Black Hole Mergers From Globular Clusters Observable by LISA I: Eccentric Sources Originating From Relativistic $N$-body Dynamics

TL;DR

This paper demonstrates that a significant fraction of binary black hole mergers from globular clusters have detectable eccentricities in the LISA band, highlighting the importance of relativistic effects in modeling these sources.

Contribution

It shows that including General Relativistic corrections in N-body simulations significantly increases the predicted eccentricity of BBH mergers detectable by LISA, contrasting with previous Newtonian-based studies.

Findings

Nearly half of BBH mergers have measurable eccentricities in LISA band.

Relativistic corrections are crucial for accurate eccentricity predictions.

Eccentric mergers originate from binary-single interactions inside globular clusters.

Abstract

We show that nearly half of all binary black hole (BBH) mergers dynamically assembled in globular clusters have measurable eccentricities ($e>0.01$) in the LISA band ($10^{-2}$ Hz), when General Relativistic corrections are properly included in the $N$-body evolution. If only Newtonian gravity is included, the derived fraction of eccentric LISA sources is significantly lower, which explains why recent studies all have greatly underestimated this fraction. Our findings have major implications for how to observationally distinguish between BBH formation channels using eccentricity with LISA, which is one of the key science goals of the mission. We illustrate that the relatively large population of eccentric LISA sources reported here originates from BBHs that merge between hardening binary-single interactions inside their globular cluster. These results indicate a bright future for using LISA to probe the origin of BBH mergers.