Magnetic Field in Supernovae

A relatively modest value of the initial rotation of the iron core, a period of ~ 6-31 s, will give a very rapidly rotating protoneutron star and hence strong differential rotation with respect to the infalling matter. Under these conditions, a seed field is expected to be amplified by the MRI and to grow exponentially. Exponential growth of the field on the time scale Omega^{-1} by the magnetorotational instability (MRI) will dominate the linear growth process of field line "wrapping" with the same characteristic time. The shear is strongest at the boundary of the newly formed protoneutron star. 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 10^{15} - 10^{16} G develop ~ 300 msec after bounce with an associated MHD luminosity of ~ 10^{49} - 10^{53} erg s^{-1}. Bi-polar flows driven by this MHD power can affect or even cause the explosions associated with core-collapse supernovae. If the initial rotation is too slow, then there will not be enough rotational energy to power the supernova despite the high luminosities. The MRI should be active and may qualitatively alter the flow if a black hole forms directly or after a fall-back delay.