# Hierarchical analysis of gravitational-wave measurements of binary black hole spin-orbit misalignments

## TL;DR

This paper develops a hierarchical analysis method to interpret gravitational-wave data, enabling the identification of sub-populations of binary black holes with different spin-orbit misalignments, which sheds light on their formation channels.

## Contribution

It introduces a hierarchical analysis framework applied to simulated gravitational-wave data to distinguish and quantify sub-populations of binary black holes based on spin orientations.

## Key findings

- Tens of observations can differentiate subpopulations based on spin orientations.
- 100 observations allow estimating the fraction of isotropic spin directions with ~40% uncertainty.
- Only 5 observations suffice to distinguish extreme models of spin alignment.

## Abstract

Binary black holes may form both through isolated binary evolution and through dynamical interactions in dense stellar environments. The formation channel leaves an imprint on the alignment between the black hole spins and the orbital angular momentum. Gravitational waves from these systems directly encode information about the spin--orbit misalignment angles, allowing them to be (weakly) constrained. Identifying sub-populations of spinning binary black holes will inform us about compact binary formation and evolution. We simulate a mixed population of binary black holes with spin--orbit misalignments modelled under a range of assumptions. We then develop a hierarchical analysis and apply it to mock gravitational-wave observations of these populations. Assuming a population with dimensionless spin magnitudes of $\chi = 0.7$, we show that tens of observations will make it possible to distinguish the presence of subpopulations of coalescing binary black holes based on their spin orientations. With $100$ observations it will be possible to infer the relative fraction of coalescing binary black holes with isotropic spin directions (corresponding to dynamical formation in our models) with a fractional uncertainty of $\sim 40\%$. Meanwhile, only $\sim 5$ observations are sufficient to distinguish between extreme models---all binary black holes either having exactly aligned spins or isotropic spin directions.