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

TL;DR

This paper models the evolution of supermassive black hole binaries with retrograde circumbinary disks, showing how accretion-driven eccentricity growth influences gravitational wave signals detectable by pulsar timing arrays.

Contribution

It provides a detailed calculation of binary evolution under retrograde accretion, highlighting the impact on gravitational wave emission and waveform characteristics.

Findings

Eccentricity rapidly grows to near unity due to retrograde accretion.

High eccentricity shifts gravitational wave power to lower frequencies.

Retrograde accretion can drive binaries into GW-dominated regimes before disk alignment.

Abstract

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 $a(1-e)$. The high-eccentricity waveforms redistribute the peak gravitational wave power from the nHz to $\mu$Hz bands, substantially affecting the signal that might be detected with pulsar timing arrays. We also estimate the torque coupling binaries of arbitrary eccentricity with obliquely aligned circumbinary disks. If the outer edge of the disk is not an extremely large multiple of the binary separation, retrograde accretion can drive the binary into the gravitational wave-dominated state before these torques align the binary with the angular momentum of the mass supply.