The mass distribution of neutron stars and stellar-mass black holes provides vital clues into the nature of stellar core collapse and the physical engine responsible for supernova explosions. A number of supernova engines have been proposed: neutrino- or oscillation-driven explosions enhanced by early (developing in 10-50?ms) and late-time (developing in 200?ms) convection as well as magnetic field engines (in black hole accretion disks or neutron stars). Using our current understanding of supernova engines, we derive mass distributions of stellar compact remnants. We provide analytic prescriptions for both single-star models (as a function of initial star mass) and for binary-star models—prescriptions for compact object masses for major population synthesis codes. These prescriptions have implications for a range of observations: X-ray binary populations, supernova explosion energies, and gravitational wave sources. We show that advanced gravitational radiation detectors (like LIGO/VIRGO or the Einstein Telescope) will be able to further test the supernova explosion engine models once double black hole inspirals are detected.
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