The Kepler Mission, combined with ground based radial velocity (RV) follow-up and dynamical analyses of transit timing variations, has revolutionized the observational constraints on sub-Neptunesize planet compositions. The results of an extensive Kepler follow-up program including multiple Doppler measurements for 22 planet-hosting stars more than doubles the population of sub-Neptunesized transiting planets that have RV mass constraints. This unprecedentedly large and homogeneous sample of planets with both mass and radius constraints opens the possibility of a statistical study of the underlying population of planet compositions. We focus on the intriguing transition between rocky exoplanets (comprised of iron and silicates) and planets with voluminous layers of volatiles (H/He and astrophysical ices). Applying a hierarchical Bayesian statistical approach to the sample of Kepler transiting sub-Neptune planets with Keck RV follow-up, we constrain the fraction of close-in planets (with orbital periods less than ∼ 50 days) that are sufficiently dense to be rocky, as a function of planet radius. We show that the majority of 1.6 R ⊕ planets are too low density to be comprised of Fe and silicates alone. At larger radii, the constraints on the fraction of rocky planets are even more stringent. These insights into the size demographics of rocky and volatile-rich planets offer empirical constraints to planet formation theories, and guide the range of planet radii to be considered in studies of the occurrence rate of "Earth-like" planets, η ⊕ .

We report the distribution of planets as a function of planet radius, orbital period, and stellar effective temperature for orbital periods less than 50 days around Solar-type (GK) stars. These results are based on the 1,235 planets (formally "planet candidates") from the Kepler mission that include a nearly complete set of detected planets as small as 2 R ⊕ . For each of the 156,000 target stars we assess the detectability of planets as a function of planet radius, R p , and orbital period, P , using a measure of the detection efficiency for each star. We also correct for the geometric probability of transit, R ⋆ /a. We consider first Kepler target stars within the "solar subset" having T eff = 4100-6100 K, log g = 4.0-4.9, and Kepler magnitude Kp < 15 mag, i.e. bright, main sequence GK stars. We include only those stars having photometric noise low enough to permit detection of planets down to 2 R ⊕ . We count planets in small domains of R p and P and divide by the included target stars to calculate planet occurrence in each domain. The resulting occurrence of planets varies by more than three orders of magnitude in the radius-orbital period plane and increases substantially down to the smallest radius (2 R ⊕ ) and out to the longest orbital period (50 days, ∼0.25 AU) in our study. For P < 50 days, the distribution of planet radii is given by a power law, df /d log R = k R R α with k R = 2.9 +0.5 −0.4 , α = −1.92 ± 0.11, and R = R p /R ⊕ . This rapid increase in planet occurrence with decreasing planet size agrees with the prediction of core-accretion formation, but disagrees with population synthesis models that predict a desert at super-Earth and Neptune sizes for close-in orbits. Planets with orbital periods shorter than 2 days are extremely rare; for R p > 2 R ⊕ we measure an occurrence of less than 0.001 planets per star. For all planets with orbital periods less than 50 days, we measure occurrence of 0.130 ± 0.008, 0.023 ± 0.003, and 0.013 ± 0.002 planets per star for planets with radii 2-4, 4-8, and 8-32 R ⊕ , in agreement with Doppler surveys. We fit occurrence as a function of P to a power law model with an exponential cutoff below a critical period P 0 . For smaller planets, P 0 has larger values, suggesting that the "parking distance" for migrating planets moves outward with decreasing planet size. We also measured planet occurrence over a broader stellar T eff range of 3600-7100 K, spanning M0 to F2 dwarfs. Over this range, the occurrence of 2-4 R ⊕ planets in the Kepler field linearly increases with decreasing T eff , making these small planets seven times more abundant around cool stars (3600-4100 K) than the hottest stars in our sample (6600-7100 K).

Kepler has found hundreds of Neptune-size (2-6 R ⊕ ) planet candidates within 0.5 AU of their stars. The nature of the vast majority of these planets is not known because their masses have not been measured. Using theoretical models of planet formation, evolution and structure, we explore the range of minimum plausible masses for low-density exo-Neptunes. We focus on highly irradiated planets with T eq ≥ 500 K. We consider two separate formation pathways for low-mass planets with voluminous atmospheres of light gases: core nucleated accretion and outgassing of hydrogen from dissociated ices. We show that Neptune-size planets at T eq = 500 K with masses as small as a few times that of Earth can plausibly be formed core nucleated accretion coupled with subsequent inward migration. We also derive a limiting low-density mass-radius relation for rocky planets with outgassed hydrogen envelopes but no surface water. Rocky planets with outgassed hydrogen envelopes typically have computed radii well below 3 R ⊕ . For both planets with H/He envelopes from core nucleated accretion and planets with outgassed hydrogen envelopes, we employ planet interior models to map the range of planet mass-envelope mass-equilibrium temperature parameter space that is consistent with Neptune-size planet radii. Atmospheric mass loss mediates which corners of this parameter space are populated by actual planets and ultimately governs the minimum plausible mass at a specified transit radius. We find that Kepler's 2-6 R ⊕ planet candidates at T eq = 500-1000 K could potentially have masses 4 M ⊕ . Although our quantitative results depend on several assumptions, our qualitative finding that warm Neptune-size planets can have masses substantially smaller than those given by interpolating the masses and radii of planets within our Solar System is robust.

In the solar system, the planets' compositions vary with orbital distance, with rocky planets in close orbits and lower-density gas giants in wider orbits. The detection of close-in giant planets around other stars was the first clue that this pattern is not universal and that planets' orbits can change substantially after their formation. Here, we report another violation of the orbit-composition pattern: two planets orbiting the same star with orbital distances differing by only 10% and densities differing by a factor of 8. One planet is likely a rocky "super-Earth," whereas the other is more akin to Neptune. These planets are 20 times more closely spaced and have a larger density contrast than any adjacent pair of planets in the solar system.

The Kepler Mission has discovered thousands of planets with radii <4 Å R , paving the way for the first statistical studies of the dynamics, formation, and evolution of these sub-Neptunes and super-Earths. Planetary masses are an important physical property for these studies, and yet the vast majority of Kepler planet candidates do not have theirs measured. A key concern is therefore how to map the measured radii to mass estimates in this Earth-toNeptune size range where there are no Solar System analogs. Previous works have derived deterministic, one-toone relationships between radius and mass. However, if these planets span a range of compositions as expected, then an intrinsic scatter about this relationship must exist in the population. Here we present the first probabilistic mass-radius relationship (M-R relation) evaluated within a Bayesian framework, which both quantifies this intrinsic dispersion and the uncertainties on the M-R relation parameters. We analyze how the results depend on the radius range of the sample, and on how the masses were measured. Assuming that the M-R relation can be described as a power law with a dispersion that is constant and normally distributed, we find that) , a scatter in mass of Å M 1.9 , and a mass constraint to physically plausible densities, is the "best-fit" probabilistic M-R relation for the sample of RV-measured transiting sub-Neptunes (R pl < 4 Å R ). More broadly, this work provides a framework for further analyses of the M-R relation and its probable dependencies on period and stellar properties.