Simulations of eccentric disks in close binary systems

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 $0.05 \le q \le 0.3$ 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 $0.01{-}0.06$ and dimensionless kinematic viscosity ν in the range $3.3 \times 10^{-6}{-}10^{-4}$. 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 $0.3{-}0.5$ 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. Conclusions. Eccentric disks readily develop in close binary systems with $ 0.05 \le q \le 0.3.$ 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.