Circumbinary disc self-gravity governing supermassive black hole binary mergers

TL;DR

This study uses 3D simulations to show that self-gravity in circumbinary discs consistently causes supermassive black hole binaries to shrink, regardless of disc mass or temperature, impacting models of their merger evolution.

Contribution

It demonstrates that disc self-gravity governs binary orbital decay across various conditions, highlighting its importance in supermassive black hole merger models.

Findings

Self-gravity causes binary semi-major axis to decrease regardless of disc mass or temperature.

More massive discs accelerate binary shrinking and eccentricity growth.

Initial cavity size influences the rate of binary orbital decay.

Abstract

Understanding the interaction of massive black hole binaries with their gaseous environment is crucial since at sub-parsec scales the binary is too wide for gravitational wave emission to take over and to drive the two black holes to merge. We here investigate the interaction between a massive black hole binary and a self-gravitating circumbinary disc using 3D smoothed particle hydrodynamics simulations. We find that, when the disc self-gravity regulates the angular momentum transport, the binary semi-major axis decreases regardless the choice of disc masses and temperatures, within the range we explored. In particular, we find that the disc initial temperature (hence the disc aspect ratio) has little effect on the evolution of the binary since discs with the same mass self-regulate towards the same temperature. Initially warmer discs cause the binary to shrink on a slightly shorter timescale until the disc has reached the self-regulated equilibrium temperature. More massive discs drive the binary semi-major axis to decrease at a faster pace compared to less massive discs and result in faster binary eccentricity growth even after the initial-condition-dependent transient evolution. Finally we investigate the effect that the initial cavity size has on the binary-disc interaction and we find that, in the self-gravitating regime, an initially smaller cavity leads to a much faster binary shrinking, as expected. Our results are especially important for very massive black hole binaries such as those in the PTA band, for which gas self gravity cannot be neglected.