a time series of nonlinear force-free field (NLFFF) extrapolations for the active region 11515, which underwent significant changes in the photospheric fields and produced five C-class flares and one M-class flare over five hours on 2012 July 2. NLFFF extrapolation was performed for the uninterrupted 5 hour period from the 12 minute cadence vector magnetograms of the Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory. According to the time-dependent NLFFF model, there was an elongated, highly sheared magnetic flux rope structure that aligns well with an Hα filament. This long filament splits sideways into two shorter segments, which further separate from each other over time at a speed of 1-4 km s-1, much faster than that of the footpoint motion of the magnetic field. During the separation, the magnetic arcade arching over the initial flux rope significantly decreases in height from ~4.5 Mm to less than 0.5 Mm. We discuss the reality of this modeled magnetic restructuring by relating it to the observations of the magnetic cancellation, flares, a filament eruption, a penumbra formation, and magnetic flows around the magnetic polarity inversion line. Title: First use of synoptic vector magnetograms for global nonlinear, force-free coronal magnetic field models Authors: Tadesse, T.; Wiegelmann, T.; Gosain, S.; MacNeice, P.; Pevtsov, A. A. Bibcode: 2014A&A...562A.105T Altcode: 2013arXiv1309.5853T Context. The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently, there are several modelling techniques being used to calculate three-dimensional field lines into the solar atmosphere.
Aims: For the first time, synoptic maps of a photospheric-vector magnetic field synthesized from the vector spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model the coronal magnetic field and estimate free magnetic energy in the global scale. The free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions.
Methods: We solve the nonlinear force-free field equations using an optimization principle in spherical geometry. The resulting three-dimensional magnetic fields are used to estimate the magnetic free energy content Efree = Enlfff - Epot, which is the difference of the magnetic energies between the nonpotential field and the potential field in the global solar corona. For comparison, we overlay the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the atmospheric imaging assembly (AIA) on board the Solar Dynamics Observatory (SDO).
Results: For a single Carrington rotation 2121, we find that the global nonlinear force-free field (NLFFF) magnetic energy density is 10.3% higher than the potential one. Most of this free energy is located in active regions. Title: Topological study of active region 11158 Authors: Zhao, Jie; Li, Hui; Pariat, Etienne; Schmieder, Brigitte; Guo, Yang; Wiegelmann, Thomas Bibcode: 2014IAUS..300..479Z Altcode: With the cylindrical equal area (CEA) projection data from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO), we reconstructed the three-dimensional (3D) magnetic fields in the corona, using a non-linear force-free field (NLFFF) extrapolation method every 12 minutes during five days, to calculate the squashing degree factor Q in the volume. The results show that this AR has an hyperbolic flux tube (HFT) configuration, a typical topology of quadrupole, which is stable even during the two large flares (M6.6 and X2.2 class flares). Title: Force-free Field Modeling of Twist and Braiding-induced Magnetic Energy in an Active-region Corona Authors: Thalmann, J. K.; Tiwari, S. K.; Wiegelmann, T. Bibcode: 2014ApJ...780..102T Altcode: 2013arXiv1311.3413T The theoretical concept that braided magnetic field lines in the solar corona may dissipate a sufficient amount of energy to account for the brightening observed in the active-region (AR) corona has only recently been substantiated by high-resolution observations. From the analysis of coronal images obtained with the High Resolution Coronal Imager, first observational evidence of the braiding of magnetic field lines was reported by Cirtain et al. (hereafter CG13). We present nonlinear force-free reconstructions of the associated coronal magnetic field based on Solar Dynamics Observatory/Helioseismic and Magnetic Imager vector magnetograms. We deliver estimates of the free magnetic energy associated with a braided coronal structure. Our model results suggest (~100 times) more free energy at the braiding site than analytically estimated by CG13, strengthening the possibility of the AR corona being heated by field line braiding. We were able to appropriately assess the coronal free energy by using vector field measurements and we attribute the lower energy estimate of CG13 to the underestimated (by a factor of 10) azimuthal field strength. We also quantify the increase in the overall twist of a flare-related flux rope that was noted by CG13. From our models we find that the overall twist of the flux rope increased by about half a turn within 12 minutes. Unlike another method to which we compare our results, we evaluate the winding of the flux rope's constituent field lines around each other purely based on their modeled coronal three-dimensional field line geometry. To our knowledge, this is done for the first time here. Title: Evidence for Solar Tether-cutting Magnetic Reconnection from Coronal Field Extrapolations Authors: Liu, Chang; Deng, Na; Lee, Jeongwoo; Wiegelmann, Thomas; Moore, Ronald L.; Wang, Haimin Bibcode: 2013ApJ...778L..36L Altcode: 2013arXiv1310.5098L Magnetic reconnection is one of the primary mechanisms for triggering solar eruptive events, but direct observation of this rapid process has been a challenge. In this Letter, using a nonlinear force-free field (NLFFF) extrapolation technique, we present a visualization of field line connectivity changes resulting from tether-cutting reconnection over about 30 minutes during the 2011 February 13 M6.6 flare in NOAA AR 11158. Evidence for the tether-cutting reconnection was first collected through multiwavelength observations and then by analysis of the field lines traced from positions of four conspicuous flare 1700 Å footpoints observed at the event onset. Right before the flare, the four footpoints are located very close to the regions of local maxima of the magnetic twist index. In particular, the field lines from the inner two footpoints form two strongly twisted flux bundles (up to ~1.2 turns), which shear past each other and reach out close to the outer two footpoints, respectively. Immediately after the flare, the twist index of regions around the footpoints diminishes greatly and the above field lines become low-lying and less twisted (lsim0.6 turns), overarched by loops linking the two flare ribbons formed later. About 10% of the flux (~3 × 1019 Mx) from the inner footpoints undergoes a footpoint exchange. This portion of flux originates from the edge regions of the inner footpoints that are brightened first. These rapid changes of magnetic field connectivity inferred from the NLFFF extrapolation are consistent with the tether-cutting magnetic reconnection model. Title: Magnetic structure of solar active region NOAA 11158 Authors: Vemareddy, P.; Ambastha, A.; Wiegelmann, T. Bibcode: 2013BASI...41..183V Altcode: 2013arXiv1310.6895V Magnetic fields in the solar corona are responsible for a wide range of phenomena. However, any direct measurements of the coronal magnetic fields are very difficult due to lack of suitable spectral lines, weak magnetic fields, and high temperatures. Therefore, one extrapolates photospheric field measurements into the corona. Owing to low coronal plasma β, we can apply a force-free model in lowest order to study the slow evolution of active region (AR) magnetic fields. On applying these models to AR 11158 and compared with coronal plasma tracers, we found that (1) the approximation of potential field to coronal structures over large length scales is a reasonable one, 2) linear force-free (LFF) assumption to AR coronal fields may not be applicable model as it assumes uniform twist over the entire AR, and 3) for modeling fields at sheared, stressed locations where energy release in the form of flares are usually observed, non-linear force free fields (NLFFF) seem to provide a good approximation. The maximum available free-energy profile shows step-wise decrease that is sufficient to power an M-class flare as observed. Title: Modeling coronal magnetic field using spherical geometry: cases with several active regions Authors: Tadesse, Tilaye; Wiegelmann, T.; MacNeice, P. J.; Olson, K. Bibcode: 2013Ap&SS.347...21T Altcode: 2013Ap&SS.tmp..221T; 2013arXiv1301.7522T The magnetic fields in the solar atmosphere structure the plasma, store free magnetic energy and produce a wide variety of active solar phenomena, like flare and coronal mass ejections (CMEs). The distribution and strength of magnetic fields are routinely measured in the solar surface (photosphere). Therefore, there is considerable interest in accurately modeling the 3D structure of the coronal magnetic field using photospheric vector magnetograms. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma. Nonlinear force-free field (NLFFF) models are thought to be viable tools for those task. Usually those models use Cartesian geometry. However, the spherical nature of the solar surface cannot be neglected when the field of view is large. In this work, we model the coronal magnetic field above multiple active regions using NLFFF extrapolation code using vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS)/Vector Spectromagnetograph (VSM) as a boundary conditions. We compare projections of the resulting magnetic field lines solutions with their respective coronal EUV-images from the Atmospheric Imaging Assembly (SDO/AIA) observed on October 15, 2011 and November 13, 2012. This study has found that the NLFFF model in spherical geometry reconstructs the magnetic configurations for several active regions which agrees to some extent with observations. During October 15, 2011 observation, there are substantial number of trans-equatorial loops carrying electric current. Title: Fragmentation of electric currents in the solar corona by plasma flows Authors: Nickeler, D. H.; Karlický, M.; Wiegelmann, T.; Kraus, M. Bibcode: 2013A&A...556A..61N Altcode: 2013arXiv1306.5155N
Aims: We consider a magnetic configuration consisting of an arcade structure and a detached plasmoid, resulting from a magnetic reconnection process, as is typically found in connection with solar flares. We study spontaneous current fragmentation caused by shear and vortex plasma flows.
Methods: An exact analytical transformation method was applied to calculate self-consistent solutions of the nonlinear stationary magnetohydrodynamic equations. The assumption of incompressible field-aligned flows implies that both the Alfvén Mach number and the mass density are constant on field lines. We first calculated nonlinear magnetohydrostatic equilibria with the help of the Liouville method, emulating the scenario of a solar eruptive flare configuration with plasmoids (magnetic ropes or current-carrying loops in 3D) and flare arcade. Then a Mach number profile was constructed that describes the upflow along the open magnetic field lines and implements a vortex flow inside the plasmoid. This Mach number profile was used to map the magnetohydrostatic equilibrium to the stationary one.
Results: We find that current fragmentation takes place at different locations within our configuration. Steep gradients of the Alfvén Mach number are required, implying the strong influence of shear flows on current amplification and filamentation of the magnetohydrostatic current sheets. Crescent- or ring-like structures appear along the outer separatrix, butterfly structures between the upper and lower plasmoids, and strong current peaks close the lower boundary (photosphere). Furthermore, impressing an intrinsic small-scale structure on the upper plasmoid results in strong fragmentation of the plasmoid. Hence fragmentation of current sheets and plasmoids is an inherent property of magnetohydrodynamic theory.
Conclusions: Transformations from magnetohydrostatic into magnetohydrodynamic steady-states deliver fine-structures needed for plasma heating and acceleration of particles and bulk plasma flows in dissipative events that are typically connected to magnetic reconnection processes in flares and coronal mass ejections. Title: Comparison of Force-free Coronal Magnetic Field Modeling Using Vector Fields from Hinode and Solar Dynamics Observatory Authors: Thalmann, J. K.; Tiwari, S. K.; Wiegelmann, T. Bibcode: 2013ApJ...769...59T Altcode: 2013arXiv1304.3619T Photospheric magnetic vector maps from two different instruments are used to model the nonlinear force-free coronal magnetic field above an active region. We use vector maps inferred from polarization measurements of the Solar Dynamics Observatory/Helioseismic and Magnetic Imager (HMI) and the Solar Optical Telescope's Spectropolarimeter (SP) on board Hinode. Besides basing our model calculations on HMI data, we use both SP data of original resolution and scaled down to the resolution of HMI. This allows us to compare the model results based on data from different instruments and to investigate how a binning of high-resolution data affects the model outcome. The resulting three-dimensional magnetic fields are compared in terms of magnetic energy content and magnetic topology. We find stronger magnetic fields in the SP data, translating into a higher total magnetic energy of the SP models. The net Lorentz forces of the HMI and SP lower boundaries verify their force-free compatibility. We find substantial differences in the absolute estimates of the magnetic field energy but similar relative estimates, e.g., the fraction of excess energy and of the flux shared by distinct areas. The location and extension of neighboring connectivity domains differ and the SP model fields tend to be higher and more vertical. Hence, conclusions about the magnetic connectivity based on force-free field models are to be drawn with caution. We find that the deviations of the model solution when based on the lower-resolution SP data are small compared to the differences of the solutions based on data from different instruments. Title: Evolution of the Fine Structure of Magnetic Fields in the Quiet Sun: Observations from Sunrise/IMaX and Extrapolations Authors: Wiegelmann, Thomas; Solanki, Sami; Borrero, Juan; Peter, Hardi; Sunrise Team Bibcode: 2013EGUGA..15.5251W Altcode: Observations with the balloon-borne Sunrise/ Imaging Magnetograph eXperiment (IMaX) provide high spatial resolution (roughly 100 km at disk center) measurements of the magnetic field in the photosphere of the quiet Sun. To investigate the magnetic structure of the chromosphere and corona, we extrapolate these photospheric measurements into the upper solar atmosphere and analyse a 22-minute long time series with a cadence of 33 seconds. Using the extrapolated magnetic-field lines as tracer, we investigate temporal evolution of the magnetic connectivity in the quiet Sun's atmosphere. The majority of magnetic loops are asymmetric in the sense that the photospheric field strength at the loop footpoints is very different. We find that the magnetic connectivity of the loops changes rapidly with a typical connection recycling time of about 3 ± 1 minutes in the upper solar atmosphere and 12 ± 4 minutes in the photosphere. This is considerably shorter than previously found. Nonetheless, our estimate of the energy released by the associated magnetic-reconnection processes is not likely to be the sole source for heating the chromosphere and corona in the quiet Sun. Title: Evolution of the Fine Structure of Magnetic Fields in the Quiet Sun: Observations from Sunrise/IMaX and Extrapolations Authors: Wiegelmann, T.; Solanki, S. K.; Borrero, J. M.; Peter, H.; Barthol, P.; Gandorfer, A.; Martínez Pillet, V.; Schmidt, W.; Knölker, M. Bibcode: 2013SoPh..283..253W Altcode: Observations with the balloon-borne Sunrise/Imaging Magnetograph eXperiment (IMaX) provide high spatial resolution (roughly 100 km at disk center) measurements of the magnetic field in the photosphere of the quiet Sun. To investigate the magnetic structure of the chromosphere and corona, we extrapolate these photospheric measurements into the upper solar atmosphere and analyze a 22-minute long time series with a cadence of 33 seconds. Using the extrapolated magnetic-field lines as tracer, we investigate temporal evolution of the magnetic connectivity in the quiet Sun's atmosphere. The majority of magnetic loops are asymmetric in the sense that the photospheric field strength at the loop foot points is very different. We find that the magnetic connectivity of the loops changes rapidly with a typical connection recycling time of about 3±1 minutes in the upper solar atmosphere and 12±4 minutes in the photosphere. This is considerably shorter than previously found. Nonetheless, our estimate of the energy released by the associated magnetic-reconnection processes is not likely to be the sole source for heating the chromosphere and corona in the quiet Sun. Title: Force-free coronal magnetic field modeling using vector fields from Hinode and SDO Authors: Thalmann, Julia K.; Tiwari, Sanjiv K.; Wiegelmann, Thomas Bibcode: 2013EGUGA..15.1368T Altcode: Given the lack of routine direct measurements of the magnetic field in the solar corona, force-free reconstruction methods are a promising tool for the diagnostics of the magnetic structure there. Routine photospheric magnetic field measurements which monitor the temporal evolution of an active region and contain information on the non-potentiality of the field above are used as an input. Based on the assumption that magnetic forces dominate the solar atmosphere, these models allow estimates of the total and free magnetic energy content and the structure of the magnetic field above active regions. The outcome of force-free field modeling strongly depends on the vector magnetic field data used as boundary condition. We compare the model results based on simultaneously observed vector maps from the Helioseismic and Magnetic Imager (HMI) on board Solar Dynamics Observatory and from the Solar Optical Telescope Spectropolarimeter (SP) on board Hinode. We find substantial differences in the absolute estimates of the magnetic field energy but very similar relative estimates, e.g., the fraction of energy to be set free during an eruption or the fraction of flux linking distinct areas within an active region. Our study reveals that only relative estimates of coronal physical quantities from force-free models might be save and conclusions about the magnetic field topology might be drawn with caution. Title: Magnetic Energy Partition between the Coronal Mass Ejection and Flare from AR 11283 Authors: Feng, L.; Wiegelmann, T.; Su, Y.; Inhester, B.; Li, Y. P.; Sun, X. D.; Gan, W. Q. Bibcode: 2013ApJ...765...37F Altcode: On 2011 September 6, an X-class flare and a halo coronal mass ejection (CME) were observed from Earth erupting from the same active region AR 11283. The magnetic energy partition between them has been investigated. SDO/HMI vector magnetograms were used to obtain the coronal magnetic field using the nonlinear force-free field (NLFFF) extrapolation method. The free magnetic energies before and after the flare were calculated to estimate the released energy available to power the flare and the CME. For the flare energetics, thermal and nonthermal energies were derived using the RHESSI and GOES data. To obtain the radiative output, SDO/EVE data in the 0.1-37 nm waveband were utilized. We have reconstructed the three-dimensional (3D) periphery of the CME from the coronagraph images observed by STEREO-A, B, and SOHO. The mass calculations were then based on a more precise Thomson-scattering geometry. The subsequent estimate of the kinetic and potential energies of the CME took advantage of the more accurate mass, and the height and speed in a 3D frame. The released free magnetic energy resulting from the NLFFF model is about 6.4 × 1031 erg, which has a possible upper limit of 1.8 × 1032 erg. The thermal and nonthermal energies are lower than the radiative output of 2.2 × 1031 erg from SDO/EVE for this event. The total radiation covering the whole solar spectrum is probably a few times larger. The sum of the kinetic and potential energy of the CME could go up to 6.5 × 1031 erg. Therefore, the free energy is able to power the flare and the CME in AR 11283. Within the uncertainty, the flare and the CME may consume a similar amount of free energy. Title: 2D and 3D Polar Plume Analysis from the Three Vantage Positions of STEREO/EUVI A, B, and SOHO/EIT Authors: de Patoul, Judith; Inhester, Bernd; Feng, Li; Wiegelmann, Thomas Bibcode: 2013SoPh..283..207D Altcode: 2011arXiv1111.4123D; 2011SoPh..tmp..415D Polar plumes appear as elongated objects starting at the solar polar regions. Here we analyze these objects from a sequence of images taken simultaneously by the three spacecraft telescopes STEREO/EUVI A and B, and SOHO/EIT. We establish a method capable of automatically identifying plumes in solar EUV images close to the limb at 1.01 - 1.39 R⊙ in order to study their temporal evolution. This plume-identification method is based on a multiscale Hough-wavelet analysis. Then two methods to determine the 3D localization and structure of the plumes are discussed: first, tomography using filtered back-projection and including the differential rotation of the Sun and, second, conventional stereoscopic triangulation. We show that tomography and stereoscopy are complementary for studying polar plumes. We also show that this systematic 2D identification and the proposed methods of 3D reconstruction are well suited to identify plumes individually and also to analyze the distribution of plumes and inter-plume regions. Finally, the results are discussed, focusing on plume position and cross-sectional area. Title: Full-disk nonlinear force-free field extrapolation of SDO/HMI and SOLIS/VSM magnetograms Authors: Tadesse, T.; Wiegelmann, T.; Inhester, B.; MacNeice, P.; Pevtsov, A.; Sun, X. Bibcode: 2013A&A...550A..14T Altcode: 2012arXiv1210.3668T Context. The magnetic field configuration is essential for understanding solar explosive phenomena, such as flares and coronal mass ejections. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Two complications of this approach are that the measured photospheric magnetic field is not force-free and that one has to apply a preprocessing routine to achieve boundary conditions suitable for the force-free modeling. Furthermore the nonlinear force-free extrapolation code should take uncertainties into account in the photospheric field data. They occur due to noise, incomplete inversions, or azimuth ambiguity-removing techniques.
Aims: Extrapolation codes in Cartesian geometry for modeling the magnetic field in the corona do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, e.g., a single active region. Here we apply a method for nonlinear force-free coronal magnetic field modeling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure to full disk vector magnetograms. We compare the analysis of the photospheric magnetic field and subsequent force-free modeling based on full-disk vector maps from Helioseismic and Magnetic Imager (HMI) onboard the solar dynamics observatory (SDO) and Vector Spectromagnetograph (VSM) of the Synoptic Optical Long-term Investigations of the Sun (SOLIS).
Methods: We used HMI and VSM photospheric magnetic field measurements to model the force-free coronal field above multiple solar active regions, assuming magnetic forces to dominate. We solved the nonlinear force-free field equations by minimizing a functional in spherical coordinates over a full disk and excluding the poles. After searching for the optimum modeling parameters for the particular data sets, we compared the resulting nonlinear force-free model fields. We compared quantities, such as the total magnetic energy content, free magnetic energy, the longitudinal distribution of the magnetic pressure, and surface electric current density, using our spherical geometry extrapolation code.
