Disk-Satellite Interaction via Density Waves and the Eccentricity Evolution of Bodies Embedded in Disks

Abstract

Using a generalized torque formula for Lindblad resonances in non-self-gravitating gaseous disks we study the interaction of disks with small, embedded bodies (not able to open a gap). For satellites on circular orbits, the generalized torque formula reproduces exactly the torque cutoff occurring at high azimuthal number m of the potential harmonics, originally found seminumerically by Goldreich & Tremaine (1980) in the shearing coordinates representation. The cutoff is attributable to the shift in the effective Lindblad resonance position with respect to the nominal resonant radius given by the usual period commensurabilty requirement. We apply the theory to the problem of orbital eccentricity evolution of embedded satellites. We relax some of the assumptions implicit in previous calculations related to this problem, most importantly that of a spatially smooth perturbing potential. We treat the co-orbital and the external Lindblad resonances within a unified formalism. We calculate the total rate of eccentricity damping due to co-orbital resonances and the excitation due to external resonances, the former exceeding the latter by a factor roughly equal to 3, independent of the method of averaging over the vertical disk structure. In application to a solar nebula with embedded planetesimals, the timescales of eccentricity damping for a wide range of planetesimal masses are much shorter than those corresponding to either gas drag, planetesimal growth, or nebular lifetime, and thus relevant to the scenarios of planetary system formation. In application to large (radius > 10 m) particles in Saturn's rings we estimate that the eccentricity is damped on the orbital timescale