Probing the Delay Time of Supermassive Black Hole Binary Mergers With Gravitational Waves

TL;DR

This paper proposes a method to determine the delay time of supermassive black hole binary mergers by combining gravitational wave data with galaxy merger rates, aiding in testing binary evolution models.

Contribution

It introduces a hierarchical Bayesian framework to infer delay time distributions from mock gravitational wave data and galaxy surveys, accounting for model uncertainties.

Findings

Method successfully recovers delay time distributions in simulations

Bayesian model selection distinguishes between different evolution models

Incorporates astrophysical uncertainties into the inference process

Abstract

Merging supermassive black hole binaries is expected as a consequence of galaxy mergers, yet the detailed evolution path and underlying merging mechanisms of these binaries are still subject to large theoretical uncertainties. In this work, we propose to combine the (future) gravitational wave measurements of supermassive black hole binary merger events with the galaxy merger rate distributions from galaxy surveys/cosmological simulations, to infer the delay time of binary mergers, as a function of binary mass. The delay time encodes key information about binary evolution, which can be used to test the predictions of various evolution models. With a Mock data set of supermassive black hole binary merger events, we discuss how to infer the distribution of delay time with hierarchical Bayesian inference and test evolution models with the Bayesian model selection method. The astrophysical model uncertainties are also considered in the hierarchical Bayesian inference and Bayesian model selection.