The evolution of a binary in a retrograde circular orbit embedded in an accretion disk

TL;DR

This paper investigates the inward migration and accretion processes of a small-mass ratio binary in a retrograde orbit within an accretion disk, combining semi-analytic and numerical methods to understand their evolution and observational signatures.

Contribution

It develops the theory of type I migration for retrograde binaries and compares semi-analytic and numerical approaches, providing new insights into their orbital evolution and accretion behavior.

Findings

Inward migration occurs on a timescale related to secondary mass accretion.

Accretion onto the secondary has minor impact on orbital evolution.

Migration can help resolve the final parsec problem.

Abstract

Supermassive black hole binaries may form as a consequence of galaxy mergers. Both prograde and retrograde orbits have been proposed. We study a binary of a small mass ratio, q, in a retrograde orbit immersed in and interacting with a gaseous accretion disk in order to estimate time scales for inward migration leading to coalescence and the accretion rate to the secondary component. We employ both semi-analytic methods and two dimensional numerical simulations, focusing on the case where the binary mass ratio is small but large enough to significantly perturb the disk. We develop the theory of type I migration for this case and determine conditions for gap formation finding that then inward migration occurs on a time scale equal to the time required for one half of the secondary mass to be accreted through the unperturbed disk, with accretion onto the secondary playing only a minor role. The semi-analytic and fully numerical approaches are in good agreement, the former being applicable over long time scales. Inward migration induced by interaction with the disk alleviates the final parsec problem. Accretion onto the secondary does not significantly affect the orbital evolution, but may have observational consequences for high accretion efficiency. The binary may then appear as two sources of radiation rotating around each other. This study should be extended to consider orbits with significant eccentricity and the effects of gravitational radiation at small length scales. Note too that torques acting between a circumbinary disk and a retrograde binary orbit may cause the mutual inclination to increase on a timescale that can be similar to, or smaller than that for orbital evolution, depending on detailed parameters. This is also an aspect for future study (abridged).