Viscous hydrodynamics simulations of circumbinary accretion discs: variability, quasi-steady state and angular momentum transfer

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 longterm integrations to ensure that the disc reaches a quasi-steady state, in which the time-averaged mass accretion rate onto the binary, Ṁ , matches the mass supply rate at the outer disc. We focus on binaries with comparable masses and a wide range of eccentricities (e B ). For e B 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 6a B ) generally becomes coherently eccentric. For low and high e B , the disc line of apsides precesses around the binary, but for intermediate e 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, J . The specific angular momentum, l 0 = J / Ṁ , depends non-monotonically on e B . Contrary to previous claims, we find that l 0 is positive for most e 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 B (0.2 − 0.4), corresponding to the regime where the inner eccentric disc is apsidally aligned with the binary.

Circumbinary discs: Numerical and physical behaviour

“…In contrast, Miranda et al (2017) find for their disk setup (h = 0.1, α = 0.1) that the disk does not precess for binary eccentricities between 0.2 and 0.4. We do not find this behaviour for our disk models, but note that we use a disk with a lower aspect ratio and a smaller α-value.…”

“…During our work we became aware of other simulations that were tackling similar problems. In October 2016 alone three publications appeared on astro-ph that described numerical simulations of circumbinary disks (Fleming & Quinn 2017;Miranda et al 2017;Mutter et al 2017). While the first paper considered SPH-simulations in the latter two papers grid-codes were used and in both the boundary condition at R min is discussed in more detail.…”

“…At the inner radial boundary the standard condition is the zero-gradient outflow condition as in Kley & Haghighipour (2014) or Miranda et al (2017) but we test also different possibilities such as closed boundaries or the viscous outflow condition (Kley & Nelson 2008;Mutter et al 2017).…”

“…This means that for simulations where the binary orbit is not included in the computational domain, the boundary condition at the inner radius has to allow for flow into the inner cavity, at least approximately. Two boundary conditions are usually used in circumbinary disk simulations: closed boundaries (Lines et al 2015;Pierens & Nelson 2013) and outflow boundaries (Kley & Haghighipour 2014Miranda et al 2017).…”

“…We do not find this behaviour for our disk models, but note that we use a disk with a lower aspect ratio and a smaller α-value. To investigate this further we set up a simulation with the same numerical parameters as Miranda et al (2017) and used a physical setup where they did not observe a precession of the disk (q bin = 1.0, e bin = 0.4, h = 0.1 and α = 0.1). We carried out two simulations, one with an inner radius of R min = (1 + e bin )a bin and one with an inner radius of R min = 1.136 a bin .…”