Results: The magnetic field lines obtained from nonlinear force-free extrapolation based on HMI and VSM data show good agreement. However, the nonlinear force-free extrapolation based on HMI data contain more total magnetic energy, free magnetic energy, the longitudinal distribution of the magnetic pressure, and surface electric current density than do the VSM data. Title: Double Power-law Distribution of Magnetic Energy in the Solar Corona over an Active Region Authors: Shen, Jinhua; Ji, Haisheng; Wiegelmann, Thomas; Inhester, Bernd Bibcode: 2013ApJ...764...86S Altcode: In this paper, we study the magnetic energy (ME) structure contained in the solar corona over the active region NOAA 11158. The time period is chosen as from 0:00 to 06:00 UT on 2011 February 15, during which an X-class flare occurred. The nonlinear force-free field (NLFFF) and the potential field extrapolation are carried out to model the coronal magnetic field over this active region, using high-quality photospheric vector magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory as boundary conditions. We find that the volume distribution for the density of the ME (B 2/8π) and the ohmic dissipation power (ODP, j 2/σ), in which j is the electric current density (c/4π∇ × B) and σ is the conductivity in the corona, can be readily fitted by a broken-down double-power law. The turn-over density for the spectrum of the ME and ODP is found to be fixed at ~1.0 × 104 erg cm-3 and ~2.0 × 10-15 W cm-3 (assuming σ = 105 Ω-1 m-1), respectively. Compared with their first power-law spectra (fitted below the corresponding turn-over value) which remain unchanged, the second power-law spectra (fitted above the corresponding turn-over value) for the NLFFF's ME and ODP show flare-associated changes. The potential field remains steady. These results indicate that a magnetic field with energy density larger than the turn-over energy density plays a dominant role in powering the flare. Title: On the Comparison of Nonlinear Force-free Models Based on Vector-magnetograms from Different Instruments Authors: Thalmann, J. K.; Wiegelmann, T.; Tiwari, S. K.; Sun, X. Bibcode: 2012AGUFMSH41C2120T Altcode: We investigate the three-dimensional structure of the magnetic field in the outer solar atmosphere with the help of photospheric magnetic vector maps based on measurements from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory and of the Solar Optical Telescope Spectral-polarimeter (SP) on board the Hinode spacecraft. HMI and SP magnetic vector maps of NOAA AR 11382 on 21-22 December 2011 are used as lower boundary condition for nonlinear force-free field reconstructions. We compare the resulting three-dimensional coronal magnetic field models in terms of the energy content, the magnetic pressure, the vertical distribution of the magnetic field and associated electric current density, as well as the magnetic field line configuration and compare the latter to the loops visible in coronal images from the SDO Atmospheric Imaging Assembly. Title: Doppler shift of hot coronal lines in a moss area of an active region Authors: Dadashi, N.; Teriaca, L.; Tripathi, D.; Solanki, S. K.; Wiegelmann, T. Bibcode: 2012A&A...548A.115D Altcode: 2012arXiv1211.5473D The moss is the area at the footpoint of the hot (3 to 5 MK) loops forming the core of the active region where emission is believed to result from the heat flux conducted down to the transition region from the hot loops. Studying the variation of Doppler shift as a function of line formation temperatures over the moss area can give clues on the heating mechanism in the hot loops in the core of the active regions. We investigate the absolute Doppler shift of lines formed at temperatures between 1 MK and 2 MK in a moss area within active region NOAA 11243 using a novel technique that allows determining the absolute Doppler shift of EUV lines by combining observations from the SUMER and EIS spectrometers. The inner (brighter and denser) part of the moss area shows roughly constant blue shift (upward motions) of 5 km s-1 in the temperature range of 1 MK to 1.6 MK. For hotter lines the blue shift decreases and reaches 1 km s-1 for Fe xv 284 Å (~2 MK). The measurements are discussed in relation to models of the heating of hot loops. The results for the hot coronal lines seem to support the quasi-steady heating models for nonsymmetric hot loops in the core of active regions. Title: How Should One Optimize Nonlinear Force-Free Coronal Magnetic Field Extrapolations from SDO/HMI Vector Magnetograms? Authors: Wiegelmann, T.; Thalmann, J. K.; Inhester, B.; Tadesse, T.; Sun, X.; Hoeksema, J. T. Bibcode: 2012SoPh..281...37W Altcode: 2012SoPh..tmp...67W; 2012arXiv1202.3601W The Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) provides photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semianalytic and numeric equilibria and applied to vector magnetograms from Hinode and ground-based observations. Recently we implemented a new version which takes into account measurement errors in photospheric vector magnetograms. Photospheric field measurements are often affected by measurement errors and finite nonmagnetic forces inconsistent for use as a boundary for a force-free field in the corona. To deal with these uncertainties, we developed two improvements: i) preprocessing of the surface measurements to make them compatible with a force-free field, and ii) new code which keeps a balance between the force-free constraint and deviation from the photospheric field measurements. Both methods contain free parameters, which must be optimized for use with data from SDO/HMI. In this work we describe the corresponding analysis method and evaluate the force-free equilibria by how well force-freeness and solenoidal conditions are fulfilled, by the angle between magnetic field and electric current, and by comparing projections of magnetic field lines with coronal images from the Atmospheric Imaging Assembly (SDO/AIA). We also compute the available free magnetic energy and discuss the potential influence of control parameters. Title: Coronal Magnetic Field Structure and Evolution for Flaring AR 11117 and Its Surroundings Authors: Tadesse, Tilaye; Wiegelmann, T.; Inhester, B.; Pevtsov, A. Bibcode: 2012SoPh..281...53T Altcode: 2011arXiv1109.4889T; 2012SoPh..tmp...60T In this study, photospheric vector magnetograms obtained with the Synoptic Optical Long-term Investigations of the Sun (SOLIS) survey are used as boundary conditions to model three-dimensional nonlinear force-free (NLFF) coronal magnetic fields as a sequence of NLFF equilibria in spherical geometry. We study the coronal magnetic field structure inside an active region and its temporal evolution. We compare the magnetic field configuration obtained from NLFF extrapolation before and after the flaring event in active region (AR) 11117 and its surroundings observed on 27 October 2010, and we also compare the magnetic field topologies and the magnetic energy densities and study the connectivities between AR 11117 and its surroundings. During the investigated time period, we estimate the change in free magnetic energy from before to after the flare to be 1.74×1032 erg, which represents about 13.5 % of the NLFF magnetic energy before the flare. In this study, we find that electric currents from AR 11117 to its surroundings were disrupted after the flare. Title: First 4D Reconstruction of an Eruptive Prominence Using Three Simultaneous View Directions Authors: Chifu, I.; Inhester, B.; Mierla, M.; Chifu, V.; Wiegelmann, T. Bibcode: 2012SoPh..281..121C Altcode: 2012SoPh..tmp..213C Data from the STEREO (Solar Terrestrial Relations Observatory) mission are intensively used for 3D reconstruction of solar coronal structures. After the launch of the SDO (Solar Dynamic Observatory) satellite, its additional observations give the possibility to have a third eye for more accurate 3D reconstruction in the very low corona (< 1.5 R⊙). With our reconstruction code MBSR (Multi-view B-spline Stereoscopic Reconstruction), we use three view directions (STEREO A, B, and SDO) to perform the 3D reconstruction and evolution of a prominence which triggered a CME on 1 August 2010. In the paper we present the reconstruction of this prominence from the moment it starts to erupt until it leaves the field of view of the coronagraph. We also determine the evolution of the leading edge of the CME. Based on the temporal evolution, we analyze some of its properties, such as velocity, acceleration, opening and rotation angles and evolution of the cavity. Title: Modeling Magnetic Field Structure of a Solar Active Region Corona Using Nonlinear Force-free Fields in Spherical Geometry Authors: Guo, Y.; Ding, M. D.; Liu, Y.; Sun, X. D.; DeRosa, M. L.; Wiegelmann, T. Bibcode: 2012ApJ...760...47G Altcode: 2012arXiv1210.0998G We test a nonlinear force-free field (NLFFF) optimization code in spherical geometry using an analytical solution from Low and Lou. Several tests are run, ranging from idealized cases where exact vector field data are provided on all boundaries, to cases where noisy vector data are provided on only the lower boundary (approximating the solar problem). Analytical tests also show that the NLFFF code in the spherical geometry performs better than that in the Cartesian one when the field of view of the bottom boundary is large, say, 20° × 20°. Additionally, we apply the NLFFF model to an active region observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory (SDO) both before and after an M8.7 flare. For each observation time, we initialize the models using potential field source surface (PFSS) extrapolations based on either a synoptic chart or a flux-dispersal model, and compare the resulting NLFFF models. The results show that NLFFF extrapolations using the flux-dispersal model as the boundary condition have slightly lower, therefore better, force-free, and divergence-free metrics, and contain larger free magnetic energy. By comparing the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly on board SDO, we find that the NLFFF performs better than the PFSS not only for the core field of the flare productive region, but also for large EUV loops higher than 50 Mm. Title: LEMUR: Large European module for solar Ultraviolet Research. European contribution to JAXA's Solar-C mission Authors: Teriaca, Luca; Andretta, Vincenzo; Auchère, Frédéric; Brown, Charles M.; Buchlin, Eric; Cauzzi, Gianna; Culhane, J. Len; Curdt, Werner; Davila, Joseph M.; Del Zanna, Giulio; Doschek, George A.; Fineschi, Silvano; Fludra, Andrzej; Gallagher, Peter T.; Green, Lucie; Harra, Louise K.; Imada, Shinsuke; Innes, Davina; Kliem, Bernhard; Korendyke, Clarence; Mariska, John T.; Martínez-Pillet, Valentin; Parenti, Susanna; Patsourakos, Spiros; Peter, Hardi; Poletto, Luca; Rutten, Robert J.; Schühle, Udo; Siemer, Martin; Shimizu, Toshifumi; Socas-Navarro, Hector; Solanki, Sami K.; Spadaro, Daniele; Trujillo-Bueno, Javier; Tsuneta, Saku; Dominguez, Santiago Vargas; Vial, Jean-Claude; Walsh, Robert; Warren, Harry P.; Wiegelmann, Thomas; Winter, Berend; Young, Peter Bibcode: 2012ExA....34..273T Altcode: 2011ExA...tmp..135T; 2011arXiv1109.4301T The solar outer atmosphere is an extremely dynamic environment characterized by the continuous interplay between the plasma and the magnetic field that generates and permeates it. Such interactions play a fundamental role in hugely diverse astrophysical systems, but occur at scales that cannot be studied outside the solar system. Understanding this complex system requires concerted, simultaneous solar observations from the visible to the vacuum ultraviolet (VUV) and soft X-rays, at high spatial resolution (between 0.1'' and 0.3''), at high temporal resolution (on the order of 10 s, i.e., the time scale of chromospheric dynamics), with a wide temperature coverage (0.01 MK to 20 MK, from the chromosphere to the flaring corona), and the capability of measuring magnetic fields through spectropolarimetry at visible and near-infrared wavelengths. Simultaneous spectroscopic measurements sampling the entire temperature range are particularly important. These requirements are fulfilled by the Japanese Solar-C mission (Plan B), composed of a spacecraft in a geosynchronous orbit with a payload providing a significant improvement of imaging and spectropolarimetric capabilities in the UV, visible, and near-infrared with respect to what is available today and foreseen in the near future. The Large European Module for solar Ultraviolet Research (LEMUR), described in this paper, is a large VUV telescope feeding a scientific payload of high-resolution imaging spectrographs and cameras. LEMUR consists of two major components: a VUV solar telescope with a 30 cm diameter mirror and a focal length of 3.6 m, and a focal-plane package composed of VUV spectrometers covering six carefully chosen wavelength ranges between 170 Å and 1270 Å. The LEMUR slit covers 280'' on the Sun with 0.14'' per pixel sampling. In addition, LEMUR is capable of measuring mass flows velocities (line shifts) down to 2 km s - 1 or better. LEMUR has been proposed to ESA as the European contribution to the Solar C mission. Title: Solar Force-free Magnetic Fields Authors: Wiegelmann, Thomas; Sakurai, Takashi Bibcode: 2012LRSP....9....5W Altcode: The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces like plasma pressure gradient and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relation between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently of large interests, as accurate measurements of the photospheric field become available from ground-based (for example SOLIS) and space-born (for example Hinode and SDO) instruments. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma. Title: The Formation of a Magnetic Channel by Emergence of Current-Carrying Magnetic Fields Authors: Lim, E. -K.; Chae, J.; Jing, J.; Wang, H.; Wiegelmann, T. Bibcode: 2012ASPC..454..185L Altcode: The term magnetic channel indicates a series of polarity reversals separating elongated flux threads with opposite polarities. We studied the formation process of the magnetic channel in AR 10930 using time sequence SP data taken by SOT/Hinode. As a result, we detected both upflows (-0.5 to -1.0 km s-1) and downflows (+1.5 to +2.0 km s-1) within the channel site, and a pair of strong vertical current threads of opposite polarity along the channel. We also analyzed coronal magnetic fields computed from the non-linear force-free field extrapolation, and found that the current density in the lower corona increased as the channel structure evolved. These findings support the idea that the magnetic channel represents the emergence of the twisted flux tube. Title: Nonlinear Force-free Field Modeling of a Solar Active Region Using SDO/HMI and SOLIS/VSM Data Authors: Thalmann, J. K.; Pietarila, A.; Sun, X.; Wiegelmann, T. Bibcode: 2012AJ....144...33T Altcode: 2012arXiv1206.1141T We use SDO/HMI and SOLIS/VSM photospheric magnetic field measurements to model the force-free coronal field above a solar active region, assuming magnetic forces dominate. We take measurement uncertainties caused by, e.g., noise and the particular inversion technique, into account. After searching for the optimum modeling parameters for the particular data sets, we compare the resulting nonlinear force-free model fields. We show the degree of agreement of the coronal field reconstructions from the different data sources by comparing the relative free energy content, the vertical distribution of the magnetic pressure, and the vertically integrated current density. Though the longitudinal and transverse magnetic flux measured by the VSM and HMI is clearly different, we find considerable similarities in the modeled fields. This indicates the robustness of the algorithm we use to calculate the nonlinear force-free fields against differences and deficiencies of the photospheric vector maps used as an input. We also depict how much the absolute values of the total force-free, virial, and the free magnetic energy differ and how the orientation of the longitudinal and transverse components of the HMI- and VSM-based model volumes compare to each other. Title: Reconstruction of 3D Coronal Magnetic Structures from THEMIS/MTR and Hinode/SOT Vector Maps Authors: Schmieder, B.; Guo, Y.; Aulanier, G.; Démoulin, P.; Török, T.; Bommier, V.; Wiegelmann, T.; Gosain, S. Bibcode: 2012ASPC..454..363S Altcode: Coordinated campaigns using THEMIS, Hinode, and other instruments have allowed us to study the magnetic fields of faculae, filaments, and active regions. In a first case, we modelled the 3D magnetic field in a flaring active region with a nonlinear force-free field extrapolation, using magnetic vectors observed by THEMIS/MTR as boundary condition. In order to construct a consistent bottom boundary for the model, we first removed the 180 degree ambiguity of the transverse fields and minimized the force and torque in the observed vector fields. We found a twisted magnetic flux rope, well aligned with the polarity inversion line and a part of an Hα filament, and located where a large flare is initiated about two hours later. In a second case, Hinode/SOT allowed us to detect fine flux concentrations in faculae, while MTR provided us with magnetic information at different levels in the atmosphere. The polarimetry analysis of the MTR and SOT data gave consistent results, using both UNNOFIT and MELANIE inversion codes. Title: Evolution of Relative Magnetic Helicity and Current Helicity in NOAA Active Region 11158 Authors: Jing, Ju; Park, Sung-Hong; Liu, Chang; Lee, Jeongwoo; Wiegelmann, Thomas; Xu, Yan; Deng, Na; Wang, Haimin Bibcode: 2012ApJ...752L...9J Altcode: Both magnetic and current helicities are crucial ingredients for describing the complexity of active-region magnetic structure. In this Letter, we present the temporal evolution of these helicities contained in NOAA active region 11158 during five days from 2011 February 12 to 16. The photospheric vector magnetograms of the Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory were used as the boundary conditions for the coronal field extrapolation under the assumption of nonlinear force-free field, from which we calculated both relative magnetic helicity and current helicity. We construct a time-altitude diagram in which altitude distribution of the magnitude of current helicity density is displayed as a function of time. This diagram clearly shows a pattern of upwardly propagating current helicity density over two days prior to the X2.2 flare on February 15 with an average propagation speed of ~36 m s-1. The propagation is synchronous with the emergence of magnetic flux into the photosphere, and indicative of a gradual energy buildup for the X2.2 flare. The time profile of the relative magnetic helicity shows a monotonically increasing trend most of the time, but a pattern of increasing and decreasing magnetic helicity above the monotonic variation appears prior to each of two major flares, M6.6 and X2.2, respectively. The physics underlying this bump pattern is not fully understood. However, the fact that this pattern is apparent in the magnetic helicity evolution but not in the magnetic flux evolution makes it a useful indicator in forecasting major flares. Title: First Results from the SUNRISE Mission Authors: Solanki, S. K.; Barthol, P.; Danilovic, S.; Feller, A.; Gandorfer, A.; Hirzberger, J.; Jafarzadeh, S.; Lagg, A.; Riethmüller, T. L.; Schüssler, M.; Wiegelmann, T.; Bonet, J. A.; González, M. J. M.; Pillet, V. M.; Khomenko, E.; Yelles Chaouche, L.; Iniesta, J. C. d. T.; Domingo, V.; Palacios, J.; Knölker, M.; González, N. B.; Borrero, J. M.; Berkefeld, T.; Franz, M.; Roth, M.; Schmidt, W.; Steiner, O.; Title, A. M. Bibcode: 2012ASPC..455..143S Altcode: The SUNRISE balloon-borne solar observatory consists of a 1m aperture Gregory telescope, a UV filter imager, an imaging vector polarimeter, an image stabilization system, and further infrastructure. The first science flight of SUNRISE yielded high-quality data that reveal the structure, dynamics, and evolution of solar convection, oscillations, and magnetic fields at a resolution of around 100 km in the quiet Sun. Here we describe very briefly the mission and the first results obtained from the SUNRISE data, which include a number of discoveries. Title: Rapid Changes of Photospheric Magnetic Field after Tether-cutting Reconnection and Magnetic Implosion Authors: Liu, Chang; Deng, N.; Liu, R.; Lee, J.; Wiegelmann, T.; Jing, J.; Xu, Y.; Wang, S.; Wang, H. Bibcode: 2012AAS...22051605L Altcode: A rapid and persistent change of the photospheric magnetic field co-temporal with the impulsive phase of solar flare emissions has been recognized as an important element of the flare process from both observational and theoretical points of view. Using the state-of-the-art photospheric vector magnetograms acquired by HMI and Hinode, we have studied such a change associated with the 2011 February 13 M6.6 flare in NOAA AR 11158. Our aim is not only to identify the field change but also to understand it in the context of magnetic reconnection involved with the flare. In our analysis, (1) the rapid change is detected in a compact region lying at the central neutral line, where the mean horizontal field strength increased significantly by 28% in 30 minutes. The field also becomes more sheared and inclined to the surface. (2) Sunspot umbrae with opposite polarity lying on the two sides of the compact region experienced sudden perturbations, moving in opposite directions at an apparent velocity of 3 km/s against the long-term evolution. (3) The field variation induces a downward Lorentz-force change acting on the compact region and two opposite horizontal components of the Lorentz-force change consistent with the sunspot motions. (4) Four conspicuous UV flare kernels appear at the event onset and are linked to ribbon-like hard X-ray emissions in the impulsive phase. The compact region lies between the central two kernels that are co-spatial with the central feet of the sigmoid according to the nonlinear force-free field (NLFFF) model. (5) The NLFFF model further shows that strong coronal currents are concentrated immediately above the compact region and undergo apparent downward collapse after the sigmoid eruption. These results are discussed in favor of both the tether-cutting reconnection producing the flare and the ensuing implosion (collapse) of the coronal field resulting from the energy release. Title: Evolution of Coronal Relative Magnetic Helicity and Current Helicity in NOAA Active Region 11158 Authors: Jing, Ju; Park, S.; Liu, C.; Wiegelmann, T.; Xu, Y.; Deng, N.; Wang, H. Bibcode: 2012AAS...22041102J Altcode: The evolution of relative magnetic helicity contained in an active region is a crucial ingredient to describe the complexity in solar atmosphere. In this paper we present the temporal evolution of relative magnetic helicity (Hr) in NOAA active region 11158 during a 4-day period of February 12-15, 2011. The photospheric vector magnetograms of the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO) are used as the boundary conditions to extrapolate the three-dimensional (3D) non-linear force-free (NLFF) coronal magnetic field, based on which Hr inside the 3D coronal volume is deduced. A bump pattern in Hr prior to two major flares is noted and may be a precursor of major flares. We compare the temporal variation of Hr with that of the accumulated amount of helicity injected through the photosphere that is inferred independently by tracking the apparent motion of magnetic footpoints at the photosphere from a line-of-sight HMI magnetogram series. The good consistency between Hr and the injected helicity suggests that the helicity is generated largely below the photosphere and is well conserved from the subsurface into the corona. In addition, the altitude-time diagram of the average unsigned current helicity displays a clear propagation pattern over two days prior to the X2.2 flare of February 15, with an average propagation rate of 36 m/s. The propagation is synchronous with the emergence of magnetic flux, and indicative of a gradual energy buildup for the flares. Title: A First Look at Magnetic Field Data Products from SDO/HMI Authors: Liu, Y.; Scherrer, P. H.; Hoeksema, J. T.; Schou, J.; Bai, T.; Beck, J. G.; Bobra, M.; Bogart, R. S.; Bush, R. I.; Couvidat, S.; Hayashi, K.; Kosovichev, A. G.; Larson, T. P.; Rabello-Soares, C.; Sun, X.; Wachter, R.; Zhao, J.; Zhao, X. P.; Duvall, T. L., Jr.; DeRosa, M. L.; Schrijver, C. J.; Title, A. M.; Centeno, R.; Tomczyk, S.; Borrero, J. M.; Norton, A. A.; Barnes, G.; Crouch, A. D.; Leka, K. D.; Abbett, W. P.; Fisher, G. H.; Welsch, B. T.; Muglach, K.; Schuck, P. W.; Wiegelmann, T.; Turmon, M.; Linker, J. A.; Mikić, Z.; Riley, P.; Wu, S. T. Bibcode: 2012ASPC..455..337L Altcode: The Helioseismic and Magnetic Imager (HMI; Scherrer & Schou 2011) is one of the three instruments aboard the Solar Dynamics Observatory (SDO) that was launched on February 11, 2010 from Cape Canaveral, Florida. The instrument began to acquire science data on March 24. The regular operations started on May 1. HMI measures the Doppler velocity and line-of-sight magnetic field in the photosphere at a cadence of 45 seconds, and the vector magnetic field at a 135-second cadence, with a 4096× 4096 pixels full disk coverage. The vector magnetic field data is usually averaged over 720 seconds to suppress the p-modes and increase the signal-to-noise ratio. The spatial sampling is about 0".5 per pixel. HMI observes the Fe i 6173 Å absorption line, which has a Landé factor of 2.5. These data are further used to produce higher level data products through the pipeline at the HMI-AIA Joint Science Operations Center (JSOC) - Science Data Processing (Scherrer et al. 2011) at Stanford University. In this paper, we briefly describe the data products, and demonstrate the performance of the HMI instrument. We conclude that the HMI is working extremely well. Title: Evolution of Magnetic Field and Energy in a Major Eruptive Active Region Based on SDO/HMI Observation Authors: Sun, Xudong; Hoeksema, J. Todd; Liu, Yang; Wiegelmann, Thomas; Hayashi, Keiji; Chen, Qingrong; Thalmann, Julia Bibcode: 2012ApJ...748...77S Altcode: 2012arXiv1201.3404S We report the evolution of the magnetic field and its energy in NOAA active region 11158 over five days based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). Fast flux emergence and strong shearing motion led to a quadrupolar sunspot complex that produced several major eruptions, including the first X-class flare of Solar Cycle 24. Extrapolated nonlinear force-free coronal fields show substantial electric current and free energy increase during early flux emergence near a low-lying sigmoidal filament with a sheared kilogauss field in the filament channel. The computed magnetic free energy reaches a maximum of ~2.6 × 1032 erg, about 50% of which is stored below 6 Mm. It decreases by ~0.3 × 1032 erg within 1 hr of the X-class flare, which is likely an underestimation of the actual energy loss. During the flare, the photospheric field changed rapidly: the horizontal field was enhanced by 28% in the core region, becoming more inclined and more parallel to the polarity inversion line. Such change is consistent with the conjectured coronal field "implosion" and is supported by the coronal loop retraction observed by the Atmospheric Imaging Assembly (AIA). The extrapolated field becomes more "compact" after the flare, with shorter loops in the core region, probably because of reconnection. The coronal field becomes slightly more sheared in the lowest layer, relaxes faster with height, and is overall less energetic. Title: On the Role of the Background Overlying Magnetic Field in Solar Eruptions Authors: Nindos, A.; Patsourakos, S.; Wiegelmann, T. Bibcode: 2012ApJ...748L...6N Altcode: The primary constraining force that inhibits global solar eruptions is provided by the overlying background magnetic field. Using magnetic field data from both the Helioseismic and Magnetic Imager aboard the Solar Dynamics Observatory and the spectropolarimeter of the Solar Optical Telescope aboard Hinode, we study the long-term evolution of the background field in active region AR11158 that produced three major coronal mass ejections (CMEs). The CME formation heights were determined using EUV data. We calculated the decay index -(z/B)(∂B/∂z) of the magnetic field B (i.e., how fast the field decreases with height, z) related to each event from the time of the active region emergence until well after the CMEs. At the heights of CME formation, the decay indices were 1.1-2.1. Prior to two of the events, there were extended periods (of more than 23 hr) where the related decay indices at heights above the CME formation heights either decreased (up to -15%) or exhibited small changes. The decay index related to the third event increased (up to 118%) at heights above 20 Mm within an interval that started 64 hr prior to the CME. The magnetic free energy and the accumulated helicity into the corona contributed the most to the eruptions by their increase throughout the flux emergence phase (by factors of more than five and more than two orders of magnitude, respectively). Our results indicate that the initiation of eruptions does not depend critically on the temporal evolution of the variation of the background field with height. Title: Magnetic Connectivity Between Active Regions 10987, 10988, and 10989 by Means of Nonlinear Force-Free Field Extrapolation Authors: Tadesse, Tilaye; Wiegelmann, T.; Inhester, B.; Pevtsov, A. Bibcode: 2012SoPh..277..119T Altcode: 2011SoPh..tmp..167T; 2011arXiv1104.2246T; 2011SoPh..tmp..236T; 2011SoPh..tmp..102T Extrapolation codes for modelling the magnetic field in the corona in Cartesian geometry do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, e.g., a single active region. We apply a method for nonlinear force-free coronal magnetic field modelling of photospheric vector magnetograms in spherical geometry which allows us to study the connectivity between multi-active regions. We use Vector Spectromagnetograph (VSM) data from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) survey to model the coronal magnetic field, where we study three neighbouring magnetically connected active regions (ARs 10987, 10988, 10989) observed on 28, 29, and 30 March 2008, respectively. We compare the magnetic field topologies and the magnetic energy densities and study the connectivities between the active regions. We have studied the time evolution of the magnetic field over the period of three days and found no major changes in topologies, as there was no major eruption event. From this study we have concluded that active regions are much more connected magnetically than the electric current. Title: Relation between current sheets and vortex sheets in stationary incompressible MHD Authors: Nickeler, D. H.; Wiegelmann, T. Bibcode: 2012AnGeo..30..545N Altcode: 2012arXiv1203.5493N Magnetohydrodynamic configurations with strong localized current concentrations and vortices play an important role in the dissipation of energy in space and astrophysical plasma. Within this work we investigate the relation between current sheets and vortex sheets in incompressible, stationary equilibria. For this approach it is helpful that the similar mathematical structure of magnetohydrostatics and stationary incompressible hydrodynamics allows us to transform static equilibria into stationary ones. The main control function for such a transformation is the profile of the Alfvén-Mach number MA, which is always constant along magnetic field lines, but can change from one field line to another. In the case of a global constant MA, vortices and electric current concentrations are parallel. More interesting is the nonlinear case, where MA varies perpendicular to the field lines. This is a typical situation at boundary layers like the magnetopause, heliopause, the solar wind flowing around helmet streamers and at the boundary of solar coronal holes. The corresponding current and vortex sheets show in some cases also an alignment, but not in every case. For special density distributions in 2-D, it is possible to have current but no vortex sheets. In 2-D, vortex sheets of field aligned-flows can also exist without strong current sheets, taking the limit of small Alfvén Mach numbers into account. The current sheet can vanish if the Alfvén Mach number is (almost) constant and the density gradient is large across some boundary layer. It should be emphasized that the used theory is not only valid for small Alfvén Mach numbers MA << 1, but also for MA ≲ 1. Connection to other theoretical approaches and observations and physical effects in space plasmas are presented. Differences in the various aspects of theoretical investigations of current sheets and vortex sheets are given. Title: Particle kinetic analysis of a polar jet from SECCHI COR data Authors: Feng, L.; Inhester, B.; de Patoul, J.; Wiegelmann, T.; Gan, W. Q. Bibcode: 2012A&A...538A..34F Altcode: 2011arXiv1112.2255F
Aims: We analyze coronagraph observations of a polar jet observed by the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) instrument suite onboard the Solar TErrestrial RElations Observatory (STEREO) spacecraft.
