A Solution to the Peas-in-a-Pod Problem for Extrasolar Planetary Systems

Motivated by the trends found in the observed sample of extrasolar planets, this talk discusses 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 superearth-class planets, we show that energy optimization leads to nearly equal mass planets, with circular orbits confined to a plane. We then generalize the treatment to include the self-gravity of the planetary bodies. For systems with sufficiently large total mass 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 40 earth masses (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.