Merging of unequal mass binary black holes in non-axisymmetric galactic nuclei

TL;DR

This study uses advanced simulations to analyze how unequal mass supermassive black hole binaries evolve in merging galactic nuclei, revealing that asymmetric binaries merge much faster, impacting gravitational wave detection.

Contribution

The paper provides the first comprehensive N-body simulation analysis of unequal mass SMBH binaries in rotating, non-axisymmetric galactic nuclei, extending previous results to larger particle numbers.

Findings

No 'final-parsec problem' observed, SMBHs pair and shrink efficiently.

Merger times for highly asymmetric binaries are up to four orders of magnitude shorter.

Binary hardening depends on the mass ratio through a single parameter function.

Abstract

In this work, we study the stellar-dynamical hardening of unequal mass supermassive black hole (SMBH) binaries in the central regions of merging galactic nuclei. We present a comprehensive set of direct $N$-body simulations of the problem, varying both the total mass and the mass ratio of the SMBH binary (SMBHB). Simulations were carried out with the $\varphi-$GPU $N$-body code, which enabled us to fully exploit supercomputers equipped with graphic processing units (GPUs). As a model for the galactic nuclei, we adopted initial axisymmetric, rotating models, aimed at reproducing the properties of a galactic nucleus emerging from a galaxy merger event, containing two SMBHs which were unbound initially. We found no 'final-parsec problem', as our SMBHs tend to pair and shrink without showing significant signs of stalling. This confirms earlier results and extends them to large particle numbers and rotating systems. We find that the SMBHB hardening depends on the binary-reduced mass ratio via a single parameter function. Our results suggest that, at a fixed value for the SMBHB primary mass, the merger time of highly asymmetric binaries is up to four order of magnitudes smaller than the equal-mass binaries. This can significantly affect the population of SMBHs potentially detectable as gravitational wave sources.