Viscous Hydrodynamics Simulations of Circumbinary Accretion Discs: Variability, Quasi-Steady State, and Angular Momentum Transfer

TL;DR

This study uses detailed numerical simulations to analyze circumbinary accretion discs, revealing how binary eccentricity influences accretion variability, disc eccentricity, and angular momentum transfer, with implications for binary evolution.

Contribution

It provides the first comprehensive analysis of angular momentum transfer and disc behavior across a range of binary eccentricities using long-term viscous hydrodynamics simulations.

Findings

Mass accretion rate modulated at binary period or higher for low eccentricity.

Inner disc becomes eccentric and precesses or locks with binary depending on eccentricity.

Binary generally gains angular momentum, potentially increasing separation.

Abstract

We carry out numerical simulations of circumbinary discs, solving the viscous hydrodynamics equations on a polar grid covering an extended disc outside the binary co-orbital region. We use carefully controlled outer boundary conditions and long-term integrations to ensure that the disc reaches a quasi-steady state, in which the time-averaged mass accretion rate onto the binary, $\langle\dot{M}\rangle$, matches the mass supply rate at the outer disc. We focus on binaries with comparable masses and a wide range of eccentricities ($e_\mathrm{B}$). For $e_\mathrm{B} \lesssim 0.05$, the mass accretion rate of the binary is modulated at about $5$ times the binary period; otherwise it is modulated at the binary period. The inner part of the circumbinary disc ($r \lesssim 6 a_\mathrm{B}$) generally becomes coherently eccentric. For low and high $e_\mathrm{B}$, the disc line of apsides precesses around the binary, but for intermediate $e_\mathrm{B}$ ($0.2 - 0.4$), it instead becomes locked with that of the binary. By considering the balance of angular momentum transport through the disc by advection, viscous stress, and gravitational torque, we determine the time-averaged net angular momentum transfer rate to the binary, $\langle\dot{J}\rangle$. The specific angular momentum, $l_0 = \langle\dot{J}\rangle/\langle\dot{M}\rangle$, depends non-monotonically on $e_\mathrm{B}$. Contrary to previous claims, we find that $l_0$ is positive for most $e_\mathrm{B}$, implying that the binary receives net angular momentum, which may cause its separation to grow with time. The minimum $l_0$ occurs at intermediate $e_\mathrm{B}$ ($0.2 - 0.4$), corresponding to the regime where the inner eccentric disc is apsidally aligned with the binary.