Dynamical formation signatures of black hole binaries in the first detected mergers by LIGO

TL;DR

This paper investigates how dynamical interactions in dense stellar environments influence the formation and detection rates of massive black hole binaries by LIGO, revealing a strong mass dependence and potential for inferring initial black hole populations.

Contribution

It introduces a model linking dynamical formation processes to black hole merger rates and mass distributions, highlighting the impact of mass segregation and multibody interactions.

Findings

Merger rate scales as ~M_tot^beta with beta > 4.

LIGO is most sensitive to binaries with total mass <~ 80 solar masses.

Approximately 5% of mergers involve black holes 2-3 times the initial maximum mass.

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^beta, with beta >~ 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 solar masses. We find that for power-law BH mass functions dN/dM ~ M^-alpha with alpha <~ 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.