Dynamical Evolution of Planetesimals in Protoplanetary Disks

The current picture of terrestrial planet formation relies heavily on ourunderstanding of the dynamical evolution of planetesimals -- asteroid-likebodies thought to be planetary building blocks. In this study we investigatethe growth of eccentricities and inclinations of planetesimals in spatiallyhomogeneous protoplanetary disks using methods of kinetic theory. We exploredisks with a realistic mass spectrum of planetesimals evolving in time, similarto that obtained in self-consistent simulations of planetesimal coagulation. Wecalculate the behavior of planetesimal random velocities as a function of theplanetesimal mass spectrum both analytically and numerically; results obtainedby the two approaches agree quite well. Scaling of random velocity with masscan always be represented as a combination of power laws corresponding todifferent velocity regimes (shear- or dispersion-dominated) of planetesimalgravitational interactions. For different mass spectra we calculateanalytically the exponents and time dependent normalizations of these powerlaws, as well as the positions of the transition regions between differentregimes. It is shown that random energy equipartition between differentplanetesimals can only be achieved in disks with very steep mass distributions(differential surface number density of planetesimals falling off steeper thanm^{-4}), or in the runaway tails. In systems with shallow mass spectra(shallower than m^{-3}) random velocities of small planetesimals turn out to beindependent of their masses. We also discuss the damping effects of inelasticcollisions between planetesimals and of gas drag, and their importance inmodifying planetesimal random velocities.Comment: 20 pages, 17 figures, 1 table, submitted to A