Simulations of eccentric disks in close binary systems

TL;DR

This study uses two-dimensional simulations to explore how eccentric accretion disks develop and behave in close binary systems, highlighting the influence of viscosity, boundary conditions, and mass transfer.

Contribution

It provides detailed parameter studies on eccentric disk formation, emphasizing the sensitivity to boundary conditions and mass transfer, and supports the mode-coupling mechanism near the 3:1 resonance.

Findings

Eccentric disks with mean eccentricity 0.3-0.5 form readily in simulations.

A critical viscosity exists below which disks remain circular.

Mass transfer streams can stabilize disks and match observed precession rates.

Abstract

We study the development of finite eccentricity in accretion disks in close binary systems using a two-dimensional grid-based numerical scheme. We perform detailed parameter studies to explore the dependence on viscosity, disk aspect ratio, the inclusion of a mass-transfer stream and the role of the boundary conditions. We consider mass ratios 0.05<q<0.3 appropriate to superoutbursting cataclysmic binary systems. Instability to the formation of a precessing eccentric disk that attains a quasi-steady state with mean eccentricity in the range 0.3-0.5 occurs readily. The shortest growth times are ~15 binary orbits for the largest viscosities and the instability mechanism is for the most part consistent with the mode-coupling mechanism associated with the 3:1 resonance proposed by Lubow. However, the results are sensitive to the treatment of the inner boundary and to the incorporation of the mass-transfer stream. In the presence of a stream we found a critical viscosity below which the disk remains circular. Incorporation of a mass-transfer stream tends to impart stability for small enough viscosity (or, equivalently, mass-transfer rate through the disk) and does assist in obtaining a prograde precession rate that is in agreement with observations. For the larger q the location of the 3:1 resonance is pushed outwards towards the Roche lobe where higher-order mode couplings and nonlinearity occur. It is likely that three-dimensional simulations that properly resolve the disk's vertical structure are required to make significant progress in this case.