Accretion Disks Around Binary Black Holes: A Quasistationary Model

TL;DR

This paper develops an analytic, quasistationary model of accretion disks around binary black holes, describing the disk structure and electromagnetic emission prior to binary decoupling, with implications for simulations and observations.

Contribution

It introduces a simple Newtonian, steady-state model for thin, Keplerian disks around binary black holes, incorporating tidal and viscous torques through a key nondimensional parameter.

Findings

Disk structure depends on the ratio of tidal to viscous torque.

The model reduces to the standard Shakura-Sunyaev profile for small tidal effects.

Provides analytic solutions useful for initial conditions in numerical simulations.

Abstract

Tidal torques acting on a gaseous accretion disk around a binary black hole can create a gap in the disk near the orbital radius. At late times, when the binary inspiral timescale due to gravitational wave emission becomes shorter than the viscous timescale in the disk, the binary decouples from the disk and eventually merges. Prior to decoupling the balance between tidal and viscous torques drives the disk to a quasistationary equilibrium state, perturbed slightly by small amplitude, spiral density waves emanating from the edges of the gap. We consider a black hole binary with a companion of smaller mass and construct a simple Newtonian model for a geometrically thin, Keplerian disk in the orbital plane of the binary. We solve the disk evolution equations in steady state to determine the quasistationary, (orbit-averaged) surface density profile prior to decoupling. We use our solution, which is analytic up to simple quadratures, to compute the electromagnetic flux and approximate radiation spectrum during this epoch. A single nondimensional parameter Td/Tvis, equal to the ratio of the tidal to viscous torque at the orbital radius, determines the disk structure, including the surface density profile, the extent of the gap, the existence of an inner disk, and the accretion rate. The solution reduces to the Shakura-Sunyaev profile for a stationary accretion disk around a single black hole in the limit of small Td/Tvis. Our solution may be useful for choosing physical parameters and setting up quasistationary disk initial data for detailed numerical simulations that begin prior to decoupling and track the subsequent evolution of a black hole binary-disk system.