Retrograde Accretion and Merging Supermassive Black Holes

TL;DR

This paper demonstrates that retrograde circumbinary gas discs are highly effective in shrinking supermassive black hole binaries, leading to coalescence within a timescale proportional to the secondary black hole's mass over the gas inflow rate.

Contribution

It reveals that retrograde discs facilitate binary coalescence by absorbing negative angular momentum, overcoming limitations of prograde disc interactions.

Findings

Retrograde discs are more effective than prograde discs in binary shrinking.

Binary coalescence occurs once angular momentum equal to the secondary's mass is absorbed.

Coalescence timescale is approximately the secondary mass divided by the inflow rate.

Abstract

We investigate whether a circumbinary gas disc can coalesce a supermassive black hole binary system in the centre of a galaxy. This is known to be problematic for a prograde disc. We show that in contrast, interaction with a retrograde circumbinary disc is considerably more effective in shrinking the binary because there are no orbital resonances. The binary directly absorbs negative angular momentum from the circumbinary disc by capturing gas into a disc around the secondary black hole, or discs around both holes if the binary mass ratio is close to unity. In many cases the binary orbit becomes eccentric, shortening the pericentre distance as the eccentricity grows. In all cases the binary coalesces once it has absorbed the angular momentum of a gas mass comparable to that of the secondary black hole. Importantly, this conclusion is unaffected even if the gas inflow rate through the disc is formally super--Eddington for either hole. The coalescence timescale is therefore always $\sim M_2/\dot M$, where $M_2$ is the secondary black hole mass and $\dot M$ the inflow rate through the circumbinary disc.