Author name code: ferriz-mas ADS astronomy entries on 2022-09-14 author:"Ferriz-Mas, Antonio" ------------------------------------------------------------------------ Title: Can Stochastic Resonance Explain Recurrence of Grand Minima? Authors: Albert, Carlo; Ferriz-Mas, Antonio; Gaia, Filippo; Ulzega, Simone Bibcode: 2021ApJ...916L...9A Altcode: The amplitude of the 11 yr solar cycle is well known to be subject to long-term modulation, including sustained periods of very low activity known as Grand Minima. Stable long-period cycles found in proxies of solar activity have given new momentum to the debate about a possible influence of the tiny planetary tidal forcing. Here, we study the solar cycle by means of a simple zero-dimensional dynamo model, which includes a delay caused by meridional circulation as well as a quenching of the α-effect at toroidal magnetic fields exceeding an upper threshold. Fitting this model to the sunspot record, we find a set of parameters close to the bifurcation point at which two stable oscillatory modes emerge. One mode is a limit cycle resembling normal solar activity including a characteristic kink in the decaying limb of the cycle. The other mode is a weak sub-threshold cycle that could be interpreted as Grand Minimum activity. Adding noise to the model, we show that it exhibits Stochastic Resonance, which means that a weak external modulation can toss the dynamo back and forth between these two modes, whereby the periodicities of the modulation get strongly amplified. Title: Response to: "Critical Analysis of a Hypothesis of the Planetary Tidal Influence on Solar Activity" by S. Poluianov and I. Usoskin Authors: Abreu, J. A.; Albert, C.; Beer, J.; Ferriz-Mas, A.; McCracken, K. G.; Steinhilber, F. Bibcode: 2014SoPh..289.2343A Altcode: 2014SoPh..tmp...21A No abstract at ADS Title: Introduction Authors: Ferriz-Mas, Antonio; Hollerbach, Rainer; Stefani, Frank; Tilgner, Andreas Bibcode: 2013GApFD.107..383F Altcode: No abstract at ADS Title: Evidence for a planetary influence on solar activity? Authors: Beer, Jürg; Abreu, Jose A.; Ferriz-Mas, Antonio; McCracken, Kenneth G.; Steinhilber, Friedhelm Bibcode: 2013EGUGA..1510282B Altcode: In a recent paper Abreu et al. put forward the hypothesis of a planetary influence on the solar activity. This is based on a surprisingly good agreement between decadal to centennial solar cycles found in proxy records of solar activity of the past 10,000 years and the cycles present in the calculated torque exerted by the planets to a non-spherical tachocline. The evidence and its significance for such a planetary influence are discussed. If correct this hypothesis has some interesting implications for space climate. Title: Is there a planetary influence on solar activity? Authors: Abreu, Jose A.; Beer, Jürg; Ferriz-Mas, Antonio; McCracken, Kenneth G.; Steinhilber, Friedhelm Bibcode: 2013EGUGA..1510070A Altcode: Recently Abreu et al. have put forward the hypothesis of a planetary influence on solar activity. They developed a simple physical model for describing the time dependent torque exerted by the planets on a non-spherical tachocline and compared the corresponding power spectrum with the one obtained from a 9300 y long reconstruction of solar activity. They found an excellent agreement between the long-term cycles in proxies of solar activity and the periodicities in the planetary torque If correct, this hypothesis has important implications for solar physics and the solar terrestrial relationship. Title: Is there a planetary influence on solar activity? Authors: Abreu, J. A.; Beer, J.; Ferriz-Mas, A.; McCracken, K. G.; Steinhilber, F. Bibcode: 2012A&A...548A..88A Altcode: Context. Understanding the Sun's magnetic activity is important because of its impact on the Earth's environment. Direct observations of the sunspots since 1610 reveal an irregular activity cycle with an average period of about 11 years, which is modulated on longer timescales. Proxies of solar activity such as 14C and 10Be show consistently longer cycles with well-defined periodicities and varying amplitudes. Current models of solar activity assume that the origin and modulation of solar activity lie within the Sun itself; however, correlations between direct solar activity indices and planetary configurations have been reported on many occasions. Since no successful physical mechanism was suggested to explain these correlations, the possible link between planetary motion and solar activity has been largely ignored.
Aims: While energy considerations clearly show that the planets cannot be the direct cause of the solar activity, it remains an open question whether the planets can perturb the operation of the solar dynamo. Here we use a 9400 year solar activity reconstruction derived from cosmogenic radionuclides to test this hypothesis.
Methods: We developed a simple physical model for describing the time-dependent torque exerted by the planets on a non-spherical tachocline and compared the corresponding power spectrum with that of the reconstructed solar activity record.
Results: We find an excellent agreement between the long-term cycles in proxies of solar activity and the periodicities in the planetary torque and also that some periodicities remain phase-locked over 9400 years.
