Isolated Binary Black Hole Formation and Merger Rates from Galaxy Evolution

TL;DR

This paper models the formation and merger rates of binary black holes from galaxy evolution, considering metallicity distributions and stellar evolution, to explain observed gravitational wave events and mass distributions.

Contribution

It introduces a population model for BBHs based on galaxy metallicities and stellar evolution, analyzing the impact of delay-time distribution and mass gap predictions.

Findings

Merger rate spectral shape is affected by the DTD power-law index.

Top-heavy IMF or dynamical formation is needed to explain certain mass distributions.

Mass gap due to pair instability causes a sharp decline in BBH numbers above 50 M_sun.

Abstract

The LIGO-Virgo-KAGRA (LVK) collaboration has detected over 150 confirmed gravitational wave events through O4a. Binary black hole (BBH) systems represent the overwhelming majority of these observations. We construct a model for the population of the BBHs based on the 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 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 (DTD) 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 IMF in dwarf galaxies must be top heavy, or most of the 30-40 $\rm M_\odot$ black holes must be formed through a dynamical capture mechanism. For masses greater than about $50 \, \rm M_\odot$, the predicted number of BBH systems plummet to zero, revealing the well-known mass gap due to the pair instability mechanism and mass loss in binary systems.