Handy Relation Between Binary Black Hole Merger Times and Host Galaxy Properties

TL;DR

This paper presents new scaling relations derived from high-resolution simulations that link black hole merger timescales to observable properties of host galaxies, aiding in more accurate cosmological merger rate estimates.

Contribution

It introduces a set of empirically informed scaling relations for black hole merger timescales based on galaxy properties, improving modeling in cosmological studies.

Findings

Merger timescales depend on galaxy shape, structure, and kinematics.

Scaling relations enable quick estimation of merger timescales from observables.

Results can be integrated into cosmological models for event rate predictions.

Abstract

Over the past 15 years, the evidence has clearly demonstrated that massive black hole (MBH) binary merger timescales depend strongly on the structural and kinematic properties of their host galaxy. Stellar density, gas content, shape and kinematics all play a role, combining in non-linear ways to effect the evolution of the binary. The binary properties themselves, such as eccentricity, mass ratio, and orbital plane, all matter as well. This makes it nontrivial to estimate accurate cosmological MBH binary merger rates, or to generate merger rate ranges that reflect the distribution of galaxy hosts and orbits. Using an extensive set of high-resolution direct N-body simulations in which the shape, structure, and kinematics of each galaxy host are directly informed by observations, we map out MBH binary merger timescales over a range of galaxy hosts and MBH binary orbits. This yields a convenient set of scaling relations to determine MBH binary merger timescales -- and the range of merger timescales -- as functions of basic observables. Such scaling relations can be readily employed as a subgrid model in cosmological or semi-analytic studies, for example, to model event rates for LISA or pulsar timing.