Isolated Binary Black Hole Formation and Merger Rates from Galaxy Evolution

Abstract The LIGO–Virgo–KAGRA collaboration has detected over 150 confirmed gravitational-wave events through Observing Run 4a. Binary black hole (BBH) systems represent the overwhelming majority of these observations. We construct a model for the population of BBHs based on the distribution of metallicities in galaxies and state-of-the-art stellar evolution models implemented through the Stellar Evolution N -body code. We calculate the redshift evolution of the total merger rate of BBHs and the differential rates with respect to primary mass, secondary mass, and the mass ratio. We explore variations in the delay-time distribution’s power-law index and show that it affects the total merger rate’s spectral shape, but primarily acts as an amplitude shift on the differential rates. When comparing to the primary mass distribution, our results indicate that either the average initial mass function in dwarf galaxies must be top heavy, or most of the 30–40 M ⊙ BHs must be formed through a dynamical capture mechanism. For masses greater than about 50 M ⊙ , the predicted number of BBH systems plummets to zero, revealing the well-known mass gap due to the pair instability mechanism and mass loss in binary systems.