Black-hole mergers in disklike environments could explain the observed $q$-$\chi_\mathrm{eff}$ correlation

TL;DR

This paper proposes that the observed correlation between black-hole binary mass ratio and effective spin can be explained by the environment's symmetry, especially in disk-like settings such as AGN disks, through a toy model.

Contribution

It introduces a toy model demonstrating how environment symmetry influences black-hole merger properties, explaining the observed $q$-$ff$ correlation.

Findings

The environment's symmetry is key to understanding the $q$-$ff$ correlation.

A toy model qualitatively reproduces the observed correlation.

Migration traps in AGN disks are potential sites for hierarchical mergers.

Abstract

Current gravitational-wave data from stellar-mass black-hole binary mergers suggest a correlation between the binary mass ratio $q$ and the effective spin $\chi_\mathrm{eff}$: more unequal-mass binaries consistently show larger and positive values of the effective spin. Multiple generations of black-hole mergers in dense astrophysical environments may provide a way to form unequal-mass systems, but they cannot explain the observed correlation on their own. We show that the symmetry of the astrophysical environment is a crucial feature to shed light on this otherwise puzzling piece of observational evidence. We present a toy model that reproduces, at least qualitatively, the observed correlation. The model relies on axisymmetric, disk-like environments where binaries participating in hierarchical mergers share a preferential direction. Migration traps in AGN disks are a prime candidate for this setup, hinting at the exciting possibility of constraining their occurrence with gravitational-wave data.