Hydrodynamical Evolution of Black-Hole Binaries Embedded in AGN Discs
  Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus
(AGN) discs are possible progenitors of black-hole mergers detected in
gravitational waves by LIGO/VIRGO. To better understand the hydrodynamical
evolution of BBHs interacting with the disc gas, we perform a suite of
high-resolution 2D simulations of binaries in local disc (shearing-box) models,
considering various binary mass ratios, eccentricities and background disc
properties. We use the $\gamma$-law equation of state and adopt a robust
post-processing treatment to evaluate the mass accretion rate, torque and
energy transfer rate on the binary to determine its long-term orbital
evolution. We find that circular comparable-mass binaries contract, with an
orbital decay rate of a few times the mass doubling rate. Eccentric binaries
always experience eccentricity damping. Prograde binaries with higher
eccentricities or smaller mass ratios generally have slower orbital decay
rates, with some extreme cases exhibiting orbital expansion. The averaged
binary mass accretion rate depends on the physical size of the accretor. The
accretion flows are highly variable, and the dominant variability frequency is
the apparent binary orbital frequency (in the rotating frame around the central
massive BH) for circular binaries but gradually shifts to the radial epicyclic
frequency as the binary eccentricity increases. Our findings demonstrate that
the dynamics of BBHs embedded in AGN discs is quite different from that of
isolated binaries in their own circumbinary discs. Furthermore, our results
suggest that the hardening timescales of the binaries are much shorter than
their migration timescales in the disc, for all reasonable binary and disc
parameters.