Conclusions: Based on these observations we put forward the idea that the long-term solar magnetic activity is modulated by planetary effects. If correct, our hypothesis has important implications for solar physics and the solar-terrestrial connection. Title: Coupled spin models for magnetic variation of planets and stars Authors: Nakamichi, A.; Mouri, H.; Schmitt, D.; Ferriz-Mas, A.; Wicht, J.; Morikawa, M. Bibcode: 2012MNRAS.423.2977N Altcode: 2011arXiv1104.5093N Geomagnetism is characterized by intermittent polarity reversals and rapid fluctuations. We have recently proposed a coupled macro-spin model to describe these dynamics based on the idea that the whole dynamo mechanism is described by the coherent interactions of many local elements. In this paper, we further develop this idea and construct the minimal model for magnetic variations. This simple model naturally yields many of the observed features of geomagnetism: its time evolution, the power spectrum, the frequency distribution of stable polarity periods etc. This model is characterized by two coexisting phases of spins: i.e. the cluster phase which determines the global dipole magnetic moment, and the expanded phase which gives random perpetual perturbations that yield the intermittent polarity flip of the dipole moment. This model can also describe the synchronization of the spin oscillations. This corresponds to the case of our Sun and the model well describes the quasi-regular cycles of the solar magnetism. Furthermore, by analysing the relevant terms of magnetohydrodynamic equations based on our model, we have obtained a scaling relation for the magnetism for planets, satellites and the Sun. Comparing it with various observations, we can estimate the relevant scale of the macro-spins. Title: A domino model for geomagnetic field reversals Authors: Mori, N.; Schmitt, D.; Ferriz-Mas, A.; Wicht, J.; Mouri, H.; Nakamichi, A.; Morikawa, M. Bibcode: 2011arXiv1110.5062M Altcode: We solve the equations of motion of a one-dimensional planar Heisenberg (or Vaks-Larkin) model consisting of a system of interacting macro-spins aligned along a ring. Each spin has unit length and is described by its angle with respect to the rotational axis. The orientation of the spins can vary in time due to random forcing and spin-spin interaction. We statistically describe the behaviour of the sum of all spins for different parameters. The term "domino model" in the title refers to the interaction among the spins. We compare the model results with geomagnetic field reversals and find strikingly similar behaviour. The aggregate of all spins keeps the same direction for a long time and, once in a while, begins flipping to change the orientation by almost 180 degrees (mimicking a geomagnetic reversal) or to move back to the original direction (mimicking an excursion). Most of the time the spins are aligned or anti-aligned and deviate only slightly with respect to the rotational axis (mimicking the secular variation of the geomagnetic pole with respect to the geographic pole). Reversals are fast compared to the times in between and they occur at random times, both in the model and in the case of the Earth's magnetic field. Title: Past and Future Solar Activity from Cosmogenic Radionuclides Authors: Abreu, J. A.; Beer, J.; Ferriz-Mas, A. Bibcode: 2010ASPC..428..287A Altcode: The sunspot record since 1610 shows cycles of magnetic activity with an irregular distribution of amplitudes and with a period around 11 years. They are modulated on longer timescales and were interrupted by the Maunder minimum in the 17th century. During the past several cycles the average solar activity was very high. This raises the question whether the present grand maximum is likely to terminate soon or even to be followed by another (Maunder-like) grand minimum. Cosmogenic radionuclides stored in natural archives such as 10Be in ice cores and 14C in tree rings have proven to be a valuable tool in reconstructing past solar activity and changes in the geomagnetic field intensity over several millennia. At present, this is the only method to extend back the record of solar activity beyond the instrumental period. The main properties of solar activity will be discussed for the past 10,000 years. A detailed statistical analysis of this record allows us to derive the life expectancy of the present grand maximum, which will come soon to an end. By using the same approach applied to the intervals between grand minima, we expect a grand minimum in solar activity to occur within the next 100 years. Title: How to Reach Superequipartition Field Strengths in Solar Magnetic Flux Tubes Authors: Ferriz-Mas, A.; Steiner, O. Bibcode: 2007SoPh..246...31F Altcode: A number of independent arguments indicate that the toroidal flux system responsible for the sunspot cycle is stored at the base of the convection zone in the form of flux tubes with field strength close to 105 G. Although the evidence for such strong fields is quite compelling, how such field strength can be reached is still a topic of debate. Flux expulsion by convection should lead to about the equipartition field strength, but the magnetic energy density of a 105-G field is two orders of magnitude larger than the mean kinetic energy density of convective motions. Line stretching by differential rotation (i.e., the "Ω effect" in the classical mean-field dynamo approach) probably plays an important role, but arguments based on energy considerations show that it does not seem feasible that a 105-G field can be produced in this way. An alternative scenario for the intensification of the toroidal flux system in the overshoot layer is related to the explosion of rising, buoyantly unstable magnetic flux tubes, which opens a complementary mechanism for magnetic-field intensification. A parallelism is pointed out with the mechanism of "convective collapse" for the intensification of photospheric magnetic flux tubes up to field strengths well above equipartition; both mechanisms, which are fundamentally thermal processes, are reviewed. Title: Flow instabilities of magnetic flux tubes. I. Perpendicular flow Authors: Schüssler, M.; Ferriz Mas, A. Bibcode: 2007A&A...463...23S Altcode: Context: The stability properties of filamentary magnetic structures are relevant for the storage and dynamics of magnetic fields in stellar convection zones and possibly also in other astrophysical contexts.
