The 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 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 generates pseudo-adiabatic regions within radiative zones, which pushes the radiative-convective boundaries inward. This decreases the cooling luminosity and enhances the Kelvin–Helmholtz (KH) timescale. For a given lifetime of protoplanetary disks (PPDs), there exists a critical threshold for the turbulent diffusivity, ν critical . If ν turb  >  ν critical , the KH timescale is longer than the disk lifetime and the planet becomes a super-Earth, rather than a gas giant. We find that even a small value of turbulent diffusion has influential effects on the evolution of super-Earths. The ν critical increases with the core mass. We further ascertain that, within the minimum-mass extrasolar nebula, ν critical increases with the semimajor axis. This may explain the feature that super-Earths are common in inner PPD regions, while gas giants are common in outer PPD regions. The predicted envelope mass fraction 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.