Methods: In our analysis we compare the brightness distribution of the jet in white-light coronagraph images with a dedicated kinetic particle model. We obtain a consistent estimate of the time that the jet was launched from the solar surface and an approximate initial velocity distribution in the jet source. The method also allows us to check the consistency of the kinetic model. In this first application, we consider only gravity as the dominant force on the jet particles along the magnetic field.
Results: We find that the kinetic model explains the observed brightness evolution well. The derived initiation time is consistent with the jet observations by the EUVI telescope at various wavelengths. The initial particle velocity distribution is fitted by Maxwellian distributions and we find deviations of the high-energy tail from the Maxwellian distributions. We estimated the jet's total electron content to have a mass between 3.2 × 1014 and 1.8 × 1015 g. Mapping the integrated particle number along the jet trajectory to its source region and assuming a typical source region size, we obtain an initial electron density between 8 × 109 and 5 × 1010 cm-3 that is characteristic for the lower corona or the upper chromosphere. The total kinetic energy of all particles in the jet source region amounts from 2.1 × 1028 to 2.4 × 1029 erg. Title: Computer Vision for the Solar Dynamics Observatory (SDO) Authors: Martens, P. C. H.; Attrill, G. D. R.; Davey, A. R.; Engell, A.; Farid, S.; Grigis, P. C.; Kasper, J.; Korreck, K.; Saar, S. H.; Savcheva, A.; Su, Y.; Testa, P.; Wills-Davey, M.; Bernasconi, P. N.; Raouafi, N. -E.; Delouille, V. A.; Hochedez, J. F.; Cirtain, J. W.; DeForest, C. E.; Angryk, R. A.; De Moortel, I.; Wiegelmann, T.; Georgoulis, M. K.; McAteer, R. T. J.; Timmons, R. P. Bibcode: 2012SoPh..275...79M Altcode: 2011SoPh..tmp..144M; 2011SoPh..tmp..213M; 2011SoPh..tmp....8M In Fall 2008 NASA selected a large international consortium to produce a comprehensive automated feature-recognition system for the Solar Dynamics Observatory (SDO). The SDO data that we consider are all of the Atmospheric Imaging Assembly (AIA) images plus surface magnetic-field images from the Helioseismic and Magnetic Imager (HMI). We produce robust, very efficient, professionally coded software modules that can keep up with the SDO data stream and detect, trace, and analyze numerous phenomena, including flares, sigmoids, filaments, coronal dimmings, polarity inversion lines, sunspots, X-ray bright points, active regions, coronal holes, EIT waves, coronal mass ejections (CMEs), coronal oscillations, and jets. We also track the emergence and evolution of magnetic elements down to the smallest detectable features and will provide at least four full-disk, nonlinear, force-free magnetic field extrapolations per day. The detection of CMEs and filaments is accomplished with Solar and Heliospheric Observatory (SOHO)/Large Angle and Spectrometric Coronagraph (LASCO) and ground-based Hα data, respectively. A completely new software element is a trainable feature-detection module based on a generalized image-classification algorithm. Such a trainable module can be used to find features that have not yet been discovered (as, for example, sigmoids were in the pre-Yohkoh era). Our codes will produce entries in the Heliophysics Events Knowledgebase (HEK) as well as produce complete catalogs for results that are too numerous for inclusion in the HEK, such as the X-ray bright-point metadata. This will permit users to locate data on individual events as well as carry out statistical studies on large numbers of events, using the interface provided by the Virtual Solar Observatory. The operations concept for our computer vision system is that the data will be analyzed in near real time as soon as they arrive at the SDO Joint Science Operations Center and have undergone basic processing. This will allow the system to produce timely space-weather alerts and to guide the selection and production of quicklook images and movies, in addition to its prime mission of enabling solar science. We briefly describe the complex and unique data-processing pipeline, consisting of the hardware and control software required to handle the SDO data stream and accommodate the computer-vision modules, which has been set up at the Lockheed-Martin Space Astrophysics Laboratory (LMSAL), with an identical copy at the Smithsonian Astrophysical Observatory (SAO). Title: Rapid Changes of Photospheric Magnetic Field after Tether-cutting Reconnection and Magnetic Implosion Authors: Liu, Chang; Deng, Na; Liu, Rui; Lee, Jeongwoo; Wiegelmann, Thomas; Jing, Ju; Xu, Yan; Wang, Shuo; Wang, Haimin Bibcode: 2012ApJ...745L...4L Altcode: 2011arXiv1112.3598L The rapid, irreversible change of the photospheric magnetic field has been recognized as an important element of the solar flare process. This Letter reports such a rapid change of magnetic fields during the 2011 February 13 M6.6 flare in NOAA AR 11158 that we found from the vector magnetograms of the Helioseismic and Magnetic Imager (HMI) with 12 minute cadence. High-resolution magnetograms of Hinode that are available at ~-5.5, -1.5, 1.5, and 4 hr relative to the flare maximum are used to reconstruct a three-dimensional coronal magnetic field under the nonlinear force-free field (NLFFF) assumption. UV and hard X-ray images are also used to illuminate the magnetic field evolution and energy release. The rapid change is mainly detected by HMI in a compact region lying in the center of the magnetic sigmoid, where the mean horizontal field strength exhibited a significant increase of 28%. The region lies between the initial strong UV and hard X-ray sources in the chromosphere, which are cospatial with the central feet of the sigmoid according to the NLFFF model. The NLFFF model further shows that strong coronal currents are concentrated immediately above the region, and that, more intriguingly, the coronal current system underwent an apparent downward collapse after the sigmoid eruption. These results are discussed in favor of both the tether-cutting reconnection producing the flare and the ensuing implosion of the coronal field resulting from the energy release. Title: Nonlinear Force-Free Extrapolation of Vector Magnetograms into the Corona Authors: Thalmann, J. K.; Wiegelmann, T.; Sun, X.; Hoeksema, J. T.; Liu, Y.; Tadesse, T. Bibcode: 2011AGUFMSH33C..05T Altcode: To investigate the structure and evolution of the coronal magnetic field, we extrapolate measurements of the photospheric magnetic field vector into the corona based on the force-free assumption. A complication of this approach is that the measured photospheric magnetic field is not force-free and that one has to apply a preprocessing routine in order to achieve boundary conditions suitable for the force-free modelling. Furthermore the nonlinear force-free extrapolation code takes errors in the photospheric field data into account which occur due to noise, incomplete inversions or ambiguity removing techniques. Within this work we compare extrapolations from SDO/HMI and SOLIS vector magnetograms and explain how to find optimum parameters for handling the data of a particular instrument. The resulting coronal magnetic field lines are quantitatively compared with coronal EUV-images from SDO/AIA. Title: Evolution of the fine structure of magnetic fields in the quiet Sun: Combining Sunrise observations and modelling Authors: Wiegelmann, T.; Solanki, S.; Borrero, J.; Martinez Pillet, V.; Sunrise Team Bibcode: 2011AGUFMSH41B..06W Altcode: Observations with the balloon borne SUNRISE/IMAX instrument provide us with unprecedented high spatial resolution (pixel size 40 km) measurements of the magnetic field in the photosphere of the quiet Sun. To investigate the magnetic structure of the chromosphere and corona we extrapolate these photospheric measurements into the upper solar atmosphere and analyse a timeseries with a cadence of 33s. We find that the majority of closed loops which reach into the chromosphere or corona have one foot point in strong photospheric magnetic field regions (B>300 G). Most loops are asymmetric and the weaker foot point is often located in the internetwork. We find that the magnetic connectivity of the loops changes rapidly with a typical recycling time of about 2 min in the upper solar atmosphere and 14 min in the photosphere. We discuss, to which extend the observed topological changes can be interpreted as evidence for magnetic reconnection and the relevance of these processes for coronal heating. Title: Evolution of Magnetic Field in the Flaring Active Region AR 11158 Based on SDO/HMI Observation Authors: Sun, X.; Hoeksema, J. T.; Liu, Y.; Wiegelmann, T.; Hayashi, K. Bibcode: 2011AGUFMSH31A1993S Altcode: We report the evolution of magnetic field and its energy in NOAA active region 11158 based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). Over 5 days, the quadrupolar sunspot complex produced multiple eruptions, including the first X-class flare of the current solar cycle. Extrapolated non-linear force-free coronal fields suggest substantial electric current and free energy injection during early flux emergence along a newly-formed, pronounced filament. About 75% of the inferred free energy is stored below 10 Mm; the total decreased by 0.25E32 erg (10%) within 1 hour of the X-class flare, which is likely an underestimation of the actual energy loss. During the flare, photospheric flux underwent rapid redistribution: horizontal flux density was enhanced by 28% in the AR core region. Extrapolation shows that such change is consistent with the conjectured coronal field "implosion". Multiple coronal loops retraction were indeed observed for 5 minutes over 10 Mm during the impulsive phase. Modeling indicates that the coronal field becomes more compact after the flare, its lower layers more energetic but overall less so. Title: Nonpotentiality of Chromospheric Fibrils in NOAA Active Regions 11092 and 9661 Authors: Jing, Ju; Yuan, Yuan; Reardon, Kevin; Wiegelmann, Thomas; Xu, Yan; Wang, Haimin Bibcode: 2011ApJ...739...67J Altcode: In this paper, we present a method to automatically segment chromospheric fibrils from Hα observations and further identify their orientation. We assume that chromospheric fibrils are aligned with the magnetic field. By comparing the orientation of the fibrils with the azimuth of the embedding chromospheric magnetic field extrapolated from a potential field model, the shear angle, a measure of nonpotentiality, along the fibrils is readily deduced. Following this approach, we make a quantitative assessment of the nonpotentiality of fibrils in two NOAA active regions (ARs): (1) the relatively simple AR 11092, observed with very high resolution by Interferometric Bidimensional Spectrometer, and (2) a β-γ-δ AR 9661, observed with median resolution by Big Bear Solar Observatory before and after an X1.6 flare. Title: Evolution of Magnetic Field and Energy in A Major Eruptive Active Region Based on SDO/HMI Observation Authors: Sun, Xudong; Hoeksema, Todd; Liu, Yang; Wiegelmann, Thomas; Hayashi, Keiji; Chen, Qingrong; Thalmann, Julia Bibcode: 2011sdmi.confE..63S Altcode: We report the evolution of magnetic field and its energy in NOAA AR 11158 based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI). Fast flux emergence and strong shearing motion created a quadrupolar sunspot complex that produced several major eruptions, including the first X-class flare of solar cycle 24. Extrapolated non-linear force-free coronal field shows substantial electric current and free energy increase during early flux emergence along a newly-formed, low-lying filament with a typical 1000 G field strength and 0.45 Mm^(-1) alpha-parameter at its center. The computed magnetic free energy reaches a maximum of 2.62E32 erg, about 50% stored below 6 Mm. This free energy decreases by 0.33E32 erg within 1 hour of the X-class flare, which is likely an underestimation of the actual energy loss. During the flare, photospheric field changed rapidly: the horizontal field was enhanced by 28% in the AR core region. Such change is consistent with the conjectured coronal field "implosion", and is in line with both the reconnection signatures and the coronal loop retraction observed by the Atmospheric Image Assembly (AIA). Extrapolation indicates that the coronal field relaxes more rapidly with height after the flare and becomes overall less energetic. These preliminary results demonstrate the capability to quantitatively study the AR field topology and energetics using SDO data- although difficulties still abound. Title: Estimating the Relative Helicity of Coronal Magnetic Fields Authors: Thalmann, J. K.; Inhester, B.; Wiegelmann, T. Bibcode: 2011SoPh..272..243T Altcode: To quantify changes of the solar coronal field connectivity during eruptive events, one can use magnetic helicity, which is a measure of the shear or twist of a current-carrying (non-potential) field. To find a physically meaningful quantity, a relative measure, giving the helicity of a current-carrying field with respect to a reference (potential) field, is often evaluated. This requires a knowledge of the three-dimensional vector potential. We present a method to calculate the vector potential for a solenoidal magnetic field as the sum of a Laplacian part and a current-carrying part. The only requirements are the divergence freeness of the Laplacian and current-carrying magnetic field and the sameness of their normal field component on the bounding surface of the considered volume. Title: A filament supported by different magnetic field configurations Authors: Guo, Y.; Schmieder, B.; Démoulin, P.; Wiegelmann, T.; Aulanier, G.; Török, T.; Bommier, V. Bibcode: 2011IAUS..273..328G Altcode: A nonlinear force-free magnetic field extrapolation of vector magnetogram data obtained by THEMIS/MTR on 2005 May 27 suggests the simultaneous existence of different magnetic configurations within one active region filament: one part of the filament is supported by field line dips within a flux rope, while the other part is located in dips within an arcade structure. Although the axial field chirality (dextral) and the magnetic helicity (negative) are the same along the whole filament, the chiralities of the filament barbs at different sections are opposite, i.e., right-bearing in the flux rope part and left-bearing in the arcade part. This argues against past suggestions that different barb chiralities imply different signs of helicity of the underlying magnetic field. This new finding about the chirality of filaments will be useful to associate eruptive filaments and magnetic cloud using the helicity parameter in the Space Weather Science. Title: The Sun at high resolution: first results from the Sunrise mission Authors: Solanki, S. K.; Barthol, P.; Danilovic, S.; Feller, A.; Gandorfer, A.; Hirzberger, J.; Lagg, A.; Riethmüller, T. L.; Schüssler, M.; Wiegelmann, T.; Bonet, J. A.; Pillet, V. Martínez; Khomenko, E.; del Toro Iniesta, J. C.; Domingo, V.; Palacios, J.; Knölker, M.; González, N. Bello; Borrero, J. M.; Berkefeld, T.; Franz, M.; Roth, M.; Schmidt, W.; Steiner, O.; Title, A. M. Bibcode: 2011IAUS..273..226S Altcode: The Sunrise balloon-borne solar observatory consists of a 1m aperture Gregory telescope, a UV filter imager, an imaging vector polarimeter, an image stabilization system and further infrastructure. The first science flight of Sunrise yielded high-quality data that reveal the structure, dynamics and evolution of solar convection, oscillations and magnetic fields at a resolution of around 100 km in the quiet Sun. Here we describe very briefly the mission and the first results obtained from the Sunrise data, which include a number of discoveries. Title: Nonpotentiality of Chromospheric Fibrils in the Active Regions NOAA 9661 and NOAA 11092 Authors: Jing, Ju; Yuan, Y.; Reardon, K.; Wiegelmann, T.; Deng, N.; Xu, Y.; Wang, H. Bibcode: 2011SPD....42.1738J Altcode: 2011BAAS..43S.1738J We have developed a method to automatically segment chromospheric fibrils from Halpha observations and further identify their orientation. We assume that chromospheric fibrils are magnetic field-aligned. By comparing the orientation of the fibrils with the azimuth of the embedding chromospheric magnetic field extrapolated from the photosphere or chromosphere with the help of a potential field model, the shear angle, a measure of nonpotentiality, along the fibrils is readily deduced. Following this approach, we make a quantitative assessment of the nonpotentiality of fibrils in the active region NOAA 9661 and NOAA 11092. The spatial distribution and the histogram of the shear angle along fibrils are presented. Title: Evolution of Magnetic Field in the Flaring Active Region 11158 Observed by SDO/HMI Authors: Sun, Xudong; Hoeksema, T.; Liu, Y.; Wiegelmann, T.; Hayashi, K. Bibcode: 2011SPD....42.2101S Altcode: 2011BAAS..43S.2101S We report the evolution of the magnetic field in NOAA AR11158 over 5 days (2011 Feb 12-16) using preliminary vector magnetograms from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). This region consisted of two pairs of major sunspots and displayed a complex quadrupolar field topology. It produced multiple major flares and eruptions, including the first X-class flare of the current solar cycle. Strong shear motion and flux emergence were both present, with apparent emergence preceding each major flare. We reconstruct the coronal field from a series of vector data using a non-linear force-free (NLFF) extrapolation. The estimated free magnetic energy shows a great increase during the early emergence of the current-carrying flux, while a significant, permanent decrease ( 0.5e32 erg, or 20%) is found after the X-class flare despite continuous flux injection. We relate this decrease to a previously reported, sudden change of the photospheric field after the flare. The extrapolated coronal field structure correspondingly becomes more "compact": the low-lying of field appears more sheared and stores more free energy, and higher-altitude field decays faster with height and becomes more potential. The coronal field overall becomes less-energetic. Title: Nonlinear force-free field extrapolation in spherical geometry: improved boundary data treatment applied to a SOLIS/VSM vector magnetogram Authors: Tadesse, T.; Wiegelmann, T.; Inhester, B.; Pevtsov, A. Bibcode: 2011A&A...527A..30T Altcode: 2010arXiv1011.6285T Context. Understanding the 3D structure of coronal magnetic field is important to understanding: the onset of flares and coronal mass ejections, and the stability of active regions, and to monitoring the magnetic helicity and free magnetic energy and other phenomena in the solar atmosphere. Routine measurements of the solar magnetic field are mainly carried out in the photosphere. Therefore, one has to infer the field strength in the upper layers of the solar atmosphere from the measured photospheric field based on the assumption that the corona is force-free. Meanwhile, those measured data are inconsistent with the above force-free assumption. Therefore, one has to apply some transformations to these data before nonlinear force-free extrapolation codes can be applied.
Aims: Extrapolation codes in Cartesian geometry for modelling the magnetic field in the corona do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, e.g., a single active region. Here we apply a method for nonlinear force-free coronal magnetic field modelling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure.
Methods: We solve the nonlinear force-free field equations by minimizing a functional in spherical coordinates over a restricted area of the Sun. We extend the functional by an additional term, which allows us to incorporate measurement errors and treat regions lacking observational data. We use vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS) to model the coronal magnetic field. We study two neighbouring magnetically connected active regions observed on May 15 2009.
Results: For vector magnetograms with variable measurement precision and randomly scattered data gaps (e.g., SOLIS/VSM), the new code yields field models that satisfy the solenoidal and force-free condition significantly better as it allows deviations between the extrapolated boundary field and observed boundary data within the measurement errors. Data gaps are assigned an infinite error. We extend this new scheme to spherical geometry and apply it for the first time to real data. Title: Mesogranulation and the Solar Surface Magnetic Field Distribution Authors: Yelles Chaouche, L.; Moreno-Insertis, F.; Martínez Pillet, V.; Wiegelmann, T.; Bonet, J. A.; Knölker, M.; Bellot Rubio, L. R.; del Toro Iniesta, J. C.; Barthol, P.; Gandorfer, A.; Schmidt, W.; Solanki, S. K. Bibcode: 2011ApJ...727L..30Y Altcode: 2010arXiv1012.4481Y The relation of the solar surface magnetic field with mesogranular cells is studied using high spatial (≈100 km) and temporal (≈30 s) resolution data obtained with the IMaX instrument on board SUNRISE. First, mesogranular cells are identified using Lagrange tracers (corks) based on horizontal velocity fields obtained through local correlation tracking. After ≈20 minutes of integration, the tracers delineate a sharp mesogranular network with lanes of width below about 280 km. The preferential location of magnetic elements in mesogranular cells is tested quantitatively. Roughly 85% of pixels with magnetic field higher than 100 G are located in the near neighborhood of mesogranular lanes. Magnetic flux is therefore concentrated in mesogranular lanes rather than intergranular ones. Second, magnetic field extrapolations are performed to obtain field lines anchored in the observed flux elements. This analysis, therefore, is independent of the horizontal flows determined in the first part. A probability density function (PDF) is calculated for the distribution of distances between the footpoints of individual magnetic field lines. The PDF has an exponential shape at scales between 1 and 10 Mm, with a constant characteristic decay distance, indicating the absence of preferred convection scales in the mesogranular range. Our results support the view that mesogranulation is not an intrinsic convective scale (in the sense that it is not a primary energy-injection scale of solar convection), but also give quantitative confirmation that, nevertheless, the magnetic elements are preferentially found along mesogranular lanes. Title: A comparison of preprocessing methods for solar force-free magnetic field extrapolation Authors: Fuhrmann, M.; Seehafer, N.; Valori, G.; Wiegelmann, T. Bibcode: 2011A&A...526A..70F Altcode: 2010arXiv1010.6015F Context. Extrapolations of solar photospheric vector magnetograms into three-dimensional magnetic fields in the chromosphere and corona are usually done under the assumption that the fields are force-free. This condition is violated in the photosphere itself and a thin layer in the lower atmosphere above. The field calculations can be improved by preprocessing the photospheric magnetograms. The intention here is to remove a non-force-free component from the data.
Aims: We compare two preprocessing methods presently in use, namely the methods of Wiegelmann et al. (2006, Sol. Phys., 233, 215) and Fuhrmann et al. (2007, A&A, 476, 349).
Methods: The two preprocessing methods were applied to a vector magnetogram of the recently observed active region NOAA AR 10 953. We examine the changes in the magnetogram effected by the two preprocessing algorithms. Furthermore, the original magnetogram and the two preprocessed magnetograms were each used as input data for nonlinear force-free field extrapolations by means of two different methods, and we analyze the resulting fields.
