Orbital Evolution of Bodies Crossing Disks Due to Density and Bending Wave Excitation

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Abstract
Theories of density and bending wave excitation in geometrically thin gaseous or particulate astrophysical disks by disk-crossing, pointlike perturbers on slightly elliptical and inclined orbits are presented. The perturber is assumed to be too small to truncate or otherwise strongly modify the disk. The theories are linear and rely on Fourier techniques for the representation of both the wave dynamics and the external potential. The problematic WKB approximation (assuming waves to be tightly wrapped everywhere) is relaxed, along with the assumption of a smooth forcing potential. The theories enable explicit calculation of the so-called torque cutoffs at high azimuthal number m of the perturbing potential. The dominant ("kinetic") cutoff at m ≍ 0.5/(I2 + e2)1/2 occurs when the inclination I and/or eccentricity e are larger than the ratio of disk thickness to radius and operates independently of the disk properties. It is caused by weakening of the driving potential above the indicated m. Angular momentum and energy flow between the perturber and the disk in such a proportion that the relative epicyclic motion, measured by (I2 + e2), suffers decay. This result stands in sharp contrast to the evolution of satellites large enough to truncate the disk but agrees qualitatively (and quantitatively to within a factor of order unity) with the effects of the hydrodynamical Bondi-Hoyle drag acting during the passages through a gaseous disk. In most cases, when e ̃ I, the resonant interaction is roughly 3 times weaker than the hydrodynamical drag. In case of e ≫ I, the two effects provide comparable inclination damping. The simple results of our theory are relevant, for example, to star trapping in the disks of active galactic nuclei. Suggestions on the interaction of stars with protostellar disks are briefly discussed.

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