Gravitational waves from eccentric intermediate-mass black hole binaries

TL;DR

This paper investigates the dynamical evolution and gravitational wave signatures of eccentric intermediate-mass black hole binaries in dense stellar clusters, highlighting their detectability by LISA and the potential for measurable eccentricities.

Contribution

It combines N-body and three-body relativistic scattering simulations to show that such binaries can have significant eccentricities in the LISA band, contrary to standard assumptions.

Findings

Eccentricities in the LISA band can reach 0.2-0.3.

Binary mergers occur within less than 100 million years.

Cluster structure is only mildly affected by the binary.

Abstract

If binary intermediate-mass black holes (IMBHs; with masses between 100 and $10^4 \Msun$) form in dense stellar clusters, their inspiral will be detectable with the planned Laser Interferometer Space Antenna (LISA) out to several Gpc. Here we present a study of the dynamical evolution of such binaries using a combination of direct $N$-body techniques (when the binaries are well separated) and three-body relativistic scattering experiments (when the binaries are tight enough that interactions with stars occur one at a time). We find that for reasonable IMBH masses there is only a mild effect on the structure of the surrounding cluster even though the binary binding energy can exceed the binding energy of the cluster. We demonstrate that, contrary to standard assumptions, the eccentricity in the LISA band can be in {\em some} cases as large as $\sim 0.2 - 0.3$ and that it induces a measurable phase difference from circular binaries in the last year before merger. We also show that, even though energy input from the binary decreases the density of the core and slows down interactions, the total time to coalescence is short enough (typically less than a hundred million years) that such mergers will be unique snapshots of clustered star formation.