A linear distribution of orbits in compact planetary systems?

Abstract

Abstract We report a linear ordering of orbits in a sample of multiple extrasolar planetary systems with super-Earth planets. We selected 20 cases, mostly discovered by the Kepler mission, hosting at least four planets within ∼0.5 au. The semimajor axis an of an nth planet in each system of this sample obeys a(n) = a1 + (n − 1) Δa, where a1 is the semimajor axis of the innermost orbit and Δa is a spacing between subsequent planets, which are specific for a particular system. For instance, the Kepler-33 system hosting five super-Earth planets exhibits the relative deviations between the observed and linearly predicted semimajor axes of only a few per cent. At least half of systems in the sample fulfil the linear law with a similar accuracy. We explain the linear distribution of semimajor axes as a natural implication of multiple chains of mean-motion resonances between subsequent planets, which emerge due to planet–disc interactions and convergent migration at early stages of their evolution.