Thermal properties of magnetic flux tubes II. Storage of flux in the solar overshoot region

We consider the consequences of radiative heating for the storage of magnetic flux in the overshoot region at the bottom of the solar convection zone. In the first part of the paper, we study the evolution of axisymmetric flux tubes (flux rings), which are initially in neutrally buoyant mechanical equilibrium. Radiative heating leads to a slow upward drift of the flux ring with a velocity depending on the degree of subadiabaticity of the stratification. Maintaining the flux tubes within the overshoot region for time intervals comparable with the solar cycle period requires a strongly subadiabatic stratification with δ = ∇-∇_ad < - 10^-4, which is not predicted by most current overshoot models (e.g., Skaley & Stix 1991; van Ballegooijen 1982; Schmitt et al. 1984). The drag force exerted by equatorward flow due to meridional circulation permits states of mechanical and thermal equilibrium in the overshoot region, but these apply only to very thin magnetic flux tubes containing less than 1% of the flux of a large sunspot. In the second part, we consider the influence of radiative heating (and cooling) on magnetic flux stored in the form of a magnetic layer. In contrast to the case of isolated flux tubes, the suppression of the convective energy transport within the magnetic layer affects the overall stratification of the overshoot region. In the case of a quenching of the convective heat conductivity by a factor of the order 100, the overshoot layer receives a net cooling leading to a stronger subadiabaticity, so that values of δ < -10^-4 are reached. The stabilization of the stratification relaxes the conditions for flux storage. Stronger quenching of the heat conductivity leads to larger temperature perturbations (of both signs) and to the destabilization of the upper part of the overshoot layer, with the likely consequence of rapid magnetic flux loss.