[Paper Review] Hydrodynamical Evolution of Black-Hole Binaries Embedded in AGN Discs

Rixin Li, Dong Lai|arXiv (Cornell University)|Feb 15, 2022

Astrophysical Phenomena and Observations4 citations

TL;DR

This study uses high-resolution 2D hydrodynamical simulations in a shearing-box framework to model the evolution of stellar-mass black-hole binaries (BBHs) embedded in active galactic nucleus (AGN) discs. It finds that circular comparable-mass BBHs contract rapidly—hardening on timescales a few times the mass doubling rate—while eccentric binaries experience eccentricity damping; orbital decay is faster than migration for all realistic parameters, and accretion is highly variable, with variability frequency shifting from binary orbital to radial epicyclic frequency as eccentricity increases.

ABSTRACT

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 $γ$-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.

Motivation & Objective

• To understand the hydrodynamical evolution of stellar-mass black-hole binaries (BBHs) embedded in gaseous AGN discs, a potential formation channel for LIGO/Virgo gravitational wave mergers.
• To resolve the conflicting results in prior studies regarding whether BBHs in AGN discs harden or expand, particularly due to differences in numerical resolution and accretion modeling.
• To quantify the effects of binary mass ratio, eccentricity, and disc properties on accretion rates, torques, and orbital evolution.
• To determine whether the hardening timescale of BBHs in AGN discs is shorter than their migration timescale, a key question for merger formation efficiency.

Proposed method

• Conducting high-resolution 2D hydrodynamical simulations using a shearing-box approximation to model local regions of AGN discs around a central supermassive black hole.
• Employing a γ-law equation of state and a robust post-processing method to compute mass accretion rate, torque, and energy transfer rate on the binary.
• Using a small gravitational softening length (~0.08 of binary separation) and high spatial resolution to properly resolve circum-single discs (CSDs) around each binary component.
• Simulating binaries with varying mass ratios (q = 0.1 to 1.0), eccentricities (e = 0.0 to 0.5), and disc parameters (h = 0.01, λ = 2.5), with time-averaged quantities computed over the final 300 orbital periods.
• Evaluating orbital evolution via time-averaged rates of change in semimajor axis, eccentricity, and binary specific energy.
• Applying a consistent post-processing framework to extract accretion and torque rates from simulation outputs, ensuring reliable estimation of long-term evolution.

Experimental results

Research questions

• RQ1 Does the orbital decay rate of BBHs in AGN discs exceed their migration timescale, and under what conditions?
• RQ2 How does the binary mass ratio affect the accretion rate and orbital evolution of BBHs in AGN discs?
• RQ3 What is the role of binary eccentricity in determining the dominant variability frequency in accretion and the rate of eccentricity damping?
• RQ4 How do high-resolution simulations with properly resolved CSDs alter the previously reported expansion of BBHs in AGN discs compared to lower-resolution studies?
• RQ5 Does the thermodynamic state of the circum-single disc (e.g., temperature) influence the net torque and thus the hardening or expansion of the binary?

Key findings

• Circular comparable-mass BBHs contract rapidly, with an orbital decay rate of a few times the mass doubling rate, indicating fast hardening.
• Eccentric binaries always experience eccentricity damping, and prograde binaries with higher eccentricities or smaller mass ratios exhibit slower orbital decay, with some cases showing orbital expansion.
• The averaged mass accretion rate depends on the physical size of the accretor, with higher accretion rates for larger sink radii.
• Accretion variability is dominated by the apparent binary orbital frequency in the rotating frame for circular binaries, but shifts toward the radial epicyclic frequency as eccentricity increases.
• The hardening timescale of BBHs in AGN discs is significantly shorter than their migration timescale for all reasonable parameter combinations, favoring rapid merger formation.
• The results demonstrate that BBH dynamics in AGN discs differ fundamentally from isolated binaries in circumbinary discs, with stronger gas torques and distinct accretion signatures.