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 hydrogenhelium envelopes. We provide model radii for planets 1-20 M ⊕ , with envelope fractions from 0.01-20%, levels of irradiation 0.1-1000× 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 composition, radii show little dependence on mass for planets with more than ∼1% of their mass in their envelope. Consequently, planetary radius is to first order a proxy for planetary composition 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.

We use models of coupled thermal evolution and photo-evaporative mass loss to understand the formation and evolution of the Kepler-36 system. We show that the large contrast in mean planetary density observed by Carter et al. (2012) can be explained as a natural consequence of photo-evaporation from planets that formed with similar initial compositions. However, rather than being due to differences in XUV irradiation between the planets, we find that this contrast is due to the difference in the masses of the planets' rock/iron cores and the impact that this has on mass loss evolution. We explore in detail how our coupled models depend on irradiation, mass, age, composition, and the efficiency of mass loss. Based on fits to large numbers of coupled evolution and mass loss runs, we provide analytic fits to understand threshold XUV fluxes for significant atmospheric loss, as a function of core mass and mass loss efficiency. Finally we discuss these results in the context of recent studies of the radius distribution of Kepler candidates. Using our parameter study, we make testable predictions for the frequency of sub-Neptune sized planets. We show that 1.8-4.0 R ⊕ planets should become significantly less common on orbits within 10 days and discuss the possibility of a narrow "occurrence valley" in the radius-flux distribution. Moreover, we describe how photo-evaporation provides a natural explanation for the recent observations of Ciardi et al. (2013) that inner planets are preferentially smaller within the systems.

We use models of thermal evolution and extreme ultraviolet (XUV) driven mass loss to explore the composition and history of low-mass, low-density transiting planets. We investigate the Kepler-11 system in detail and provide estimates of both the current and past planetary compositions. We find that an H/He envelope on Kepler-11b is highly vulnerable to mass loss. By comparing to formation models, we show that in situ formation of the system is extremely difficult. Instead we propose that it is a water-rich system of sub-Neptunes that migrated from beyond the snow line. For the broader population of observed planets, we show that there is a threshold in bulk planet density and incident flux above which no low-mass transiting planets have been observed. We suggest that this threshold is due to the instability of H/He envelopes to XUV-driven mass loss. Importantly, we find that this mass-loss threshold is well reproduced by our thermal evolution/contraction models that incorporate a standard mass-loss prescription. Treating the planets' contraction history is essential because the planets have significantly larger radii during the early era of high XUV fluxes. Over time low-mass planets with H/He envelopes can be transformed into water-dominated worlds with steam envelopes or rocky super-Earths. Finally, we use this threshold to provide likely minimum masses and radial-velocity amplitudes for the general population of Kepler candidates. Likewise, we use this threshold to provide constraints on the maximum radii of low-mass planets found by radial-velocity surveys.

Exoplanet discoveries of recent years have provided a great deal of new data for studying the bulk compositions of giant planets. Here we identify 47 transiting giant planets (20M ⊕ < M < 20M J ) whose stellar insolation is low enough (F * < 2 × 10 8 erg s −1 cm −2 , or roughly T eff < 1000) that they are not affected by the hot Jupiter radius inflation mechanism(s). We compute a set of new thermal and structural evolution models and use these models in comparison with properties of the 47 transiting planets (mass, radius, age) to determine their heavy element masses. A clear correlation emerges between the planetary heavy element mass M z and the total planet mass, approximately of the form M z ∝ √ M . This finding is consistent with the core accretion model of planet formation. We also study how stellar metallicity [Fe/H] affects planetary metal-enrichment and find a weaker correlation than has been previously reported from studies with smaller sample sizes. We confirm a strong relationship between the planetary metal-enrichment relative to the parent star Z planet /Z star and the planetary mass, but see no relation in Z planet /Z star with planet orbital properties or stellar mass. The large heavy element masses of many planets (> 50 M ⊕ ) suggest significant amounts of heavy elements in H/He envelopes, rather than cores, such that metal-enriched giant planet atmospheres should be the rule. We also discuss a model of coreaccretion planet formation in a one-dimensional disk and show that it agrees well with our derived relation between mass and Z planet /Z star .