It is now clear that a subset of supernovae display evidence for jets and are observed as gamma-ray bursts. The angular momentum distribution of massive stellar endpoints provides a rare means of constraining the nature of the central engine in core-collapse explosions. Unlike supermassive black holes, the spin of stellar-mass black holes in X-ray binary systems is little affected by accretion, and accurately reflects the spin set at birth. A modest number of stellar-mass black hole angular momenta have now been measured using two independent X-ray spectroscopic techniques. In contrast, rotation-powered pulsars spin-down over time, via magnetic braking, but a modest number of natal spin periods have now been estimated. For both canonical and extreme neutron star parameters, statistical tests strongly suggest that the angular momentum distributions of black holes and neutron stars are markedly different. Within the context of prevalent models for core-collapse supernovae, the angular momentum distributions are consistent with black holes typically being produced in GRB-like supernovae with jets, and with neutron stars typically being produced in supernovae with too little angular momentum to produce jets via magnetohydrodynamic processes. It is possible that neutron stars are imbued with high spin initially, and rapidly spun-down shortly after the supernova event, but the available mechanisms may be inconsistent with some observed pulsar properties.
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