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The Non-Monotonic Dependence of Supernova and Remnant Formation on Progenitor Rotation

Traditional models of core collapse suggest the issue of successful versus failed supernova explosions and neutron star versus black hole formation depends monotonically on the mass (and metallicity) of the progenitor star. Here we argue that the issue of success or failure of the explosion or other possible outcomes may depend non--monotonically on the rotation of the progenitor star even at fixed progenitor mass and composition. We have computed "shellular" models of core collapse for a star of 15 M_solar with initial central angular velocity, Omega_0, in the range 0.1 -- 8 rad/s until a few hundred ms after bounce to explore qualitative trends. The non--monotonic behavior will be manifested in the rotation of the proto--neutron star and hence in the strength of the associated magnetic field that will be generated by shear in that rotating environment. We estimate that our maximally rotating and shearing models generate toroidal fields approaching or exceeding 10^17G, strengths nearing dynamical significance.