Bayesian analysis of LIGO-Virgo mergers: Primordial versus astrophysical black hole populations

We conduct a thorough Bayesian analysis of the possibility that the black hole merger events seen in gravitational waves are primordial black hole (PBH) mergers. Using the latest merger rate models for PBH binaries drawn from a log-normal mass function, we compute posterior parameter constraints and Bayesian evidences using data from the first two observing runs of LIGO-Virgo. We account for theoretical uncertainty due to possible disruption of the binary by surrounding PBHs, which can suppress the merger rate significantly. We also consider simple astrophysically motivated models and find that these are favored decisively over the PBH scenario, quantified by the Bayesian evidence ratio. Paying careful attention to the influence of the parameter priors and the quality of the model fits, we show that the evidence ratios can be understood by comparing the predicted chirp mass distribution to that of the data. We identify the posterior predictive distribution of chirp mass as a vital tool for discriminating between models. A model in which all mergers are PBH binaries is strongly disfavored compared with astrophysical models, in part due to the overprediction of heavy systems having M_chirp ≥ 40 M_⊙ and positive skewness over the range of observed masses which does not match the observations. We find that the fit is not significantly improved by adding a maximum mass cutoff or a bimodal mass function or imposing that PBH binaries form at late times. We argue that a successful PBH model must either modify the log-normal shape of the initial mass function significantly or abandon the hypothesis that all observed merging binaries are primordial. We develop and apply techniques for analyzing PBH models with gravitational wave data, which will be necessary for robust statistical inference as the gravitational wave source sample size increases.