Magnetorotational instability in proto-neutron stars

Departament de Física Aplicada, Universitat d'Alacant, Ap. Correus 99, 03080 Alacant, Spain A.F. Ioffe Institute of Physics and Technology, 194021 St. Petersburg, Russia Isaac Newton Institute of Chile, Branch in St. Petersburg, 194021 St. Petersburg, Russia

Received: 14 July 2009
Accepted: 1 October 2009

Abstract

Context. Magneto-rotational instability (MRI) has been suggested to lead to a rapid growth of the magnetic field in core collapse supernovae and produce departures from spherical symmetry that are important in determining the explosion mechanism.

Aims. We address the problem of stability in differentially rotating magnetized proto-neutron stars at the beginning of their evolution.

Methods. To do this, we consider a linear stability taking into account non-linear effects of the magnetic field and strong gravity.

Results. Criteria for MRI are derived without simplifying assumptions about a weak magnetic field. In proto-neutron stars, these criteria differ qualitatively from the standard condition where Ω is the angular velocity and s the cylindrical radius. If the magnetic field is strong, the MRI can occur only in the neighbourhood of the regions where the spherical radial component of the magnetic field vanishes. The growth rate of the MRI is relatively low except for perturbations with very small scales which usually are not detected in numerical simulations. We find that MRI in proto-neutron stars grows more slowly than the double diffusive instability analogous the Goldreich-Schubert-Fricke instability in ordinary stars.