Accelerated orbital decay of supermassive black hole binaries in merging nuclear star clusters

TL;DR

This study uses N-body simulations to show that nuclear star clusters significantly accelerate the merger of supermassive black hole binaries, making coalescence within a Hubble time more likely and enhancing gravitational wave detection prospects.

Contribution

It demonstrates the impact of nuclear star clusters on SMBH binary evolution, revealing a faster orbital decay process not accounted for in traditional models.

Findings

SMBH binaries experience rapid orbital decay due to star cluster effects.

The presence of star clusters enables SMBH coalescence within a Hubble time.

Results support increased likelihood of detecting SMBH mergers with LISA.

Abstract

The coalescence of supermassive black holes (SMBHs) should generate the strongest sources of gravitational waves (GWs) in the Universe. However, the dynamics of their coalescence is the subject of much debate. In this study, we use a suite of $N$-body simulations to follow the merger of two nuclear star clusters (NSCs), each hosting a SMBH in their centre. We find that the presence of distinct star clusters around each SMBH has important consequences for the dynamical evolution of the SMBH binary: (i) The separation between the SMBHs decreases by a few orders of magnitude in the first few Myrs by the combined effects of dynamical friction and a drag force caused by tidally stripped stars. In fact, this is a significant speedup for equal mass ratio binaries, and becomes extreme for unequal mass ratios, e.g. 1:10 or 1:100, which traditional dynamical friction alone would not permit to bind. (ii) The subsequent binary hardening is driven by the gravitational slingshots between the SMBH binary and stars, and also depends on the mass ratio between the SMBHs. Thus, with this additional drag force, we find that all SMBHs in our suite coalesce within a Hubble time. Given that about 50% of Milky Way sized galaxies host NSCs, our results are encouraging for upcoming GW observations with the Laser Interferometer Space Antenna -- LISA -- which will detect SMBH coalescence in the $10^4-10^7$$M_{\rm \odot}$ mass range.