Constraints on the formation history and composition of Kepler planets from their distribution of orbital period ratios

Abstract

Context. The Kepler high-precision planetary sample has revealed a ‘radius valley’ separating compact super-Earths from sub-Neptunes with lower densities. Super-Earths are generally assumed to be rocky planets that were probably born in situ, while the composition and formation of sub-Neptunes remains debated. Numerous statistical studies have explored planetary and stellar properties and their correlations to provide observational clues. However, no conclusive result on the origin of the radius valley or the composition of sub-Neptunes has been derived to date. Aims. To provide more constraints, our aim is to investigate the distributions of the orbital spacing of sub-Neptunes and super-Earth planets in Kepler systems and compare their distributions with theoretical predictions of planet pairs of different formation pathways and compositions in synthetic planetary systems. Methods. Based on the Kepler planetary sample, we derived the distributions of period ratios of sub-Neptune and super-Earth planet pairs. Using synthetic planetary systems generated by the Generation III Bern Model, we also obtained theoretical predictions of period ratio distributions of planet pairs of different compositions and origins. Results. We find that Kepler sub-Neptune pairs show a significant preference to be near first-order mean motion resonances by a factor of 1.7−0.3+0.3. This is smaller than the model predictions for ‘water-rich’ pairs but larger than that of ‘water-poor’ pairs by confidence levels of ~2σ. Kepler super-Earth pairs show no significant preference for mean motion resonances from a random distribution. The derived normalised fraction of near first-order resonances of actual Kepler super-Earth pairs is consistent with that of synthetic water-poor planet pairs but significantly (≳3σ) smaller than that of synthetic water-rich planet pairs. Conclusions. The orbital migration has been more important for sub-Neptunes than for super-Earths, suggesting a partial ex situ formation of the former and an origin of the radius valley caused in part by distinct formation pathways. However, the model comparisons also show that sub-Neptunes in Kepler multiple systems are not likely (~2σ) to all be water-rich planets born ex situ but a mixture of the two (in situ and ex situ) pathways. Whereas, Kepler super-Earth planets are predominantly composed of water-poor planets that were born inside the ice line, likely through a series of giant impacts without large-scale migration.