DYNAMICS OF ECCENTRIC DISKS WITH APPLICATION TO SUPERHUMP BINARIES

We investigate some issues regarding the nature of eccentric accretion disks in close binary systems. We also relate some methods developed here to the theory of planetary rings. Recent analytic studies and simulations have demonstrated that eccentricity can be generated at the 3:1 resonance in an accretion disk. We extend such work to analyze several issues of interest. 1. We investigate the role of nonresonant tidal effects at weakening the eccentric instability produced by a pure m = 3 tidal potential phi3 at the 3:1 resonance. Using SPH simulations, we show that the m = 2 component of the tidal potential, phi2, is primarily responsible for weakening the instability by repelling matter from the resonant region. 2. We develop an analytic model for disk precession that incorporates the effects of direct tidal effects, gas pressure, and resonant wave stresses.We show that tidal effects dominate for conditions appropriate for superhump binaries and produce a net prograde precession. Gas pressure produces a retrograde contribution. For fast growing eccentricity (growth times of order 5 orbital periods) wave stresses contribute significantly. This latter effect can cause the precession rate to decrease in time, as is found in some SPH simulations. During the later stages of eccentricity evolution, the observed decrease in the precession rate may be due to secular disk contraction. 3. We investigate the effects of the phi4 tidal field at the 2:1 resonance as a test of the mode-coupling model of eccentric instability. We demonstrate with simulations that a three-armed wave is launched at resonance, whose properties are in agreement with the mode-coupling model.