# Constraining Formation Models of Binary Black Holes with Gravitational-Wave Observations

## TL;DR

This paper uses gravitational-wave data and hierarchical Bayesian modeling to constrain binary black hole formation channels and physical parameters, demonstrating that about 100 detections can distinguish between different formation scenarios and natal kick prescriptions.

## Contribution

It introduces a hierarchical Bayesian framework to analyze GW data, constraining formation models and natal kicks with mass measurements from synthetic samples.

## Key findings

- Approximately 100 detections suffice to distinguish formation channels.
- Mass measurements can constrain natal kick prescriptions.
- The framework is extendable to other formation scenarios and properties.

## Abstract

Gravitational waves (GWs) from binary black hole (BBH) mergers provide a new probe of massive-star evolution and the formation channels of binary compact objects. By coupling the growing sample of BBH systems with population synthesis models, we can begin to constrain the parameters of such models and glean unprecedented knowledge about the inherent physical processes that underpin binary stellar evolution. In this study, we apply a hierarchical Bayesian model to mass measurements from a synthetic GW sample to constrain the physical prescriptions in population models and the relative fraction of systems generated from various channels. We employ population models of two canonical formation scenarios in our analysis --- isolated binary evolution involving a common-envelope phase and dynamical formation within globular clusters --- with model variations for different black hole natal kick prescriptions. We show that solely with chirp mass measurements, it is possible to constrain natal kick prescriptions and the relative fraction of systems originating from each formation channel with $\mathcal{O}(100)$ of confident detections. This framework can be extended to include additional formation scenarios, model parameters, and measured properties of the compact binary.