[Paper Review] Dynamics and spin alignment in massive, gravito-turbulent circumbinary discs around supermassive black hole binaries

Martin A. Bourne, Davide Fiacconi+3 more|arXiv (Cornell University)|Nov 28, 2023

Astrophysical Phenomena and Observations4 citations

TL;DR

This study presents 3D hydrodynamic simulations of massive, gravito-turbulent circumbinary discs (CBDs) around supermassive black hole binaries, using super-Lagrangian refinement and a sub-grid Shakura-Sunyaev disc model to self-consistently track black hole mass and spin evolution. Unlike prior works, it finds no preferential accretion onto the secondary black hole, leading to constant mass ratios and weaker gravitational wave backgrounds, while spin alignment occurs rapidly even in low mass ratio systems, though misaligned mini-discs may prevent alignment in chaotic accretion scenarios.

ABSTRACT

Parsec-scale separation supermassive black hole binaries in the centre of gas-rich galaxy merger remnants could be surrounded by massive circumbinary discs (CBDs). Black hole mass and spin evolution during the gas-rich binary inspiral are crucial in determining the direction and power of relativistic jets that radio observations with LOFAR and SKAO will probe, and for predicting gravitational wave (GW) emission that IPTA and LISA will measure. We present 3D hydrodynamic simulations capturing gas-rich, self-gravitating CBDs around a $2 imes 10^6$ M$_{\odot}$ supermassive black hole binary, that probe different mass ratios, eccentricities and inclinations. We employ a sub-grid Shakura-Sunyaev accretion disc to self-consistently model black hole mass and spin evolution together with super-Lagrangian refinement techniques to resolve gas flows, streams and mini-discs within the cavity, which play a fundamental role in torquing and feeding the binary. We find that higher mass ratio and eccentric binaries result in larger cavities, while retrograde binaries result in smaller cavities. All of the simulated binaries are expected to shrink with net gravitational torques being negative. Unlike previous simulations, we do not find preferential accretion onto the secondary black hole. This implies smaller chirp masses at coalescence and hence a weaker GW background. Critically this means that spin-alignment is faster than the binary inspiral timescale even for low mass ratios. When considering initially misaligned systems, the orientation of the mini-discs around each black hole can vary significantly. We discuss the implications of this behaviour for black hole spin alignment and highlight the need for broader parameter space studies of misaligned systems to understand the impact on black hole recoil velocities.

Motivation & Objective

• To understand the dynamics and spin evolution of supermassive black hole binaries in massive, self-gravitating circumbinary discs (CBDs) during the gas-rich phase of galaxy mergers.
• To investigate how binary mass ratio, eccentricity, and inclination affect cavity structure, gas inflow, and accretion patterns in CBDs.
• To determine whether accretion preferentially feeds the secondary black hole, as suggested in prior studies, and its implications for chirp mass and gravitational wave emission.
• To assess the timescale of black hole spin alignment relative to binary inspiral, especially in misaligned systems, and its impact on recoil velocities and host galaxy displacement.
• To evaluate the role of mini-discs and stream dynamics in torquing black hole spins and influencing long-term binary evolution.

Proposed method

• 3D hydrodynamic simulations using the adaptive mesh refinement code, with super-Lagrangian refinement to resolve gas flows, streams, and mini-discs within the circumbinary cavity.
• Incorporation of a sub-grid Shakura-Sunyaev accretion disc model to self-consistently evolve black hole mass and spin via viscous torques.
• Use of an adiabatic equation of state with slow β-cooling to model gas thermodynamics and maintain disc stability.
• Systematic variation of binary parameters: mass ratio (q = 1, 1/3, 1/10), eccentricity (e = 0, 0.5), and inclination (i = 0°, 45°, 180°) across 12 simulation setups.
• Tracking of gravitational torques on the binary from gas at different radii (R < a and R > a) to determine net inspiral rates.
• Analysis of mini-disc formation, size, and alignment timescales relative to binary inspiral to assess spin evolution.

Experimental results

Research questions

• RQ1 Does accretion in massive, gravito-turbulent circumbinary discs preferentially feed the secondary black hole, as predicted by some prior models?
• RQ2 How do binary mass ratio, eccentricity, and inclination influence the size and structure of the circumbinary cavity and gas inflow?
• RQ3 What is the net gravitational torque on the binary, and how does it affect the inspiral timescale?
• RQ4 How rapidly do black hole spins align with the global angular momentum of the system, and is this alignment guaranteed in initially misaligned configurations?
• RQ5 What are the implications of misaligned mini-discs for black hole spin evolution and potential recoil velocities post-merger?

Key findings

• Higher mass ratio and eccentric binaries produce larger circumbinary cavities, while retrograde binaries result in smaller cavities due to stronger gas torques.
• Net gravitational torques on the binary are negative across all configurations, driving inspiral, with low mass ratio and retrograde binaries shrinking more rapidly.
• Accretion does not preferentially feed the secondary black hole; mass ratios remain approximately constant, implying lower chirp masses and weaker gravitational wave backgrounds at coalescence.
• Spin alignment occurs on timescales shorter than or comparable to the binary inspiral timescale, even for low mass ratio systems, due to efficient torquing from mini-discs.
• In initially misaligned systems, mini-discs do not align quickly, so black hole spins may remain misaligned at merger, increasing the risk of significant recoil velocities and galaxy displacement.
• The lack of preferential secondary accretion is attributed to the adiabatic equation of state, slow β-cooling, low viscosity, and differences from traditional sink particle accretion models.