In order to study the early stages of planetary accretion from a very large number of planetesimals, numerical simulations based on the techniques of the kinetic theory of gases are generally used. In these simulations, the evolution of size distributions is calculated according to the collision rate, which depends on the mean eccentricity and inclination of planetesimals. Recently, an evolution equation for mean square eccentricity and inclination has been derived for particles with the Rayleigh distribution of eccentricities and inclinations (Ohtsuki 1999, Icarus 137, 152; Stewart and Ida 2000, Icarus 143, 28). Stewart and Ida (2000) obtained analytic formulas for the stirring and dynamical friction rates of planetesimals appearing in this equation and compared the velocity evolution with N-body simulations. They found fairly good agreement, but the following discrepancies remained unexplained: (i) Evolution in the low velocity cases disagree with N-body simulations. (ii) The dynamical friction terms in the analytic formulas have to be reduced by 30% to obtain agreement with N-body simulations. In order to clarify the reason for the above discrepancies and obtain more accurate formulas for the stirring rates, we calculated the stirring and dynamical friction rates of planetesimals with the Rayleigh distribution of eccentricities and inclinations by three-body orbital integrations using the method described in Ohtsuki (1999), who calculated these rates for ring particles. We have found excellent agreement of the velocity evolution calculated by the present results based on three-body orbital integrations with N-body simulations, for both one- and two-size component systems. The newly obtained stirring and dynamical friction rates can be used to derive revised analytic formulas for these rates, which can be used to produce more accurate numerical simulations of planetesimal accumulation.
AAS/Division of Dynamical Astronomy Meeting
- Pub Date:
- May 2000