Departure from the Exact Location of Mean Motion Resonances Induced by the Gas Disk in the Systems Observed by Kepler

TL;DR

This paper investigates how gas disk depletion and structure influence the departure of planet pairs from exact mean motion resonances, explaining observed period ratio distributions in Kepler systems.

Contribution

It introduces a formation scenario where gas disk effects cause planet pairs to deviate from MMRs, aligning with observed near-resonance configurations.

Findings

Gas disk depletion and structure drive planets away from exact MMRs.

Higher disk aspect ratio increases likelihood of departure from MMRs.

Transition radius influences the innermost planet's orbital period.

Abstract

The statistical results of transiting planets show that there are two peaks around 1.5 and 2.0 in the distribution of orbital period ratios. A large number of planet pairs are found near the exact location of mean motion resonances (MMRs). In this work, we find out that the depletion and structures of gas disk play crucial roles in driving planet pairs out of exact location of MMRs. Under such scenario, planet pairs are trapped into exact MMRs during orbital migration firstly and keep migrating in a same pace. The eccentricities can be excited. Due to the existence of gas disk, eccentricities can be damped leading to the change of orbital period. It will make planet pairs depart from the exact location of MMRs. With depletion timescales larger than 1 Myr, near MMRs configurations are formed easily. Planet pairs have higher possibilities to escape from MMRs with higher disk aspect ratio. Additionally, with weaker corotation torque, planet pairs can depart farther from exact location of MMRs. The final location of the innermost planets in systems are directly related to the transition radius from optically thick region to inner optically thin disk. While the transition radius is smaller than 0.2 AU at the late stage of star evolution process, the innermost planets can reach around 10 days. Our formation scenario is a possible mechanism to explain the formation of near MMRs configuration with the innermost planet farther than 0.1 AU.