Asymmetric Orbital Distribution near Mean Motion Resonance: Application to Planets Observed by Kepler and Radial Velocities

TL;DR

This study investigates the asymmetric distribution of orbital period ratios near mean motion resonances in Kepler and radial velocity planet systems, revealing the roles of dissipation and migration in shaping these features.

Contribution

It provides an analytical and numerical analysis of orbital evolutions near MMRs, highlighting the importance of dissipation and migration in creating observed asymmetries.

Findings

Kepler planets' asymmetry near 3:2 MMR can be partly reproduced without dissipation.

Massive RV planets show pileup wide of 2:1 MMR consistent with migration scenarios.

Dissipation effects are more significant for 2:1 MMR than for 3:2 MMR.

Abstract

Many multiple-planet systems have been found by the Kepler transit survey and various radial velocity (RV) surveys. Kepler planets show an asymmetric feature, namely, there are small but significant deficits/excesses of planet pairs with orbital period spacing slightly narrow/wide of the exact resonance, particularly near the first order mean motion resonance (MMR), such as 2:1 and 3:2 MMR. Similarly, if not exactly the same, an asymmetric feature (pileup wide of 2:1 MMR) is also seen in RV planets, but only for massive ones. We analytically and numerically study planets' orbital evolutions near and in the MMR. We find that their orbital period ratios could be asymmetrically distributed around the MMR center regardless of dissipation. In the case of no dissipation, Kepler planets' asymmetric orbital distribution could be partly reproduced for 3:2 MMR but not for 2:1 MMR, implying that dissipation might be more important to the latter. The pileup of massive RV planets just wide of 2:1 MMR is found to be consistent with the scenario that planets formed separately then migrated toward the MMR. The location of the pileup infers a K value of 1-100 on the order of magnitude for massive planets, where K is the damping rate ratio between orbital eccentricity and semimajor axis during planet migration.