The Magnetorotational Instability in Core‐Collapse Supernova Explosions

Abstract

We investigate the action of the magnetorotational instability (MRI) in the context of iron-core collapse. Exponential growth of the field on the timescale Ω^-1 by the MRI will dominate the linear growth process of field-line "wrapping" with the same characteristic time. We examine a variety of initial rotation states, with solid-body rotation or a gradient in rotational velocity, that correspond to models in the literature. A relatively modest value of the initial rotation, a period of ~10 s, will give a very rapidly rotating proto-neutron star and hence strong differential rotation with respect to the infalling matter. We assume conservation of angular momentum on spherical shells. Rotational distortion and the dynamic feedback of the magnetic field are neglected in the subsequent calculation of rotational velocities. In our rotating and collapsing conditions, a seed field is expected to be amplified by the MRI and to grow exponentially to a saturation field. Results are discussed for two examples of saturation fields, a fiducial field that corresponds to v_A = rΩ and a field that corresponds to the maximum growing mode of the MRI. We find, as expected, that the shear is strong at the boundary of the newly formed proto-neutron star and, unexpectedly, that the region within the stalled shock can be subject to strong MHD activity. Modest initial rotation velocities of the iron core result in sub-Keplerian rotation and a sub-equipartition magnetic field that nevertheless produce substantial MHD luminosity and hoop stresses: saturation fields of order 10¹⁵-10¹⁶ G can develop ~300 ms after bounce with an associated MHD luminosity of ~10⁵² ergs s^-1. Bipolar flows driven by this MHD power can affect or even cause the explosions associated with core-collapse supernovae.