Nonaxisymmetric Magnetorotational Instability in Proto–Neutron Stars

We investigate the stability of differentially rotating proto-neutron stars(PNSs) with a toroidal magnetic field. Stability criteria for nonaxisymmetricMHD instabilities are derived using a local linear analysis. PNSs are expectedto have much stronger radial shear in the rotation velocity compared to normalstars. We find that nonaxisymmetric magnetorotational instability (NMRI) with alarge azimuthal wavenumber $m$ is dominant over the kink mode ($m=1$) indifferentially rotating PNSs. The growth rate of the NMRI is of the order ofthe angular velocity $\Omega$ which is faster than that of the kink-typeinstability by several orders of magnitude. The stability criteria areanalogous to those of the axisymmetric magnetorotational instability with apoloidal field, although the effects of leptonic gradients are considered inour analysis. The NMRI can grow even in convectively stable layers if thewavevectors of unstable modes are parallel to the restoring force by theBrunt-V\"ais\"al\"a oscillation. The nonlinear evolution of NMRI could amplifythe magnetic fields and drive MHD turbulence in PNSs, which may lead toenhancement of the neutrino luminosity.Comment: 24pages, 7figures, Accepted for publication in the Astrophysical Journal (December 12, 2005