Results: Both preprocessing methods managed to significantly decrease the magnetic forces and magnetic torques that act through the magnetogram area and that can cause incompatibilities with the assumption of force-freeness in the solution domain. The force and torque decrease is stronger for the Fuhrmann et al. method. Both methods also reduced the amount of small-scale irregularities in the observed photospheric field, which can sharply worsen the quality of the solutions. For the chosen parameter set, the Wiegelmann et al. method led to greater changes in strong-field areas, leaving weak-field areas mostly unchanged, and thus providing an approximation of the magnetic field vector in the chromosphere, while the Fuhrmann et al. method weakly changed the whole magnetogram, thereby better preserving patterns present in the original magnetogram. Both preprocessing methods raised the magnetic energy content of the extrapolated fields to values above the minimum energy, corresponding to the potential field. Also, the fields calculated from the preprocessed magnetograms fulfill the solenoidal condition better than those calculated without preprocessing. Title: Driving mechanism of a failed eruption Authors: Guo, Y.; Ding, M. D.; Schmieder, B.; Li, H.; Törö, T.; Wiegelmann, T. Bibcode: 2011ASInC...2..307G Altcode: We find a magnetic flux rope before the M1.1 flare in active region 10767 on 2005 May 27 by a nonlinear force-free field extrapolation. TRACE observations of the filament eruption show that the erupting structure performed a writhing deformation and stopped rising at a certain height, suggesting that the flux rope converted some of its twist into writhe and was confined in the corona. After calculating the twist of the flux rope, we find that it was comparable to thresholds of the helical kink instability found in numerical simulations. We conclude that the activation and rise of the flux rope were triggered and initially driven by the kink instability. The decay index of the external magnetic field stays below the threshold for the torus instability within a long height range. The confinement of the eruption could be explained by the failure of the torus instability. Hard X-ray sources at the peak of the M1.1 flare coincided with the footpoints of the erupting helical structure, which indicates a high possibility that hard X-ray sources were produced more efficiently in the flux rope. Title: First Result of Field Extrapolation Based on HMI Vector Magnetic Data Authors: Sun, X.; Hoeksema, J. T.; Wiegelmann, T.; Hayashi, K.; Liu, Y. Bibcode: 2010AGUFMSH11A1607S Altcode: Magnetic field extrapolation based on photospheric field has long been used to infer the coronal field. However, past studies are often restrained by the line-of-sight nature of observation, or the inadequate spatial/temporal resolution of the few available vector data. With the new Helioseismic and Magnetic Imager (HMI), we are now able to produce full-disk, high cadence (12 min), high resolution (1 arcsec) vector data continuously for the first time. In this paper, we analyze a time sequence of HMI vector data and apply several extrapolation methods (potential-field model, nonlinear force-free model, MHD simulation, etc.) to study the evolution of overlying field structure in lower corona. Results from different methods are cross-compared and examined against coronal observations. This study will provide insight to modeling the coronal field with greater detail and better accuracy, and eventually help the understanding of dynamic processes in solar atmosphere. Title: Driving Mechanism and Onset Condition of a Confined Eruption Authors: Guo, Y.; Ding, M. D.; Schmieder, B.; Li, H.; Török, T.; Wiegelmann, T. Bibcode: 2010ApJ...725L..38G Altcode: We study a confined eruption accompanied by an M1.1 flare in solar active region (AR) NOAA 10767 on 2005 May 27, where a pre-eruptive magnetic flux rope was reported in a nonlinear force-free field (NLFFF) extrapolation. The observations show a strong writhing motion of the erupting structure, suggesting that a flux rope was indeed present and converted some of its twist into writhe in the course of the eruption. Using the NLFFF extrapolation, we calculate the twist of the pre-eruptive flux rope and find that it is in very good agreement with thresholds of the helical kink instability found in numerical simulations. We conclude that the activation and rise of the flux rope were triggered and driven by the instability. Using a potential field extrapolation, we also estimate the height distribution of the decay index of the external magnetic field in the AR 1 hr prior to the eruption. We find that the decay index stays below the threshold for the torus instability for a significant height range above the erupting flux rope. This provides a possible explanation for the confinement of the eruption to the low corona. Title: Magnetic Loops in the Quiet Sun Authors: Wiegelmann, T.; Solanki, S. K.; Borrero, J. M.; Martínez Pillet, V.; del Toro Iniesta, J. C.; Domingo, V.; Bonet, J. A.; Barthol, P.; Gandorfer, A.; Knölker, M.; Schmidt, W.; Title, A. M. Bibcode: 2010ApJ...723L.185W Altcode: 2010arXiv1009.4715W We investigate the fine structure of magnetic fields in the atmosphere of the quiet Sun. We use photospheric magnetic field measurements from SUNRISE/IMaX with unprecedented spatial resolution to extrapolate the photospheric magnetic field into higher layers of the solar atmosphere with the help of potential and force-free extrapolation techniques. We find that most magnetic loops that reach into the chromosphere or higher have one footpoint in relatively strong magnetic field regions in the photosphere. Ninety-one percent of the magnetic energy in the mid-chromosphere (at a height of 1 Mm) is in field lines, whose stronger footpoint has a strength of more than 300 G, i.e., above the equipartition field strength with convection. The loops reaching into the chromosphere and corona are also found to be asymmetric in the sense that the weaker footpoint has a strength B < 300 G and is located in the internetwork (IN). Such loops are expected to be strongly dynamic and have short lifetimes, as dictated by the properties of the IN fields. Title: The Formation of a Magnetic Channel by the Emergence of Current-carrying Magnetic Fields Authors: Lim, Eun-Kyung; Chae, Jongchul; Jing, Ju; Wang, Haimin; Wiegelmann, Thomas Bibcode: 2010ApJ...719..403L Altcode: 2010arXiv1009.0420L A magnetic channel—a series of polarity reversals separating elongated flux threads with opposite polarities—may be a manifestation of a highly non-potential magnetic configuration in active regions. To understand its formation, we have carried out a detailed analysis of the magnetic channel in AR 10930 using data taken by the Solar Optical Telescope/Hinode. As a result, we found upflows (-0.5 to -1.0 km s-1) and downflows (+1.5 to +2.0 km s-1) inside and at both tips of the thread, respectively, and a pair of strong vertical currents of opposite polarity along the channel. Moreover, our analysis of the nonlinear force-free fields constructed from the photospheric magnetic field indicates that the current density in the lower corona may have gradually increased as a result of the continuous emergence of the highly sheared flux along the channel. With these results, we suggest that the magnetic channel originates from the emergence of the twisted flux tube that has formed below the surface before the emergence. Title: Thin current sheets caused by plasma flow gradients in space and astrophysical plasma Authors: Nickeler, D. H.; Wiegelmann, T. Bibcode: 2010AnGeo..28.1523N Altcode: 2010arXiv1008.2848N Strong gradients in plasma flows play a major role in space and astrophysical plasmas. A typical situation is that a static plasma equilibrium is surrounded by a plasma flow, which can lead to strong plasma flow gradients at the separatrices between field lines with different magnetic topologies, e.g., planetary magnetospheres, helmet streamers in the solar corona, or at the boundary between the heliosphere and interstellar medium. Within this work we make a first step to understand the influence of these flows towards the occurrence of current sheets in a stationary state situation. We concentrate here on incompressible plasma flows and 2-D equilibria, which allow us to find analytic solutions of the stationary magnetohydrodynamics equations (SMHD). First we solve the magnetohydrostatic (MHS) equations with the help of a Grad-Shafranov equation and then we transform these static equilibria into a stationary state with plasma flow. We are in particular interested to study SMHD-equilibria with strong plasma flow gradients perpendicular to separatrices. We find that induced thin current sheets occur naturally in such situations. The strength of the induced currents depend on the Alfvén Mach number and its gradient, and on the magnetic field. Title: Nonlinear Force-free Modeling of Magnetic Fields in a Solar Filament Authors: Jing, Ju; Yuan, Yuan; Wiegelmann, Thomas; Xu, Yan; Liu, Rui; Wang, Haimin Bibcode: 2010ApJ...719L..56J Altcode: We present a striking filament pattern in the nonlinear force-free (NLFF) chromospheric magnetic field of the active region NOAA 10956. The NLFF chromospheric field is extrapolated from the Hinode high-resolution photospheric vector magnetogram using the weighted optimization method. The modeled structure is characterized by a highly sheared field with strong horizontal magnetic components and has a virtually identical shape and location as the filament seen in Hα. The modeled field strength agrees with the recent He I 10830 Å observations by Kuckein et al.. The unequivocal resemblance between the NLFF extrapolation and the Hα observation not only demonstrates the ability of the NLFF field to reproduce chromospheric features, but also provides a valuable diagnostic tool for the filament magnetic fields. Title: Re-flaring of a Post-flare Loop System Driven by Flux Rope Emergence and Twisting Authors: Cheng, X.; Ding, M. D.; Guo, Y.; Zhang, J.; Jing, J.; Wiegelmann, T. Bibcode: 2010ApJ...716L..68C Altcode: 2010arXiv1005.1720C In this Letter, we study in detail the evolution of the post-flare loops on 2005 January 15 that occurred between two consecutive solar eruption events, both of which generated a fast halo coronal mass ejection (CME) and a major flare. The post-flare loop system, formed after the first CME/flare eruption, evolved rapidly, as manifested by the unusual accelerating rise motion of the loops. Through nonlinear force-free field models, we obtain the magnetic structure over the active region. It clearly shows that the flux rope below the loops also kept rising, accompanied with increasing twist and length. Finally, the post-flare magnetic configuration evolved to a state that resulted in the second CME/flare eruption. This is an event in which the post-flare loops can re-flare in a short period of ~16 hr following the first CME/flare eruption. The observed re-flaring at the same location is likely driven by the rapid evolution of the flux rope caused by the magnetic flux emergence and the rotation of the sunspot. This observation provides valuable information on CME/flare models and their prediction. Title: How to deal with measurement errors and lacking data in nonlinear force-free coronal magnetic field modelling? Authors: Wiegelmann, T.; Inhester, B. Bibcode: 2010A&A...516A.107W Altcode: Context. The measured solar photospheric magnetic field vector is extrapolated into the solar corona under the assumption of a force-free plasma. In the generic case this problem is nonlinear.
Aims: We aim to improve an algorithm for computing the nonlinear force-free coronal magnetic field. We are in particular interested to incorporate measurement errors and to handle lacking data in the boundary conditions.
Methods: We solve the nonlinear force-free field equations by minimizing a functional. Within this work we extend the functional by an additional term, which allows us to incorporate measurement errors and treat regions with lacking observational data. We test the new code with the help of a well known semi-analytic test case. We compare coronal magnetic field extrapolations from ideal boundary conditions and boundary conditions where the transversal magnetic field information is lacking or has a poor signal-to-noise ratio in weak field regions.
Results: For ideal boundary conditions the new code gives the same result as the old code. The advantage of the new approach, which includes an error matrix, is visible only for non-ideal boundary conditions. The force-free and solenoidal conditions are fulfilled significantly better and the solutions agrees somewhat better with the exact solution. The new approach also relaxes the boundary and allows a deviation from the boundary data in poor signal-to-noise ratio areas.
Conclusions: The incorporation of measurement errors in the updated extrapolation code significantly improves the quality of nonlinear force-free field extrapolation from imperfect boundary conditions. Title: Free Magnetic Energy and Flare Productivity of Active Regions Authors: Jing, Ju; Tan, C.; Yuan, Y.; Wang, B.; Wiegelmann, T.; Xu, Y.; Wang, H. Bibcode: 2010AAS...21640415J Altcode: 2010BAAS...41..902J In this study, the photospheric vector magnetograms, obtained with the Spectro-Polarimeter of the Solar Optical Telescope on board Hinode, are used as the boundary conditions to extrapolate the three-dimensional non-linear force-free (NLFF) coronal magnetic fields. The observed non-force-free photospheric magnetic fields are preprocessed towards the nearly force-free chromospheric magnetic fields. The performance of the preprocessing procedure is evaluated by comparing with chromospheric magnetic fields obtained by the Vector SpectroMagnetograph instrument located on the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Tower. Then the weighted optimization method is applied to the preprocessed boundary data to extrapolate the NLFF fields with which we are able to estimate the free magnetic energy stored in the active regions. The magnitude scaling correlation between the free magnetic energy and the soft X-ray flare index of active regions is then studied. The latter quantifies the impending flare production of active regions over the subsequent 1-, 2- and 3-day time windows. Based on 75 samples, we find a positive correlation between the free energy and the flare index. We also study the temporal variation of free magnetic energy for three active regions, of which two are flare-active and one is flare-quiet during the observation over a period of several days. While the magnitude of free magnetic energy unambiguously differentiates between the flare-active and the flare-quiet regions, the temporal variation of free magnetic energy does not exhibit a clear and consistent pre-flare pattern. This may indicate that the trigger mechanism of flares is as important as the energy storage in active regions. Title: Computer Vision for SDO: First Results from the SDO Feature Finding Algorithms Authors: Martens, Petrus C.; Attrill, G.; Davey, A.; Engell, A.; Farid, S.; Grigis, P.; Kasper, J.; Korreck, K.; Saar, S.; Su, Y.; Testa, P.; Wills-Davey, M.; Bernasconi, P.; Raouafi, N.; Georgoulis, M.; Deforest, C.; Peterson, J.; Berghoff, T.; Delouille, V.; Hochedez, J.; Mampaey, B.; Verbeek, C.; Cirtain, J.; Green, S.; Timmons, R.; Savcheva, A.; Angryk, R.; Wiegelmann, T.; McAteer, R. Bibcode: 2010AAS...21630804M Altcode: The SDO Feature Finding Team produces robust and very efficient software modules that can keep up with the relentless SDO data stream, and detect, trace, and analyze a large number of phenomena including: flares, sigmoids, filaments, coronal dimmings, polarity inversion lines, sunspots, X-ray bright points, active regions, coronal holes, EIT waves, CME's, coronal oscillations, and jets. In addition we track the emergence and evolution of magnetic elements down to the smallest features that are detectable, and we will also provide at least four full disk nonlinear force-free magnetic field extrapolations per day.

During SDO commissioning we will install in the near-real time data pipeline the modules that provide alerts for flares, coronal dimmings, and emerging flux, as well as those that trace filaments, sigmoids, polarity inversion lines, and active regions. We will demonstrate the performance of these modules and illustrate their use for science investigations. Title: An Attempt in Incorporating Local and Global Coronal Magnetic Field Modeling Authors: Sun, Xudong; Hoeksema, J. T.; Zhao, X.; Wiegelmann, T. Bibcode: 2010AAS...21640215S Altcode: 2010BAAS...41R.875S Coronal field extrapolation models are based on observed photospheric field data. The global models (eg. MHD and potential field source surface model (PFSS)) study the large scale stable structures of the corona, whereas local models (eg. non-linear force free field model (NLFFF)) look at smaller scale events that are more dynamic, with more drastic energy build up and release. While both have been successful at explaining a variety of solar activities, fewer studies are devoted to how these two types of models could be integrated, and how large scale and small scale magnetic activities interact with each other. In this study, we demonstrate our first attempt in this direction. We plan to use (1) series of updated synchronic maps and the PFSS model and (2) series of vector magnetograms with the NLFFF model to study the magnetic structure before and after major solar events. If available, results using the newest HMI data will also illustrate the prospect of future studies. Title: Coexisting Flux Rope and Dipped Arcade Sections Along One Solar Filament Authors: Guo, Y.; Schmieder, B.; Démoulin, P.; Wiegelmann, T.; Aulanier, G.; Török, T.; Bommier, V. Bibcode: 2010ApJ...714..343G Altcode: We compute the three-dimensional magnetic field of an active region in order to study the magnetic configuration of active region filaments. The nonlinear force-free field model is adopted to compute the magnetic field above the photosphere, where the vector magnetic field was observed by THEMIS/MTR on 2005 May 27. We propose a new method to remove the 180° ambiguity of the transverse field. Next, we analyze the implications of the preprocessing of the data by minimizing the total force and torque in the observed vector fields. This step provides a consistent bottom boundary condition for the nonlinear force-free field model. Then, using the optimization method to compute the coronal field, we find a magnetic flux rope along the polarity inversion line. The magnetic flux rope aligns well with part of an Hα filament, while the total distribution of the magnetic dips coincides with the whole Hα filament. This implies that the magnetic field structure in one section of the filament is a flux rope, while the other is a sheared arcade. The arcade induced a left-bearing filament in the magnetic field of negative helicity, which is opposite to the chirality of barbs that a flux rope would induce in a magnetic field of the same helicity sign. The field strength in the center of the flux rope is about 700 G, and the twist of the field lines is ~1.4 turns. Title: Free Magnetic Energy and Flare Productivity of Active Regions Authors: Jing, Ju; Tan, Changyi; Yuan, Yuan; Wang, Benjamin; Wiegelmann, Thomas; Xu, Yan; Wang, Haimin Bibcode: 2010ApJ...713..440J Altcode: In this study, the photospheric vector magnetograms, obtained with the Spectro-Polarimeter of the Solar Optical Telescope on board Hinode, are used as the boundary conditions to extrapolate the three-dimensional nonlinear force-free (NLFF) coronal magnetic fields. The observed non-force-free photospheric magnetic fields are preprocessed toward the nearly force-free chromospheric magnetic fields. The performance of the preprocessing procedure is evaluated by comparing with chromospheric magnetic fields obtained by the Vector SpectroMagnetograph instrument located on the Synoptic Optical Long-term Investigations of the Sun Tower. Then, the weighted optimization method is applied to the preprocessed boundary data to extrapolate the NLFF fields with which we are able to estimate the free magnetic energy stored in the active regions. The magnitude scaling correlation between the free magnetic energy and the soft X-ray flare index (FI) of active regions is then studied. The latter quantifies the impending flare production of active regions over the subsequent 1, 2, and 3 day time windows. Based on 75 samples, we find a positive correlation between the free energy and the FI. We also study the temporal variation of free magnetic energy for three active regions, of which two are flare-active and one is flare-quiet during the observation over a period of several days. While the magnitude of free magnetic energy unambiguously differentiates between the flare-active and the flare-quiet regions, the temporal variation of free magnetic energy does not exhibit a clear and consistent pre-flare pattern. This may indicate that the trigger mechanism of flares is as important as the energy storage in active regions. Title: Nonlinear force-free modelling: influence of inaccuracies in the measured magnetic vector Authors: Wiegelmann, T.; Yelles Chaouche, L.; Solanki, S. K.; Lagg, A. Bibcode: 2010A&A...511A...4W Altcode: 2009arXiv0912.3002W Context. Solar magnetic fields are regularly extrapolated into the corona starting from photospheric magnetic measurements that can be affected by significant uncertainty.
Aims: We study how inaccuracies introduced into the maps of the photospheric magnetic vector by the inversion of ideal and noisy Stokes parameters influence the extrapolation of nonlinear force-free magnetic fields.
Methods: We compute nonlinear force-free magnetic fields based on simulated vector magnetograms, by the inversion of Stokes profiles that were computed by a 3-D radiation MHD simulation snapshot. These extrapolations are compared with extrapolations that originate directly in the field in the MHD simulations, which is our reference. We investigate how line formation and instrumental effects such as noise, limited spatial resolution, and the effect of employing a filter instrument influence the resulting magnetic field structure. The comparison is performed qualitatively by visually inspecting the magnetic field distribution and quantitatively by different metrics.
Results: The reconstructed field is most accurate if ideal Stokes data are inverted and becomes less accurate if instrumental effects and noise are included. The results demonstrate that the nonlinear force-free field extrapolation method tested here is relatively insensitive to the effects of noise in measured polarization spectra at levels consistent with present-day instruments.
Conclusions: Our results show that we can reconstruct the coronal magnetic field as a nonlinear force-free field from realistic photospheric measurements with an accuracy of a few percent, at least in the absence of sunspots. Title: Stereoscopic 3D reconstruction of polar plumes from the three vantage positions of STEREO/SECCHI A, B and SOHO/EIT using the Hough-wavelet transform Authors: de Patoul, Judith; Feng, Li; Inhester, Bernd; Wiegelmann, Thomas Bibcode: 2010cosp...38.2947D Altcode: 2010cosp.meet.2947D We present the results from a method to determine the 3D position and orientation of po-lar plumes from three corresponding images observed simultaneously by three spacecrafts, STEREO/SECCHI A, B, and SOHO/EIT. We have applied both conventional stereoscopic triangulation and a new detection tool based on a combination of Hough and wavelet trans-form. We show that the obtained plume orientation can help to verify magnetic field models in the pole region where surface observations are difficult and their extrapolation may be problematic. This automatic and systematic 3D reconstruction is well suited to identify plumes individually in time and to follow their intensity variation. Typical lifetimes observed were found between 1-2 days. The plumes we have reconstructed were not always rooted at a simultaneous EUV bright points and were sometime associated with a jet. Title: How do inaccuracies and unresolved structures in the measured solar photospheric magnetic vector influence the accuracy of coronal magnetic field models? Authors: Wiegelmann, Thomas; Yelles, Lotfi; Solanki, Sami; Lagg, Andreas Bibcode: 2010cosp...38.2827W Altcode: 2010cosp.meet.2827W Solar magnetic fields are usually extrapolated into the corona starting from photospheric mag-netic measurements that can suffer from significant uncertainties caused by the presence of unresolved fine structures due to a limited spatial resolution and by the limited polarimet-ric accuracy and spectral resolution. We investigate how these inaccuracies in the measured photospheric magnetic field vector influence the accuracy of the extrapolated coronal mag-netic field. We compare non-linear force-free coronal magnetic field extrapolations from a 3-D radiation MHD simulation snapshot with corresponding extrapolations from synthetic vector magnetograms. The synthetic magnetograms contain instrumental effects such as noise, limited spatial and spectral resolution and the effect of employing a filter instrument. The parameters are chosen in particular to mimic the effects of the Hinode/SOT and the future Solar Orbiter PHI instruments, respectively. We discuss, how photospheric structures, which are inherent in the MHD snapshot, but not resolved in the photospheric magnetic field measurements, influence the quality of the computed coronal magnetic field model. Title: Monitoring free magnetic energy in erupting active regions Authors: Wiegelmann, Thomas; Thalmann, Julia; Jing, Ju; Wang, Haimin Bibcode: 2010cosp...38.2960W Altcode: 2010cosp.meet.2960W In solar eruptions, like flares and coronal mass ejections, free magnetic energy stored in the solar corona is converted into kinetic energy. Unfortunately the coronal magnetic field cannot be measured directly. We can, however, reconstruct the coronal magnetic field from measurements of the photospheric magnetic field vector under the reasonable assumption of a force-free coronal plasma. With a procedure dubbed preprocessing we derive force-free consistent boundary conditions, which are extrapolated into the solar corona with a nonlinear force-free extrapolation code. The resulting 3D coronal magnetic field allows us to derive the magnetic topology and to computed the magnetic energy as well as an upper limited of the free energy available for driving eruptive phenomena. We apply our code to measurements from several ground based vector magnetographs, e.g. the Solar Flare Telescope, SOLIS and the Big Bear Solar Observatory. Within our studies we find a clear relationship between the stored magnetic energy and the strength of eruptions. In most cases not the entire free energy is converted to kinetic energy, but only a fraction. Consequently, the post-flare magnetic field configuration is usually not entirely current free, but significantly closer to a potential field as before the flare. Title: On the propagation of the polar jets from SECCHI/STEREO images Authors: Feng, Li; Inhester, Bernd; de Patoul, Judith; Wiegelmann, Thomas Bibcode: 2010cosp...38.2936F Altcode: 2010cosp.meet.2936F We present the propagation of the polar jets observed from the field of view of EUVI, COR1 to COR2 on board STEREO. We provide a method to test the free fall model both in 2D and 3D dimensions by comparing the height-time images extracted from observations with the free fall model. By assuming all the particles in polar jets are ejected at the same time when it is initiated, this method could produce the initial velocity distribution of the particles and tell us during the propagation whether the particles are ionized/recombined or experience some other processes. The derived 3D orientations of the polar jets are used to test different magnetic field models around polar regions where the observation and extrapolation are not reliable. The estimated 3D leading edge velocities by different telescopes are also investigated. Title: Automated Feature and Event Detection with SDO AIA and HMI Data Authors: Davey, Alisdair; Martens, P. C. H.; Attrill, G. D. R.; Engell, A.; Farid, S.; Grigis, P. C.; Kasper, J.; Korreck, K.; Saar, S. H.; Su, Y.; Testa, P.; Wills-Davey, M.; Savcheva, A.; Bernasconi, P. N.; Raouafi, N. -E.; Delouille, V. A.; Hochedez, J. F. .; Cirtain, J. W.; Deforest, C. E.; Angryk, R. A.; de Moortel, I.; Wiegelmann, T.; Georgouli, M. K.; McAteer, R. T. J.; Hurlburt, N.; Timmons, R. Bibcode: 2010cosp...38.2878D Altcode: 2010cosp.meet.2878D The Solar Dynamics Observatory (SDO) represents a new frontier in quantity and quality of solar data. At about 1.5 TB/day, the data will not be easily digestible by solar physicists using the same methods that have been employed for images from previous missions. In order for solar scientists to use the SDO data effectively they need meta-data that will allow them to identify and retrieve data sets that address their particular science questions. We are building a comprehensive computer vision pipeline for SDO, abstracting complete metadata on many of the features and events detectable on the Sun without human intervention. Our project unites more than a dozen individual, existing codes into a systematic tool that can be used by the entire solar community. The feature finding codes will run as part of the SDO Event Detection System (EDS) at the Joint Science Operations Center (JSOC; joint between Stanford and LMSAL). The metadata produced will be stored in the Heliophysics Event Knowledgebase (HEK), which will be accessible on-line for the rest of the world directly or via the Virtual Solar Observatory (VSO) . Solar scientists will be able to use the HEK to select event and feature data to download for science studies. Title: Nonlinear force-free extrapolation of SDO/HMI vector magnetograms in to the corona Authors: Tadesse Asfaw, Tilaye; Wiegelmann, Thomas; Inhester, Bernd Bibcode: 2010cosp...38.2866T Altcode: 2010cosp.meet.2866T SDO/HMI provides us high resolution full disk measurements of the photospheric magnetic field vector.We compute the field in the higher layers of the solar atmosphere from the measured photospheric field under the assumption that the corona is force-free. However, those measured data are inconsistent with the above force-free assumption. Therefore, one has to apply some transformations dubbed preprocessing to these data before nonlinear force-free extrapolation codes can be applied. Our force-free code is based on an optimization principle and takes the spherical geometry of the sun in to account. Untill now, these extrapolations were applied only to a small surface area of the Sun so that cartesian geometry could be applied. We carry out both full disk computations as well as computations of active regions. The code has been well tested with model equilibria and used with the ground based observations from SOLIS. We plan to show first Nonlinear force-free coronal magnetic fields extrapolated from SDO/HMI in comparison with the coronal plasma in SDO/HMI. Title: Nonlinear force-free coronal magnetic field modelling and preprocessing of vector magnetograms in spherical geometry Authors: Tadesse, T.; Wiegelmann, T.; Inhester, B. Bibcode: 2009A&A...508..421T Altcode: 2009arXiv0912.1514T Context: Knowledge about the coronal magnetic field is important to the understanding of many phenomena, such as flares and coronal mass ejections. Routine measurements of the solar magnetic field vector are traditionally carried out in the photosphere. We compute the field in the higher layers of the solar atmosphere from the measured photospheric field under the assumption that the corona is force-free. However, those measured data are inconsistent with the above force-free assumption. Therefore, one has to apply some transformations to these data before nonlinear force-free extrapolation codes can be applied.