Aims: In a series of papers we study the effect of external and internal flows on the stability of magnetic flux tubes. In this paper we consider the effect of a flow perpendicular to a straight, horizontal flux tube embedded in a gravitationally stratified fluid. The flow acts on the flux tube by exerting an aerodynamic drag force and by modifying the pressure stratification in the background medium.
Methods: We carry out a Lagrangian linear stability analysis in the framework of the approximation of thin magnetic flux tubes.
Results: The external flow can drive monotonic and oscillatory instability (overstability). The stability condition depends on direction and magnitude of the external velocity as well as on its first and second derivatives with respect to depth. The range of the flow-driven instabilities typically extends to modes with much shorter wavelengths than for the buoyancy-driven undulatory Parker instability.
Conclusions: .Perpendicular flows with Alfvénic Mach number of order unity can drive monotonic as well as oscillatory instability of thin magnetic flux tubes. Such instability can affect the storage of magnetic flux in stellar interiors. Title: Connecting solar radiance variability to the solar dynamo with the virial theorem Authors: Steiner, O.; Ferriz-Mas, A. Bibcode: 2005AN....326..190S Altcode: The variability of solar radiance over a solar cycle is thought to result from a delicate balance between the radiative deficit of sunspots and the extra contribution of plage and network regions. Although the net effect is tiny, it must imply structural and thermal changes in the Sun or in partial layers of it as an unavoidable consequence of the virial theorem. Using the virial theorem for continua--including the magnetic field--it can be shown how solar radiance variability might be connected to a deeply seated flux-tube dynamo and how this connection is established on a hydrodynamical time scale. Title: The deep roots of solar radiance variability . Authors: Steiner, O.; Ferriz-Mas, A. Bibcode: 2005MmSAI..76..789S Altcode: The variability of solar radiance over a solar cycle is thought to result from a delicate balance between the radiative deficit of sunspots and the extra contribution of plage and network regions. Although the net effect is tiny, it implies structural and thermal changes in the Sun or in partial layers of it as an unavoidable consequence of the virial theorem. Using the virial theorem for continua--including the magnetic field--it can be shown how solar radiance variability might be connected to a deeply seated flux-tube dynamo and how this connection is established on a hydrodynamical time scale. Title: Where does the solar dynamo operate? Authors: Ferriz-Mas, Antonio Bibcode: 2003ESASP.535...99F Altcode: 2003iscs.symp...99F The Sun's large-scale magnetic field shows a cyclic behaviour with a period of about 22 years, but the exact origin of this cycle is not well understood yet. The observed properties of the magnetic field in the solar photosphere along with theoretical studies of magneto-convection in electrically well-conducting fluids suggest that the magnetic field in stellar convection zones is quite inhomogeneous: magnetic flux is concentrated into flux tubes embedded in a significantly less magnetized plasma. This concentration of magnetic flux has important consequences for magnetic flux storage and for modeling the solar dynamo, since dynamical aspects such as buoyancy and drag force must be taken into account. Title: Magnetic flux tubes and the dynamo problem Authors: Schüssler, Manfred; Ferriz-Mas, Antonio Bibcode: 2003and..book..123S Altcode: 2003eclm.book..123S The observed properties of the magnetic field in the solar photosphere and theoretical studies of magneto-convection in electrically well-conducting fluids suggest that the magnetic field in stellar convection zones is quite inhomogeneous: magnetic flux is concentrated into magnetic flux tubes embedded in significantly less magnetized plasma. Such a state of the magnetic field potentially has strong implications for stellar dynamo theory since the dynamics of an ensemble of flux tubes is rather different from that of a more uniform field and new phenomena like magnetic buoyancy appear.

If the diameter of a magnetic flux tube is much smaller than any other relevant length scale, the MHD equations governing its evolution can be considerably simplified in terms of the thin-flux-tube approximation. Studies of thin flux tubes in comparison with observed properties of sunspot groups have led to far-reaching conclusions about the nature of the dynamo-generated magnetic field in the solar interior. The storage of magnetic flux for periods comparable to the amplification time of the dynamo requires the compensation of magnetic buoyancy by a stably stratified medium, a situation realized in a layer of overshooting convection at the bottom of the convection zone. Flux tubes stored in mechanical force equilibrium in this layer become unstable with respect to an undular instability once a critical field strength is exceeded, flux loops rise through the convection zone and erupt as bipolar magnetic regions at the surface. For parameter values relevant for the solar case, the critical field strength is of the order of 105 G. A field of similar strength is also required to prevent the rising unstable flux loops from being strongly deflected poleward by the action of the Coriolis force and also from `exploding' in the middle of the convection zone. The latter process is caused by the superadiabatic stratification.

The magnetic energy density of a field of 105 G is two orders of magnitude larger than the kinetic energy density of the convective motions in the lower solar convection zone. This raises serious doubts whether the conventional turbulent dynamo process based upon cyclonic convection can work on the basis of such a strong field. Moreover, it is unclear whether solar differential rotation is capable of generating a toroidal magnetic field of 105 G; it is conceivable that thermal processes like an entropy-driven outflow from exploded flux tubes leads to the large field strength required.

