Evolution of random velocities of planetesimals in the course of accretion

Abstract

The role of accretion in the random velocity evolution of planetesimals is examined. By combining the equation for velocity change caused by accretion and the coagulation equation for the mass distribution function, we derive an equation for random velocity evolution in the course of accretion, which is described in terms of eccentricity and inclination of planetesimal orbits in the framework of the Hill's approximations. We find that dissipation of random velocity due to accretion has the tendency to lead to equipartition of kinetic energy of random motion between planetesimals with different masses. We also compare the three effects on velocity evolution, that is, gas drag of the solar nebula, gravitational scattering, and accretion. At the Earth's orbit, all these three effects seem to contribute to velocity evolution at early stages of planetesimal accumulation. However, when the typical size of planetesimals becomes larger than 10 20 g, the effect of accretion on velocity evolution becomes less effective, and it is considered that planetesimals have certain equilibrium velocities determined by the balance between gravitational scattering and gas drag. At this, or at a slightly later stage, the onset of runaway growth of several protoplanets seems more probable.