Effects of Planetesimal Scattering: Explaining the Observed Offsets from Period Ratios 3:2 and 2:1

Abstract

The observed deficit and excess of adjacent planet pairs with period ratios narrow and wide of 3:2 and 2:1, the nominal values for the corresponding mean motion resonances (MMRs), have intrigued many. Previously, using a suite of simulations, Chatterjee & Ford (2015) showed that the excess above the 2:1 MMR can be naturally explained if planet pairs, initially trapped in the 2:1 MMR, dynamically interact with nearby planetesimals in a disk. We build on this work by: a) updating the census of discovered planet pairs, b) extending the study to initially non-resonant as well as resonant planet pairs, c) using initial planet and orbital properties directly guided by those observed, and d) extending the initial period ratios to include both 2:1 and 3:2. We find that 1) interactions with planetesimals typically increase the period ratios of both initially resonant and non-resonant planet pairs; 2) starting from an initially flat period ratio distribution for systems across 3:2 and 2:1, these interactions can naturally create the deficits observed narrow of these period ratios; 3) contribution from initially resonant planet pairs is needed to explain the observed levels of excess wide of 3:2; 4) a mixture model where about 25% (1%) planet pairs were initially trapped into 3:2 (2:1) MMRs is favored to explain both the observed deficit and excess of systems across these period ratios, however, up to a few percent of planet pairs are expected to remain in MMR today.