MASS-SPECTRUM AND VELOCITY DISPERSIONS DURING PLANETESIMAL ACCUMULATION .1. ACCRETION

The accumulation of the planetesimals has been investigated taking account of the simultaneous evolution of mass distribution and velocity dispersions. Under the assumption that collision frequencies are much smaller than the orbital frequency ω the velocity dispersions are determined from a previously developed formalism (Hornung et al. 1985, Barge and Pellat 1990) which works as long as the velocity dispersions remain approximately greater than the "Hill velocity" ωRH; this formalism is extended to the lower velocities through a model based on the numerical computations of Ida (1990). On the other hand the evolution of the mass distribution is derived from the simplified Oort-Van de Hulst formulation of the coagulation equation, which is sufficient to investigate the main trends of the accumulation of the planetesimals. It It is found that: • -A runaway growth of the largest bodies occurs with the formation of massive embryos (the mass can grow by a factor of one million on a time scale of the order of 0.1 million years); this is in contrast with the results of the Moscow "school" (Safronov and others) which assumes that mass and velocity are decoupled. • -Velocity dispersions increase with growing planetesimals; this is in contrast with the numerical simulation of Greenberg et al. (1978) and with the more recent work of Wetherill and Stewart (1989) whose computations are outside the range of validity of the formalism. These conclusions result from the yet unsuspected importance of viscous stirring of gravitational encounters which plays the major role in the collisional evolution of planetesimals by the transfer of significant amounts of orbital energy into random motions. The increase of the velocity dispersions reveals also that the fragmentation could play an important role in the final evolution of the planetesimals toward the planetary stage. © 1991.