On some aspects of the stirring rate of planetesimal velocities by a protoplanet

Abstract

We discuss some aspects of the evolution of the relative velocities of a swarm of planetesimals stirred by a protoplanet. We show that the prescriptions most commonly used in semi-analytical `oligarchic growth' models overestimate the relative velocities of planetesimals by a non-negligible factor. We discuss the probable origin of this discrepancy, proposing a correction factor that provides good agreement between these prescriptions and the results of numerical experiments. The proposed correction factor can be easily implemented in semi-analytical accretion models.