Physical Models for the Astrophysical Population of Black Holes: Application to the Bump in the Mass Distribution of Gravitational-wave Sources

Gravitational-wave observations of binary black holes have revealed unexpected structure in the black hole mass distribution. Previous studies employ physically motivated phenomenological models and infer the parameters that control the features of the mass distribution that are allowed in their model, associating the constraints on those parameters with their physical motivations a posteriori. In this work, we take an alternative approach in which we introduce a model parameterizing the underlying stellar and core-collapse physics and obtaining the remnant black hole distribution as a derived by-product. In doing so, we constrain the stellar physics necessary to explain the astrophysical distribution of black hole properties under a given model. We apply this to the mapping between initial mass and remnant black hole mass, accounting for mass-dependent mass loss using a simple parameterized description. Allowing the parameters of the initial mass-remnant mass relationship to evolve with redshift permits correlated and physically reasonable changes to features in the mass function. We find that the current data are consistent with no redshift evolution in the core-remnant mass relationship, but place only weak constraints on the change of these parameters. This procedure can be applied to modeling any physical process underlying the astrophysical distribution. We illustrate this by applying our model to the pulsational pair instability supernova (PPISN) process, previously proposed as an explanation for the observed excess of black holes at similar to 35 M circle dot. Placing constraints on the reaction rates necessary to explain the PPISN parameters, we concur with previous results in the literature that the peak observed at similar to 35 M circle dot is unlikely to be a signature from the PPISN process as presently understood.