Shaping binary black hole merger efficiency with gravitational wave observations

Abstract

Gravitational wave (GW) astronomy offers unprecedented insights into binary black hole (BBH) coalescence. However, many of the key quantities involved remain inaccessible to direct observations. The BBH merger rate density is deeply linked to both the merger efficiency and the distribution of delay time between binary formation and merger, neither of which is directly constrained by observations. Disentangling their impact on the merger rate represents a highly non-trivial endeavour. Here we present a semi-parametric BBH population model, based on population synthesis simulations of both isolated and dynamically-formed BBHs, anchored on an observation-driven, metallicity-dependent star formation history. We parametrise the merger efficiency of these two formation channels, fitting the model to GW events from the Gravitational-Wave Transient Catalog 5.0 within a hierarchical Bayesian framework. Our analysis suggests that the isolated BBH merger efficiency should be lowered by a factor $\mathcal{O}(10)$ relative to standard population synthesis results. The dynamical channel requires an efficiency more than an order of magnitude larger than the isolated one to reproduce current GW observations. Nevertheless, we find that the two channels provide comparable contributions to the observed number of events. Finally, we introduce a parametrisation for the delay time distribution of the isolated BBHs. We derive a distribution consistent with the observed local merger rate and show its degeneracy with the merger efficiency.