http://arxiv.org/abs/1404.3562
With a linear theory the instability of a toroidal background field system with dipolar parity for inner stellar radiative zones under the presence of density stratification, differential rotation and for realistically small Prandtl numbers is analyzed. The physical parameters are the normalized latitudinal shear $a$ and the normalized field amplitude $b \simeq \Omega_A/\Omega$. Only the solutions for the wavelengths with the maximal growth rates are considered. If these scales are combined to the radial values of velocity one finds that for $b \gsim 0.1$ the (very small) radial velocity does only slightly depend on $a$ and $b$ so that it can be used as the free parameter of the eigenvalue system.
The resulting instability-generated tensors of magnetic diffusivity and eddy viscosity are highly anisotropic. The eddy diffusivity in latitudinal direction exceeds the eddy diffusivity in radial direction by orders of magnitude. Its latitudinal profile shows a strong concentration to the poles and (for rigid rotation) a numerical value of $10^{12}$ cm$^2$/s. On the other hand, the instability pattern transports angular momentum equatorward even for rigid rotation producing a slightly faster rotation of the equator of the radiative zone. The resulting effective magnetic Prandtl number reaches values of $O(10^3)$ so that differential rotation decays much faster than the toroidal background field which is {\em the} necessary condition to explain the observed slow rotation of the early red-giant and subgiant cores by means of magnetic instabilities.
G. Rudiger, M. Schultz and L. Kitchatinov
Tue, 15 Apr 14
64/73
You must be logged in to post a comment.