Aims: Extrapolation codes of cartesian geometry for medelling the magnetic field in the corona do not take the curvature of the Sun's surface into account. Here we develop a method for nonlinear force-free coronal magnetic field medelling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure.
Methods: We describe a newly developed code for the extrapolation of nonlinear force-free coronal magnetic fields in spherical coordinates over a restricted area of the Sun. The program uses measured vector magnetograms on the solar photosphere as input and solves the force-free equations in the solar corona. We develop a preprocessing procedure in spherical geometry to drive the observed non-force-free data towards suitable boundary conditions for a force-free extrapolation.
Results: We test the code with the help of a semi-analytic solution and assess the quality of our reconstruction qualitatively by magnetic field line plots and quantitatively with a number of comparison metrics for different boundary conditions. The reconstructed fields from the lower boundary data with the weighting function are in good agreement with the original reference fields. We added artificial noise to the boundary conditions and tested the code with and without preprocessing. The preprocessing recovered all main structures of the magnetogram and removed small-scale noise. The main test was to extrapolate from the noisy photospheric vector magnetogram with and without preprocessing. The preprocessing was found to significantly improve the agreement between the extrapolated and the exact field.
Title: Internetwork Horizontal Magnetic Fields in the Quiet Sun Chromosphere: Results from a Joint Hinode/VTT Study Authors: Lagg, A.; Ishikawa, R.; Merenda, L.; Wiegelmann, T.; Tsuneta, S.; Solanki, S. K. Bibcode: 2009ASPC..415..327L Altcode: We present results from a joint Hinode/VTT campaign (May 2008). Spectropolarimetric data of a quiet Sun super-granular network cell at a heliocentric angle of 28° in the He I 10830 Å line were analyzed using an inversion code incorporating Hanle and Zeeman effects (HeLIx^+) to retrieve magnetic field strength and direction in the upper chromosphere. Simultaneously recorded Hinode SOT/SP data reveal the photospheric magnetic field morphology, clearly showing magnetic flux concentrations in the internetwork. The photospheric magnetic field maps are used to feed potential field extrapolations similar to the work by Schrijver & Title (2003). The extrapolated magnetic field structure is compared with the magnetic field configuration resulting from the He 10830 inversions. These inversions also reveal horizontal magnetic structures extending over a length of up to 20 Mm above the internetwork, indicative of the presence of a magnetic canopy. The photospheric magnetic flux concentrations in the internetwork are obviously not sufficiently strong to prevent the formation of a canopy at chromospheric heights. Title: Coronal hole boundaries evolution at small scales. I. EIT 195 Å  and TRACE 171 Å view Authors: Madjarska, M. S.; Wiegelmann, T. Bibcode: 2009A&A...503..991M Altcode: 2009arXiv0906.2556M Aims: We aim to study the small-scale evolution at the boundaries of an equatorial coronal hole connected with a channel of open magnetic flux to the polar region and an “isolated” one in the extreme-ultraviolet spectral range. We determine the spatial and temporal scale of these changes.
Methods: Imager data from TRACE in the Fe ix/x 171 Å passband and EIT on-board Solar and Heliospheric Observatory in the Fe xii 195 Å passband were analysed.
Results: We found that small-scale loops known as bright points play an essential role in coronal hole boundary evolution at small scales. Their emergence and disappearance continuously expand or contract coronal holes. The changes appear to be random on a time scale comparable to the lifetime of the loops seen at these temperatures. No signature was found for a major energy release during the evolution of the loops.
Conclusions: Although coronal holes seem to maintain their general shape during a few solar rotations, a closer look at their day-by-day and even hour-by-hour evolution demonstrates significant dynamics. The small-scale loops (10´´-40´´ and smaller) which are abundant along coronal hole boundaries contribute to the small-scale evolution of coronal holes. Continuous magnetic reconnection of the open magnetic field lines of the coronal hole and the closed field lines of the loops in the quiet Sun is more likely to take place.

Movies are only available in electronic form at http://www.aanda.org Title: Stereoscopic Polar Plume Reconstructions from STEREO/SECCHI Images Authors: Feng, L.; Inhester, B.; Solanki, S. K.; Wilhelm, K.; Wiegelmann, T.; Podlipnik, B.; Howard, R. A.; Plunkett, S. P.; Wuelser, J. P.; Gan, W. Q. Bibcode: 2009ApJ...700..292F Altcode: 2009arXiv0908.2365F We present stereoscopic reconstructions of the location and inclination of polar plumes of two data sets based on the two simultaneously recorded images taken by the EUVI telescopes in the SECCHI instrument package onboard the Solar TErrestrial RElations Observatory spacecraft. The 10 plumes investigated show a superradial expansion in the coronal hole in three dimensions (3D) which is consistent with the two-dimensional results. Their deviations from the local meridian planes are rather small with an average of 6fdg47. By comparing the reconstructed plumes with a dipole field with its axis along the solar rotation axis, it is found that plumes are inclined more horizontally than the dipole field. The lower the latitude is, the larger is the deviation from the dipole field. The relationship between plumes and bright points has been investigated and they are not always associated. For the first data set, based on the 3D height of plumes and the electron density derived from SUMER/SOHO Si VIII line pair, we found that electron densities along the plumes decrease with height above the solar surface. The temperature obtained from the density scale height is 1.6-1.8 times larger than the temperature obtained from Mg IX line ratios. We attribute this discrepancy to a deviation of the electron and the ion temperatures. Finally, we have found that the outflow speeds studied in the O VI line in the plumes corrected by the angle between the line of sight and the plume orientation are quite small with a maximum of 10 km s-1. It is unlikely that plumes are a dominant contributor to the fast solar wind. Title: Solar stereoscopy - where are we and what developments do we require to progress? Authors: Wiegelmann, T.; Inhester, B.; Feng, L. Bibcode: 2009AnGeo..27.2925W Altcode: 2009arXiv0912.1267W Observations from the two STEREO-spacecraft give us for the first time the possibility to use stereoscopic methods to reconstruct the 3-D solar corona. Classical stereoscopy works best for solid objects with clear edges. Consequently an application of classical stereoscopic methods to the faint structures visible in the optically thin coronal plasma is by no means straight forward and several problems have to be treated adequately: 1) First there is the problem of identifying one-dimensional structures - e.g. active region coronal loops or polar plumes- from the two individual EUV-images observed with STEREO/EUVI. 2) As a next step one has the association problem to find corresponding structures in both images. This becomes more difficult as the angle between STEREO-A and B increases. 3) Within the reconstruction problem stereoscopic methods are used to compute the 3-D-geometry of the identified structures. Without any prior assumptions, e.g., regarding the footpoints of coronal loops, the reconstruction problem has not one unique solution. 4) One has to estimate the reconstruction error or accuracy of the reconstructed 3-D-structure, which depends on the accuracy of the identified structures in 2-D, the separation angle between the spacecraft, but also on the location, e.g., for east-west directed coronal loops the reconstruction error is highest close to the loop top. 5) Eventually we are not only interested in the 3-D-geometry of loops or plumes, but also in physical parameters like density, temperature, plasma flow, magnetic field strength etc. Helpful for treating some of these problems are coronal magnetic field models extrapolated from photospheric measurements, because observed EUV-loops outline the magnetic field. This feature has been used for a new method dubbed "magnetic stereoscopy". As examples we show recent application to active region loops. Title: Hanle Effect Diagnostics of the Coronal Magnetic Field: A Test Using Realistic Magnetic Field Configurations Authors: Raouafi, N. -E.; Solanki, S. K.; Wiegelmann, T. Bibcode: 2009ASPC..405..429R Altcode: 2008arXiv0801.2202R Our understanding of coronal phenomena, such as coronal plasma thermodynamics, faces a major handicap caused by missing coronal magnetic field measurements. Several lines in the UV wavelength range present suitable sensitivity to determine the coronal magnetic field via the Hanle effect. The latter is a largely unexplored diagnostic of coronal magnetic fields with a very high potential. Here we study the magnitude of the Hanle-effect signal to be expected outside the solar limb due to the Hanle effect in polarized radiation from the H I Lyα and β lines, which are among the brightest lines in the off-limb coronal FUV spectrum. For this purpose we use a magnetic field structure obtained by extrapolating the magnetic field starting from photospheric magnetograms. The diagnostic potential of these lines for determining the coronal magnetic field, as well as their limitations are studied. We show that these lines, in particular H I Lyβ, are useful for such measurements. Title: Computer Vision for The Solar Dynamics Observatory Authors: Martens, Petrus C.; Angryk, R. A.; Bernasconi, P. N.; Cirtain, J. W.; Davey, A. R.; DeForest, C. E.; Delouille, V. A.; De Moortel, I.; Georgoulis, M. K.; Grigis, P. C.; Hochedez, J. E.; Kasper, J.; Korreck, K. E.; Reeves, K. K.; Saar, S. H.; Savcheva, A.; Su, Y.; Testa, P.; Wiegelmann, T.; Wills-Davey, M. Bibcode: 2009SPD....40.1711M Altcode: NASA funded a large international consortium last year to produce a comprehensive system for automated feature recognition in SDO images. The data we consider are all AIA and EVE data plus surface magnetic field images from HMI. Helioseismology is addressed by another group.

We will produce robust and very efficient software modules that can keep up with the relentless SDO data stream and detect, trace, and analyze a large number of phenomena, including: flares, sigmoids, filaments, coronal dimmings, polarity inversion lines, sunspots, X-ray bright points, active regions, coronal holes, EIT waves, CME's, coronal oscillations, and jets. In addition we will track the emergence and evolution of magnetic elements down to the smallest features that are detectable, and we will also provide at least four full disk nonlinear force-free magnetic field extrapolations per day.

A completely new software element that rounds out this suite is a trainable feature detection module, which employs a generalized image classification algorithm to produce the texture features of the images analyzed. A user can introduce a number of examples of the phenomenon looked and the software will return images with similar features. We have tested a proto-type on TRACE data, and were able to "train" the algorithm to detect sunspots, active regions, and loops. Such a module can be used to find features that have not even been discovered yet, as, for example, sigmoids were in the pre-Yohkoh era.

Our codes will produce entries in the Helio Events Knowledge base, and that will permit users to locate data on individual events as well as carry out statistical studies on large numbers of events, using the interface provided by the Virtual Solar Observatory. Title: Formation Heights of Extreme Ultraviolet Lines in an Active Region Derived by Correlation of Doppler Velocity and Magnetic Field Authors: Guo, Y.; Ding, M. D.; Jin, M.; Wiegelmann, T. Bibcode: 2009ApJ...696.1526G Altcode: 2009arXiv0903.4343G We study the correlation heights, which indicate the formation height of Extreme Ultraviolet (EUV) lines in an active region using observations from the EUV Imaging Spectrometer and Solar Optical Telescope on board Hinode. The nonlinear force-free field optimization method is adopted to extrapolate the three-dimensional magnetic fields to higher layers. Three subregions with different characteristics are selected in the active region for this study. The results show that the formation heights in different subregions vary with their different magnetic fields or velocity patterns. After solving the line blending problem between the He II 256.32 Å and Si X 256.37 Å lines by the double Gaussian curve fitting, we find that the transition region lies higher in a strong magnetic area. In a preflare heating area, there possibly exist multithermal loops as implied by comparing the Doppler velocity and the magnetic field on the solar disk. Title: Temporal Evolution of Free Magnetic Energy Associated with Four X-Class Flares Authors: Jing, Ju; Chen, P. F.; Wiegelmann, Thomas; Xu, Yan; Park, Sung-Hong; Wang, Haimin Bibcode: 2009ApJ...696...84J Altcode: We study the temporal variation of free magnetic energy E free around the time of four X-class flares. The high-cadence photospheric vector magnetograms obtained by the digital vector magnegograph system at the Big Bear Solar Observatory are used as the boundary conditions to reconstruct the three-dimensional nonlinear force-free (NLFF) coronal field. In order to remove the effect of the net Lorentz force and torque acting in the photosphere, the vector magnetograms are preprocessed using the method devised by Wiegelmann et al.. Then a well-tested multigrid-like optimization code by Wiegelmann is applied to the preprocessed boundary data to extrapolate the NLFF coronal field with which we are able to estimate the free energy E free. In all the four events, we find a significant drop of E free starting ~15 minutes before the peak time of the associated nonthermal flare emission, although long-term trend varies from event to event. We discuss the physical implication of the result, i.e., the magnetic relaxation is already going on in the corona well before the flare reconnection. Title: Nonlinear Force-Free Magnetic Field Modeling of AR 10953: A Critical Assessment Authors: De Rosa, Marc L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.; Lites, B. W.; Aschwanden, M. J.; Amari, T.; Canou, A.; McTiernan, J. M.; Régnier, S.; Thalmann, J. K.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung, M. C. M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T. Bibcode: 2009SPD....40.3102D Altcode: Nonlinear force-free field (NLFFF) modeling seeks to provide accurate representations of the structure of the magnetic field above solar active regions, from which estimates of physical quantities of interest (e.g., free energy and helicity) can be made. However, the suite of NLFFF algorithms have failed to arrive at consistent solutions when applied to (thus far, two) cases using the highest-available-resolution vector magnetogram data from Hinode/SOT-SP (in the region of the modeling area of interest) and line-of-sight magnetograms from SOHO/MDI (where vector data were not available). One issue is that NLFFF models require consistent, force-free vector magnetic boundary data, and vector magnetogram data sampling the photosphere do not satisfy this requirement. Consequently, several problems have arisen that are believed to affect such modeling efforts. We use AR 10953 to illustrate these problems, namely: (1) some of the far-reaching, current-carrying connections are exterior to the observational field of view, (2) the solution algorithms do not (yet) incorporate the measurement uncertainties in the vector magnetogram data, and/or (3) a better way is needed to account for the Lorentz forces within the layer between the photosphere and coronal base. In light of these issues, we conclude that it remains difficult to derive useful and significant estimates of physical quantities from NLFFF models. Title: A Critical Assessment of Nonlinear Force-Free Field Modeling of the Solar Corona for Active Region 10953 Authors: De Rosa, Marc L.; Schrijver, Carolus J.; Barnes, Graham; Leka, K. D.; Lites, Bruce W.; Aschwanden, Markus J.; Amari, Tahar; Canou, Aurélien; McTiernan, James M.; Régnier, Stéphane; Thalmann, Julia K.; Valori, Gherardo; Wheatland, Michael S.; Wiegelmann, Thomas; Cheung, Mark C. M.; Conlon, Paul A.; Fuhrmann, Marcel; Inhester, Bernd; Tadesse, Tilaye Bibcode: 2009ApJ...696.1780D Altcode: 2009arXiv0902.1007D Nonlinear force-free field (NLFFF) models are thought to be viable tools for investigating the structure, dynamics, and evolution of the coronae of solar active regions. In a series of NLFFF modeling studies, we have found that NLFFF models are successful in application to analytic test cases, and relatively successful when applied to numerically constructed Sun-like test cases, but they are less successful in application to real solar data. Different NLFFF models have been found to have markedly different field line configurations and to provide widely varying estimates of the magnetic free energy in the coronal volume, when applied to solar data. NLFFF models require consistent, force-free vector magnetic boundary data. However, vector magnetogram observations sampling the photosphere, which is dynamic and contains significant Lorentz and buoyancy forces, do not satisfy this requirement, thus creating several major problems for force-free coronal modeling efforts. In this paper, we discuss NLFFF modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT, STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process illustrate three such issues we judge to be critical to the success of NLFFF modeling: (1) vector magnetic field data covering larger areas are needed so that more electric currents associated with the full active regions of interest are measured, (2) the modeling algorithms need a way to accommodate the various uncertainties in the boundary data, and (3) a more realistic physical model is needed to approximate the photosphere-to-corona interface in order to better transform the forced photospheric magnetograms into adequate approximations of nearly force-free fields at the base of the corona. We make recommendations for future modeling efforts to overcome these as yet unsolved problems. Title: Free Magnetic Energy and Flare Productivity of Active Regions Authors: Jing, Ju; Tan, C.; Wiegelmann, T.; Xu, Y.; Wang, H. Bibcode: 2009SPD....40.2009J Altcode: We study the magnitude scaling correlation between coronal free magnetic energy and flare productivity of active regions. The vector magnetograms from Hinode are used as the boundary conditions to extrapolate the 3-dimensional nonlinear force-free (NLFF) coronal magnetic fields and the potential fields. Free magnetic energy of NLFF fields is calculated as the excess magnetic energy above the potential fields over the volume of the computational box. For each active region, we select one vector magnetogram in which the active region is viewed as close to the disk center as possible. The flare productivity of active regions is quantified by the soft X-ray flare index for two different time windows: one covers the entire disk passage of active regions, the other covers 3 days starting from the time of the analyzed magnetogram. Based on the limited samples we have studied so far, we find a positive correlation between free energy and flare index. The correlation confirms the physical link between the quantities and carries important statistical information for the flare forecasting.

