Isolated Binary Black Hole Formation and Merger Rates from Galaxy Evolution

Abstract: The LIGO-Virgo-KAGRA (LVK) collaboration has detected 90 gravitational wave events and will detect many more in its fourth observing run. Binary black hole (BBH) systems represent the overwhelming majority of these observations. We build a model for the population of the BBHs based on the observed distribution of metallicities in galaxies and state-of-the-art stellar evolution models implemented through the Stellar EVolution N-body (SEVN) code. We calculate the primary mass spectrum and merger rates of BBHs and find general agreement with the redshift evolution and mass ratio distribution inferred by the LVK collaboration. When comparing to the primary mass distribution, our results indicate that either the average IMF in dwarf galaxies must be top heavy, or most of the $30-40 \, M_\odot$ black holes must be formed through a dynamical capture mechanism. For masses greater than about $50 \, M_\odot$, the predicted number of BBH systems plummet to zero, revealing the well-known mass gap due to the pair instability mechanism and the mass loss in binary systems. We estimate the probability needed to fill part of the mass gap with mergers of dynamically-formed BBHs originating from the single black hole population.