A Method to Identify the Boundary Between Rocky and Gaseous Exoplanets from Tidal Theory and Transit Durations

Abstract

The determination of an exoplanet as rocky is critical for the assessment of planetary habitability. Observationally, the number of small-radius, transiting planets with accompanying mass measurements is insufficient for a robust determination of the transitional mass or radius. Theoretically, models predict that rocky planets can grow large enough to become gas giants when they reach ~10 Earth-masses, but the transitional mass remains unknown. Here I show how transit data, interpreted in the context of tidal theory, can reveal the critical radius that separates rocky and gaseous exoplanets. Standard tidal models predict that rocky exoplanets' orbits are tidally circularized much more rapidly than gaseous bodies', suggesting the former will tend to be found on circular orbits at larger semi-major axes than the latter. Well-sampled transits can provide a minimum eccentricity of the orbit, allowing a measurement of this differential circularization. I show that this effect should be present in the data from the Kepler spacecraft, but is not apparent. Instead, it appears that there is no evidence of tidal circularization at any planetary radius, probably because the publicly-available data, particularly the impact parameters, are not accurate enough. I also review the bias in the transit duration toward values that are smaller than that of planets on circular orbits, stressing that the azimuthal velocity of the planet determines the transit duration. The ensemble of Kepler planet candidates may be able to determine the critical radius between rocky and gaseous exoplanets, tidal dissipation as a function of planetary radius, and discriminate between tidal models.