The instability of magnetic flux tubes stored in the overshoot region suggests an alternative dynamo mechanism based upon growing helical waves propagating along the tubes. Since this process operates only for field strengths exceeding a critical value, such a dynamo can fall into a `grand minimum' once the field strength is globally driven below this value, for instance by magnetic flux pumped at random from the convection zone into the dynamo region in the overshoot layer. The same process may act as a (re-)starter of the dynamo operation. Other non-conventional dynamo mechanisms based upon the dynamics of magnetic flux tubes are also conceivable. Title: Advances in Nonlinear Dynamos Authors: Ferriz-Mas, Antonio; Núñez, Manuel Bibcode: 2003and..book.....F Altcode: No abstract at ADS Title: Variable Solar and Stellar Activity by a Flux Tube Dynamo Authors: Schmitt, D.; Ferriz-Mas, A. Bibcode: 2003PADEU..13...89S Altcode: The dynamo action of unstable magnetic flux tubes due to magnetic buoyancy in a rotating stellar convection zone is summarized and the implications of a flux tube dynamo with a threshold in field strength for dynamo action is discussed in connection with the observed variability of solar and stellar magnetic activity. Title: The need for very high resolution spectroscopy for the study of hot subdwarfs Authors: Ulla, A.; Manteiga, M.; Thejll, P.; Saffer, R. A.; Pérez Hernández, F.; MacDonald, J.; Ferriz-Mas, A.; Elkin, V.; Oreiro Rey, R. Bibcode: 2003RMxAC..16..313U Altcode: Hot subdwarf stars (hot sds) are blue subluminous objects at high galactic latitudes. They split into two well-separated spectroscopic sequences: the O (sdOs) and B-type (sdBs), according to composition and effective temperature. As they are immediate progenitors of white dwarfs (WDs), this resembles the spectroscopic H (DA)/He (DB) distinction between these. Among the various theories for the origin and final fate of hot sds, both single and close binary evolution have been suggested but the issue is still debated. Only a few determinations are available to date regarding the study of such aspects as rotation and microturbulent velocities (Heber et al.~2000) or the magnetic nature of these objects (Elkin 1996). Title: Hot Subdwarfs: Magnetic, Oscillatory and Other Physical Properties Authors: Oreiro, R.; Pérez Hernández, F.; Manteiga, M.; Ulla, A.; González Pérez, J. M.; Zapatero Osorio, M. R.; GarcÍa López, R.; MacDonald, J.; Thejll, P.; Ferriz-Mas, A.; Saffer, R. A.; Elkin, V. Bibcode: 2003Ap&SS.284..269O Altcode: Hot subdwarf stars (hot sds) are blue subluminous objects. Only a few determinations are available to date regarding the study of such aspects as rotation, microturbulent velocities or the magnetic nature of these objects. Over 26 sdBs are known to date to be multiperiodic rapid oscillators. This project presents preliminary results of new observations and models of a sample of pulsating and non-pulsating hot sds, including considerations on mass loss and eventual magnetic properties. Title: Studying the Asymmetry of Bipolar Active Regions by Means of the Thin Flux-Tube Approximation Authors: Ferriz-Mas, Antonio Bibcode: 2002smra.progE...4F Altcode: No abstract at ADS Title: Solar Interior: Convection Zone Flux Tubes Authors: Ferriz-Mas, A. Bibcode: 2000eaa..bookE2244F Altcode: The magnetic field at the solar surface reflects the presence of isolated flux tubes below the photosphere. The magnetic field is not diffusively distributed over the entire surface but is concentrated into regions of rather intense field, ranging from SUNSPOTS—with diameters of approximately 20 000 km and field strengths of 3000 G—down to smaller magnetic elements (100-200 km and 1000 G). The e... Title: Stellar Dynamos: Nonlinearity and Chaotic Flows Authors: Nunez, Manuel; Ferriz-Mas, Antonio Bibcode: 1999ASPC..178.....N Altcode: 1999sdnc.conf.....N No abstract at ADS Title: On the Asymmetry of Bipolar Active Regions Authors: Ferriz-Mas, A.; Schüssler, M. Bibcode: 1998ASPC..155...14F Altcode: 1998sasp.conf...14F No abstract at ADS Title: Variability of Solar and Stellar Activity by Two Interacting Hydromagnetic Dynamos Authors: Schmitt, D.; Schussler, M.; Ferriz-Mas, A. Bibcode: 1998ASPC..154.1324S Altcode: 1998csss...10.1324S We propose a combination of two dynamos for solar and stellar magnetic activity. A strong-field dynamo operating in the overshoot layer at the base of the convection zone generating superequipartition fields concentrated in isolated flux tubes is responsible for cyclic activity (e.g., sunspots), while a turbulent weak-field dynamo in the convection zone produces a more irregular field. The combination of a threshold in field strength for dynamo action due to instability of magnetic flux tubes in the overshoot layer and random fluctuations due to magnetic fields from the turbulent convection zone leads, in the case of the Sun and solar-type stars, to activity cycles with strong amplitude variations and the occasional appearance of grand minima. Stronger fluctuations may destroy the cyclic behaviour of the overshoot layer dynamo and lead to increased but irregular activity. Such activity is observed in fast rotating cool stars. On the other hand, stars with low and non-variable magnetic activity may be in a state with only the turbulent convection zone dynamo active. Title: Long-term Variation of Solar Activity by a Dynamo Based on