Stirring of a planetesimal swarm: The role of distant encounters

Planetesimals have random velocities (eccentric and inclined orbits) induced by their mutual gravitational perturbations. The viscous stirring algorithm of Stewart and Wetherill (1988, Icarus 74, 542-553) includes only scattering by close encounters of bodies in crossing orbits. A completetreatment should also include the effect of more distant bodies in noncrossing orbits. This paper presents expressions for the stirring rate due to distant encounters, derived with three-body formalism. The stirring rate has the same mass dependence as that for close encounters; the relative importance of the two mechanisms depends on the Safronov number θ. For small θ, close encounters dominate the stirring rate, but distant encounters may dominate for θ ≳ 10 ². Perturbations by a planetary embryo in scenarios involving "runaway growth" may affect the evolution of planetesimals in noncrossing orbits.