Kepler planets around resonances: in-situ planet formation

The orbital architecture of multi-planet systems discovered by Kepler encode information about their formation history and evolution. One intriguing observation comes from the period ratio distribution of neighboring planets (see figure below from Fabrycky et al. 2014). Most remarkably, this distribution is overall smooth, while it presents an intriguing features around the 2:1 and 3:2 orbital resonances: planets avoid being slightly inside the resonance, while they prefer being slightly wide of it.

These observations are interesting because in the standard theory of planet migration by disk-driven torques, planets are generally expected to be locked in orbital resonances with the 2:1 and 3:2 being the most prominent ones. Thus, resonances provide useful information about the planetary system evolution when the gas disk was still present, i.e. when the planetary system was at least ~1000 times younger than currently observed!.

In Petrovich, Malhotra & Tremaine 2013 we have studied the orbital dynamics of a very simple model of planet formation in which planets grow without orbital migration nor any dissipative process. Quite remarkably, this model develops an assymetric redistribution of orbital periods around first-order mean motion resonances that resembles a 'P-Cygni' profile (see figures) with a gap around the nominal resonance and a pile-up wide of the resonance, similar to that observed in the Kepler sample. This naturally shows that both dissipation or migration are not needed to account for the resonant features seen in Kepler (at least qualitatively), supporting an in-situ formation scenario of planets.