Magnetic Flux Tubes Authors: Schussler, M.; Schmitt, D.; Ferriz-Mas, A. Bibcode: 1997ASPC..118...39S Altcode: 1997fasp.conf...39S We show that cyclic activity and Maunder-type grand minima can be explained by a dynamo driven by the instability of magnetic flux tubes in the overshoot layer at the bottom of the solar convection zone. The combination of a threshold in field strength for dynamo action and random fluctuations due to magnetic fields from the turbulent convection zone leads to activity cycles with strong amplitude variations and the occasional appearance of grand minima. Title: Distribution of starspots on cool stars. I. Young and main sequence stars of 1Msun_. Authors: Schuessler, M.; Caligari, P.; Ferriz-Mas, A.; Solanki, S. K.; Stix, M. Bibcode: 1996A&A...314..503S Altcode: Sunspots are restricted to a latitude band within 30degof the solar equator. In contrast, the latitudes of spots on the surfaces of rapidly rotating cool stars can range from their polar regions, for RS CVn systems and for T Tauri stars leaving the Hayashi track, to mid latitudes for stars close to or on the main sequence. In order to find an explanation for these observed spot latitudes we have applied the criteria for the undulatory instability (Parker instability) of a toroidal magnetic flux tube embedded in the convective overshoot layer below the outer convection zone and calculated the non-linear evolution of the rising magnetic loops formed by this instability. We describe the results for a star of one solar mass in different phases of its evolution before and on the main sequence. We find that there usually is a range of latitudes at which magnetic flux can emerge on the stellar surface. The mean latitude of emergence shifts towards the poles for increasingly rapid rotation. The internal structure of the star, however, plays an almost equally important role in determining the latitude of magnetic emergence. For stars of solar mass only the youngest objects, with extremely deep convection zones, should show spots emerging at the stellar poles. Pre-main sequence stars at an age of 10^7^ y (convection zone reaching down half-way to the centre) exhibit high latitude, but not truly polar spots, while a main sequence star of one solar mass, even at high rotation rates, only shows intermediate latitude spots. These results are found to be in good agreement with Doppler images of young rapid rotators. Title: Enhanced inertia of thin magnetic flux tubes. Authors: Moreno-Insertis, F.; Schuessler, M.; Ferriz-Mas, A. Bibcode: 1996A&A...312..317M Altcode: Accelerated bodies immersed in a fluid experience enhanced inertia due to the associated co-acceleration of a certain volume of fluid in their environment. We discuss the concept of enhanced inertia in the framework of the approximation of thin flux tubes, which is widely used to describe the dynamics of concentrated magnetic structures in astrophysical objects. Previous attempts to incorporate this effect have used a local approach, in which the reaction force of the external medium on a given tube mass element solely depends on the relative acceleration of tube and environment at that element. We show that those previous formulations are inconsistent (either on physical or geometrical grounds). We present here an alternative derivation of the enhanced inertia term by geometrical means, still within a local treatment of the problem but avoiding the pitfalls of previous works. Our formulation, on the other hand, reveals a basic problem: all local approaches are bound to give incorrect answers for the reaction force in as far as they disregard the variation of the external flow in the direction parallel to the flux tube: in doing so, they generally fail to provide for global momentum conservation. An exact solution and detailed analysis for an instance of this failure is given. The discussion of this paper may be of use also in the hydrodynamical framework of vortex tube dynamics. Title: Intermittent solar activity by an on-off dynamo. Authors: Schmitt, D.; Schuessler, M.; Ferriz-Mas, A. Bibcode: 1996A&A...311L...1S Altcode: We show that the alteration between intervals of cyclic activity and grand minima like the Maunder minimum in the 17th century, which is characteristic for the long-term variation of the solar activity, can be described as on-off intermittency arising in a dymano driven by the instability of magnetic flux tubes in the overshoot layer below the convection zone. The combination of a threshold in field strength for dynamo action and random fluctuations due to magnetic fields from a turbulent convection zone dynamo leads to activity cycles with strong amplitude variations and the occasional appearance of grand minima of very low activity. The resulting pattern is in qualitative agreement with the long-term records of solar activity. Title: On the Storage of Magnetic Flux Tubes at the Base of the Solar Convection Zone Authors: Ferriz-Mas, Antonio Bibcode: 1996ApJ...458..802F Altcode: The study of the storage of toroidal flux tubes at the base of the convection zone is of interest in connection with the operation of a solar αΩ-type dynamo. The natural equilibrium state for an isolated flux tube is that of neutral buoyancy (so that there is a mass flow along the tube in the direction of solar rotation); flux tubes in thermal equilibrium must be ruled out for magnetic fluxes Φ ≳ 1019 Mx.

