Characterizing the dependence of the orbital architectures and formation environments on the eccentricity distribution of planets is vital for understanding planet formation. In this work, we perform statistical eccentricity studies of transiting exoplanets using transit durations measured via Kepler combined with precise and accurate stellar radii from the California-Kepler Survey and Gaia. Compared to previous works that characterized the eccentricity distribution from transit durations, our analysis benefits from both high-precision stellar radii (∼3%) and a large sample of ∼1000 planets. We observe that systems with only a single observed transiting planet have a higher mean eccentricity () than systems with multiple transiting planets (), in agreement with previous studies. We confirm the preference for high- and low-eccentricity subpopulations among the single transiting systems. Finally, we show suggestive new evidence that high-e planets in the Kepler sample are preferentially found around high-metallicity ([Fe/H] > 0) stars. We conclude by discussing the implications on planetary formation theories.

Small planets, 1-4× the size of Earth, are extremely common around Sun-like stars, and surprisingly so, as they are missing in our solar system. Recent detections have yielded enough information about this class of exoplanets to begin characterizing their occurrence rates, orbits, masses, densities, and internal structures. The Kepler mission finds the smallest planets to be most common, as 26% of Sun-like stars have small, 1-2 R⊕ planets with orbital periods under 100 d, and 11% have 1-2 R⊕ planets that receive 1-4× the incident stellar flux that warms our Earth. These Earth-size planets are sprinkled uniformly with orbital distance (logarithmically) out to 0.4 the Earth-Sun distance, and probably beyond. Mass measurements for 33 transiting planets of 1-4 R⊕ show that the smallest of them, R < 1.5 R⊕, have the density expected for rocky planets. Their densities increase with increasing radius, likely caused by gravitational compression. Including solar system planets yields a relation: ρ = 2:32 + 3:19 R=R ⊕ [g cm(-3)]. Larger planets, in the radius range 1.5-4.0 R⊕, have densities that decline with increasing radius, revealing increasing amounts of low-density material (H and He or ices) in an envelope surrounding a rocky core, befitting the appellation ''mini-Neptunes.'' The gas giant planets occur preferentially around stars that are rich in heavy elements, while rocky planets occur around stars having a range of heavy element abundances. Defining habitable zones remains difficult, without benefit of either detections of life elsewhere or an understanding of life's biochemical origins.

The California-Kepler Survey (CKS) catalog contains precise stellar and planetary properties for the \Kepler\ planet candidates, including systems with multiple detected transiting planets ("multis") and systems with just one detected transiting planet ("singles," although additional planets could exist). We compared the stellar and planetary properties of the multis and singles in a homogenous subset of the full CKS-Gaia catalog. We found that sub-Neptune sized singles and multis do not differ in their stellar properties or planet radii. In particular: (1.) The distributions of stellar properties $M_\star$, [Fe/H], and $v\mathrm{sin}i$ for the Kepler sub Neptune-sized singles and multis are statistically indistinguishable. (2.) The radius distributions of the sub-Neptune sized singles and multis with $P > 3$ days are indistinguishable, and both have a valley at $\sim1.8~R_\oplus$. However, there are significantly more detected short-period ($P < 3$ days), sub-Neptune sized singles than multis. The similarity of the host star properties, planet radii, and radius valley for singles and multis suggests a common origin. The similar radius valley, which is likely sculpted by photo-evaporation from the host star within the first 100 Myr, suggests that planets in both singles and multis spend much of the first 100 Myr near their present, close-in locations. One explanation that is consistent with the similar fundamental properties of singles and multis is that many of the singles are members of multi-planet systems that underwent planet-planet scattering.

Probing the connection between a star's metallicity and the presence and properties of any associated planets offers an observational link between conditions during the epoch of planet formation and mature planetary systems. We explore this connection by analyzing the metallicities of Kepler target stars and the subset of stars found to host transiting planets. After correcting for survey incompleteness, we measure planet occurrence: the number of planets per 100 stars with a given metallicity M. Planet occurrence correlates with metallicity for some, but not all, planet sizes and orbital periods. For warm super-Earths having P = 10-100 days and RP = 1.0-1.7 R⊕, planet occurrence is nearly constant over metallicities spanning -0.4 to + 0.4 dex. We find 20 warm super-Earths per 100 stars, regardless of metallicity. In contrast, the occurrence of warm sub-Neptunes (RP= 1.7-4.0 R⊕) doubles over that same metallicity interval, from 20 to 40 planets per 100 stars. We model the distribution of planets as df ∝ 10βM DM, where β characterizes the strength of any metallicity correlation. This correlation steepens with decreasing orbital period and increasing planet size. For warm super-Earths β = -0.3-0.2+0.2, while for hot Jupiters β = +3.40.8+0.9. High metallicities in protoplanetary disks may increase the mass of the largest rocky cores or the speed at which they are assembled, enhancing the production of planets larger than 1.7 R⊕. The association between high metallicity and short-period planets may reflect disk density profiles that facilitate the inward migration of solids or higher rates of planet-planet scattering.

