Evolution of a Binary Black Hole with a Retrograde Circumbinary Accretion Disk

Understand

We consider the evolution of a supermassive black hole binary (SMBHB) surrounded by a retrograde accretion disk.

• Assuming the disk is exactly in the binary plane and transfers energy and angular momentum to the binary via direct gas accretion, we calculate the time evolution of the binary's semi-major axis $a$ and eccentricity $e$.
• Because the gas is predominantly transferred when the binary is at apocenter, we find the eccentricity grows rapidly while maintaining constant $a(1+e)$.
• After accreting only a fraction of the secondary's mass, the eccentricity grows to nearly unity; from then on, gravitational wave emission dominates the evolution, preserving constant $a(1-e)$.