In this paper we study the equilibrium and stability properties of toroidal flux tubes in the equatorial plane of the Sun. To that end, we use a solar model which includes a consistently calculated overshoot region at the bottom of the convection zone, based on a nonlocal mixing length formalism. As a consequence of the nonlocal treatment, the superadiabaticity already becomes negative in the lowest part (≃26,000 km) of the convection zone proper, which is defined as the region in which the convective flux, is positive. In the present model, the underlying overshoot region extends over some 10,000 km, and the total extent of the subadiabatic layer is about 36,000 km. For the angular velocity distribution, we use a semiempirical formula based on helioseismological results. Flux tubes with field strengths of about 105 G can be stored only in the overshoot region, while tubes with equipartition field strength could be kept in a subadiabatic layer at the bottom of the convection zone proper. The results of the stability analysis are compared with those of previous studies. Title: Instabilities of Magnetic Flux Tubes in a Stellar Convection Zone Authors: Ferriz-Mas, A.; Schüssler, M. Bibcode: 1996ApL&C..34....1F Altcode: No abstract at ADS Title: Instabilities of magnetic flux tubes in a stellar convection zone II. Flux rings outside the equatorial plane Authors: Ferriz-Mas, A.; Schüssler, M. Bibcode: 1995GApFD..81..233F Altcode: Motivated by the problems of magnetic flux storage and dynamo action in stars with convection zones, we study the equilibrium and stability of magnetic flux tubes under the influence of differential rotation and stratification. The formalism developed in the first paper in this series is applied to axisymmetric, toroidal flux tubes (flux rings) lying in planes parallel to the equator at an arbitrary latitude. We assume mechanical force equilibrium, which requires neutral buoyancy of the flux tube and a longitudinal internal flow in the direction of stellar rotation. Stability against isentropic perturbations is investigated by considering both axisymmetric and non-axisymmetric, three-dimensional displacements of the equilibrium configuration. For axisymmetric modes, we find qualitative differences between the stability criteria for flux tubes within and outside the equatorial plane, where instability is generally easier to excite and overstable modes appear. In the case of non-axisymmetric perturbations, the results of a numerical study with parameter values corresponding to the bottom of the solar convection zone are discussed. The stability properties depend in a complicated way on the various parameters (e.g., latitude, magnetic field, superadiabaticity of the stratification, angular velocity and its gradient). While the magnetic field value for the onset of undulatory (Parker) instability with large growth rates is mainly determined by the stratification and the rotation rate, instabilities at somewhat lower field strengths with relatively small growth rates depend strongly on the sign and the value of the angular velocity gradient. Title: Waves and Instabilities of a Toroidal Magnetic Flux Tube in a Rotating Star Authors: Ferriz-Mas, A.; Schuessler, M. Bibcode: 1994ApJ...433..852F Altcode: The oscillation modes and instabilities of a toroidal flux tube lying in the equatorial plane of a differentially rotating star are investigated using the thin flux-tube approximation. The behavior of the frequencies as functions of the magnetic field strength and of the superadiabaticity is explored for both axisymmetric and nonaxisymmetric modes. In limiting cases, the modes can be identified with known normal modes of simple configurations (e.g., a plane-parallel atmosphere with constant gravity or a magnetic flux tube embedded in a homogeneous medium). The axisymmetric modes are essentially radial modes oscillating with a magnetically modified Brunt-Vaisala frequency. As to the nonaxisymmetric modes in the limit of rapid rotation (or of weak magnetic field) there is one pair of stable inertial waves, which are due to the Coriolis force, and one pair of magnetospheric modes, which are longitudinal slow modes modified by rotation. In the general case (intermediate rotation rates), the modes do not have a definite character, but their properties can be investigated analytically. The corresponding bifurcation diagrams are discussed. Title: A dynamo effect due to instability of magnetic flux tubes. Authors: Ferriz-Mas, A.; Schmitt, D.; Schuessler, M. Bibcode: 1994A&A...289..949F Altcode: We show that a non-axisymmetric instability of toroidal magnetic flux tubes in a rotating star provides a dynamo effect. The instability occurs in the form of propagating helical waves; their growth in amplitude causes a phase shift between the perturbations of magnetic field and velocity, which leads to an electric field (anti)parallel to the direction of the unperturbed field. Together with differential rotation, this effect is capable of driving a dynamo of the α{OMEGA}-type. In contrast to the conventional α-effect in cyclonic convection, this dynamo effect operates in strong (super-equipartition) magnetic fields which resist against distortion by convective flows. We calculate the induced electric field using results from linear stability analysis and a model of the solar convection zone which consistently includes an overshoot layer. We find that for growing magnetic field the dynamo effect occurs first in high latitudes (near the poles) in a region of weak instability which moves towards the equator as the field strength increases further. The dependence of the dynamo effect on the location of the flux tubes (in depth and latitude) and on the rotation rate is discussed. Title: Forces on Magnetic Flux Tubes Moving in Inhomogeneous Flows Authors: Moreno-Insertis, F.; Ferriz-Mas, A.; Schussler, M. Bibcode: 1994ApJ...422..652M Altcode: The back-reaction of an incompressible two-dimensional flow of constant strain to the accelerated motion of a straight cylinder is calculated in the general case that the flow is inhomogeneous, nonstationary, and with nonvanishing (although constant) vorticity. The