Gravitational wave sources from inspiralling globular clusters in the Galactic Centre and similar environments

TL;DR

This study models the inspiral of globular clusters into galactic centers to understand the formation of gravitational wave sources, revealing how galaxy profiles influence merger rates of black hole binaries and IMBHs.

Contribution

It provides new insights into how globular cluster infalls contribute to gravitational wave sources, including IMBH-SMBH mergers and extreme-mass-ratio inspirals, with detailed simulation results.

Findings

IMBH-SMBH merger rate of 2.8×10^{-3} yr^{-1} Gpc^{-3}

EMRI merger rate of 0.25 yr^{-1} Gpc^{-3}

Black hole binary merger rate of 0.4-4 yr^{-1} Gpc^{-3}

Abstract

We model the inspiral of globular clusters (GCs) towards a galactic nucleus harboring a supermassive black hole (SMBH), a leading scenario for the formation of nuclear star clusters. We consider the case of GCs containing either an intermediate-mass black hole (IMBH) or a population of stellar mass black holes (BHs), and study the formation of gravitational wave (GW) sources. We perform direct summation $N$-body simulations of the infall of GCs with different orbital eccentricities in the live background of a galaxy with either a shallow or steep density profile. We find that the GC acts as an efficient carrier for the IMBH, facilitating the formation of a bound pair. The hardening and evolution of the binary depends sensitively on the galaxy's density profile. If the host galaxy has a shallow profile the hardening is too slow to allow for coalescence within a Hubble time, unless the initial cluster orbit is highly eccentric. If the galaxy hosts a nuclear star cluster, the hardening leads to coalescence by emission of GWs within $3-4$ Gyr. In this case, we find a IMBH-SMBH merger rate of $\Gamma_{\rm IMBH-SMBH} = 2.8\times 10^{-3}$ yr$^{-1}$ Gpc$^{-3}$. If the GC hosts a population of stellar BHs, these are deposited close enough to the SMBH to form extreme-mass-ratio-inspirals with a merger rate of $\Gamma_{\rm EMRI} = 0.25$ yr$^{-1}$ Gpc$^{-3}$. Finally, the SMBH tidal field can boost the coalescence of stellar black hole binaries delivered from the infalling GCs. The merger rate for this merging channel is $\Gamma_{\rm BHB} = 0.4-4$ yr$^{-1}$ Gpc$^{-3}$.