The competing effect of gas and stars in massive black hole binaries evolution

TL;DR

This study models the evolution of massive black hole binaries considering both stellar and gaseous influences, revealing that gas-driven outspiral is limited and does not significantly delay coalescence for gravitational wave detection.

Contribution

It introduces a semi-analytical model combining stellar and gas effects on binary evolution, showing gas outspiral is limited and coalescence occurs within a few hundred million years.

Findings

Gas-driven outspiral occurs only at high accretion rates.

Binaries eventually coalesce within a few hundred million years.

Gas effects do not significantly hinder gravitational wave detection.

Abstract

Massive black hole binaries are predicted to form during the hierarchical assembly of cosmic structures and will represent the loudest sources of low-frequency gravitational waves (GWs) detectable by present and forthcoming GW experiments. Before entering the GW-driven regime, their evolution is driven by the interaction with the surrounding stars and gas. While stellar interactions are found to always shrink the binary, recent studies predict the possibility of binary outspiral mediated by the presence of a gaseous disk, which could endlessly delay the coalescence and impact the merger rates of massive binaries. Here we implement a semi-analytical treatment that follows the binary evolution under the combined effect of stars and gas. We find that binaries may outspiral only if they accrete near or above their Eddington limit and only until their separation reaches the gaseous disk self-gravitating radius. Even in case of an outspiral, the binary eventually reaches a large enough mass for GW to take over and drive it to coalescence. The combined action of stellar hardening, mass growth and GW-driven inspiral brings binaries to coalescence in few hundreds Myr at most, implying that gas-driven expansion will not severely affect the detection prospects of upcoming GW facilities.