Formation of close in Super-Earths \& Mini-Neptunes: Required Disk Masses \& Their Implications

Abstract

Recent observations by the {\it Kepler} space telescope have led to the discovery of more than 4000 exoplanet candidates consisting of many systems with Earth- to Neptune-sized objects that reside well inside the orbit of Mercury, around their respective host stars. How and where these close-in planets formed is one of the major unanswered questions in planet formation. Here we calculate the required disk masses for {\it in situ} formation of the {\it Kepler} planets. We find that, if close-in planets formed as {\it isolation masses}, then standard gas-to-dust ratios yield corresponding gas disks that are gravitationally unstable for a significant fraction of systems, ruling out such a scenario. We show that the maximum width of a planet's accretion region in the absence of any migration is $2 v_{esc}/\Omega$, where $v_{esc}$ is the escape velocity of the planet and $\Omega$ the Keplerian frequency and use it to calculate the required disk masses for {\it in situ} formation with giant impacts. Even with giant impacts, formation without migration requires disk surface densities in solids at semi-major axes less than 0.1~AU of $10^3-10^5 \rm{~g~cm^{-2}}$ implying typical enhancements above the minimum-mass solar nebular (MMSN) by at least a factor of 20. Corresponding gas disks are below, but not far from, the gravitational stability limit. In contrast, formation beyond a few AU is consistent with MMSN disk masses. This suggests that migration of either solids or fully assembled planets is likely to have played a major role in the formation of close-in super-Earths and mini-Neptunes.