Ultra-short-period (USP) planets are a newly recognized class of planets with periods shorter than one day and radii smaller than about 2 R ⊕. It has been proposed that USP planets are the solid cores of hot Jupiters that have lost their gaseous envelopes due to photo-evaporation or Roche lobe overflow. We test this hypothesis by asking whether USP planets are associated with metal-rich stars, as has long been observed for hot Jupiters. We find the metallicity distributions of USP-planet and hot-Jupiter hosts to be significantly different (p = 310-4) based on Keck spectroscopy of Kepler stars. Evidently, the sample of USP planets is not dominated by the evaporated cores of hot Jupiters. The metallicity distribution of stars with USP planets is indistinguishable from that of stars with short-period planets with sizes between 2 and 4 R ⊕. Thus, it remains possible that the USP planets are the solid cores of formerly gaseous planets that are smaller than Neptune.

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.

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.

We have established precise planet radii, semimajor axes, incident stellar fluxes, and stellar masses for 909 planets in 355 multi-planet systems discovered by Kepler. In this sample, we find that planets within a single multi-planet system have correlated sizes: each planet is more likely to be the size of its neighbor than a size drawn at random from the distribution of observed planet sizes. In systems with three or more planets, the planets tend to have a regular spacing: the orbital period ratios of adjacent pairs of planets are correlated. Furthermore, the orbital period ratios are smaller in systems with smaller planets, suggesting that the patterns in planet sizes and spacing are linked through formation and/or subsequent orbital dynamics. Yet, we find that essentially no planets have orbital period ratios smaller than 1.2, regardless of planet size. Using empirical mass-radius relationships, we estimate the mutual Hill separations of planet pairs. We find that 93% of the planet pairs are at least 10 mutual Hill radii apart, and that a spacing of ∼20 mutual Hill radii is most common. We also find that when comparing planet sizes, the outer planet is larger in 65% ± 0.4% of cases, and the typical ratio of the outer to inner planet size is positively correlated with the temperature difference between the planets. This could be the result of photo-evaporation.