# Constraining the fraction of binary black holes formed in isolation and young star clusters with gravitational-wave data

## TL;DR

This paper uses gravitational-wave data and Bayesian hierarchical modeling to estimate the proportion of binary black holes formed in isolation versus young star clusters, projecting improved constraints with future detections.

## Contribution

It introduces a method to constrain black hole binary formation channels using current and future gravitational-wave observations, combining population synthesis and N-body simulations.

## Key findings

- Current data mildly constrain the formation channel fraction
- Projected data will reduce fractional errors to 10-20%
- Method integrates population synthesis and hierarchical modeling

## Abstract

Ten binary black-hole mergers have already been detected during the first two observing runs of advanced LIGO and Virgo, and many more are expected to be observed in the near future. This opens the possibility for gravitational-wave astronomy to better constrain the properties of black hole binaries, not only as single sources, but as a whole astrophysical population. In this paper, we address the problem of using gravitational-wave measurements to estimate the proportion of merging black holes produced either via isolated binaries or binaries evolving in young star clusters. To this end, we use a Bayesian hierarchical modeling approach applied to catalogs of merging binary black holes generated using state-of-the-art population synthesis and N-body codes. In particular, we show that, although current advanced LIGO/Virgo observations only mildly constrain the mixing fraction $f \in [0,1]$ between the two formation channels, we expect to narrow down the fractional errors on $f$ to $10-20\%$ after a few hundreds of detections.