The Mass Ratio Distribution of Tertiary Induced Binary Black Hole Mergers

TL;DR

This paper investigates how tertiary companions in hierarchical triples can enhance black hole merger rates via the eccentric Kozai mechanism, especially for binaries with small mass ratios, and compares the resulting mass ratio distribution with observations.

Contribution

It provides analytical criteria and numerical analysis for octupole-enhanced binary black hole mergers, highlighting the impact on mass ratio distributions.

Findings

Merger fraction increases significantly for smaller mass ratios.

Mass ratio distribution from this scenario is in tension with LIGO/VIRGO observations.

Analytical criteria for the strength of octupole enhancement are provided.

Abstract

Many proposed scenarios for black hole (BH) mergers involve a tertiary companion that induces von Zeipel-Lidov-Kozai (ZLK) eccentricity cycles in the inner binary. An attractive feature of such mechanisms is the enhanced merger probability when the octupole-order effects, also known as the eccentric Kozai mechanism, are important. This can be the case when the tertiary is of comparable mass to the binary components. Since the octupole strength [$\propto (1-q)/(1+q)$] increases with decreasing binary mass ratio $q$, such ZLK-induced mergers favor binaries with smaller mass ratios. We use a combination of numerical and analytical approaches to fully characterize the octupole-enhanced binary BH mergers and provide analytical criteria for efficiently calculating the strength of this enhancement. We show that for hierarchical triples with semi-major axis ratio $a/a_{\rm out}\gtrsim 0.01$-$0.02$, the binary merger fraction can increase by a large factor (up to $\sim 20$) as $q$ decreases from unity to $0.2$. The resulting mass ratio distribution for merging binary BHs produced in this scenario is in tension with the observed distribution obtained by the LIGO/VIRGO collaboration, although significant uncertainties remain about the initial distribution of binary BH masses and mass ratios.