Planetesimal disk evolution driven by planetesimal-planetesimal gravitational scattering

We investigate the process of inhomogeneous planetesimal disk evolution caused by planetesimal-planetesimal gravitational scattering. We develop a rather general approach based on kinetic theory that self-consistently describes the evolution in time and space of both the disk's surface density and its kinematic properties dispersions of eccentricity and inclination. The gravitational scattering of planetesimals is assumed to be in the dispersion-dominated regime, which considerably simplifies the analytical treatment. The resultant equations are of the advection-diffusion type. Distance-dependent scattering coefficients entering these equations are calculated analytically under the assumption of two-body scattering to leading order in the Coulomb logarithm. They are essentially nonlocal in nature. Our approach allows one to explore the dynamics of nonuniform planetesimal disks with arbitrary mass and random-velocity distributions. It can also naturally include other physical mechanisms that are important for the evolution of such disks gas drag, migration, and so on.