Stirring and dynamical friction rates of planetesimals in the solar gravitational field

Abstract The random velocity (eccentricity and inclination) change of planetesimals due to mutual gravitational scattering is investigated, taking into account the solar gravitational field. Viscous stirring and dynamical friction rates are presented with three-body formalism (using eccentricity and inclination), and calculated through a large number ∼10 7−8 ) of three-body orbital integrations. The results are summarized as follows: (1) The role of distant encounters is not important. (2) In the low energy cases where Keplerian shear dominates, eccentricity grows much more rapidly than inclination, and dynamical friction is not effective. The viscous stirring time scale for eccentricity is much greater than the two-body relaxation time. (3) In the high energy cases where random motion dominates, a 2:1 ratio of eccentricity to inclination is spontaneously attained. Both stirring and dynamical friction time scales are almost given by the two-body relaxation time, and dynamical friction is effective for the larger planetesimals, which should lead to “runaway growth” of protoplanets.

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