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

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 ${\Gamma }_{\mathrm{IMBH}-\mathrm{SMBH}}=2.8\times 10^{-3}$ 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 ${\Gamma }_{\mathrm{EMRI}}=0.25$ 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 ${\Gamma }_{\mathrm{BHB}}=0.4-4$ yr${}^{-1}$ Gpc${}^{-3}$.

arXiv comment21 pages, 29 figures, 6 tables. Accepted for publication in MNRAS

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