Single-event likelihood of star cluster properties with LIGO-Virgo-Kagra binary black hole observations

TL;DR

This paper develops a method to infer star cluster properties from individual binary black hole merger observations, revealing correlations between primary mass and cluster mass, and discusses physical mechanisms behind these trends.

Contribution

It introduces a formalism to construct single-event likelihoods of star cluster properties from gravitational wave data, focusing on dynamical formation in star clusters.

Findings

Primary mass correlates with star cluster mass.

Hierarchical mergers are more efficient in massive clusters.

Massive first-generation binaries are suppressed in smaller clusters.

Abstract

The population of binary black hole mergers observed in gravitational waves, together with astrophysical simulations, can help us to understand the properties of the progenitors and the binary formation mechanisms in different astrophysical scenarios. Here we focus on dynamical formation in star clusters. We use the third gravitational-wave transient catalog (GWTC-3) and Rapster, a rapid code to simulate cluster dynamics, to show that it is possible to construct the single-event likelihood of star cluster properties from individual observations. We find that the measured primary mass in a binary black hole merger correlates with the measured star cluster mass, because the mass spectrum of the primary component increases with the mass of the cluster. This trend may be caused by two physical mechanisms: (i) the more efficient production of hierarchical mergers with primary mass above $\sim 40~M_{\odot}$ for cluster masses of $\gtrsim 10^6~M_{\odot}$, and (ii) the suppression of more massive first-generation binaries, which happens because ejected binaries do not merge within the lookback time for cluster masses of $\lesssim 10^5~M_{\odot}$. The formalism presented here can be generalized to infer the population properties of binary progenitors in more realistic scenarios involving multiple formation channels.