The observed samples of supernovae (SN) and double compact objects (DCOs) provide several critical constraints on population-synthesis models: the parameters of these models must be carefully chosen to reproduce, among other factors, (i) the formation rates of double neutron star (NS-NS) binaries and of white dwarf-neutron star (WD-NS) binaries, estimated from binary samples, and (ii) the type II and Ib/c supernova rates. Even allowing for extremely conservative accounting of the uncertainties in observational and theoretical predictions, we find only a few plausible population synthesis models (roughly 9%) are consistent with DCO and SN rates empirically determined from observations. As a proof of concept, we describe the information that can be extracted about population synthesis models given such stringent observational tests, including surprisingly good agreement with the neutron star kick distributions inferred from pulsar proper-motion measurements. In the present study, we find that the current observational constraints favor: kicks described by a single Maxwellian with a typical velocity of about 300km/s; mass-loss fractions during non-conservative, but stable, mass transfer episodes of about 90%; and common envelope parameters of about 0.2-0.5. Finally, we use the subset of astrophysically consistent models to predict the rates at which black hole-neutron star (BH-NS) and NS-NS binaries merge in the Milky Way and the nearby Universe, assuming Milky-Way-like galaxies dominate. (Abridged)
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