The Growth Rate of Tidally Excited Waves in Accretion Disks

Accretion disks in close binary systems are subject to a tidally driven parametric instability which leads to the growth of internal waves near the outer edges of such disks (Goodman 1993). These waves are important in understanding the torque exerted on a disk by tidal forces and may play a role in the structure of the disk at small radii. Here we calculate the growth rate of this instability, including the effects of vertical structure and fluid compressibility. We find growth rates which are only slightly different from Goodman's original results, except that near the vertical resonance radius the growth rate can have an extremely broad and strong peak when the disk is stably stratified in the vertical direction. Higher order modes, in the sense of increasing number of vertical nodes, have similar growth rates. Our results differ from a previous calculation along these lines by Lubow et al. (1993). The difference is mostly due to their neglect of radial gradients in the tidally distorted streamlines.