Evolution of Massive Black Hole Binaries in Collisionally Relaxed Nuclear Star Clusters -- Impact of Mass Segregation

TL;DR

This study uses high-resolution N-body simulations to explore how mass segregation in collisional nuclear star clusters influences the evolution and merger timescales of massive black hole binaries, revealing effects dependent on mass ratio.

Contribution

It provides the first detailed analysis of collisional relaxation effects on MBH binary dynamics in realistic, high-particle-number NSC models with mass spectra.

Findings

Mass segregation accelerates binary hardening in low mass ratio cases.

Higher mass ratio binaries experience slower hardening due to relaxation.

Relaxed models show lower eccentricities and longer merger timescales.

Abstract

Massive Black Hole (MBH) binaries are considered to be one of the most important sources of Gravitational Waves (GW) that can be detected by GW detectors like LISA. However, there are a lot of uncertainties in the dynamics of MBH binaries in the stages leading up to the GW-emission phase. It has been recently suggested that Nuclear Star Clusters (NSCs) could provide a viable route to overcome the final parsec problem for MBH binaries at the center of galaxies. NSCs are collisional systems where the dynamics would be altered by the presence of a mass spectrum. In this study, we use a suite of high-resolution $N$-body simulations with over 1 million particles to understand how collisional relaxation under the presence of a mass spectrum of NSC particles affects the dynamics of the MBH binary under the merger of two NSCs. We consider MBH binaries with different mass ratios and additional non-relaxed models. We find that mass-segregation driven by collisional relaxation can lead to accelerated hardening in lower mass ratio binaries but has the opposite effect in higher mass ratio binaries. Crucially, the relaxed models also demonstrate much lower eccentricities at binary formation and negligible growth during hardening stages leading to longer merger timescales. The results are robust and highlight the importance of collisional relaxation on changing the dynamics of the binary. Our models are state-of-the-art, use zero softening, and high enough particle numbers to model NSCs realistically.