The Nonmonotonic Dependence of Supernova and Compact Remnant Formation on Progenitor Rotation

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Abstract
Traditional models of core collapse suggest that 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, with mass above some cutoff leading to black holes with or without attendant supernova explosions. Here we argue that the issue of success or failure of the explosion or other possible outcomes may depend nonmonotonically on the rotation of the progenitor star even for fixed progenitor mass and composition. We have computed "shellular" models of core collapse for a star of 15 M☉ with initial central angular velocity, Ω0, in the range 0.1-8 rad s-1 until a few hundred milliseconds after bounce to explore qualitative trends. The resulting rotational velocity of the proto-neutron star is a nonmonotonic function of the initial rotational velocity. The model with Ω0 = 4 rad s-1 gives the maximum postbounce rotation, with rotation comparable to that necessary for secular or dynamical instability to occur. Models with Ω0 > 4 rad s-1 bounce at subnuclear density with γ ~ 4/3 and subsequently slowly contract. The nonmonotonic 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 1017 G, strengths nearing dynamical significance. One implication of this nonmonotonicity is that the process of rotating, magnetic core collapse may itself provide a filter to select specific outcomes from the distribution of initial rotation states. Possible outcomes are black hole, neutron star, and black hole, as the initial angular momentum of the progenitor increases. Within the regime of successful explosions leaving neutron stars behind, a subset may spin rapidly enough, either initially or during the subsequent deleptonization contraction phase, to drive an α-Ω dynamo and hence produce the large dipole field associated with magnetars.