We present the discovery of Kepler-88 d (Pd = 1403 ± 14 days, M sin id =965 ± 44⊕ = 3.04 ± 0.13 MJ, ed = 0.41 ± 0.03) based on six years of radial velocity (RV) follow-up from the W. M. Keck Observatory High Resolution Echelle Spectrometer spectrograph. Kepler-88 has two previously identified planets. Kepler-88 b (KOI-142.01) transits in the NASA Kepler photometry and has very large transit timing variations (TTVs). Nesvorný et al. performed a dynamical analysis of the TTVs to uniquely identify the orbital period and mass of the perturbing planet (Kepler-88 c), which was later was confirmed with RVs from the Observatoire de Haute-Provence (OHP). To fully explore the architecture of this system, we performed photodynamical modeling on the Kepler photometry combined with the RVs from Keck and OHP and stellar parameters from spectroscopy and Gaia. Planet d is not detectable in the photometry, and long-baseline RVs are needed to ascertain its presence. A photodynamical model simultaneously optimized to fit the RVs and Kepler photometry yields the most precise planet masses and orbital properties yet for b and c: Pb=10.91647 ± 0.00014 days, Mb=9.5 ± 1.2 M⊕ Pc=22.2649±0.0007 days, and Mc=214.0±5.3 M⊕. The photodynamical solution also finds that planets b and c have low eccentricites and low mutual inclination, are apsidally anti-aligned, and have conjunctions on the same hemisphere of the star. Continued RV follow-up of systems with small planets will improve our understanding of the link between inner planetary system architectures and giant planets.

Understanding the relationship between long-period giant planets and multiple smaller short-period planets is critical for formulating a complete picture of planet formation. This work characterizes three such systems. We present Kepler-65, a system with an eccentric (e = 0.28 ±0.07) giant planet companion discovered via radial velocities (RVs) exterior to a compact, multiply transiting system of sub-Neptune planets. We also use precision RVs to improve mass and radius constraints on two other systems with similar architectures, Kepler-25 and Kepler-68. In Kepler-68 we propose a second exterior giant planet candidate. Finally, we consider the implications of these systems for planet formation models, particularly that the moderate eccentricity in Kepler-65's exterior giant planet did not disrupt its inner system.

We present stellar and planetary properties for 1305 Kepler Objects of Interest hosting 2025 planet candidates observed as part of the California-Kepler Survey. We combine spectroscopic constraints, presented in Paper I, with stellar interior modeling to estimate stellar masses, radii, and ages. Stellar radii are typically constrained to 11%, compared to 40% when only photometric constraints are used. Stellar masses are constrained to 4%, and ages are constrained to 30%. We verify the integrity of the stellar parameters through comparisons with asteroseismic studies and Gaia parallaxes. We also recompute planetary radii for 2025 planet candidates. Because knowledge of planetary radii is often limited by uncertainties in stellar size, we improve the uncertainties in planet radii from typically 42% to 12%. We also leverage improved knowledge of stellar effective temperature to recompute incident stellar fluxes for the planets, now precise to 21%, compared to a factor of two when derived from photometry.

Measuring precise planet masses, densities, and orbital dynamics in individual planetary systems is an important pathway toward understanding planet formation. The WASP-47 system has an unusual architecture that motivates a complex formation theory. The system includes a hot Jupiter ("b") neighbored by interior ("e") and exterior ("d") sub-Neptunes, and a long-period eccentric giant planet ("c"). We simultaneously modeled transit times from the Kepler K2 mission and 118 radial velocities to determine the precise masses, densities, and Keplerian orbital elements of the WASP-47 planets. Combining RVs and TTVs provides a better estimate of the mass of planet d () than that obtained with only RVs () or TTVs (). Planets e and d have high densities for their size, consistent with a history of photoevaporation and/or formation in a volatile-poor environment. Through our RV and TTV analysis, we find that the planetary orbits have eccentricities similar to the solar system planets. The WASP-47 system has three similarities to our own solar system: (1) the planetary orbits are nearly circular and coplanar, (2) the planets are not trapped in mean motion resonances, and (3) the planets have diverse compositions. None of the current single-process exoplanet formation theories adequately reproduce these three characteristics of the WASP-47 system (or our solar system). We propose that WASP-47, like the solar system, formed in two stages: first, the giant planets formed in a gas-rich disk and migrated to their present locations, and second, the high-density sub-Neptunes formed in situ in a gas-poor environment.

The size of a planet is an observable property directly connected to the physics of its formation and evolution. We used precise radius measurements from the California-Kepler Survey to study the size distribution of 2025 Kepler planets in fine detail. We detect a factor of ≥2 deficit in the occurrence rate distribution at 1.5-2.0 R⊕. This gap splits the population of close-in (P < 100 days) small planets into two size regimes: Rp < 1.5⊕ and RP = 2.0-3.0R⊕, with few planets in between. Planets in these two regimes have nearly the same intrinsic frequency based on occurrence measurements that account for planet detection efficiencies. The paucity of planets between 1.5 and 2.0 R⊕ supports the emerging picture that close-in planets smaller than Neptune are composed of rocky cores measuring 1.5 R⊕ or smaller with varying amounts of low-density gas that determine their total sizes.

The California-Kepler Survey (CKS) is an observational program developed to improve our knowledge of the properties of stars found to host transiting planets by NASA's Kepler Mission. The improvement stems from new high-resolution optical spectra obtained using HIRES at the W. M. Keck Observatory. The CKS stellar sample comprises 1305 stars classified as Kepler objects of interest, hosting a total of 2075 transiting planets. The primary sample is magnitude-limited (Kp < 14.2) and contains 960 stars with 1385 planets. The sample was extended to include some fainter stars that host multiple planets, ultra-short period planets, or habitable zone planets. The spectroscopic parameters were determined with two different codes, one based on template matching and the other on direct spectral synthesis using radiative transfer. We demonstrate a precision of 60 K in Teff, 0.10 dex in log g, 0.04 dex in [Fe/H], and 1.0km s-1 in V sin i. In this paper, we describe the CKS project and present a uniform catalog of spectroscopic parameters. Subsequent papers in this series present catalogs of derived stellar properties such as mass, radius, and age; revised planet properties; and statistical explorations of the ensemble. CKS is the largest survey to determine the properties of Kepler stars using a uniform set of high-resolution, high signal-to-noise ratio spectra. The HIRES spectra are available to the community for independent analyses.