Semi-analytic Formulas for the Stirring Rates of Planetesimals

Astronomy and Astrophysics – Astronomy

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Scientific paper

We obtain the stirring and dynamical friction rates of planetesimals with the Rayleigh distribution of eccentricities and inclinations, using three-body orbital integrations. We find that the stirring rates obtained by orbital integrations for a given pair of eccentricity and inclination agree well with the analytic results of Tanaka and Ida (1996, Icarus 120, 371) when both eccentricity and inclination are large enough. As for the stirring rates averaged over the Rayleigh distribution, fairy good agreement with the analytic results of Stewart and Ida (2000, Icarus 143, 28) is found for high velocity cases, but significant deviation is also found for intermediate and low velocity cases. We derive semi-analytic formulas for the stirring and dynamical friction rates based on our numerical results. We calculate evolution of root mean square eccentricities and inclinations using our new formulas to compare with N-body simulations, and find excellent agreement for both one- and two-component systems.

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