Understanding the Mass-Radius Relation for Sub-neptunes: Radius as a Proxy for Composition

Transiting planet surveys like Kepler have provided a wealth of information on the distribution of planetary radii, particularly for the new populations of super-Earth- and sub-Neptune-sized planets. In order to aid in the physical interpretation of these radii, we compute model radii for low-mass rocky planets with hydrogen-helium envelopes. We provide model radii for planets 1-20 M _⊕, with envelope fractions 0.01%-20%, levels of irradiation 0.1-1000 times Earth's, and ages from 100 Myr to 10 Gyr. In addition we provide simple analytic fits that summarize how radius depends on each of these parameters. Most importantly, we show that at fixed H/He envelope fraction, radii show little dependence on mass for planets with more than ~1% of their mass in their envelope. Consequently, planetary radius is to a first order a proxy for planetary composition, i.e., H/He envelope fraction, for Neptune- and sub-Neptune-sized planets. We recast the observed mass-radius relationship as a mass-composition relationship and discuss it in light of traditional core accretion theory. We discuss the transition from rocky super-Earths to sub-Neptune planets with large volatile envelopes. We suggest ~1.75 R _⊕ as a physically motivated dividing line between these two populations of planets. Finally, we discuss these results in light of the observed radius occurrence distribution found by Kepler.