Period ratios in multi-planetary systems discovered by Kepler are consistent with planet migration

The Kepler planet candidates are an interesting testbed for planet formation scenarios. We present results from N-body simulations of multi-planetary systems that resemble those observed by Kepler. We add both smooth (Type I/II) and stochastic migration forces. The observed period ratio distribution is inconsistent with either of those two scenarios on its own. However, applying both stochastic and smooth migration forces to the planets simultaneously results in a period ratio distribution that is similar to the observed one. This is a natural scenario if planets form in a turbulent proto-planetary disk where these forces are always present. We show how the observed period ratio and eccentricity distribution can constrain the relative strength of these forces, a parameter which has been notoriously hard to predict for decades. We make the source code of our simulations and the initial conditions freely available to enable the community to expand this study and include effect other than planetary migration.