Energy optimization in extrasolar planetary systems: the transition from peas-in-a-pod to runaway growth

Motivated by the trends found in the observed sample of extrasolar planets, this paper determines tidal equilibrium states for forming planetary systems - subject to conservation of angular momentum, constant total mass, and fixed orbital spacing. In the low mass limit, valid for super-Earth-class planets with masses of order m(p) similar to 10 M-circle plus, previous work showed that energy optimization leads to nearly equal mass planets, with circular orbits confined to a plane. The present treatment generalizes previous results by including the self-gravity of the planetary bodies. For systems with a sufficiently large total mass m(T) in planets, the optimized energy state switches over from the case of nearly equal mass planets to a configuration where one planet contains most of the material. This transition occurs for a critical mass threshold of approximately m(T) greater than or similar to m(C) similar to 40 M-circle plus (where the value depends on the semimajor axes of the planetary orbits, the stellar mass, and other system properties). These considerations of energy optimization apply over a wide range of mass scales, from binary stars to planetary systems to the collection of moons orbiting the giant planets in our Solar system.