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Co-orbital Oligarchy

We present a systematic examination of the changes in semi-major axis caused by the mutual interactions of a group of massive bodies orbiting a central star in the presence of eccentricity dissipation. For parameters relevant to the oligarchic stage of planet formation, dynamical friction keeps the typical eccentricities small and prevents orbit crossing. Interactions at impact parameters greater than several Hill radii cause the protoplanets to repel each other; if the impact parameter is instead much less than the Hill radius, the protoplanets shift slightly in semi-major axis but remain otherwise unperturbed. If the orbits of two or more protoplanets are separated by less than a Hill radius, they are each pushed towards an equilibrium spacing between their neighbors and can exist as a stable co-orbital system. In the shear-dominated oligarchic phase of planet formation we show that the feeding zones contain several oligarchs instead of only one. Growth of the protoplanets in the oligarchic phase drives the disk to an equilibrium configuration that depends on the mass ratio of protoplanets to planetesimals, $Σ/σ$. Early in the oligarchic phase, when $Σ/σ$ is low, the spacing betw