resulting enhanced inertia of the cylinder is basically given by its relative acceleration with respect to the background flow. Further force terms that appear because of the nonstationary and inhomogeneity of the background flow are the following: a force identical to that experienced by the mass elements of the unperturbed flow at the position of the axis of the cylinder; the customary lift force because of the circulation around the body; finally, a force term that appears only with nonvanishing relative speed between the body and the background flow and which is related to the energy which has to be imparted by the body to the surrounding fluid in order to adapt the perturbation to the new local velocity. The results have application to the dynamics of magnetic flux tubes in the convection zone and atmosphere of the Sun as well as to other astrophysical problems. Title: Alpha-effect due to instability of magnetic flux tubes and the solar dynamo Authors: Schmitt, D.; Ferriz-Mas, A.; Schüssler, M. Bibcode: 1994smf..conf..101S Altcode: No abstract at ADS Title: Instability and eruption of magnetic flux tubes Authors: Caligari, P.; Ferriz-Mas, A.; Moreno-Insertis, F.; Schüssler, M. Bibcode: 1994smf..conf..139C Altcode: No abstract at ADS Title: Instability and eruption of magnetic flux tubes in the solar convection zone. Authors: Schussler, M.; Caligari, P.; Ferriz-Mas, A.; Moreno-Insertis, F. Bibcode: 1994A&A...281L..69S Altcode: We present a consistent model of storage, instability and dynamical eruption of magnetic flux tubes in the solar convection zone and underlying overshoot region. Using a convection zone model with self-consistent overshoot layer, we calculate equilibrium configurations of magnetic flux tubes and determine their linear stability properties, taking into consideration the effects of stratification and rotation. Instability of flux tubes stored in the overshoot layer with growth times below one year requires field strengths of the order of 105 G; in many cases, the dominant mode has an azimuthal wave number of m = 2. Numerical simulations are used to follow the nonlinear evolution of such unstable flux tubes and their rise through the convection zone, from which they emerge to form active regions. The results are in accordance with the following two requirements, based on observational facts: (a) the upward motion of the tubes is not significantly deflected by the Coriolis force so that they can emerge at low latitudes, (b) their inclination with respect to the East-West direction (tilt angle) as a function of the latitude of emergence is consistent with observations of acitve regions. Title: Storage of Magnetic Flux in the Overshoot Region Authors: Moreno-Insertis, F.; Schussler, M.; Ferriz-Mas, A. Bibcode: 1993IAUS..157...41M Altcode: No abstract at ADS Title: Instabilities of magnetic flux tubes in a stellar convection zone I. Equatorial flux rings in differentially rotating stars Authors: Ferriz-Mas, A.; Schüssler, M. Bibcode: 1993GApFD..72..209F Altcode: The stability properties of magnetic flux tubes in stellar convection zones including overshoot regions is of considerable interest in connection with the problems of magnetic flux storage and hydromagnetic dynamo action in the Sun and other cool stars. We have developed a general formalism based on the approximation of thin flux tubes which provides a basis for a linear stability analysis of arbitrary flux tube equilibria. As a first application, the stability of axisymmetric, toroidal flux tubes (flux rings) located in the equatorial plane of a star under the influence of differential rotation and stratification has been considered. Arbitrary angular velocity differences between the interior of the flux ring and its environment are permitted. It is found that the linear evolution of radial and azimuthal perturbations (i.e., within the equatorial plane) is decoupled from that of latitudinal perturbations (perpendicular to the plane). The latitudinal instability ('poleward slip') is found to be suppressed if the matter within the flux tube rotates faster than its environment by a sufficient amount. For perturbations within the equatorial plane, both stratification (sub-order superadiabatic) of the external gas and rotation are crucial. Angular momentum conservation tends to suppress axisymmetric modes. This effect is enhanced by a faster rotation of the gas within the flux tube. Non-axisymmetric modes are more unstable since the constraint of angular momentum conservation is broken. For these modes, a slower internal rotation rate has a stabilizing effect. Within a certain range of magnetic field strengths, a second region of stability exists within the region of unstable configurations, which can extend into the superadiabatically stratified (convectively unstable) region. The character of the different modes is discussed in conjunction with the topology of the stability diagram. Title: On the Stability of Magnetic Flux Tubes in the Equator of a Star Authors: Ferriz-Mas, A.; Schussler, M. Bibcode: 1993IAUS..157...45F Altcode: No abstract at ADS Title: Modes of a flux ring lying in the equator of a star. Authors: Ferriz-Mas, A.; Schüssler, M. Bibcode: 1993spd..conf...69F Altcode: No abstract at ADS Title: Shock wave propagation in a magnetic flux tube Authors: Ferriz-Mas, A.; Moreno-Insertis, F. Bibcode: 1992PhFlA...4.2700F Altcode: 1992PhFl....4.2700F The propagation of a shock wave in a magnetic flux tube is studied within the framework of the Brinkley-Kirkwood theory adapted to a radiating gas. Simplified thermodynamic paths along which the compressed plasma returns to its initial state are considered. It is assumed that the undisturbed medium is uniform and that the flux tube is optically thin. The shock waves investigated, which are described with the aid of the thin flux-tube approximation, are essentially slow magnetohydrodynamic shocks modified by the constraint of lateral pressure balance between the flux tube and the surrounding field-free fluid; the confining external pressure must be balanced by the internal gas plus magnetic pressures. Exact analytical solutions giving the evolution