Eccentric Black Hole Mergers Forming in Globular Clusters

TL;DR

This paper calculates the likelihood of eccentric black hole mergers in globular clusters, revealing a significant fraction detectable by gravitational wave observatories and linking merger eccentricity to cluster properties.

Contribution

It introduces a method to estimate the rate of eccentric BBH mergers in stellar clusters, highlighting the importance of relativistic effects in accurate modeling.

Findings

Eccentric BBH mergers can constitute up to 5% of total mergers in globular clusters.

Eccentric mergers are more likely in denser, more compact clusters.

The eccentricity distribution of mergers can reveal their formation environment.

Abstract

We derive the probability for a newly formed binary black hole (BBH) to undergo an eccentric gravitational wave (GW) merger during binary-single interactions inside a stellar cluster. By integrating over the hardening interactions such a BBH must undergo before ejection, we find that the observable rate of BBH mergers with eccentricity $>0.1$ at $10\ \rm{Hz}$ relative to the rate of circular mergers can be as high as $\sim 5\%$ for a typical globular cluster (GC). This further suggests that BBH mergers forming through GW captures in binary-single interactions, eccentric or not, are likely to constitute $\sim 10\%$ of the total BBH merger rate from GCs. Such GW capture mergers can only be probed with an $N$-body code that includes General Relativistic corrections, which explains why recent Newtonian cluster studies not have been able to resolve this population. Finally, we show that the relative rate of eccentric BBH mergers depends on the compactness of their host cluster, suggesting that an observed eccentricity distribution can be used to probe the origin of BBH mergers.