Magneto‐seismology of the solar atmosphere

Magnetohydrodynamic (MHD) waves in solar coronal loops, which were previously only predicted by theory have actually been detected with space‐borne instruments. These observations have given an important and novel tool to measure fundamental parameters in the magnetically embedded solar corona. This paper will illustrate how information about the magnetic and density structure along coronal loops can be determined by measuring the frequency or amplitude profiles of standing fast kink mode oscillations. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The problem of phase mixed shear Alfvén waves in the solar corona revisited

The problem of phase mixing of shear Alfvén waves is revisited taking into account dissipative phenomena specific for the solar corona. In regions of space plasmas where the dynamics is controlled by the magnetic field, transport coefficients become anisotropic with transport mechanism having different behavior and magnitude depending on the orientation with respect to the ambient magnetic field. Taking into account realistic values for dissipative coefficients we obtain that the previous results derived in context of torsional Alfvén wave phase mixing are actually heavily underestimated so phase mixing cannot be used to explain the damping of torsional Alfvén waves and heating of open coronal structures. The presented results indicate that in order for phase mixing to still be a viable mechanism to explain heating or wave damping unrealistic assumptions have to be made. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

MHD waves at a spherical interface modelling EIT waves

Eruptive events such as flares and coronal mass ejections (CMEs) are known to generate global waves propagating over distances comparable to the solar radius in different layers of the solar atmosphere. Here we investigate the propagation of coronal EIT waves, modelled as fast magnetoacoustic modes propagating at a spherical interface in the presence of a purely radial magnetic field. Based on a simplified equilibrium we derive the dispersion relation of the waves. The generation and propagation of EIT waves at the spherical interface is studied numerically for different values of spherical degree and preliminary conclusions are reached regarding the properties of EIT waves. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

MHD waves in the solar north polar coronal hole

The effects, hitherto not treated, of the temperature and the number density gradients, both in the parallel and the perpendicular direction to the magnetic field, of O VI ions, on the MHD wave propagation characteristics in the solar North Polar Coronal Hole are investigated. We investigate the magnetosonic wave propagation in a resistive MHD regime where only the thermal conduction is taken into account. Heat conduction across the magnetic field is treated in a non‐classical approach wherein the heat is assumed to be conducted by the plasma waves emitted by ions and absorbed at a distance from the source by other ions. Anisotropic temperature and the number density distributions of O VI ions revealed the chaotic nature of MHD standing wave, especially near the plume/interplume lane borders. Attenuation length scales of the fast mode is shown not to be smoothly varying function of the radial distance from the Sun (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On global solar dynamo simulations

Global dynamo simulations solving the equations of magnetohydrodynamics (MHD) have been a tool of astrophysicists who try to understand the magnetism of the Sun for several decades now. During recent years many fundamental issues in dynamo theory have been studied in detail by means of local numerical simulations that simplify the problem and allow the study of physical effects in isolation. Global simulations, however, continue to suffer from the age‐old problem of too low spatial resolution, leading to much lower Reynolds numbers and scale separation than in the Sun. Reproducing the internal rotation of the Sun, which plays a crucial role in the dynamo process, has also turned out to be a very difficult problem. In the present paper the current status of global dynamo simulations of the Sun is reviewed. Emphasis is put on efforts to understand how the large‐scale magnetic fields, i.e. whose length scale is greater than the scale of turbulence, are generated in the Sun. Some lessons from mean‐field theory and local simulations are reviewed and their possible implications to the global models are discussed. Possible remedies to some current issues of solar simulations are put forward (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Meridional circulation and dynamo waves

The effect of meridional circulation on spherical shell dynamos is considered in the Parker approximation. We demonstrate that the type of the exited solution crucially depend on the intensity of the meridional circulation. If the circulation is equatorward or if it is polarward however do not exceed some critical value, an oscillating solution in form of an equatorward traveling wave is excited. If the polarward meridional circulation becomes too intensive the solution becomes steady growing. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear interaction between Alfvén and acoustic-gravity waves in the solar atmosphere

Based on a plane-parallel isothermal model solar atmosphere permeated by a uniform magnetic field directed against the action of gravity, we considered the nonlinear interaction between vertically propagating Alfvén and acoustic-gravity waves. We established that Alfvén waves are efficiently generated at the difference and sum frequencies. We ascertained that no acoustic-gravity waves are formed at the corresponding combination frequencies. A horizontal magnetohydrodynamic wind whose direction changes with height was found to be formed in the solar atmosphere at zero difference frequency.     

