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

Abstract

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 that the depletion and structures of the gas disk play crucial roles in driving planet pairs out of the exact location of MMRs. Under such a scenario, planet pairs are trapped into exact MMRs during orbital migration first and keep migrating at the same pace. The eccentricities can be excited. Due to the existence of a gas disk, eccentricities can be damped, leading to a change in orbital period, which will make planet pairs depart from the exact location of MMRs. With depletion timescales larger than 1 Myr, near-MMR configurations are formed easily. Planet pairs have higher possibilities of escaping from MMRs with a higher disk aspect ratio. Additionally, with a weaker corotation torque, planet pairs can depart farther from the exact location of MMRs. The final location of the innermost planets in the systems are directly related to the transition radius from the optically thick region to the outer optically thin disk. While the transition radius is smaller than 0.2 au at the late stage of the star evolution process, the period of the inner planets can reach around 10 days. Our formation scenario is a possible mechanism for explaining the formation of near-MMR configurations with the innermost planet farther than 0.1 au.