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 of the mass distribution employ physically-motivated phenomenological models and infer the parameters that directly control the features of the mass distribution that are allowed in their model, associating the constraints on those parameters with their physical motivations. 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 byproduct. In doing so, we directly constrain the stellar physics necessary to explain the astrophysical distribution of black hole properties under a given model. We apply this approach to modeling the mapping between stellar core mass and remnant black hole mass, including the effects of mass loss due to the pulsational pair instability supernova (PPISN) process, which has been proposed as an explanation for the observed excess of black holes at $\sim 35 M_\odot$. Placing constraints on the nuclear reaction rates necessary to explain the PPISN parameters, we conclude that the peak observed at $\sim 35 M_\odot$ is highly unlikely to be a signature from the PPISN process. This procedure can be applied to modeling any physical process that underlies the astrophysical mass distribution. Allowing the parameters of the core-remnant mass relationship to evolve with redshift permits correlated and physically reasonable changes in the location, shape, and amplitude of features in the mass function. We find that the current data are consistent with no redshift evolution in the core-remnant mass relationship, but ultimately place only weak constraints on the change of these parameters.