Alleviation of catastrophic quenching in solar dynamo model with nonlocal alpha‐effect

The nonlocal alpha‐effect of Babcock‐Leighton type is not prone to the catastrophic quenching due to conservation of magnetic helicity. This is shown with a dynamo model, which jointly applies the nonlocal alpha‐effect, the diamagnetic pumping, and dynamical equation for the magnetic alpha‐effect. The same model shows catastrophic quenching when the alpha‐effect is changed to its local formulation. The nonlocal model shows a preferred excitation of magnetic fields of dipolar symmetry, which oscillate with a period of about ten years and have a toroidal‐to‐polar fields ratio of about a thousand (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ambipolar diffusion in the solar atmosphere

The process of non-linear ambipolar diffusion in the region overlying the solar surface can be an effective mechanism for producing sharp magnetic structures and current sheets. These may be the sites responsible for the occurrence of connectivity of magnetic field lines, and the subsequent explosive input of energy for heating of some of the features in the atmosphere of the Sun..     

Force-free magnetic fields in the solar atmosphere

Reliable measurements of the solar magnetic field are restricted to the level of the photosphere. For about half a century attempts have been made to calculate the field in the layers above the photosphere, i.e. in the chromosphere and in the corona, from the measured photospheric field. The procedure is known as magnetic field extrapolation. In the superphotospheric parts of active regions the magnetic field is approximately force-free, i.e. electric currents are aligned with the magnetic field. The practical application to solar active regions has been largely confined to constant-α or linear force-free fields, with a spatially constant ratio, α, between the electric current and the magnetic field. We review results obtained from extrapolations with constant-α force-free fields, in particular on magnetic topologies favourable for flares and on magnetic and current helicities. Presently, different methods are being developed to calculate non-constant-α or nonlinear force-free fields from photospheric vector magnetograms. We also briefly discuss these methods and present a comparison of a linear and a nonlinear force-free magnetic field extrapolation applied to the same photospheric boundary data. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

3-D non-linear evolution of a magnetic flux tube in a spherical shell: The isentropic case

We present recent 3-D MHD numerical simulations of the non-linear dynamical evolution of magnetic flux tubes in an adiabatically stratified convection zone in spherical geometry, using the anelastic spherical harmonic (ASH) code.We seek to understand the mechanism of emergence of strong toroidal fields from the base of the solar convection zone to the solar surface as active regions. We confirm the results obtained in cartesian geometry that flux tubes that are not twisted split into two counter vortices before reaching the top of the convection zone. Moreover, we find that twisted tubes undergo the poleward-slip instability due to an unbalanced magnetic curvature force which gives the tube a poleward motion both in the non-rotating and in the rotating case. This poleward drift is found to be more pronounced on tubes originally located at high latitudes. Finally, rotation is found to decrease the rise velocity of the flux tubes through the convection zone, especially when the tube is introduced at low latitudes. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamo action in simulations of penetrative solar convection with an imposed tachocline

We summarize new and continuing three-dimensional spherical shell simulations of dynamo action by convection allowed to penetrate downward into a tachocline of rotational shear. The inclusion of an imposed tachocline allows us to examine several processes believed to be essential in the operation of the global solar dynamo, including differential rotation, magnetic pumping, and the stretching and organization of fields within the tachocline. In the stably stratified core, our simulations reveal that strong axisymmetric magnetic fields (of ∼ 3000 G strength) can be built, and that those fields generally exhibit a striking antisymmetric parity, with fields in the northern hemisphere largely of opposite polarity to those in the southern hemisphere. In the convection zone above, fluctuating fields dominate over weaker mean fields. New calculations indicate that the tendency toward toroidal fields of antisymmetric parity is relatively insensitive to initial magnetic field configurations; they also reveal that on decade-long timescales, the magnetic fields can briefly enter (and subsequently emerge from) states of symmetric parity.We have not yet observed any overall reversals of the field polarity, nor systematic latitudinal propagation. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability of toroidal magnetic fields in the solar tachocline and beneath

Stability of toroidal magnetic field in a stellar radiation zone is considered for the cases of uniform and differential rotation. In the rigidly rotating radiative core shortly below the tachocline, the critical magnetic field for instability is about 600 G. The unstable disturbances for slightly supercritical fields have short radial scales ∼1 Mm. Radial mixing produced by the instability is estimated to conclude that the internal field of the sun can exceed the critical value of 600 G only marginally. Otherwise, the mixing is too strong and not compatible with the observed lithium abundance. Analysis of joint instability of differential rotation and toroidal field leads to the conclusion that axisymmetric models of the laminar solar tachocline are stable to nonaxisymmetric disturbances. The question of whether sun-like stars can posses tachoclines is addressed with positive answer for stars with rotation periods shorter than about two months. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Probability distribution functions for the Sun's magnetic field

