Simulations of eccentric disks in close binary systems

¹ Institut für Astronomie & Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany e-mail: wilhelm.kley@uni-tuebingen.de; kley@tat.physik.uni-tuebingen.de
² Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA, UK

Received: 11 April 2008
Accepted: 23 June 2008

Abstract

Context. Eccentric accretion disks in superoutbursting cataclysmic and other binary systems.

Aims. We study the development of finite eccentricity in accretion disks in close binary systems using a 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.

Methods. Using a two-dimensional grid-based scheme we study the instability of accretion disks in close binary systems that causes them to attain a quasi-steady state with finite eccentricity. Mass ratios appropriate to superoutbursting cataclysmic binary systems are considered.

Results. Our grid-based scheme enables us to study the development of eccentric disks for disk aspect ratio h in the range and dimensionless kinematic viscosity ν in the range . Previous studies using particle-based methods were limited to the largest values for these parameters on account of their diffusive nature. Instability to the formation of a precessing eccentric disk that attains a quasi-steady state with mean eccentricity in the range 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.

Conclusions. Eccentric disks readily develop in close binary systems with Incorporation of a mass-transfer stream tends to impart stability for small enough viscosity (or, equivalently, mass-transfer rate through the disk) and to 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.