ACCRETION RATES OF PROTOPLANETS .2. GAUSSIAN DISTRIBUTIONS OF PLANETESIMAL VELOCITIES

We calculate the growth rate of a protoplanet embedded in a uniform surface density disk of planetesimals having a triaxial Gaussian velocity dispersion. The longitudes of the apses and nodes of the planetesimals are uniformly distributed, and the protoplanet is on a circular orbit. The accretion rate in the two-body approximation is enhanced by a factor of ∼3, compared to the case where all planetesimals have eccentricity and inclination equal to the root mean square (r.m.s.) values of those variables in a disk with locally Gaussian velocity dispersion. Numerical three-body integrations show comparable enhancements, except when the r.m.s. initial planetesimal eccentricities are very small. This enhancement in the accretion rate should be incorporated by all models, analytical or numerical, which assume a single random velocity for all planetesimals, in lieu of a Gaussian distribution. © 1992.