The work is supported by NSF under grant ATM 07-16950 and NASA under grant NNX08AQ89G. Title: Source region of the 18 November 2003 coronal mass ejection that led to the strongest magnetic storm of cycle 23 Authors: Srivastava, Nandita; Mathew, Shibu K.; Louis, Rohan E.; Wiegelmann, Thomas Bibcode: 2009JGRA..114.3107S Altcode: 2008arXiv0812.5046S; 2009JGRA..11403107S The superstorm of 20 November 2003 was associated with a high-speed coronal mass ejection (CME) which originated in the NOAA AR 10501 on 18 November. This coronal mass ejection had severe terrestrial consequences leading to a geomagnetic storm with Dst index of -472 nT, the strongest of the current solar cycle. In this paper, we attempt to understand the factors that led to the coronal mass ejection on 18 November. We have also studied the evolution of the photospheric magnetic field of NOAA AR 10501, the source region of this coronal mass ejection. For this purpose, the Michelson Doppler Imager line-of-sight magnetograms and vector magnetograms from Solar Flare Telescope, Mitaka, obtained during 17-19 November 2003 were analyzed. In particular, quantitative estimates of the temporal variation in magnetic flux, energy, and magnetic field gradient were estimated for the source active region. The evolution of these quantities was studied for the 3-day period with an objective to understand the preflare configuration leading up to the moderate flare which was associated with the geoeffective coronal mass ejection. We also examined the chromospheric images recorded in H α from Udaipur Solar Observatory to compare the flare location with regions of different magnetic field and energy. Our observations provide evidence that the flare associated with the CME occurred at a location marked by high magnetic field gradient which led to release of free energy stored in the active region. Title: Multiple-spacecraft study of an extended magnetic structure in the solar wind Authors: Ruan, P.; Korth, A.; Marsch, E.; Inhester, B.; Solanki, S.; Wiegelmann, T.; Zong, Q. -G.; Bucik, R.; Fornacon, K. -H. Bibcode: 2009JGRA..114.2108R Altcode: 2009JGRA..11402108R An extended magnetic structure was observed consecutively by five spacecraft (ACE, WIND, STEREO A and B, and CLUSTER) in the solar wind on 15 January 2007. The similar bipolar magnetic field variations from five spacecraft suggest that the magnetic structure is two-dimensional. The abrupt disappearance of the beam electrons in the core of the structure suggests that the core of the structure is magnetically isolated from the surrounding environment. Our analysis shows that this magnetic structure is a magnetic flux rope, which extends over at least 180 R E in space. The length and orientation of the flux rope were determined by a local minimum variance analysis (MVA) from individual spacecraft observations of the magnetic field and a timing analysis based on the joint observations by all five spacecraft. The results show that the orientation of the flux rope stays constant in space and time. The flux rope is embedded in a corotating interaction region (CIR), which followed a magnetic cloud. Title: Magnetic Field Extrapolation of Flaring Active Regions Authors: Thalmann, J. K.; Wiegelmann, T. Bibcode: 2009CEAB...33..131T Altcode: The solar corona is structured by magnetic fields. As direct measurements of the coronal magnetic field are not routinely available, it is extrapolated from photospheric vector magnetograms. When magnetic flux emerges from below the solar surface and expands into the corona, the coronal magnetic field is destabilized, leading to explosive phenomena like flares or coronal mass ejections. Our aim is to get insights in the coronal magnetic field structure in active regions and to study its temporal evolution. We are in particular interested to investigate the magnetic configuration of active regions in the course of flares. Therefore, we study the temporal evolution of the flaring active regions NOAA 10540 and NOAA 10960 as observed in January 2004 and June 2007, respectively. We are in particular interested in the free magnetic energy available to power the flares associated with it. To investigate AR 10540 we used photospheric vector magnetograms measured with the Solar Flare Telescope VectorMagnetograph and for AR 10960 we used data provided by the Synoptic Optical Long-term Investigations of the Sun VectorSpectroMagnetograph. We extrapolated these measurements into the corona with the help of a nonlinear force-free field model based on a well-tested multigrid-like optimization code with which we were able to estimate the energy content of the 3D coronal fields, as well as an upper limit for its free magnetic energy. Title: Nonlinear Force-Free Magnetic Field Modeling of the Solar Corona: A Critical Assessment Authors: De Rosa, M. L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.; Lites, B. W.; Aschwanden, M. J.; McTiernan, J. M.; Régnier, S.; Thalmann, J.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung, M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T. Bibcode: 2008AGUFMSH41A1604D Altcode: Nonlinear force-free field (NLFFF) modeling promises to provide accurate representations of the structure of the magnetic field above solar active regions, from which estimates of physical quantities of interest (e.g., free energy and helicity) can be made. However, the suite of NLFFF algorithms have so far failed to arrive at consistent solutions when applied to cases using the highest-available-resolution vector magnetogram data from Hinode/SOT-SP (in the region of the modeling area of interest) and line-of-sight magnetograms from SOHO/MDI (where vector data were not been available). It is our view that the lack of robust results indicates an endemic problem with the NLFFF modeling process, and that this process will likely continue to fail until (1) more of the far-reaching, current-carrying connections are within the observational field of view, (2) the solution algorithms incorporate the measurement uncertainties in the vector magnetogram data, and/or (3) a better way is found to account for the Lorentz forces within the layer between the photosphere and coronal base. In light of these issues, we conclude that it remains difficult to derive useful and significant estimates of physical quantities from NLFFF models. Title: A First Step Towards a Nonlinear and Self-consistent Modelling of the Interface Region Between Photosphere, Chromosphere and Corona Authors: Wiegelmann, T.; Neukirch, T. Bibcode: 2008AGUFMSH51C..02W Altcode: The interface region between the solar photosphere and corona is an interesting environment which is, however, difficult to model. Low and high plasma-beta regions are present in this layer side by side and require that the magnetic field and plasma are modelled self-consistently in one model. A popular simplification used to model the low beta solar corona is the assumption of force-free magnetic fields, but this approach is not justified in the mixed beta interface region. We can, however, generalize numerical schemes developed for nonlinear force-free magnetic field extrapolations. Here we report a first step towards such an approach based on an optimization principle which solves the non-force-free magneto-hydrostatic equations by minimizing a functional. As a result we get a self-consistent equilibrium of magnetic field, plasma density and plasma pressure. Measured quantities, e.g. the photospheric magnetic field vector, are used as boundary condition. We test our code with the help of a semi-analytic magneto-hydro-static equilibrium. The quality of the reconstruction was judged by comparing the exact and reconstructed solution qualitatively by magnetic field-line plots and artificial plasma-images and quantitatively by several different numerical criteria. Our code is able to reconstruct this semi-analytic test equilibrium with high accuracy. The strongly varying plasma-beta environment requires, however, a smaller time step and longer computing time compared with low beta force-free field extrapolations. Title: A MHS model in the solar corona Authors: Ruan, P.; Wiegelmann, T.; Inhester, B.; Neukirch, T. Bibcode: 2008AGUFMSH13B1521R Altcode: Since direct measurements of the solar coronal magnetic field and plasma are extremely difficult and inaccurate, we use a modeling approach based on observational quantities, e.g. the measured photospheric magnetic field, to reconstruct the structure of the global solar corona.An analytic magnetohydrostatic (MHS) model (Neukirch 95) was taken to extrapolate the magnetic field in the corona from photospheric magnetic field measurement from the Wilcox Solar Observatory. The boundary conditions are given by a synoptic magnetogram on the photosphere and by a source surface at the outer boundary. In the model, the electric current density was decomposed into two components: one component is aligned with the magnetic field lines, whereas the other component flows in spherical shells. The second component of the current generates finite Lorentz forces, which are balanced by the plasma pressure gradient and the gravity force. So the 3D distribution of the magnetic field and plasma can be derived self-consistently in one model. The magnetic field distribution of our model differs noticeably from both potential and force-free field models for the same boundary conditions. The plasma density in the MHS model is higher in the equatorial plane than in the polar region, which gives a reasonable result. Title: Evolution of two Flaring Active Regions With CME Association Authors: Thalmann, J. K.; Wiegelmann, T. Bibcode: 2008AGUFMSH23B1642T Altcode: We study the coronal magnetic field structure of two active regions, one during solar activity minimum (June 2007) and another one during a more active time (January 2004). The temporal evolution was explored with the help of nonlinear force-free coronal magnetic field extrapolations of SOLIS/VSM and NAOJ/SFT photospheric vector magnetograms. We study the active region NOAA 10960 observed on 2007 June 7 with three SOLIS/VSM snapshots taken during a small C1.0 flare of time cadence 10 minutes and six snapshots during a quiet period. The total magnetic energy in the active region was approximately 3 × 1025 J. Before the flare the free magnetic energy was about 5~% of the potential field energy. A part of this excess energy was released during the flare, producing almost a potential configuration at the beginning of the quiet period. The return to an almost potential structure can be assigned to a CME as recorded by the SoHO/LASCO instrument on 2007 June 07 around 10 minutes after the flare peaked, so that whatever magnetic helicity was bodily removed from the structure. This was compared with active region 10540 observed on 2004 January 18 -- 21, which was analyzed with the help of vector magnetograph data from the Solar Flare Telescope in Japan of time cadence of about 1 day. The free energy was Efree≈ 66~% of the total energy which was sufficiently high to power a M6.1 flare on January 20, which was associated with a CME 20 minutes later. The activity of AR 10540 was significantly higher than for AR 10960, as was the total magnetic energy. Furthermore, we found the common feature that magnetic energy accumulates before the flare/CME and a significant part of the excess energy is released during the eruption. Title: 3D Reconstruction of Polar Plumes From STEREO/SECCHI Images. Authors: Feng, L.; de Patoul, J.; Inhester, B.; Wiegelmann, T. Bibcode: 2008AGUFMSH44A..05F Altcode: We provide a newly developed approach to determine the 3D structure of high latitude open magnetic fields as visible in polar plumes. Our data are image pairs taken by the SECCHI-EUVI telescopes on board of the two STEREO spacecraft. From these image pairs we identify the plumes by two different methods. The first method identifies the plume axes by the local intensity maxima and the second method uses image processing tools such as the Hough Transform. The Hough Transform transfers plumes from images into points, called Hough coordinates, which can directly be used to calculate the 3D location of the plume. The automatic plume detection by the Hough transform method is well suited to study their temporal evolution. The capability of our code has been investigated with synthetic images taken from a 3D magnetohydrostatic corona model (Neukirch, 1995) and we apply our methods to study polar plumes observed from two vantage viewpoints. We identify the locations of the footpoints of the polar plumes in the photosphere as well as their inclination relative to the line-of-sight and to their local radial direction. The relationship between plume and bright point are investigated. With the help of SOHO/SUMER observations we derive the density scale height in the plumes. We found that plumes are not the main contributor to the fast solar wind. Title: Study of Magnetic Channel Structure in Active Region 10930 Authors: Wang, Haimin; Jing, Ju; Tan, Changyi; Wiegelmann, Thomas; Kubo, Masahito Bibcode: 2008ApJ...687..658W Altcode: The concept of "magnetic channel" was first introduced by Zirin & Wang. They were defined as a series of oppositely directed vertical-field inversions separated by extremely narrow elongated transverse fields. In this paper, we utilized unprecedented filtergraph and spectropolarimetry observations from Hinode, and studied the evolution and physical properties of channel structure of AR 10930 in detail. We found the following: (1) Channels are associated with new flux emergence in the middle of existing penumbra connecting the δ sunspot. (2) The width of each channel is in the order of 1'' or less. (3) The line-of-sight magnetic gradient is highest in the channel, 2.4-4.9 G km-1. (4) The fields are highly sheared and inclined with a median shear angle around 64° and inclination angle around 25°. (5) Using nonlinear force-free field (NLFF) extrapolation, we derive a near surface current system carrying electric current in the order of 5 × 1011 A. (6) The X3.4 flare on 2006 December 13 occurred during the period that the channels rapidly formed, but a few hours before the maximum phase of channel structure development. Based on the observational evidence, we propose that the channels are formed during the emergence of a sequence of magnetic bipoles that are squeezed in the compact penumbra of the δ sunspot and they are highly nonpotential. Formation of channels might be a precursor of major flares. Title: Plasma Flows Guided by Strong Magnetic Fields in the Solar Corona Authors: Marsch, Eckart; Tian, Hui; Sun, Jian; Curdt, Werner; Wiegelmann, Thomas Bibcode: 2008ApJ...685.1262M Altcode: In this study new results are presented regarding the relationships between the coronal magnetic field and the intensities and Doppler shifts of ultraviolet emission lines. This combination of magnetic field and spectroscopic data is used here to study material flows in association with the coronal field. We introduce the term "coronal circulation" to describe this flow, and to indicate that the plasma is not static but flows everywhere in the extended solar atmosphere. The blueshifts and redshifts often seen in transition region and coronal ultraviolet emission lines are interpreted as corresponding to upflows and downflows of the plasma on open (funnels) and closed (loops) coronal magnetic field lines, which tightly confine and strongly lead the flows in the low-beta plasma. Evidence for these processes exists in the ubiquitous redshifts mostly seen at both legs of loops on all scales, and the sporadic blueshifts occurring in strong funnels. Therefore, there is no static magnetically stratified plasma in the corona, since panta rhei, but rather a continuous global plasma circulation, being the natural perpetuation of photospheric convection which ultimately is the driver. Title: Loop Morphology and Flows and their Relation to the Magnetic Field Authors: Teriaca, L.; Wiegelmann, T.; Lagg, A.; Solanki, S. K.; Curdt, W.; Sekii, T. Bibcode: 2008ASPC..397..196T Altcode: In November 2006 we obtained several rasters of a large sunspot and its trailing region using the SUMER spectrometer on SOHO. The observations consist of spectroheliograms in the continuum around 142 nm and in several spectral lines formed between 80000 K and 0.6 MK, covering the temperature range from the chromosphere to the lower corona. The observed profiles provide LOS velocity and Doppler width maps. TRACE images in the EUV passbands and in the 160 nm continuum provide a clear picture of the coronal loops and the chromosphere near their footpoints. The same target was also observed by all the instruments aboard Hinode and, in particular, by the SOT spectro-polarimeter measuring the photospheric magnetic vector. We combined SOT and MDI data (covering a larger FOV) to infer the coronal magnetic field of the active region by a nonlinear force-free field extrapolation. The observed radiance and velocity patterns at the various heights/temperatures throughout the solar atmosphere are compared with the field topology. Title: First nonlinear force-free field extrapolations of SOLIS/VSM data Authors: Thalmann, J. K.; Wiegelmann, T.; Raouafi, N. -E. Bibcode: 2008A&A...488L..71T Altcode: 2008arXiv0809.1428T Aims: We study the coronal magnetic field structure inside active regions and its temporal evolution. We attempt to compare the magnetic configuration of an active region in a very quiet period with that for the same region during a flare.
Methods: Probably for the first time, we use vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS) to model the coronal magnetic field as a sequence of nonlinear force-free equilibria. We study the active region NOAA 10960 observed on 2007 June 7 with three snapshots taken during a small C1.0 flare of time cadence 10 min and six snapshots during a quiet period.
Results: The total magnetic energy in the active region was approximately 3 × 1025 J. Before the flare the free magnetic energy was about 5% of the potential field energy. A part of this excess energy was released during the flare, producing almost a potential configuration at the beginning of the quiet period.
Conclusions: During the investigated period, the coronal magnetic energy was only a few percent higher than that of the potential field and consequently only a small C1.0 flare occurred. This was compared with an earlier investigated active region 10540, where the free magnetic energy was about 60% higher than that of the potential field producing two M-class flares. However, the free magnetic energy accumulates before and is released during the flare which appears to be the case for both large and small flares. Title: Preprocessing of Hinode/SOT Vector Magnetograms for Nonlinear Force-Free Coronal Magnetic Field Modeling Authors: Wiegelmann, T.; Thalmann, J. K.; Schrijver, C. J.; De Rosa, M. L.; Metcalf, T. R. Bibcode: 2008ASPC..397..198W Altcode: 2008arXiv0801.2884W The solar magnetic field is key to understanding the physical processes in the solar atmosphere. Nonlinear force-free codes have been shown to be useful in extrapolating the coronal field from underlying vector boundary data (for an overview see Schrijver et al. (2006)). However, we can only measure the magnetic field vector routinely with high accuracy in the photosphere with, e.g., Hinode/SOT, and unfortunately these data do not fulfill the force-free consistency condition as defined by Aly (1989). We must therefore apply some transformations to these data before nonlinear force-free extrapolation codes can be legitimately applied. To this end, we have developed a minimization procedure that uses the measured photospheric field vectors as input to approximate a more chromospheric like field (The method was dubbed preprocessing. See Wiegelmann et al. (2006) for details). The procedure includes force-free consistency integrals and spatial smoothing. The method has been intensively tested with model active regions (see Metcalf et al. 2008) and been applied to several ground based vector magnetogram data before. Here we apply the preprocessing program to photospheric magnetic field measurements with the Hinode/SOT instrument. Title: 3D Magnetic Field Configuration of the 2006 December 13 Flare Extrapolated with the Optimization Method Authors: Guo, Y.; Ding, M. D.; Wiegelmann, T.; Li, H. Bibcode: 2008ApJ...679.1629G Altcode: The photospheric vector magnetic field of the active region NOAA 10930 was obtained with the Solar Optical Telescope (SOT) on board the Hinode satellite with a very high spatial resolution (about 0.3''). Observations of the two-ribbon flare on 2006 December 13 in this active region provide us a good sample to study the magnetic field configuration related to the occurrence of the flare. Using the optimization method for nonlinear force-free field (NLFFF) extrapolation proposed by Wheatland et al. and recently developed by Wiegelmann, we derive the three-dimensional (3D) vector magnetic field configuration associated with this flare. The general topology can be described as a highly sheared core field and a quasi-potential envelope arch field. The core field clearly shows some dips supposed to sustain a filament. Free energy release in the flare, calculated by subtracting the energy contained in the NLFFF and the corresponding potential field, is 2.4 × 1031 ergs, which is ~2% of the preflare potential field energy. We also calculate the shear angles, defined as the angles between the NLFFF and potential field, and find that they become larger at some particular sites in the lower atmosphere, while they become significantly smaller in most places, implying that the whole configuration gets closer to the potential field after the flare. The Ca II H line images obtained with the Broadband Filter Imager (BFI) of the SOT and the 1600 Å images with the Transition Region and Coronal Explorer (TRACE) show that the preflare heating occurs mainly in the core field. These results provide evidence in support of the tether-cutting model of solar flares. Title: Evolution of the flaring active region NOAA 10540 as a sequence of nonlinear force-free field extrapolations Authors: Thalmann, J. K.; Wiegelmann, T. Bibcode: 2008A&A...484..495T Altcode: Context: The solar corona is structured by magnetic fields. As direct measurements of the coronal magnetic field are not routinely available, it is extrapolated from photospheric vector magnetograms. When magnetic flux emerges from below the solar surface and expands into the corona, the coronal magnetic field is destabilized, leading to explosive phenomena like flares or coronal mass ejections.
Aims: We study the temporal evolution of the flaring active region NOAA 10540 and are in particular interested in the free magnetic energy available to power the flares associated with it.
Methods: We extrapolated photospheric vector magnetograms measured with the Solar Flare Telescope, located in Tokyo, into the corona with the help of a nonlinear force-free field model. This coronal magnetic field model is based on a well-tested multigrid-like optimization code with which we were able to estimate the energy content of the 3D coronal field, as well as an upper limit for its free magnetic energy. Furthermore, the evolution of the energy density with height and time was studied.
Results: The coronal magnetic field energy in active region 10540 increases slowly during the three days before an M6.1 flare and drops significantly after it. We estimated the energy that was set free during this event as ∝1025 J. A sequence of nonlinear force-free extrapolations of the coronal magnetic field shows a build up of magnetic energy before a flare and release of energy during the flare. The drop in magnetic energy of the active region is sufficient to power an M6.1 flare. Title: First stereoscopic polar plume reconstructions from STEREO/SECCHI images Authors: Feng, L.; Inhester, B.; Solanki, S. K.; Wiegelmann, T.; Podlipnik, B.; Howard, R.; Plunkett, S.; Wuelser, J.; Gan, W. Bibcode: 2008AGUSMSH23A..01F Altcode: We present the first stereoscopic reconstruction of the three-dimensional structures of polar plumes based on the two simultaneously recorded images taken by the EUVI telescopes in the SECCHI instrument package onboard the recently launched STEREO mission. The reconstructed polar plumes were observed on April 7th, 2007 when the two spacecraft were well below the solar equatorial plane, an appropriate time for the observation of the plumes in the south polar coronal hole. The heliocentric separation of the two spacecraft was 3.6 degrees at that time. We determine locations of the footpoints of five EUV polar plumes on the solar surface as well as their inclinations relative to the line-of-sight and to their local radial directions. The five plumes are all within 21 degrees of the south pole and their inclinations to the line-of-sight of STEREO A(head) and radial directions are on average 107 degrees and 28 degrees, respectively. A simple dipole model for the south pole's magnetic field does not provide a good correspondence with the obtained inclinations. Of the three plumes in front of the limb only one is associated with an EUV bright point. Title: Changes of Magnetic Structure in 3-D Associated with the X3.4 Flare of 2006 December 13 Authors: Jing, J.; Wiegelmann, T.; Suematsu, Y.; Kubo, M.; Wang, H. Bibcode: 2008AGUSMSP51C..02J Altcode: Recent observations demonstrated that sunspot structure can change rapidly and irreversibly after flares. One of the most puzzling results is the increase in magnetic shear around flaring magnetic polarity inversion line after flares. However, all these observations were made at the photosphere level. We study the altitude variation of the non-potentiality of the magnetic fields associated with the 4B/X3.4 flare of 2006 December 13. The vector magnetograms with unprecedented quality from Hinode before and after the flare are used as the boundary conditions to extrapolate the 3-dimensional non-linear force-free magnetic fields and the potential fields. The former are computed with the optimization algorithm and the latter with Green's function method. At the photosphere boundary, magnetic shear increases after the flare in a local area close to the flaring magnetic polarity inversion line. Two measures of the magnetic non-potentiality, the weighted mean shear θw and the total magnetic shear θwB, are calculated in this area at progressively higher altitude. By comparing their altitude variation profiles before and after the flare, we find that the non-potentiality of the local area increases after the flare below ~8 Mm and decreases from that height to ~70 Mm. Beyond 70 Mm, the magnetic fields approach potential for both times. Title: Non-Linear Force-Free Field Modeling of a Solar Active Region Around the Time of a Major Flare and Coronal Mass Ejection Authors: De Rosa, M. L.; Schrijver, C. J.; Metcalf, T. R.; Barnes, G.; Lites, B.; Tarbell, T.; McTiernan, J.; Valori, G.; Wiegelmann, T.; Wheatland, M.; Amari, T.; Aulanier, G.; Démoulin, P.; Fuhrmann, M.; Kusano, K.; Régnier, S.; Thalmann, J. Bibcode: 2008AGUSMSP31A..06D Altcode: Solar flares and coronal mass ejections are associated with rapid changes in coronal magnetic field connectivity and are powered by the partial dissipation of electrical currents that run through the solar corona. A critical unanswered question is whether the currents involved are induced by the advection along the photosphere of pre-existing atmospheric magnetic flux, or whether these currents are associated with newly emergent flux. We address this problem by applying nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA Active Region 10930 around the time of a powerful X3.4 flare in December 2006. We compute 14 NLFFF models using 4 different codes having a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We do find agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the ~1032~erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection. We discuss the relative merits of these models in a general critique of our present abilities to model the coronal magnetic field based on surface vector field measurements. Title: A first step in reconstructing the solar corona self-consistently with a magnetohydrostatic model during solar activity minimum Authors: Ruan, P.; Wiegelmann, T.; Inhester, B.; Neukirch, T.; Solanki, S. K.; Feng, L. Bibcode: 2008A&A...481..827R Altcode: Aims: We compute the distribution of the magnetic field and the plasma in the global corona with a self-consistent magnetohydrostatic (MHS) model.
Methods: Because direct measurements of the solar coronal magnetic field and plasma are extremely difficult and inaccurate, we use a modeling approach based on observational quantities, e.g. the measured photospheric magnetic field, to reconstruct the structure of the global solar corona. We take an analytic magnetohydrostatic model to extrapolate the magnetic field in the corona from photospheric magnetic field measurement. In the model, the electric current density can be decomposed into two components: one component is aligned with the magnetic field lines, whereas the other component flows in spherical shells. The second component of the current produces finite Lorentz forces that are balanced by the pressure gradient and the gravity force. We derive the 3D distribution of the magnetic field and plasma self-consistently in one model. The boundary conditions are given by a synoptic magnetogram on the inner boundary and by a source surface model at the outer boundary.
