Eccentric Black Hole Mergers Forming in Globular Clusters

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.

Eccentric Black Hole Mergers in Globular Clusters

This paper by Johan Samsing investigates the probability and characteristics of eccentric black hole mergers within globular clusters (GCs), focusing on binary black holes (BBHs) undergoing gravitational wave (GW) captures during binary-single interactions. These interactions occur frequently in dense stellar environments, leading to the formation of BBHs with eccentric orbits. The study highlights the importance of including general relativistic (GR) corrections in $N$-body simulations to accurately model these phenomena.

The paper derives, through a detailed integration over hardening interactions within a stellar cluster, that up to $\sim 5\%$ of BBH mergers with eccentricity greater than 0.1 at 10 Hz can be observed, relative to circular mergers, in typical GCs. Furthermore, GW capture mergers initiated from binary-single interactions may constitute approximately 10\% of the total BBH merger rate in these environments. This is a significant insight as it challenges previous studies that did not take GR effects into account and inadvertently underestimated this eccentric population.

The probability for eccentric BBH mergers correlates with the escape velocity of the host cluster, governing the relation between merger eccentricity distributions and cluster compactness. This suggests that observations of eccentricity in GWs can be instrumental in deducing the astrophysical origins of BBH mergers. Implementing GR effects is crucial as mergers originating from GW captures during such interactions are difficult to discern using traditional Newtonian models.

To provide these insights, the paper examines characteristic distances, such as $r_{f}$, $r_{\rm EM}$, and $r_{\rm cap}$, which describe pericenter distances relevant to GW frequency outputs and eccentric merger outcomes. For these distances, analytic mathematical models showcase how dynamical GW capture interactions within three-body systems lead to mergers observable in the LIGO band.

The work also compares merger probabilities in various cluster environments, revealing that denser clusters, such as galactic nuclei, might require further theoretical development to accurately model merger probabilities due to higher isolated merger potential before ejection.

In conclusion, the research implicates that eccentric mergers are more prevalent in these dynamic environments than previously thought, presenting a strong case for using eccentricity as an observational metric to probe BBH formation channels. Insights from this study can thus guide future $N$-body simulations incorporating GR corrections, impacting theoretical and observational astrophysics by precisely evaluating merger rates and distributions. Future works will extend these insights into PN corrections within $N$-body dynamics, aiming to fully parse the role of gravitational waves in stellar cluster evolution and resultant BBH mergers.