Formation of Super-Earths by Tidally-Forced Turbulence

Abstract

The Kepler observations indicate that many exoplanets are super-Earths, which brings about a puzzle for the core-accretion scenario. Since observed super-Earths are in the range of critical mass, they would accrete gas efficiently and become gas giants. Theoretically, super-Earths are predicted to be rare in the core-accretion framework. To resolve this contradiction, we propose that the tidally-forced turbulent diffusion may affect the heat transport inside the planet. Thermal feedback induced by turbulent diffusion is investigated. We find that the tidally-forced turbulence would generate pseudo-adiabatic regions within radiative zones, which pushes the radiative-convective boundaries (RCBs) inwards. This would decrease the cooling luminosity and enhance the Kelvin-Helmholtz (KH) timescale. For a given lifetime of protoplanetary disks (PPDs), there exists a critical threshold for the turbulent diffusivity, $ν_{\rm critical}$. If $ν_{\rm turb}>ν_{\rm critical} $, the KH timescale is longer than the disk lifetime and the planet would become a super-Earth rather than a gas giant. We find that even a small value of turbulent diffusion has influential effects on evolutions of super-Earths. $ν_{\rm critical}$ increases with the core mass. We further ascertain that, within the minimum mass extrasolar nebula (MMEN), $ν_{\rm critical}$ increases with the semi-major axis. This may explain the feature that super-Earths are common in inner PPD regions, while gas giants are common in the outer PPD regions. The predicted envelope mass fraction (EMF) is not fully consistent with observations. We discuss physical processes, such as late core assembly and mass loss mechanisms, that may be operating during super-Earth formation.