The effect of an isothermal atmosphere on the propagation of three-dimensional waves in a thermally stratified accretion disk

We extend our analysis of the three-dimensional response of a vertically po lytropic disk to tidal forcing at Lindblad resonances by including the effe cts of a disk atmosphere. The atmosphere is modeled as an isothermal layer that joins smoothly on to an underlying polytropic layer. The launched wave progressively enters the atmosphere as it propagates away from the resonan ce. The wave never propagates vertically, however, and the wave energy rise s to a (finite) characteristic height in the atmosphere. The increase of wa ve amplitude associated with this process of wave channeling is reduced by the effect of the atmosphere. For waves of large azimuthal mode number m ge nerated by giant planets embedded in a disk, the increase in wave amplitude is still substantial enough to be likely to dissipate the wave energy by s hocks for even modest optical depths (tau greater than or similar to 10) ov er a radial distance of a few times the disk thickness. For low-m waves gen erated in circumstellar disks in binary stars, the effects of wave channeli ng are less important and the level of wave nonlinearity increases by less than a factor of 10 in going from the disk edge to the disk center. For cir cumbinary disks, the effects of wave channeling remain important, even for modest values of optical depth.