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Two aspects of solar MHD are discussed in relation to the work of the MHD simulation group at KIS. Photospheric magneto-convection, the nonlinear interaction of magnetic field and convection in a strongly stratified, radiating fluid, is a key process of general astrophysical relevance. Comprehensive numerical simulations including radiative transfer have significantly improved our understanding of the processes and have become an important tool for the interpretation of observational data. Examples of field intensification in the solar photosphere ('convective collapse') are shown. The second line of research is concerned with the dynamics of flux tubes in the convection zone, which has far-reaching implications for our understanding of the solar dynamo. Simulations indicate that the field strength in the region where the flux is stored before erupting to form sunspot groups is of the order of 105 G, an order of magnitude larger than previous estimates based on equipartition with the kinetic energy of convective flows.Key words. Solar physics · astrophysics and astronomy (photosphere and chromosphere; stellar interiors and dynamo theory; numerical simulation studies).

A theoretical study of storage, instability and rise of magnetic flux tubes in the outer convection zone of a cool star is presented. Special emphasis is laid on their emergence latitudes at the surface of magnetically active stars. We apply the ‘solar paradigm’ and assume toroidal magnetic flux tubes to be stored in force equilibrium within the overshoot layer underneath the convection zone. A non-axisymmetric (undulatory) instability leads to the formation of flux loops, which rise through the convection zone and emerge at the surface to form bipolar magnetic regions and starspots. Our approach combines the analytical determination of the linear stability properties of flux tubes with numerical simulations of the nonlinear evolution of the instability and the rise of magnetic flux tubes through the convection zone. It is found that for sufficiently rapidly rotating stars the magnetic flux emerges at high latitudes since the Coriolis force leads to a poleward deflection of rising flux loops. The latitude distribution of the emerging flux is determined for a number of stellar models along the evolutionary sequence of a star with one solar mass, from the pre-main sequence evolution up to the giant phase. Rapid rotation and deep convection zones favour flux emergence in high latitudes. Starspots right at the stellar (rotational) poles form either directly by flux eruption from small stellar cores (as for T Tauri stars or giants) or by a poleward slip of the sub-surface part of the flux tube after flux emergence in mid latitudes. The latter process explains the simultaneous existence of polar spots and spots at intermediate latitudes as observed on some stars.

The combined action of the subadiabatic ambient stratification in the overshoot region below the convection zone and the inertial forces associated with the solar rotation is shown to lead to the suppression of the escape of magnetic flux in the form of toroidal flux tubes both toward the surface and toward higher latitudes. We show that a flux ring initially in thermal equilibrium with its environment and rotating 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, field-free gas. We conclude that flux rings with B≲ 105 G can be kept within the overshoot region if the superadiabaticity is sufficiently negative, i.e. δ = ▿ – ▿ad≲–10−5; below that field strength the poleward drift is also reduced to a latitudinal oscillation of moderate amplitude, δθ ≲ 20 deg. Flux rings with significantly larger field strength cannot be kept in the equatorial parts of the overshoot region: their equilibrium configuration is located at high latitudes far outside the solar activity belts and, at any rate, requires unrealistic values of δ.

The structure of solar surface magnetic fields, the way they erupt from the the convection zone below, and processes like flux expulsion and fragmentation instabilities support the view that magnetic flux in a stellar convection zone is in an intermittent, fragmented state which can be described as an ensemble of magnetic flux tubes. Depending on size and field strength, the dynamics of magnetic flux tubes can strongly differ from the behavior of a passive, diffuse field which is often assumed in conventional mean-field dynamo theory. Observed properties of active regions like emergence in low latitudes, Hale's polarity rules, tilt angles, and the process of sunspot formation from smaller fragments, together with theoretical considerations of the dynamics of buoyant flux tubes indicate that the magnetic structures which erupt in an emerging active region are not passive to convection and originate in a source region (presumably an overshoot layer below the convection zone proper) with a field strength of at least 105 G, far beyond the equipartition field strength with respect to convective flows. We discuss the consequences of such a situation for dynamo theory of the solar cycle and consider the possibility of dynamo models on the basis of flux tubes. A simple, illustrative example of a flux tube dynamo is presented.

The solar meridional flow is an important ingredient in Babcock-Leighton type models of the solar dynamo. Global variations of this flow have been suggested to explain the variations in the amplitudes and lengths of the activity cycles. Recently, cycle-related variations in the amplitude of the $P_2^1$ term in the Legendre decomposition of the observed meridional flow have been reported. The result is often interpreted in terms of an overall variation in the flow amplitude during the activity cycle. Using a semi-empirical model based upon the observed distribution of magnetic flux on the solar surface, we show that the reported variations of the $P_2^1$ term can be explained by the observed localized inflows into the active region belts. No variation of the overall meridional flow amplitude is required., Comment: Accepted in ApJ

We consider the linear stability of a toroidal flux tube lying in the equatorial plane of a differentially rotating star and investigate its dependence on superadiabaticity, magnetic field strength, and gradient of angular velocity.

The structure of solar surface magnetic fields, the way they erupt from the the convection zone below, and processes like flux expulsion and fragmentation instabilities support the view that magnetic flux in a stellar convection zone is in an intermittent, fragmented state which can be described as an ensemble of magnetic flux tubes. Depending on size and field strength, the dynamics of magnetic flux tubes can strongly differ from the behavior of a passive, diffuse field which is often assumed in conventional mean-field dynamo theory. Observed properties of active regions like emergence in low latitudes, Hale’s polarity rules, tilt angles, and the process of sunspot formation from smaller fragments, together with theoretical considerations of the dynamics of buoyant flux tubes indicate that the magnetic structures which erupt in an emerging active region are not passive to convection and originate in a source region (presumably an overshoot layer below the convection zone proper) with a field strength of at least 105 G, far beyond the equipartition field strength with respect to convective flows. We discuss the consequences of such a situation for dynamo theory of the solar cycle and consider the possibility of dynamo models on the basis of flux tubes. A simple, illustrative example of a flux tube dynamo is presented.

The combined action of the subadiabatic ambient stratification in the overshoot region below the convection zone and the inertial forces associated with the solar rotation is shown to lead to the suppression of the escape of magnetic flux in the form of toroidal flux tubes both toward the surface and toward higher latitudes. We show that a flux ring initially in thermal equilibrium with its environment and rotating 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, field-free gas. We conclude that flux rings with B≲ 105 G can be kept within the overshoot region if the superadiabaticity is sufficiently negative, i.e. δ = ▽ — ▽ad≲ −10−5; below that field strength the poleward drift is also reduced to a latitudinal oscillation of moderate amplitude, ▽θ ≲ 20 deg. Flux rings with significantly larger field strength cannot be kept in the equatorial parts of the overshoot region: their equilibrium configuration is located at high latitudes far outside the solar activity belts and, at any rate, requires unrealistic values of δ.