Tidally-Induced Radius Inflation of Sub-Neptunes

Recent work suggests that many short-period super-Earth and sub-Neptune planets may have significant spin axis tilts ("obliquities"). When planets are locked in high-obliquity states, the tidal dissipation rate may increase by several orders of magnitude. This intensified heat deposition within the planets' interiors should generate significant structural consequences, including atmospheric inflation leading to larger transit radii. Using up-to-date radius estimates from Gaia Data Release 2, we show evidence for $\sim50\%$ larger average radii of planets wide of first-order mean-motion resonances, a population of planets with a theorized frequent occurrence of high obliquities. We investigate whether this radius trend could be a signature of obliquity tides. Using an adaptation of the Modules for Experiments in Stellar Astrophysics (MESA) stellar evolution toolkit, we model the atmospheric evolution of sub-Neptune-mass planets in response to additional internal heat from obliquity tides. The degree of radius inflation predicted by the models is $\sim10\%-100\%$ for tidal luminosities $\gtrsim 10^{-5}$ of the incident stellar power; this degree of inflation is broadly consistent with the observations and can approximately be described by power law relationships. We present a few case studies of very low density "super-puff" planets -- Kepler-79 d, Kepler-31 c, and Kepler-27 b -- and show that they are strong candidates for potentially having undergone tidally-induced radius inflation. We also discuss how the discrepancy between the two populations of planets with masses derived from radial velocities and transit timing variations is connected to the radius distribution features we have identified. Altogether, the calculations in this work confirm that tidal dissipation has non-negligible consequences for the structural properties of short-period sub-Neptunes.