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 nonaxisymmetric MHD instabilities are derived using a local linear analysis. PNSs are expected to have much stronger radial shear in the rotation velocity compared to normal stars. We find that nonaxisymmetric magnetorotational instability (NMRI) with a large azimuthal wavenumber m is dominant over the kink mode (m = 1) in differentially rotating PNSs. The growth rate of the NMRI is of order the angular velocity Omega, which is faster than that of the kink-type instability by several orders of magnitude. The stability criteria are analogous to those of the axisymmetric magnetorotational instability with a poloidal field, although the effects of leptonic gradients are considered in our analysis. The NMRI can grow even in convectively stable layers if the wavevectors of unstable modes are parallel to the restoring force by the Brunt-Vaisala oscillation. The nonlinear evolution of NMRI could amplify the magnetic fields and drive MHD turbulence in PNSs, which may lead to enhancement of the neutrino luminosity.