Vertically driven resonances in accretion disks

The three-dimensional response of an accretion disk in a close binary system to tidal forcing is investigated. It is noted that both horizontal and vertical motions are generated in the disk and that resonances occur at radii where the tidal forcing frequency matches a natural frequency in the disk. It is found that for every value of the azimuthal wavenumber m, resonances involving vertical motions lie closer to the disk center than the corresponding horizontal resonances. For a wide range of mass ratios of the binary, the m = 2 vertical resonance is found to lie inside the maximum disk radius suggested by Paczynski (1971) where the simple periodic orbits begin to intersect. This resonance in most cases lies outside the inviscid disk radius determined by a no-slip condition between the stream and disk edge. It is noted that if this resonance lies inside the disk, horizontally propagating waves are generated which travel toward the disk center. The process of wave generation transfers disk angular momentum to the orbital angular momentum of the stars and therefore has important consequences on the dynamics of disk accretion.