Brownian motion of massive black hole binaries and the final parsec problem

TL;DR

This study investigates whether Brownian motion artificially influences the evolution of massive black hole binaries in galaxy mergers, concluding that in high-resolution simulations, it does not significantly impact the binary hardening process.

Contribution

The paper demonstrates that Brownian motion has negligible effects on BHB evolution in simulations with over a million particles, emphasizing the role of collisionless loss cone refilling.

Findings

Brownian motion does not significantly affect BHB evolution in high-N simulations.

Collisionless loss cone refilling drives binary hardening.

Simulations with over one million particles accurately model BHB dynamics.

Abstract

Massive black hole binaries (BHBs) are expected to be one of the most powerful sources of gravitational waves (GWs) in the frequency range of the pulsar timing array and of forthcoming space-borne detectors. They are believed to form in the final stages of galaxy mergers, and then harden by slingshot ejections of passing stars. However, evolution via the slingshot mechanism may be ineffective if the reservoir of interacting stars is not readily replenished, and the binary shrinking may come to a halt at roughly a parsec separation. Recent simulations suggest that the departure from spherical symmetry, naturally produced in merger remnants, leads to efficient loss cone refilling, preventing the binary from stalling. However, current N-body simulations able to accurately follow the evolution of BHBs are limited to very modest particle numbers. Brownian motion may artificially enhance the loss cone refilling rate in low-N simulations, where the binary encounters a larger population of stars due its random motion. Here we study the significance of Brownian motion of BHBs in merger remnants in the context of the final parsec problem. We simulate mergers with various particle numbers (from 8k to 1M) and with several density profiles. Moreover, we compare simulations where the BHB is fixed at the centre of the merger remnant with simulations where the BHB is free to random walk. We find that Brownian motion does not significantly affect the evolution of BHBs in simulations with particle numbers in excess of one million, and that the hardening measured in merger simulations is due to collisionless loss cone refilling.