of the shock wave are obtained for the case of weak shocks. Title: Storage of magnetic flux tubes in a convective overshoot region Authors: Moreno-Insertis, F.; Schuessler, M.; Ferriz-Mas, A. Bibcode: 1992A&A...264..686M Altcode: Consideration is given to the suppression of the radial and polar escape of magnetic flux in the form of toroidal flux tubes (flux rings) from low latitudes in the overshoot region below the solar convection zone through the combined action of the subadiabatic ambient stratification and the rotationally induced forces. It is shown that a flux ring which is initially in thermal equilibrium with its environment and rotates with the ambient angular velocity moves radially and latitudinally towards an equilibrium configuration of lower internal temperature and larger internal rotation rate with respect to the surrounding nonmagnetic gas. Flux rings perform superposed buoyancy and inertial oscillations around their equilibrium positions. From a study of the frequencies and amplitudes of these oscillations, it is concluded that flux rings with B of less than about 100,000 G can be kept within the overshoot region if the superadiabaticity is sufficiently negative, i.e., less than about -0.00004. Title: Damping of Shocks in Magnetic Flux Tubes Authors: Ferriz Mas, A.; Moreno Insertis, F. Bibcode: 1991mcch.conf..417F Altcode: No abstract at ADS Title: Dynamics of magnetic flux concentrations - The second-order thin flux tube approximation Authors: Ferriz-Mas, A.; Schuessler, M.; Anton, V. Bibcode: 1989A&A...210..425F Altcode: The thin flux tube approximation for the dynamics of magnetic flux concentrations is extended up to second order in the radial expansion to consistently include azimuthal velocities and twisted magnetic fields. The linear wave modes of a flux tube as described by the new set of equations are calculated and compared with the results of the conventional zeroth-order thin flux tube approximation. By comparison with exact solutions which are available for a uniform flux tube in a non-stratified medium, it is shown that the thin flux tube approximation (based on an expansion approach) is best suited to describe surface modes of a magnetic structure while body waves are not so well represented. Title: Radial expansion of the magnetohydrodynamic equations for axially symmetric configurations Authors: Ferriz-Mas, A.; Schüsler, M. Bibcode: 1989GApFD..48..217F Altcode: We introduce a general expansion approach to obtain a fully consistent closed set of magnetohydrodynamic equations in two independent variables, which is particularly useful to describe axially symmetric, time-dependent problems with weak variation of all quantities in the radial direction. This is done by considering the hierarchy of expanded magnetofluid equations in cylindrical coordinates and equating terms with equal powers in the radial coordinate r. From geometrical considerations it is shown that the radial expansions of the pertaining physical quantities are either even series or odd series in r; this introduces a significant reduction in the number of variables and equations. The closure of the system is provided by appropriate boundary conditions. Among other possible applications, the method is relevant for the analysis of structure and dynamics of magnetic field concentrations in stellar atmospheres. Title: Estudio de la dinámica de tubos de flujo magnético mediante el desarrollo en serie de las ecuaciones magnetohidrodinámicas Title: Estudio de la dinámica de tubos de flujo magnético mediante el desarrollo en serie de las ecuaciones magnetohidrodinámicas Title: Study of the dynamics of magnetic flux tubes through series expansion of the magnetohydrodynamic equations; Authors: Ferriz Mas, Antonio Bibcode: 1989PhDT.......119F Altcode: No abstract at ADS Title: Nonlinear flows along magnetic flux tubes: Mathematical structure and exact simple wave solutions Authors: Ferriz-Mas, A. Bibcode: 1988PhFl...31.2583F Altcode: The mathematical structure of nonlinear, isentropic longitudinal flows of an ideal magnetohydrodynamic plasma confined to a magnetic flux tube embedded in a quiescent nonmagnetic fluid is investigated. Exact analytical solutions are derived for a special type of nonlinear flow in the absence of gravity: the simple waves, for which all the unknowns depend on single functions of space and time. These exhibit analytically the formation of shock waves. Emphasis is placed on new features introduced by the magnetic distensibility, which acts as an additional restoring force, as compared with the hydrodynamic flow of gas along a rigid tube. Introducing a series expansion in a suitable parameter, it is shown that the hydrodynamic problem can be considered as the zeroth-order approach to the magnetic flux tube problem. Finally, the motion in a magnetic flux tube under the action of a piston advancing in a prescribed manner has been briefly considered. This problem is of current interest in relation to the generation of tube-guided waves in the solar atmosphere. Title: An analytical study of shock waves in thin magnetic flux tubes Authors: Ferriz-Mas, A.; Moreno-Insertis, F. Bibcode: 1987A&A...179..268F Altcode: The jump conditions across a shock front in a thin magnetic flux tube are studied by purely analytical means. Some properties of magnetohydrodynamic shock waves in extended media are shown also to hold in the more complicated case of thin magnetic flux tubes. It is shown that flux tube shock waves are always compressive, thus being accompanied by a weakening of the magnetic field strength and increase of the tube radius. Some consequences of this are examined, such as the sub- or supercritical character of the flow velocity with respect to the Alfvén, sound and "tube" speeds. The range of variation of the ratios of the different variables across the shock front is determined along with the equivalent of the Hugoniot curve and further properties of the shocks in magnetic flux tubes. The analogies and differences with HD and MHD shocks in extended media are pointed out. Finally, some implications of the shock wave structure for the solar atmosphere are briefly discussed.