# Circumbinary discs: Numerical and physical behaviour

## TL;DR

This study uses hydrodynamical simulations to analyze the physical and numerical behavior of circumbinary disks, revealing how binary and disk parameters influence disk eccentricity, precession, and gap size.

## Contribution

It provides detailed insights into the impact of binary eccentricity, mass ratio, and disk parameters on circumbinary disk dynamics using multiple simulation codes.

## Key findings

- Inner grid radius should be near the binary's semi-major axis.
- Disks become eccentric and precess with periods depending on parameters.
- Gap size remains constant across different mass ratios, but precession period varies.

## Abstract

We study the evolution of circumbinary disks under the gravitational influence of the binary using two-dimensional hydrodynamical simulations to investigate the impact of disk and binary parameters on the dynamical aspects of the disk. To distinguish between physical and numerical effects we apply three hydrodynamical codes. First we analyse in detail numerical issues concerning the conditions at the boundaries and grid resolution. We then perform a series of simulations with different binary (eccentricity, mass ratio) and disk parameters (viscosity, aspect ratio) starting from a reference model with Kepler-16 parameters. Concerning the numerical aspects we find that the inner grid radius must be of the order of the binary semi-major axis, with free outflow conditions applied such that mass can flow onto the central binary. A closed inner boundary leads to unstable evolutions. We find that the inner disk turns eccentric and precesses for all investigated physical parameters. The precession rate is slow with periods ($T_\mathrm{prec}$) starting at around 500 binary orbits ($T_\mathrm{bin}$) for high viscosity and large $H/R$ where the inner hole is smaller and more circular. Reducing $\alpha$ and $H/R$ increases the gap size and $T_\mathrm{prec}$ reaches 2500 $T_\mathrm{bin}$. For varying binary mass ratios $q_\mathrm{bin}$ the gap size remains constant whereas $T_\mathrm{prec}$ decreases for increasing $q_\mathrm{bin}$. For varying binary eccentricities $e_\mathrm{bin}$ we find two separate branches in the gap size and eccentricity diagram. The bifurcation occurs at around $e_\mathrm{crit} \approx 0.18$ where the gap is smallest with the shortest $T_\mathrm{prec}$. For $e_\mathrm{bin}$ smaller and larger than $e_\mathrm{crit}$ the gap size and $T_\mathrm{prec}$ increase. Circular binaries create the most eccentric disks.