Günther Rüdiger

The Differential Solar Rotation

Theory and observations of the solar differential rotation are reviewed, concentrating on recent developments. Reynolds stresses produced by stratified rotating turbulence have recently become available as fully nonlinear functions of the angular velocity. A model based on this theory has reproduced the solar rotation; almost no tuning of the theory to the observations was required. By taking into account the rotationally-produced anisotropy of the turbulent heat transport, it is even possible to resolve the “Taylor number puzzle”. Temporal variations in the solar rotation during different periods in the past and their relation to magnetic activity are briefly discussed.

Magnetic pinch-type instability in stellar radiative zones

The solar tachocline is shown as hydrodynamically stable against nonaxisymmetric disturbances if it is true that no cos 4 θ term exists in its rotation law. We also show that the toroidal field of 200 Gauss amplitude which produces the tachocline in the magnetic theory of Rudiger & Kitchatinov (1997) is stable against nonaxisymmetric MHD disturbances – but it becomes unstable for rotation periods slightly slower than 25 days. The instability of such weak fields lives from the high thermal diffusivity of stellar radiation zones compared with the magnetic diffusivity. The growth times, however, result as very long (of order of 10 5 rotation times). With estimations of the chemical mixing we find the maximal possible field amplitude to be ~500 Gauss in order to explain the observed lithium abundance of the Sun. Dynamos with such low field amplitudes should not be relevant for the solar activity cycle. With nonlinear simulations of MHD Taylor-Couette flows it is shown that for the rotation-dominated magnetic instability the resulting eddy viscosity is only of the order of the molecular viscosity. The Schmidt number as the ratio of viscosity and chemical diffusion grows to values of ~20. For the majority of the stellar physics applications, the magnetic-dominated Tayler instability will be quenched by the stellar rotation.