Retrograde binaries of massive black holes in circum-binary accretion discs

TL;DR

This study investigates how counter-rotating gas discs influence the orbital decay and eccentricity evolution of massive black hole binaries, revealing that accretion prescriptions significantly impact binary dynamics.

Contribution

It introduces detailed hydrodynamical simulations with varied accretion models to understand binary hardening and eccentricity growth in retrograde circumbinary discs.

Findings

Realistic accretion models alter disc surface densities and binary evolution.

Initially circular binaries gain small eccentricities during hardening.

Eccentric binaries tend to become more eccentric over time.

Abstract

We explore the hardening of a massive black hole binary embedded in a circum-binary gas disc when the binary and the gas are coplanar and the gas is counter-rotating. The secondary black hole, revolving in the direction opposite to the gas, experiences a drag from gas-dynamical friction and from direct accretion of part of it. Using two-dimensional (2D) hydrodynamical grid simulations we investigate the effect of changing the accretion prescriptions on the dynamics of the secondary black hole which in turn affect the binary hardening and eccentricity evolution. We find that realistic accretion prescriptions lead to results that differ from those inferred assuming accretion of all the gas within the Roche Lobe of the secondary black hole. Different accretion prescriptions result in different disc's surface densities which alter the black hole's dynamics back. Full 3D SPH realizations of a number of representative cases, run over a shorter interval of time, validate the general trends observed in the less computationally demanding 2D simulations. Initially circular black hole binaries increase only slightly their eccentricity which then oscillates around small values (<0.1) while they harden. By contrast, initially eccentric binaries become more and more eccentric. A semi-analytical model describing the black hole's dynamics under accretion only explores the late evolution stages of the binary in an otherwise unperturbed retrograde disc to illustrate how eccentricity evolves with time in relation to the shape of the underlying surface density distribution.