Iteratively Comparing Gravitational-Wave Observations to the Evolution of Massive Stellar Binaries

Gravitational-wave observations have the capability to strongly differentiate between different assumptions for how binary compact objects form. In this work, we show how to carefully interpolate a marginal likelihood between choices of binary evolution model parameters. Using the StarTrack binary evolution code, we compare one- and four-dimensional binary evolution models to the compact binary mergers reported in recent gravitational-wave observing runs. We first consider a one-dimensional model, studying the effect of supernova kick velocity (drawn from a Maxwellian with dispersion {\sigma}_eff) on the simulated population of compact binary mergers, and find support for substantial SN recoil kicks. We follow this up with a four-dimensional study of {\sigma}_eff, mass transfer efficiency (fa) and the efficiency of angular momentum depletion from ejected material (\b{eta}) during Roche-lobe accretion, and an observation-driven reduction in the mass-loss rate estimated from stellar wind models (fwind1). We find that three of them ({\sigma}_eff, fa, and fwind1) can be efficiently limited by these observational comparisons. After initially sampling from a uniform prior in the space of these parameters, we refined our sampling by iteratively estimating a Bayesian likelihood for each simulation and fitting that likelihood to a parametric model (a truncated Gaussian) in order to propose new. Our maximum likelihood simulation (K0559) has parameters: {\sigma}_eff = 108.3 km/s (indicating substantial SN recoil kicks), fa = 0.922 (indicating efficient mass transfer), and fwind1 = 0.328 (indicating support for reduced wind-driven mass loss). Note that our estimates are only valid within one particular model of compact binary formation through isolated binary evolution and do not yet take into account the impact of other uncertain pieces of stellar physics and binary evolution.