DYNAMICAL FORMATION SIGNATURES OF BLACK HOLE BINARIES IN THE FIRST DETECTED MERGERS BY LIGO

Ryan M. O’Leary,Bence Kocsis,Yohai Meiron

doi:10.3847/2041-8205/824/1/l12

Abstract

ABSTRACT The dynamical formation of stellar-mass black hole–black hole binaries has long been a promising source of gravitational waves for the Laser Interferometer Gravitational-Wave Observatory (LIGO). Mass segregation, gravitational focusing, and multibody dynamical interactions naturally increase the interaction rate between the most massive black holes in dense stellar systems, eventually leading them to merge. We find that dynamical interactions, particularly three-body binary formation, enhance the merger rate of black hole binaries with total mass M tot roughly as ∝ M tot β , with β ≳ 4. We find that this relation holds mostly independently of the initial mass function, but the exact value depends on the degree of mass segregation. The detection rate of such massive black hole binaries is only further enhanced by LIGO’s greater sensitivity to massive black hole binaries with M tot ≲ 80 M ⊙ . We find that for power-law BH mass functions dN/dM ∝ M −α with α ≤ 2, LIGO is most likely to detect black hole binaries with a mass twice that of the maximum initial black hole mass and a mass ratio near one. Repeated mergers of black holes inside the cluster result in about ∼5% of mergers being observed between two and three times the maximum initial black hole mass. Using these relations, one may be able to invert the observed distribution to the initial mass function with multiple detections of merging black hole binaries.

Highlights

After over two decades of development, the Advanced Laser Interferometer Gravitational-Wave Observatory1 has directly detected gravitational waves from an inspiralling black hole-black hole (BH-BH) binary (Abbott et al 2016b)
We find that dynamical interactions, three-body binary formation, enhance the merger rate of black hole binaries with total mass Mtot roughly as ∝ Mtβot, with β 4
We find that this relation holds mostly independently of the initial mass function, but the exact value depends on the degree of mass segregation

Summary

INTRODUCTION

After over two decades of development, the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) has directly detected gravitational waves from an inspiralling black hole-black hole (BH-BH) binary (Abbott et al 2016b). These binaries may merge within the cluster (Miller & Hamilton 2002b) or be ejected from the cluster and merge on much longer timescales (O’Leary et al 2006) Such models have presented their own theoretical obstacles, the initial mass function of BHs perhaps the largest, but ever sophisticated simulations over nearly a decade have generally found similar estimates for the expected merger rate of the binaries as well as their characteristics (Gultekin et al 2006; Moody & Sigurdsson 2009; Banerjee et al 2010; Downing et al 2010, 2011; Morscher et al 2013; Bae et al 2014; Ziosi et al 2014; Morscher et al 2015; Rodriguez et al 2015). After we have submitted our manuscript two papers appeared on the expected rates of stellar black hole mergers in globular clusters with independent methodologies, which confirm our findings (Rodriguez et al 2016; Chatterjee et al 2016)

METHODS

RESULTS

Findings

SUMMARY AND CONCLUSION