Magnetoconvection structures the Sun's magnetic field cover a vast range of scales, down to the magnetic diffusion scale that is orders of magnitude smaller than the resolution of current telescopes. The statistical properties of this structuring are governed by probability density functions (PDFs) for the flux densities and by the angular distribution functions for the orientations of the field vectors. The magnetic structuring on sub‐pixel scales greatly affects the field properties averaged over the resolution element due to the non‐linear relation between polarization and magnetic field. Here we use a Hinode SOT/SP data set for the quiet Sun disk center to explore the complex behavior of the 6301–6302 Å Stokes line profile system and identify the observables that allow us to determine the distribution functions in the most robust and least model dependent way. The angular distribution is found to be strongly peaked around the vertical direction for large flux densities but widens with decreasing flux density to become isotropic in the limit of zero flux density. The noise‐corrected PDFs for the vertical, horizontal, and total flux densities all have a narrowly peaked maximum at zero flux density that can be fitted with a stretched exponential, while the extended wings decline quadratically (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Propagation of acoustic waves in the non‐isothermal solar atmosphere

The acoustic cutoff frequency was originally introduced by Lamb in the study of the propagation of acoustic waves in a stratified, isothermal medium. In this paper, we use a new method to generalize Lamb's result for a stratified, non‐isothermal medium and obtain the local acoustic cutoff frequency, which describes the propagation of acoustic waves in such a medium. The main result is that the cutoff frequency is a local quantity and that its value at a given atmospheric height determines the frequency acoustic waves must have in order to propagate at this height. Application of this result to specific physical problems like the solar atmosphere is discussed. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The solar dynamo

The solar dynamo continues to pose a challenge to observers and theoreticians. Observations of the solar surface reveal a magnetic field with a complex, hierarchical structure consisting of widely different scales. Systematic features such as the solar cycle, the butterfly diagram, and Hale's polarity laws point to the existence of a deep-rooted large-scale magnetic field. At the other end of the scale are magnetic elements and small-scale mixed-polarity magnetic fields. In order to explain these phenomena, dynamo theory provides all the necessary ingredients including the effect, magnetic field amplification by differential rotation, magnetic pumping, turbulent diffusion, magnetic buoyancy, flux storage, stochastic variations and nonlinear dynamics. Due to advances in helioseismology, observations of stellar magnetic fields and computer capabilities, significant progress has been made in our understanding of these and other aspects such as the role of the tachocline, convective plumes and magnetic helicity conservation. However, remaining uncertainties about the nature of the deep-seated toroidal magnetic field and the effect, and the forbidding range of length scales of the magnetic field and the flow have thus far prevented the formulation of a coherent model for the solar dynamo. A preliminary evaluation of the various dynamo models that have been proposed seems to favor a buoyancy-driven or distributed scenario. The viewpoint proposed here is that progress in understanding the solar dynamo and explaining the observations can be achieved only through a combination of approaches including local numerical experiments and global mean-field modeling.Received: 5 May 2003, Published online: 15 July 2003     

Parametric generation of magnetoacoustic-gravity waves in the solar atmosphere

Based on a plane-parallel isothermal solar model atmosphere permeated by a horizontal magnetic field whose strength is proportional to the square root of the plasma density and in the approximation of a specified field for vertically propagating and nonpropagating magnetoacoustic-gravity waves, we consider the nonlinear interaction between the corresponding disturbances, to within quantities of the second order of smallness. We investigate the efficiency of the nonlinear generation of waves at difference and sum frequencies and of an acoustic flow (wind) as a function of the magnetic-field strength and the excitation frequency of the initial disturbances at the lower atmospheric boundary.     

Dispersive shock waves in the solar wind

Compressional waves in the solar wind propagating over large distances are likely to steepen into shock waves where the increase in the amplitude is balanced by dissipation. Dispersive effects caused by, e.g. Hall currents perpendicular to the ambient magnetic field can influence the generation and propagation of shock waves. In the present study the dispersion is considered weak but in time its importance can grow. When the effect of dispersion is strong enough, it can balance the nonlinear steepening of waves leading to the formation of solitons. The obtained results show that the weak dispersion will alter the amplitude and propagation speed of the shock wave. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)