A linear distribution of orbits in compact planetary systems?

TL;DR

This paper identifies a linear pattern in the semi-major axes of super-Earth planets in multiple exoplanetary systems, suggesting a common formation mechanism involving resonances and migration.

Contribution

It reveals a universal linear distribution of planetary orbits in compact systems and links it to resonance chains formed during planet migration.

Findings

At least half of the studied systems follow a linear orbital spacing law.

The linear distribution matches observed semi-major axes with a few percent deviation.

Resonance chains from planet-disk interactions likely cause the linear orbital arrangement.

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 \sim 0.5 au. The semi-major axis a_n of an n-th planet in each system of this sample obeys a(n) = a_1 + (n-1) \Delta a, where a_1 is the semi-major 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 semi-major axes of only a few percent. At least half of systems in the sample fulfill the linear law with a similar accuracy. We explain the linear distribution of semi-major axes as a natural implication of multiple chains of mean motion resonances between subsequent planets, which emerge due to planet--disk interactions and convergent migration at early stages of their evolution.