Constraining population synthesis models via empirical binary compact object merger and supernova rates

The observed samples of supernovae (SNe) 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, (1) the formation rates of double neutron star (NS-NS) binaries and white dwarf-neutron star (WD-NS) binaries, estimated from binary samples, and (2) the Type II and Ib/c SN rates. Even allowing for extremely conservative accounting of the uncertainties in observational and theoretical predictions, we find that 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 these 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 characteristic velocity of about 350 km s^_1 (i.e., at maximum likelihood; kick velocities between 100 and 700 km s^_1 remain within the 90% confidence interval of unimodal distributions), mass-loss fractions during nonconservative but stable mass transfer episodes of about 90%, and common envelope parameters of about 0.15-0.5. 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 that Milky Way-like galaxies dominate. Inevitably, the resulting probability distributions for merger rates depend on our assumed priors for the population model input parameters. In this study we adopt relatively conservative priors (flat) for all model parameters covering a rather wide range of values. However, as we gain confidence in our knowledge of these inputs, the range of merger rates consistent with our knowledge should shift and narrow.