Results: The density in the model is higher in the equatorial plane than in the polar region. We compare the magnetic field distribution of our model with potential and force-free field models for the same boundary conditions and find that our model differs noticeably from both. We discuss how to apply the model and how to improve it. Title: Theoretical modeling for the stereo mission Authors: Aschwanden, Markus J.; Burlaga, L. F.; Kaiser, M. L.; Ng, C. K.; Reames, D. V.; Reiner, M. J.; Gombosi, T. I.; Lugaz, N.; Manchester, W.; Roussev, I. I.; Zurbuchen, T. H.; Farrugia, C. J.; Galvin, A. B.; Lee, M. A.; Linker, J. A.; Mikić, Z.; Riley, P.; Alexander, D.; Sandman, A. W.; Cook, J. W.; Howard, R. A.; Odstrčil, D.; Pizzo, V. J.; Kóta, J.; Liewer, P. C.; Luhmann, J. G.; Inhester, B.; Schwenn, R. W.; Solanki, S. K.; Vasyliunas, V. M.; Wiegelmann, T.; Blush, L.; Bochsler, P.; Cairns, I. H.; Robinson, P. A.; Bothmer, V.; Kecskemety, K.; Llebaria, A.; Maksimovic, M.; Scholer, M.; Wimmer-Schweingruber, R. F. Bibcode: 2008SSRv..136..565A Altcode: 2006SSRv..tmp...75A We summarize the theory and modeling efforts for the STEREO mission, which will be used to interpret the data of both the remote-sensing (SECCHI, SWAVES) and in-situ instruments (IMPACT, PLASTIC). The modeling includes the coronal plasma, in both open and closed magnetic structures, and the solar wind and its expansion outwards from the Sun, which defines the heliosphere. Particular emphasis is given to modeling of dynamic phenomena associated with the initiation and propagation of coronal mass ejections (CMEs). The modeling of the CME initiation includes magnetic shearing, kink instability, filament eruption, and magnetic reconnection in the flaring lower corona. The modeling of CME propagation entails interplanetary shocks, interplanetary particle beams, solar energetic particles (SEPs), geoeffective connections, and space weather. This review describes mostly existing models of groups that have committed their work to the STEREO mission, but is by no means exhaustive or comprehensive regarding alternative theoretical approaches. Title: Segmentation of Loops from Coronal EUV Images Authors: Inhester, B.; Feng, L.; Wiegelmann, T. Bibcode: 2008SoPh..248..379I Altcode: 2008arXiv0801.3240I We present a procedure to extract bright loop features from solar EUV images. In terms of image intensities, these features are elongated ridge-like intensity maxima. To discriminate the maxima, we need information about the spatial derivatives of the image intensity. Commonly, the derivative estimates are strongly affected by image noise. We therefore use a regularized estimation of the derivative, which is then used to interpolate a discrete vector field of ridge points; these "ridgels" are positioned on the ridge center and have the intrinsic orientation of the local ridge direction. A scheme is proposed to connect ridgels to smooth, spline-represented curves that fit the observed loops. Finally, a half-automated user interface allows one to merge or split curves or eliminate or select loop fits obtained from this procedure. In this paper we apply our tool to one of the first EUV images observed by the SECCHI instrument onboard the recently launched STEREO spacecraft. We compare the extracted loops with projected field lines computed from near-simultaneous magnetograms measured by the SOHO/MDI Doppler imager. The field lines were calculated by using a linear force-free field model. This comparison allows one to verify faint and spurious loop connections produced by our segmentation tool and it also helps to prove the quality of the magnetic-field model where well-identified loop structures comply with field-line projections. We also discuss further potential applications of our tool such as loop oscillations and stereoscopy. Title: Changes of Magnetic Structure in Three Dimensions Associated with the X3.4 Flare of 2006 December 13 Authors: Jing, Ju; Wiegelmann, Thomas; Suematsu, Yoshinori; Kubo, Masahito; Wang, Haimin Bibcode: 2008ApJ...676L..81J Altcode: Recent observations demonstrated that sunspot structure can change rapidly and irreversibly after flares. One of the most puzzling results is the increase in magnetic shear around the flaring magnetic polarity inversion line after flares. However, all these observations were made at the photosphere level. In this Letter, we study the altitude variation of the nonpotentiality of the magnetic fields associated with the 4B/X3.4 flare of 2006 December 13. The vector magnetograms with unprecedented quality from Hinode before and after the flare are used as the boundary conditions to extrapolate the three-dimensional nonlinear force-free magnetic fields and the potential fields. The former are computed with the optimization algorithm and the latter with the Green's function method. At the photosphere boundary, magnetic shear increases after the flare in a local area close to the flaring magnetic polarity inversion line. Two measures of the magnetic nonpotentiality, the weighted mean shear θw and the total magnetic shear θwB, are calculated in this area at progressively higher altitude. By comparing their altitude variation profiles before and after the flare, we find that the nonpotentiality of the local area increases after the flare below ~8 Mm and decreases from that height to ~70 Mm. Beyond 70 Mm, the magnetic fields approach potential for both times. Title: Nonlinear Force-free Field Modeling of a Solar Active Region around the Time of a Major Flare and Coronal Mass Ejection Authors: Schrijver, C. J.; DeRosa, M. L.; Metcalf, T.; Barnes, G.; Lites, B.; Tarbell, T.; McTiernan, J.; Valori, G.; Wiegelmann, T.; Wheatland, M. S.; Amari, T.; Aulanier, G.; Démoulin, P.; Fuhrmann, M.; Kusano, K.; Régnier, S.; Thalmann, J. K. Bibcode: 2008ApJ...675.1637S Altcode: 2007arXiv0712.0023S Solar flares and coronal mass ejections are associated with rapid changes in field connectivity and are powered by the partial dissipation of electrical currents in the solar atmosphere. A critical unanswered question is whether the currents involved are induced by the motion of preexisting atmospheric magnetic flux subject to surface plasma flows or whether these currents are associated with the emergence of flux from within the solar convective zone. We address this problem by applying state-of-the-art nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA AR 10930 around the time of a powerful X3.4 flare. We compute 14 NLFFF models with four different codes and a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We discuss the relative merits of these models in a general critique of present abilities to model the coronal magnetic field based on surface vector field measurements. For our application in particular, we find a fair agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the ~1032 erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection. Title: Nonlinear force-free modeling of the solar coronal magnetic field Authors: Wiegelmann, T. Bibcode: 2008JGRA..113.3S02W Altcode: 2008arXiv0801.2902W The coronal magnetic field is an important quantity because the magnetic field dominates the structure of the solar corona. Unfortunately, direct measurements of coronal magnetic fields are usually not available. The photospheric magnetic field is measured routinely with vector magnetographs. These photospheric measurements are extrapolated into the solar corona. The extrapolated coronal magnetic field depends on assumptions regarding the coronal plasma, for example, force-freeness. Force-free means that all nonmagnetic forces like pressure gradients and gravity are neglected. This approach is well justified in the solar corona owing to the low plasma beta. One has to take care, however, about ambiguities, noise and nonmagnetic forces in the photosphere, where the magnetic field vector is measured. Here we review different numerical methods for a nonlinear force-free coronal magnetic field extrapolation: Grad-Rubin codes, upward integration method, MHD relaxation, optimization, and the boundary element approach. We briefly discuss the main features of the different methods and concentrate mainly on recently developed new codes. Title: Can We Improve the Preprocessing of Photospheric Vector Magnetograms by the Inclusion of Chromospheric Observations? Authors: Wiegelmann, T.; Thalmann, J. K.; Schrijver, C. J.; De Rosa, M. L.; Metcalf, T. R. Bibcode: 2008SoPh..247..249W Altcode: 2008arXiv0801.2707W; 2008SoPh..tmp...27W The solar magnetic field is key to understanding the physical processes in the solar atmosphere. Nonlinear force-free codes have been shown to be useful in extrapolating the coronal field upward from underlying vector boundary data. However, we can only measure the magnetic field vector routinely with high accuracy in the photosphere, and unfortunately these data do not fulfill the force-free condition. We must therefore apply some transformations to these data before nonlinear force-free extrapolation codes can be self-consistently applied. To this end, we have developed a minimization procedure that yields a more chromosphere-like field, using the measured photospheric field vectors as input. The procedure includes force-free consistency integrals, spatial smoothing, and - newly included in the version presented here - an improved match to the field direction as inferred from fibrils as can be observed in, for example, chromospheric Hα images. We test the procedure using a model active-region field that included buoyancy forces at the photospheric level. The proposed preprocessing method allows us to approximate the chromospheric vector field to within a few degrees and the free energy in the coronal field to within one percent. Title: Nonlinear Force-Free Modeling of Coronal Magnetic Fields. II. Modeling a Filament Arcade and Simulated Chromospheric and Photospheric Vector Fields Authors: Metcalf, Thomas R.; De Rosa, Marc L.; Schrijver, Carolus J.; Barnes, Graham; van Ballegooijen, Adriaan A.; Wiegelmann, Thomas; Wheatland, Michael S.; Valori, Gherardo; McTtiernan, James M. Bibcode: 2008SoPh..247..269M Altcode: 2008SoPh..tmp...17M We compare a variety of nonlinear force-free field (NLFFF) extrapolation algorithms, including optimization, magneto-frictional, and Grad - Rubin-like codes, applied to a solar-like reference model. The model used to test the algorithms includes realistic photospheric Lorentz forces and a complex field including a weakly twisted, right helical flux bundle. The codes were applied to both forced "photospheric" and more force-free "chromospheric" vector magnetic field boundary data derived from the model. When applied to the chromospheric boundary data, the codes are able to recover the presence of the flux bundle and the field's free energy, though some details of the field connectivity are lost. When the codes are applied to the forced photospheric boundary data, the reference model field is not well recovered, indicating that the combination of Lorentz forces and small spatial scale structure at the photosphere severely impact the extrapolation of the field. Preprocessing of the forced photospheric boundary does improve the extrapolations considerably for the layers above the chromosphere, but the extrapolations are sensitive to the details of the numerical codes and neither the field connectivity nor the free magnetic energy in the full volume are well recovered. The magnetic virial theorem gives a rapid measure of the total magnetic energy without extrapolation though, like the NLFFF codes, it is sensitive to the Lorentz forces in the coronal volume. Both the magnetic virial theorem and the Wiegelmann extrapolation, when applied to the preprocessed photospheric boundary, give a magnetic energy which is nearly equivalent to the value derived from the chromospheric boundary, but both underestimate the free energy above the photosphere by at least a factor of two. We discuss the interpretation of the preprocessed field in this context. When applying the NLFFF codes to solar data, the problems associated with Lorentz forces present in the low solar atmosphere must be recognized: the various codes will not necessarily converge to the correct, or even the same, solution. Title: Nonlinear force-free field models Authors: Wiegelmann, Thomas; Thalmann, Julia; Inhester, Bernd Bibcode: 2008cosp...37.3462W Altcode: 2008cosp.meet.3462W The photospheric magnetic field vector is routinely measured with high accuracy from ground based and space born instruments. We use these measurements to prescribe suitable boundary conditions for modelling the coronal magnetic field. Because of the low-beta plasma the magnetic field is in lowest order assumed to be force-free in the corona and upper chromosphere, but not in the high-beta photosphere. We developed a program package which contains a preprocessing program and a nonlinear force-free coronal magnetic extrapolation code. Both programs are based on optimization principles. The preprocessing routine uses the measured photospheric vector magnetogram as input and approximates the magnetic field vector in the force-free upper chromosphere. These data are used as boundary condition for a nonlinear force-free extrapolation of the coronal magnetic field. We applied our method to study the temporal evolution of a flaring active region as a sequence of nonlinear force-free equilibria. We found that magnetic energy was build up before the occurance of a flare and released after it. Furthermore, the 3D-magnetic field model allows us to trace the temporal evolution of the energy flows in the flaring region. Title: Optimization Approach for the Computation of 3D Magnetohydrostatic Coronal Equilibria From Multi-Spacecraft Observations Authors: Neukirch, T.; Wiegelmann, T.; Ruan, P.; Inhester, B. Bibcode: 2007AGUFMSH14B..05N Altcode: We cannot measure the 3D coronal magnetic field and plasma pressure/density distribution directly. To derive these quantities we propose a modelling approach based on observational data from multiple instruments. Our aim is to use measurements of the photospheric magnetic field vector (e.g. from Hinode/SOT and in future from SDO/HMI) and plasma images from two viewpoints -as provided by STEREO- as input for a newly developed magnetohydrostatic optimization code. The resulting 3D magnetic field and plasma distribution is a self-consistent equilibrium within the magnetohydrostatic approach. Here we test our code with the help of an exact magnetohydrostatic equilibrium and extracted synthetic observational data, which allow us to evaluate the accuracy of our method. We find that the method reconstructs the equilibrium accurately, with residual forces of the order of the discretisation error of the exact solution. The correlation with the reference solution is better than 99.9 percent and the magnetic energy is computed accurately with an error of less than 0.1 percent. We are planning to use this method with real observational data as input as soon as possible. Title: First Stereoscopic Coronal Loop Reconstructions from STEREO SECCHI Images Authors: Feng, L.; Inhester, B.; Solanki, S. K.; Wiegelmann, T.; Podlipnik, B.; Howard, R. A.; Wuelser, J. -P. Bibcode: 2007ApJ...671L.205F Altcode: 2008arXiv0802.0773F We present the first reconstruction of the three-dimensional shape of magnetic loops in an active region from two different vantage points based on simultaneously recorded images. The images were taken by the two EUVI telescopes of the SECCHI instrument on board the recently launched STEREO spacecraft when the heliocentric separation of the two space probes was 12°. We demonstrate that these data allow us to obtain a reliable three-dimensional reconstruction of sufficiently bright loops. The result is compared with field lines derived from a coronal magnetic field model extrapolated from a photospheric magnetogram recorded nearly simultaneously by SOHO MDI. We attribute discrepancies between reconstructed loops and extrapolated field lines to the inadequacy of the linear force-free field model used for the extrapolation. Title: Nonlinear Force-Free Field Extrapolation of NOAA AR 0696 Authors: Thalmann, J. K.; Wiegelmann, T. Bibcode: 2007AGUFMSH13A1095T Altcode: We investigate the 3D coronal magnetic field structure of NOAA AR 0696 in the period of November 09-11, 2004, before and after an X2.5 flare (occurring around 02:13 UT on November 10, 2004). The coronal magnetic field dominates the structure of the solar corona and consequently plays a key role for the understanding of the initiation of flares. The most accurate presently available method to derive the coronal magnetic field is currently the nonlinear force-free field extrapolation from measurements of the photospheric magnetic field vector. These vector-magnetograms were processed from stokes I, Q, U, and V measurements of the Big Bear Solar Observatory and extrapolated into the corona with the nonlinear force-free optimization code developed by Wiegelmann (2004). We analyze the corresponding time series of coronal equilibria regarding topology changes of the 3D coronal magnetic field during the flare. Furthermore, quantities such as the temporal evolution of the magnetic energy and helicity are computed. Title: First Stereoscopic Coronal Loop Reconstructions From STEREO/SECCHI Images Authors: Feng, L.; Inhester, B.; Solanki, S. K.; Wiegelmann, T.; Podlipnik, B.; Howard, R. A. Bibcode: 2007AGUFMSH41B..06F Altcode: We for the first time use simultaneously observed EUV images to reconstruct the 3D shape of magnetic loops which emerge from an active region. The images were taken by the two EUVI cameras of the SECCHI telescopes onboard the STEREO spacecraft. At the time the data was taken, the heliocentric separation of the two STEREO probes was 12 degrees. We show that under these conditions it is possible to obtain a reliable three- dimensional reconstruction of sufficiently bright loops as they usually emerge from an active region. The result is compared with field lines derived from a coronal magnetic field model extrapolated from a surface magnetogram. The magnetogram was abserved by SOHO/MDI only 9 seconds before the the EUV images were taken. Title: Can we Improve the Preprocessing of Photospheric Vectormagnetograms by the Inclusion of Chromospheric Observations? Authors: Wiegelmann, T.; Thalmann, J. K.; Schrijver, C. J.; De Rosa, M. L.; Metcalf, T. R. Bibcode: 2007AGUFMSH51C..02W Altcode: The solar magnetic field is key to understanding the physical processes in the solar atmosphere. Unfortunately, we can measure the magnetic field vector routinely with high accuracy only in the photosphere with, e.g., Hinode/SOT and in future with SDO/HMI. These measurements are extrapolated into the corona under the assumption that the field is force-free. That condition is not fulfilled in the photosphere, but is in the chromosphere and corona. In order to make the observed boundary data consistent with the force-free assumption, we therefore have to apply some transformations before nonlinear force-free extrapolation codes can be legitimately applied. We develop a minimization procedure that uses the measured photospheric field vectors as input to approximate a more chromospheric-like field. The procedure includes force-free consistency integrals, spatial smoothing, and - newly included in the version presented here - an improved match to the field direction as inferred from fibrils as can be observed in, e.g., chromospheric H-alpha images. We test the procedure using a model active-region field that included buoyancy forces at the photospheric level. We apply the combined preprocessing and nonlinear force-free extrapolation method to compute the coronal magnetic field in an active region measured with the Hinode/SOT instrument. Title: Optimization approach for the computation of magnetohydrostatic coronal equilibria in spherical geometry Authors: Wiegelmann, T.; Neukirch, T.; Ruan, P.; Inhester, B. Bibcode: 2007A&A...475..701W Altcode: 2008arXiv0801.2916W Context: This paper presents a method which can be used to calculate models of the global solar corona from observational data.
Aims: We present an optimization method for computing nonlinear magnetohydrostatic equilibria in spherical geometry with the aim to obtain self-consistent solutions for the coronal magnetic field, the coronal plasma density and plasma pressure using observational data as input.
Methods: Our code for the self-consistent computation of the coronal magnetic fields and the coronal plasma solves the non-force-free magnetohydrostatic equilibria using an optimization method. Previous versions of the code have been used to compute non-linear force-free coronal magnetic fields from photospheric measurements in Cartesian and spherical geometry, and magnetostatic-equilibria in Cartesian geometry. We test our code with the help of a known analytic 3D equilibrium solution of the magnetohydrostatic equations. The detailed comparison between the numerical calculations and the exact equilibrium solutions is made by using magnetic field line plots, plots of density and pressure and some of the usual quantitative numerical comparison measures.
Results: We find that the method reconstructs the equilibrium accurately, with residual forces of the order of the discretisation error of the analytic solution. The correlation with the reference solution is better than 99.9% and the magnetic energy is computed accurately with an error of <0.1%.
Conclusions: We applied the method so far to an analytic test case. We are planning to use this method with real observational data as input as soon as possible. Title: Non-linear Force-free Modeling Of Coronal Magnetic Fields Authors: Metcalf, Thomas R.; De Rosa, M. L.; Schrijver, C. J.; Barnes, G.; van Ballegooijen, A.; Wiegelmann, T.; Wheatland, M. S.; Valori, G.; McTiernan, J. M. Bibcode: 2007AAS...210.9102M Altcode: 2007BAAS...39..204M We compare a variety of nonlinear force-free field (NLFFF) extrapolation algorithms, including optimization, magneto-frictional, and Grad-Rubin-like codes, applied to a solar-like reference model. The model used to test the algorithms includes realistic photospheric Lorentz forces and a complex field including a weakly twisted, right helical flux bundle. The codes were applied to both forced "photospheric'' and more force-free "chromospheric'' vector magnetic field boundary data derived from the model. When applied to the

chromospheric boundary data, the codes are able to recover the presence of the flux bundle and the field's free energy, though some details of the field connectivity are lost. When the codes are applied to the forced photospheric boundary data, the reference model field is not well recovered, indicating that the Lorentz forces on the photosphere severely impact the extrapolation of the field. Preprocessing of the photospheric boundary does improve the extrapolations considerably, although the results depend sensitively on the details of the numerical codes. When applying the NLFFF codes to solar data, the problems associated with Lorentz forces present in the low solar atmosphere must be recognized: the various codes will not necessarily converge to the correct, or even the same, solution. Title: Magnetic Stereoscopy of Coronal Loops in NOAA 8891 Authors: Feng, L.; Wiegelmann, T.; Inhester, B.; Solanki, S.; Gan, W. Q.; Ruan, P. Bibcode: 2007SoPh..241..235F Altcode: The Solar TErrestrial RElations Observatory (STEREO) requires powerful tools for the three-dimensional (3D) reconstruction of the solar corona. Here we test such a program with data from SOHO and TRACE. By taking advantage of solar rotation, a newly developed stereoscopy tool for the reconstruction of coronal loops is applied to the solar active region NOAA 8891 observed from 1 March to 2 March 2000. The stereoscopic reconstruction is composed of three steps. First, we identify loop structures in two TRACE images observed from two vantage viewpoints approximately 17 degrees apart, which corresponds to observations made about 30 hours apart. In the second step, we extrapolate the magnetic field in the corona with the linear force-free field model from the photospheric line-of-sight SOHO/MDI data. Finally, combining the extrapolated field lines and one-dimensional loop curves from two different viewpoints, we obtain the 3D loop structures with the magnetic stereoscopy tool. We demonstrate that by including the magnetic modeling this tool is more powerful than pure geometrical stereoscopy, especially in resolving the ambiguities generated by classical stereoscopy. This work will be applied to the STEREO mission in the near future. Title: Computing Nonlinear Force-Free Coronal Magnetic Fields in Spherical Geometry Authors: Wiegelmann, T. Bibcode: 2007SoPh..240..227W Altcode: 2006astro.ph.12124W We describe a newly developed code for the extrapolation of nonlinear force-free coronal magnetic fields in spherical coordinates. The program uses measured vector magnetograms on the solar photosphere as input and solves the force-free equations in the solar corona. The method is based on an optimization principle and the heritage of the newly developed code is a corresponding method in Cartesian geometry. We test the newly developed code with the help of a semi-analytic solution and rate the quality of our reconstruction qualitatively by magnetic field line plots and quantitatively with a number of comparison metrics. We find that we can reconstruct the original test field with high accuracy. The method is fast if the computation is limited to low co-latitudes (say 30°≤θ≤150°), but it becomes significantly slower if the polar regions are included. Title: Evolution of a Coronal Loop System Authors: Tsiropoula, G.; Tziotziou, K.; Wiegelmann, T.; Zachariadis, Th.; Gontikakis, C.; Dara, H. Bibcode: 2007SoPh..240...37T Altcode: The temporal variation of a loop system that appears to be changing rapidly is examined. The analyzed data were obtained on 15 May 1999, with the Transition Region and Coronal Explorer (TRACE) during an observing campaign and consist of observations in the Fe IX/Fe X 171 Å and Fe XII 195 Å passbands taken at a cadence of ∼10 min. The special interest in this loop system is that it looks like one expanding loop; however, careful examination reveals that the loop consists of several strands and that new loop strands become visible successively at higher altitudes and lower loop strands fade out during the one hour of our observations. These strands have different widths, densities, and temperatures and are most probably consisting of, at least, a few unresolved thinner threads. Several geometric and physical parameters are derived for two of the strands and an effort is made to determine their 3D structure based on the extrapolation of the magnetic field lines. Electron density estimates allow us to derive radiative and conductive cooling times and to conclude that these loop strands are cooling by radiation. Title: Evolution of coronal hole boundaries seen in EIT 195 Å and TRACE 171 Å images Authors: Madjarska, M. S.; Wiegelmann, T. Bibcode: 2007msfa.conf..249M Altcode: We aim at studying the spatial and temporal scales of the small-scale evolution of coronal hole boundaries using EUV observations from TRACE (171 Å) and EIT (195 Å) on-board SoHO with a spatial resolution of 1" and 5.5", respectively, and various time cadences. We found that small-scale loops known as bright points may play an essential role in coronal hole boundaries evolution. Their emergence and disappearance continuously expand or contract coronal holes. The changes appear to be random on a time scale comparable with the lifetime of the loops seen at these temperatures. No signature was found for a major energy release during the evolution of the loops. Title: Magnetic stereoscopy of coronal loops in NOAA 8891 Authors: Feng, L.; Wiegelmann, T.; Inhester, B. Bibcode: 2007msfa.conf..269F Altcode: We present an application of the magnetic stereoscopy tool to the coronal loops observed by TRACE in the active region NOAA 8891. Designed for the newly launched STEREO mission, this tool aims to reconstruct the 3D geometry of coronal loops. Taking advantage of the solar rotation, two TRACE images observed one day apart are looked as STEREO-A and STEREO-B EUVI images. Combining with the extrapolated magnetic field lines in the corona from photospheric MDI data, the 3D geometry is reconstructed with the identified loop pair. Title: Modeling large-scale coronal structures Authors: Ruan, P.; Wiegelmann, T.; Inhester, B. Bibcode: 2007msfa.conf..363R Altcode: Current measurements provide the photospheric magnetic field (e.g., from MDI on SOHO) and line-of-sight integrated 2D coronal images (e.g., EIT). Our aim is to use these observations to reconstruct the 3D structure of the solar corona. Here we do the reconstruction in two steps. We compute a global coronal magnetic field model with the help of a potential or linear force-free model. In a subsequent step we model the coronal plasma radiation with the help of scaling laws. Scaling laws which relate loop emissivities with plasma parameters will be tested with these models. Title: Nonlinear Force-Free Magnetic Field Modelling For VIM On SO Authors: Wiegelmann, T.; Solanki, S. K.; Yelles, L.; Lagg, A. Bibcode: 2007ESASP.641E..19W Altcode: The aim of this work is to investigate how photon noise and errors in the retrieval of solar magnetic parameters from measured Stokes profiles influences the extrapolartion of nonlinear force-free coronal magnetic fields from photospheric vector magnetograms. To do so we use a nonlinear force-free extrapolation code based on an optimization principle. The extrapolation methods has been extensively tested and applied to data from various telescopes. Here we apply the code artificial vector magnetograms obtained from 3-D radiation-MHD simulations. As a reference case we compute the coronal magnetic field from an ideal magnetogram and compare the result with more realistic magnetograms based on simulated Solar Orbiter/VIM-measurements. We investigate the effect of noise, ambiguities, spatial resolution, inversion mechanism, of Stokes profiles etc. We rate the quality of the reconstructed coronal magnetic field qualitatively by magnetic field line plots and quantitatively by a number of comparison metrices, e.g., the vector correlation with the exact solution and how accurate the free magnetic energy is computed. Not surprisingly, the instrument effects and noise influence the quality of the nonlinear force-free coronal magnetic field model. The extrapolations from realistic vector magnetograms show a reasonable agreement with the ideal reconstruction, however, and are in particular significantly better than extrapolations based on line-of-sight magnetograms only. High quality VIM data will thus allow reasonably accurate extrapolations that can serve as the basis for magnetic coupling science through a comparison with observations from EUS and EUI. Title: Measuring the Magnetic Vector with the He I 10830 Å Line: A Rich New World Authors: Solanki, S. K.; Lagg, A.; Aznar Cuadrado, R.; Orozco Suárez, D.; Collados, M.; Wiegelmann, T.; Woch, J.; Sasso, C.; Krupp, N. Bibcode: 2006ASPC..358..431S Altcode: The triplet of the He I transitions around 10830 Å not only shows a rich variety of Stokes profiles, but also allows the full magnetic vector in the upper chromosphere to be probed, thus revealing the magnetic structure of loops, current sheets, finely structured supersonic downflows, the chromospheric layers of sunspots (supporting the presence of uncombed fields in the penumbra), flares, and the quiet Sun. A very brief overview of some of the observations and results obtained so far is given. Title: An optimization principle for the computation of MHD equilibria in the solar corona Authors: Wiegelmann, T.; Neukirch, T. Bibcode: 2006A&A...457.1053W Altcode: 2006astro.ph.12625W Aims.We develop an optimization principle for computing stationary MHD equilibria.
Methods: . Our code for the self-consistent computation of the coronal magnetic fields and the coronal plasma uses non-force-free MHD equilibria. Previous versions of the code have been used to compute non-linear force-free coronal magnetic fields from photospheric measurements. The program uses photospheric vector magnetograms and coronal EUV images as input. We tested our reconstruction code with the help of a semi-analytic MHD-equilibrium. The quality of the reconstruction was judged by comparing the exact and reconstructed solution qualitatively by magnetic field-line plots and EUV-images and quantitatively by several different numerical criteria.
Results: . Our code is able to reconstruct the semi-analytic test equilibrium with high accuracy. The stationary MHD optimization code developed here has about the same accuracy as its predecessor, a non-linear force-free optimization code. The computing time for MHD-equilibria is, however, longer than for force-free magnetic fields. We also extended a well-known class of nonlinear force-free equilibria to the non-force-free regime for purposes of testing the code.
Conclusions: . We demonstrate that the code works in principle using tests with analytical equilibria, but it still needs to be applied to real data. Title: Testing non-linear force-free coronal magnetic field extrapolations with the Titov-Démoulin equilibrium Authors: Wiegelmann, T.; Inhester, B.; Kliem, B.; Valori, G.; Neukirch, T. Bibcode: 2006A&A...453..737W Altcode: 2006astro.ph.12650W Context.As the coronal magnetic field can usually not be measured directly, it has to be extrapolated from photospheric measurements into the corona.
Aims.We test the quality of a non-linear force-free coronal magnetic field extrapolation code with the help of a known analytical solution.
Methods. The non-linear force-free equations are numerically solved with the help of an optimization principle. The method minimizes an integral over the force-free and solenoidal condition. As boundary condition we use either the magnetic field components on all six sides of the computational box in Case I or only on the bottom boundary in Case II. We check the quality of the reconstruction by computing how well force-freeness and divergence-freeness are fulfilled and by comparing the numerical solution with the analytical solution. The comparison is done with magnetic field line plots and several quantitative measures, like the vector correlation, Cauchy Schwarz, normalized vector error, mean vector error and magnetic energy.
Results.For Case I the reconstructed magnetic field shows good agreement with the original magnetic field topology, whereas in Case II there are considerable deviations from the exact solution. This is corroborated by the quantitative measures, which are significantly better for Case I.
