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 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 nonresonant 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 nonresonant 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) a contribution from initially resonant planet pairs is needed to explain the observed levels of excess wide of 3:2; and (4) a mixture model where about 25% (1%) of 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.