A linear distribution of orbits in compact planetary systems?

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 similar to 0.5 au. The semimajor axis an of an nth planet in each system of this sample obeys a(n) = a(1) + (n - 1) Delta a, where a(1) is the semimajor axis of the innermost orbit and Delta a 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.