Magnetic pinch-type instability in stellar radiative zones

TL;DR

This paper investigates the stability of stellar radiative zones and the solar tachocline against magnetic and hydrodynamic disturbances, finding that weak magnetic fields are stable but can become unstable under certain conditions, with implications for stellar mixing and activity.

Contribution

It provides a detailed analysis of magnetic pinch-type instabilities in stellar radiative zones, including stability criteria, growth times, and effects on chemical mixing and stellar dynamos.

Findings

Solar tachocline is hydrodynamically stable without certain rotation law terms.

Weak magnetic fields (~200 Gauss) are stable but can become unstable with slower rotation.

Maximum magnetic field amplitude consistent with lithium abundance is about 500 Gauss.

Abstract

The solar tachocline is shown as hydrodynamically stable against nonaxisymmetric disturbances if it is true that no cos^{4}\theta 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 Ruediger & 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.