Conclusions. Despite the strong nonlinearity of the considered force-free equilibrium, the optimization method of extrapolation is able to reconstruct it; however, the quality of reconstruction depends significantly on the consistency of the input data, which is given only if the known solution is provided also at the lateral and top boundaries, and on the presence or absence of flux concentrations near the boundaries of the magnetogram. Title: Magnetic Stereoscopy Authors: Wiegelmann, T.; Inhester, B. Bibcode: 2006SoPh..236...25W Altcode: 2006astro.ph.12636W The space mission Solar TErrestrial RElations Observatory (STEREO) will provide images from two viewpoints. An important aim of the STEREO mission is to get a 3D view of the solar corona. We develop a program for the stereoscopic reconstruction of 3D coronal loops from images taken with the two STEREO spacecraft. A pure geometric triangulation of coronal features leads to ambiguities because the dilute plasma emissions complicates the association of features in image 1 with features in image 2. As a consequence of these problems, the stereoscopic reconstruction is not unique and multiple solutions occur. We demonstrate how these ambiguities can be resolved with the help of different coronal magnetic field models (potential, linear, and non-linear force-free fields). The idea is that, due to the high conductivity in the coronal plasma, the emitting plasma outlines the magnetic field lines. Consequently, the 3D coronal magnetic field provides a proxy for the stereoscopy, which allows to eliminate inconsistent configurations. The combination of stereoscopy and magnetic modelling is more powerful than one of these tools alone. We test our method with the help of a model active region and plan to apply it to the solar case as soon as STEREO data become available. Title: Nonlinear Force-Free Magnetic Field Extrapolations: Comparison of the Grad Rubin and Wheatland Sturrock Roumeliotis Algorithm Authors: Inhester, Bernd; Wiegelmann, Thomas Bibcode: 2006SoPh..235..201I Altcode: 2008arXiv0801.3237I We compare the performance of two alternative algorithms which aim to construct a force-free magnetic field given suitable boundary conditions. For this comparison, we have implemented both algorithms on the same finite element grid which uses Whitney forms to describe the fields within the grid cells. The additional use of conjugate gradient and multigrid iterations result in quite effective codes. Title: Nonlinear Force-Free Modeling of Coronal Magnetic Fields Part I: A Quantitative Comparison of Methods Authors: Schrijver, Carolus J.; De Rosa, Marc L.; Metcalf, Thomas R.; Liu, Yang; McTiernan, Jim; Régnier, Stéphane; Valori, Gherardo; Wheatland, Michael S.; Wiegelmann, Thomas Bibcode: 2006SoPh..235..161S Altcode: We compare six algorithms for the computation of nonlinear force-free (NLFF) magnetic fields (including optimization, magnetofrictional, Grad-Rubin based, and Green's function-based methods) by evaluating their performance in blind tests on analytical force-free-field models for which boundary conditions are specified either for the entire surface area of a cubic volume or for an extended lower boundary only. Figures of merit are used to compare the input vector field to the resulting model fields. Based on these merit functions, we argue that all algorithms yield NLFF fields that agree best with the input field in the lower central region of the volume, where the field and electrical currents are strongest and the effects of boundary conditions weakest. The NLFF vector fields in the outer domains of the volume depend sensitively on the details of the specified boundary conditions; best agreement is found if the field outside of the model volume is incorporated as part of the model boundary, either as potential field boundaries on the side and top surfaces, or as a potential field in a skirt around the main volume of interest. For input field (B) and modeled field (b), the best method included in our study yields an average relative vector error En = « |B−b|»/« |B|» of only 0.02 when all sides are specified and 0.14 for the case where only the lower boundary is specified, while the total energy in the magnetic field is approximated to within 2%. The models converge towards the central, strong input field at speeds that differ by a factor of one million per iteration step. The fastest-converging, best-performing model for these analytical test cases is the Wheatland, Sturrock, and Roumeliotis (2000) optimization algorithm as implemented by Wiegelmann (2004). Title: Preprocessing of Vector Magnetograph Data for a Nonlinear Force-Free Magnetic Field Reconstruction Authors: Wiegelmann, T.; Inhester, B.; Sakurai, T. Bibcode: 2006SoPh..233..215W Altcode: 2006astro.ph.12641W Knowledge regarding the coronal magnetic field is important for the understanding of many phenomena, like flares and coronal mass ejections. Because of the low plasma beta in the solar corona, the coronal magnetic field is often assumed to be force-free and we use photospheric vector magnetograph data to extrapolate the magnetic field into the corona with the help of a nonlinear force-free optimization code. Unfortunately, the measurements of the photospheric magnetic field contain inconsistencies and noise. In particular, the transversal components (say Bx and By) of current vector magnetographs have their uncertainties. Furthermore, the magnetic field in the photosphere is not necessarily force free and often not consistent with the assumption of a force-free field above the magnetogram. We develop a preprocessing procedure to drive the observed non-force-free data towards suitable boundary conditions for a force-free extrapolation. As a result, we get a data set which is as close as possible to the measured data and consistent with the force-free assumption. Title: 3D visualization techniques for the STEREO-mission Authors: Wiegelmann, T.; Podlipnik, B.; Inhester, B.; Feng, L.; Ruan, P. Bibcode: 2006cosp...36..656W Altcode: 2006cosp.meet..656W The forthcoming STEREO-mission will observe the Sun from two different viewpoints We expect about 2GB data per day which ask for suitable data presentation techniques A key feature of STEREO is that it will provide for the first time a 3D-view of the Sun and the solar corona In our normal environment we see objects three dimensional because the light from real 3D objects needs different travel times to our left and right eye As a consequence we see slightly different images with our eyes which gives us information about the depth of objects and a corresponding 3D impression Techniques for the 3D-visualization of scientific and other data on paper TV computer screen cinema etc are well known e g two colour anaglyph technique shutter glasses polarization filters and head-mounted displays We discuss advantages and disadvantages of these techniques and how they can be applied to STEREO-data The 3D-visualization techniques are not limited to visual images but can be also used to show the reconstructed coronal magnetic field and energy and helicity distribution In the advent of STEREO we test the method with data from SOHO which provides us different viewpoints by the solar rotation This restricts the analysis to structures which remain stationary for several days Real STEREO-data will not be affected by these limitations however Title: Coupling of photospheric and coronal magnetic fields Authors: Wiegelmann, T.; Inhester, B. Bibcode: 2006cosp...36..436W Altcode: 2006cosp.meet..436W Information regarding the magnetic field are essential to understand the coupling of the solar interior with the photosphere and atmosphere The photospheric magnetic field is measured routinely with line-of-sight and vector magnetographs Direct measurements of chromospheric and coronal magnetic fields are usually not available except for a few individual cases We can however extrapolate the photospheric magnetic field into the corona This is by no means an easy task as the extrapolated magnetic field depends on assumptions regarding the coronal plasma e g force-freeness Force-free means that all non-magnetic forces e g pressure gradients and gravity are neglected While this assumption is well justified in the solar corona due to the low plasma beta the magnetic field is not force-free on the photosphere Ambiguities and noise in the transversal magnetic field measurements are an additional complication for reliable coronal magnetic field extrapolations A helpful property is that the emitting coronal plasma outlines the magnetic field lines As a consequence we can test and improve coronal magnetic field models by a comparison with coronal EUV-images This approach is in particular attractive if EUV-images from different viewpoints as provided by STEREO are available Photospheric magnetic field measurements and EUV-images are combined for a consistent 3D reconstruction of coronal magnetic fields and the coronal plasma Title: Non-Linear Force-Free Magnetic Fields Authors: Wiegelmann, T. Bibcode: 2005ESASP.596E..80W Altcode: 2005ccmf.confE..80W No abstract at ADS Title: Magnetic Loops: a Comparison of Extrapolations from the Photosphere with Chromospheric Measurements Authors: Wiegelmann, T.; Lagg, A.; Solanki, S.; Inhester, B.; Woch, J. Bibcode: 2005ESASP.596E...7W Altcode: 2005ccmf.confE...7W No abstract at ADS Title: How To Use Magnetic Field Information For Coronal Loop Identification Authors: Wiegelmann, T.; Inhester, B.; Lagg, A.; Solanki, S. K. Bibcode: 2005SoPh..228...67W Altcode: 2008arXiv0801.4573W The structure of the solar corona is dominated by the magnetic field because the magnetic pressure is about four orders of magnitude higher than the plasma pressure. Due to the high conductivity the emitting coronal plasma (visible, e.g., in SOHO/EIT) outlines the magnetic field lines. The gradient of the emitting plasma structures is significantly lower parallel to the magnetic field lines than in the perpendicular direction. Consequently information regarding the coronal magnetic field can be used for the interpretation of coronal plasma structures. We extrapolate the coronal magnetic field from photospheric magnetic field measurements into the corona. The extrapolation method depends on assumptions regarding coronal currents, e.g., potential fields (current-free) or force-free fields (current parallel to magnetic field). As a next step we project the reconstructed 3D magnetic field lines on an EIT-image and compare with the emitting plasma structures. Coronal loops are identified as closed magnetic field lines with a high emissivity in EIT and a small gradient of the emissivity along the magnetic field. Title: Comparing magnetic field extrapolations with measurements of magnetic loops Authors: Wiegelmann, T.; Lagg, A.; Solanki, S. K.; Inhester, B.; Woch, J. Bibcode: 2005A&A...433..701W Altcode: 2008arXiv0801.4519W We compare magnetic field extrapolations from a photospheric magnetogram with the observationally inferred structure of magnetic loops in a newly developed active region. This is the first time that the reconstructed 3D-topology of the magnetic field is available to test the extrapolations. We compare the observations with potential fields, linear force-free fields and non-linear force-free fields. This comparison reveals that a potential field extrapolation is not suitable for a reconstruction of the magnetic field in this young, developing active region. The inclusion of field-line-parallel electric currents, the so called force-free approach, gives much better results. Furthermore, a non-linear force-free computation reproduces the observations better than the linear force-free approximation, although no free parameters are available in the former case. Title: Links between magnetic fields and plasma flows in a coronal hole Authors: Wiegelmann, T.; Xia, L. D.; Marsch, E. Bibcode: 2005A&A...432L...1W Altcode: 2008arXiv0801.4724W We compare the small-scale features visible in the Ne viii Doppler-shift map of an equatorial coronal hole (CH) as observed by SUMER with the small-scale structures of the magnetic field as constructed from a simultaneous photospheric magnetogram by a potential magnetic-field extrapolation. The combined data set is analysed with respect to the small-scale flows of coronal matter, which means that the Ne viii Doppler-shift used as tracer of the plasma flow is investigated in close connection with the ambient magnetic field. Some small closed-field regions in this largely open CH are also found in the coronal volume considered. The Doppler-shift patterns are found to be clearly linked with the field topology. Title: Why are Coronal Holes Indistinguishable from the Quiet Sun in Transition Region Radiation? Authors: Wiegelmann, T.; Solanki, S. K. Bibcode: 2004ESASP.575...35W Altcode: 2004soho...15...35W No abstract at ADS Title: Coronal plasma flows and magnetic fields in solar active regions. Combined observations from SOHO and NSO/Kitt Peak Authors: Marsch, E.; Wiegelmann, T.; Xia, L. D. Bibcode: 2004A&A...428..629M Altcode: During the early days of the SOHO mission, SUMER observed a few active regions (ARs) connected with sunspots on the Sun and took their images and spectra in various EUV emission lines. In addition to these spectroscopic data magnetograms of the photospheric footpoint regions of the AR loops were available from the MDI on SOHO and the National Solar Observatory/Kitt Peak (NSO/KP), data which here are used to construct the coronal magnetic field of the ARs by force-free-field extrapolation. The combined data set is analysed with respect to the large-scale circulation of coronal matter, which means that the Dopplershifts of various lines used as tracers of the plasma flow are investigated in close connection with the ambient magnetic field, which is found to be either closed or open in the coronal volume considered. The Dopplershift pattern is found to be clearly linked with the field topology, and several regions of strong velocity shear are identified. We also estimate the coronal currents. We discuss the results of this mainly phenomenological correlative study with the perspective to understand coronal heating and mass supply to the extended corona, and with respect to the role played by the field in guiding and constraining plasma flows. Title: Similarities and Differences between Coronal Holes and the Quiet Sun: Are Loop Statistics the Key? Authors: Wiegelmann, T.; Solanki, S. K. Bibcode: 2004SoPh..225..227W Altcode: 2008arXiv0802.0120W Coronal holes (CH) emit significantly less at coronal temperatures than quiet-Sun regions (QS), but can hardly be distinguished in most chromospheric and lower transition region lines. A key quantity for the understanding of this phenomenon is the magnetic field. We use data from SOHO/MDI to reconstruct the magnetic field in coronal holes and the quiet Sun with the help of a potential magnetic model. Starting from a regular grid on the solar surface we then trace field lines, which provide the overall geometry of the 3D magnetic field structure. We distinguish between open and closed field lines, with the closed field lines being assumed to represent magnetic loops. We then try to compute some properties of coronal loops. The loops in the coronal holes (CH) are found to be on average flatter than in the QS. High and long closed loops are extremely rare, whereas short and low-lying loops are almost as abundant in coronal holes as in the quiet Sun. When interpreted in the light of loop scaling laws this result suggests an explanation for the relatively strong chromospheric and transition region emission (many low-lying, short loops), but the weak coronal emission (few high and long loops) in coronal holes. In spite of this contrast our calculations also suggest that a significant fraction of the cool emission in CHs comes from the open flux regions. Despite these insights provided by the magnetic field line statistics further work is needed to obtain a definite answer to the question if loop statistics explain the differences between coronal holes and the quiet Sun. Title: Optimization code with weighting function for the reconstruction of coronal magnetic fields Authors: Wiegelmann, T. Bibcode: 2004SoPh..219...87W Altcode: 2008arXiv0802.0124W We developed a code for the reconstruction of nonlinear force-free and non-force-free coronal magnetic fields. The 3D magnetic field is computed numerically with the help of an optimization principle. The force-free and non-force-free codes are compiled in one program. The force-free approach needs photospheric vector magnetograms as input. The non-force-free code additionally requires the line-of-sight integrated coronal density distribution in combination with a tomographic inversion code. Previously the optimization approach has been used to compute magnetic fields using all six boundaries of a computational box. Here we extend this method and show how the coronal magnetic field can be reconstructed only from the bottom boundary, where the boundary conditions are measured with vector magnetographs. The program is planed for use within the Stereo mission. Title: A Quantitative Method to Optimise Magnetic Field Line Fitting of Observed Coronal Loops Authors: Carcedo, L.; Brown, D. S.; Hood, A. W.; Neukirch, T.; Wiegelmann, T. Bibcode: 2003SoPh..218...29C Altcode: Many authors use magnetic-field models to extrapolate the field in the solar corona from magnetic data in the photosphere. The accuracy of such extrapolations is usually judged qualitatively by eye, where a less judgemental quantitative approach would be more desirable. In this paper, a robust method for obtaining the best fit between a theoretical magnetic field and intensity observations of coronal loops on the solar disk will be presented. The method will be applied to Yohkoh data using a linear force-free field as an illustration. Any other theoretical model for the magnetic field can be used, provided there is enough freedom in the model to optimize the fit. Title: Magnetic modeling and tomography: First steps towards a consistent reconstruction of the solar corona Authors: Wiegelmann, T.; Inhester, B. Bibcode: 2003SoPh..214..287W Altcode: 2008arXiv0802.0687W We undertake a first attempt towards a consistent reconstruction of the coronal magnetic field and the coronal density structure. We consider a stationary solar corona which has to obey the equations of magnetohydrostatics. We solve these equations with help of a newly developed optimization scheme. As a first step we illustrate how tomographic information can be included into the reconstruction of coronal magnetic fields. In a second step we use coronal magnetic field information to improve the tomographic inversion process. As input the scheme requires magnetic field measurements on the photosphere from vector-magnetographs and the line-of-sight integrated density distribution from coronagraphs. We test our codes with well-known analytic magnetohydrostatic equilibria and models. The program is planned for use within the STEREO mission. Title: Computing nonlinear force free coronal magnetic fields Authors: Wiegelmann, T.; Neukirch, T. Bibcode: 2003NPGeo..10..313W Altcode: 2008arXiv0801.3215W Knowledge of the structure of the coronal magnetic field is important for our understanding of many solar activity phenomena, e.g. flares and CMEs. However, the direct measurement of coronal magnetic fields is not possible with present methods, and therefore the coronal field has to be extrapolated from photospheric measurements. Due to the low plasma beta the coronal magnetic field can usually be assumed to be approximately force free, with electric currents flowing along the magnetic field lines. There are both observational and theoretical reasons which suggest that at least prior to an eruption the coronal magnetic field is in a nonlinear force free state. Unfortunately the computation of nonlinear force free fields is way more difficult than potential or linear force free fields and analytic solutions are not generally available. We discuss several methods which have been proposed to compute nonlinear force free fields and focus particularly on an optimization method which has been suggested recently. We compare the numerical performance of a newly developed numerical code based on the optimization method with the performance of another code based on an MHD relaxation method if both codes are applied to the reconstruction of a semi-analytic nonlinear force-free solution. The optimization method has also been tested for cases where we add random noise to the perfect boundary conditions of the analytic solution, in this way mimicking the more realistic case where the boundary conditions are given by vector magnetogram data. We find that the convergence properties of the optimization method are affected by adding noise to the boundary data and we discuss possibilities to overcome this difficulty. Title: Including stereoscopic information in the reconstruction of coronal magnetic fields Authors: Wiegelmann, T.; Neukirch, T. Bibcode: 2002SoPh..208..233W Altcode: 2008arXiv0801.3234W We present a method to include stereoscopic information about the three-dimensional structure of flux tubes into the reconstruction of the coronal magnetic field. Due to the low plasma beta in the corona we can assume a force-free magnetic field, with the current density parallel to the magnetic field lines. Here we use linear force-free fields for simplicity. The method uses the line-of-sight magnetic field on the photosphere as observational input. The value of α is determined iteratively by comparing the reconstructed magnetic field with the observed structures. The final configuration is the optimal linear force-free solution constrained by both the photospheric magnetogram and the observed plasma structures. As an example we apply our method to SOHO MDI/EIT data of an active region. In the future it is planned to apply the method to analyse data from the SECCHI instrument aboard the STEREO mission. Title: Tests and limits of Vlasov code simulations and its application to null-helicity and co-helicity reconnection Authors: Wiegelmann, T.; Neukirch, T.; Büchner, J. Bibcode: 2001sps..proc...58W Altcode: Magnetic reconnection is an important process in many space plasmas (e.g. geomagnetic substorms, coronal mass ejections). The large scale structure of these phenomena is usually described within MHD. Reconnection requires a non ideal region (resistivity) in the plasma. The cause of a non ideal behaviour in localized regions could for example be anomalous resistivity in thin current sheets. The formation of these thin current sheets can be understand within the framework of MHD. The further evolution of the current sheets cannot be investigated with MHD, because the sheet width becomes comparable with kinetic scales like the ion gyro radius and kinetic effects have to be taken into account. For many space plasmas, the kinetic processes are collisionless and can thus be described by the Vlasov equation. A code to solve the Vlasov equation has been developed and we report first results obtained with the code. To test the accuracy and limits of our code we carry out several consistency checks, which can be compared with analytic results, in particular phase mixing and Landau damping. We also apply our Vlasov code to collisionless magnetic reconnection in the magnetospheric plasma sheet and at the magnetopause. Title: Helmet Streamers with Triple Structures: Simulations of resistive dynamics Authors: Wiegelmann, Thomas; Schindler, Karl; Neukirch, Thomas Bibcode: 2000SoPh..191..391W Altcode: 2008arXiv0801.3187W Recent observations of the solar corona with the LASCO coronagraph on board of the SOHO spacecraft have revealed the occurrence of triple helmet streamers even during solar minimum, which occasionally go unstable and give rise to large coronal mass ejections. There are also indications that the slow solar wind is either a combination of a quasi-stationary flow and a highly fluctuating component or may even be caused completely by many small eruptions or instabilities. As a first step we recently presented an analytical method to calculate simple two-dimensional stationary models of triple helmet streamer configurations. In the present contribution we use the equations of time-dependent resistive magnetohydrodynamics to investigate the stability and the dynamical behaviour of these configurations. We particularly focus on the possible differences between the dynamics of single isolated streamers and triple streamers and on the way in which magnetic reconnection initiates both small scale and large scale dynamical behaviour of the streamers. Our results indicate that small eruptions at the helmet streamer cusp may incessantly accelerate small amounts of plasma without significant changes of the equilibrium configuration and might thus contribute to the non-stationary slow solar wind. On larger time and length scales, large coronal eruptions can occur as a consequence of large scale magnetic reconnection events inside the streamer configuration. Our results also show that triple streamers are usually more stable than a single streamer. Title: A Self-consistent Model for Coronal Streamers and their Relevance for coronal mass ejections and the slow Solar wind Authors: Wiegelmann, Thomas; Schindler, Karl; Neukirch, Thomas Bibcode: 1999AGAb...15...78W Altcode: 1999AGM....15..J23W Coronal helmet streamers are large scale magnetic field structures in the solar corona. The coronal magnetic field is approximately frozen into the plasma. Observations with the LASCO coronagraph on board of SOHO have shown that these helmet streamers show a triple structure during the solar activity minimum. The streamer regions have been identified as the source regions for the slow solar wind and new observations provide evidence that a stationary slow solar wind may not exist, but that the slow solar wind is produced by many little eruptions near the helmet streamer cusp leading to an approximately stationary plasma flow on large scales. The observations further show, that the streamer structures occasionally go unstable, leading tohuge coronal mass ejections. We present a method to calculate analytically self-consistent stationary helmet streamer configurations with triple structures. We then use these stationary configurations as input for time-dependent MHD simulations. Our simulations give evidence, that magnetic reconnection plays an important role for both the acceleration of the slow solar wind and huge coronal eruptions. Title: Numerical Simulations of Kinetic Instabilities in Space Plasmas Authors: Wiegelmann, Thomas; Büchner, Jörg Bibcode: 1999AGAb...15...83W Altcode: 1999AGM....15..L01W Spontaneous formation of structures plays an important role for the dynamics of space plasmas. Small scale turbulence may cause configuration instabilities on larger scales. Of major interest are nonlinear processes which lead to changes in the large scale struc ture of magnetic field topology as a consequence of magnetic reconnection. Magnetic reconnection is a generic process for efficient transformation of magnetic field energy in plasma. Examples of astrophysical processes where magnetic reconnection is assumed to play an important role are magnetic storms and coronal mass ejections. Recent research showed that thin current sheets play an important role for the occurrence of reconnection. To investigate the stability of these very thin current sheets we have carried out three dimensional kinetic plasma simulations with the Particle in Cell Code GISMO. We observe kinetic instabilities in the current direction (sausage instability) and perpendicular to the current direction (tearing). We investigate the growth rates and spatial scale length of these instabilities with the help of Fourier analysis. Title: Closely-spaced multi-satellite project ROY to study small-scale structures during magnetic field annihilation and strong turbulence in critical magnetospheric regions: Results of Phase A Authors: Galperin, Yu. I.; Zelenyi, L. M.; Veselov, M. V.; Savin, S. P.; Mogilevsky, M. M.; Yanovsky, M. I.; Prokhorenko, V. I.; Eismont, N. A.; Kunitsyn, V. E.; Silin, I. V.; Sosnovets, E. N.; Bûchner, J.; Nikutowski, B.; Wiegelmann, T. Bibcode: 1999ASIC..537...55G Altcode: 1999iip..conf...55G No abstract at ADS Title: Helmet Streamers with Triple Structures: Weakly Two-Dimensional Stationary States Authors: Wiegelmann, Thomas; Schindler, Karl; Neukirch, Thomas Bibcode: 1998SoPh..180..439W Altcode: 1997astro.ph.12012W Recent observations of the solar corona with the LASCO coronagraph on board the SOHO spacecraft have revealed the occurrence of triple helmet streamers even during solar minimum, which occasionally go unstable and give rise to particularly huge coronal mass ejections. We present a method to calculate (semi-)analytically self-consistent stationary configurations of triple helmet streamers which can serve as input for stability considerations and dynamical calculations. The method is based on an asymptotic expansion procedure using the elongated structure of the streamers. The method is very flexible and can be used in both Cartesian and spherical geometry. We discuss the effects of magnetic shear, gravity and field-aligned flow on open field lines. Example solutions illustrating the influence of each of these features on the solution structure are presented. Title: Solar magnetic fields: triple arcade structures Authors: Wiegelmann, Thomas Bibcode: 1998PhST...74...77W Altcode: Recent observation with the LASCO coronagraph on board the SOHO spacecraft have shown that helmet streamers may have an internal triple arcade structure. The observations suggest that this triple structure might be important for the initiation of coronal mass ejections (CME's). In this paper we undertake a first step towards the theoretical description of such triple structures by calculating self-consistent solutions of the magnetohydrostatic equations in two dimensions. For simplicity, we start with the investigations of current-free structures, leading to potential magnetic fields. We then go on to investigate the case of linear currents. These two cases have the disadvantage of being linearly stable in the framework of MHD, which makes it difficult to take them as starting-points for further investigations. Therefore, we also investigate special exact solutions of a nonlinear case and apply the method of asymptotic expansion to another nonlinear problem to obtain approximate elongated solutions, which might be useful for linear or nonlinear stability checks. Title: Helmet streamers with triple structures. Authors: Wiegelmann, T. Bibcode: 1997AGAb...13..101W Altcode: No abstract at ADS Title: Formation of thin current sheets in a quasistatic magnetotail model Authors: Wiegelmann, T.; Schindler, K. Bibcode: 1995GeoRL..22.2057W Altcode: Observations suggest that thin current sheets forming in the near-Earth magnetotail late in substorm growth phases may be a crucial part of substorm evolution. In a simple theoretical model the current density was shown to become singular for suitable external perturbations. Here, we address the same problem in a more realistic model based on the adiabatic MHD - theory developed by Schindler and Birn [1982]. We show that under suitable conditions the formation of a thin current sheet in the near-Earth tail is an intrinsic aspect of flux transfer to the magnetotail. The mechanism is based on the strong variation of flux tube volume with the magnetic flux function.