We investigate the role that planet detection order plays in the Kepler planet detection pipeline. The Kepler pipeline typically detects planets in order of descending signal strength (MES). We find that the detectability of transits experiences an additional 5.5% and 15.9% efficiency loss, for periods < 200 days and > 200 days respectively, when detected after the strongest signal transit in a multiple-planet system. We provide a method for determining the transit probability for multiple-planet systems by marginalizing over the empirical Kepler dataset. Furthermore, because detection efficiency appears to be a function of detection order, we discuss the sorting statistics that affect the radius and period distributions of each detection order. Our occurrence rate dataset includes radius measurement updates from the California Kepler Survey (CKS), Gaia DR2, and asteroseismology. Our population model is consistent with the results of Burke et al. (2015), but now includes an improved estimate of the multiplicity distribution. From our obtained model parameters, we find that only 4.0 ± 4.6% of solar-like GK dwarfs harbor one planet. This excess is smaller than prior studies and can be well modeled with a modified Poisson distribution, suggesting that the Kepler Dichotomy can be accounted for by including the effects of multiplicity on detection efficiency. Using our modified Poisson model we expect the average number of planets is 5.86 ± 0.18 planets per GK dwarf within the radius and period parameter space of Kepler.

We present a uniform transiting exoplanet candidate list for Campaign 5 of the K2 mission. This catalog contains 75 planets with 7 multi-planet systems (5 double, 1 triple, and 1 quadruple planet system). Within the range of our search, we find 8 previously undetected candidates with the remaining 66 candidates overlapping 51% of the Kruse et al. study that manually vet Campaign 5 candidates. In order to vet our potential transit signals, we introduce the Exoplanet Detection Identification Vetter (EDI-Vetter), which is a fully automated program able to determine if a transit signal should be labeled as a false positive or a planet candidate. This automation allows us to create a statistically uniform catalog, ideal for planet occurrence rate measurements. When tested, the vetting software is able to ensure our sample is 94.2% reliable against systematic false positives. Additionally, we inject artificial transits at the light-curve-level of the raw K2 data and find the maximum completeness of our pipeline is 70% before vetting and 60% after vetting. For convenience of future occurrence rate studies, we include measurements of stellar noise (CDPP) and the three-transit window function for each target. This study is part of a larger survey of the K2 data set and the methodology which will be applied to the entirety of the K2 data set.

Previous measurements of stellar properties for K2 stars in the Ecliptic Plane Input Catalog (EPIC;Huber et al. 2016) largely relied on photometry and proper motion measurements, with some added information from available spectra and parallaxes. Combining Gaia DR2 distances with spectroscopic measurements of effective temperatures, surface gravities, and metallicities from the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) DR5, we computed updated stellar radii and masses for 26,838 K2 stars. For 195,250 targets without a LAMOST spectrum, we derived stellar parameters using random forest regression on photometric colors trained on the LAMOST sample. In total, we measured spectral types, effective temperatures, surface gravities, metallicities, radii, and masses for 222,088 A, F, G, K, and M-type K2 stars. With these new stellar radii, we performed a simple reanalysis of 299 confirmed and 517 candidate K2 planet radii from Campaigns 1-13, elucidating a distinct planet radius valley around 1.9 R ⊕ , a feature thus far only conclusively identified with Kepler planets, and tentatively identified with K2 planets. These updated stellar parameters are a crucial step in the process toward computing K2 planet occurrence rates.

Using our K2 Campaign 5 fully automated planet-detection data set (43 planets), which has corresponding measures of completeness and reliability, we infer an underlying planet population model for the FGK dwarf sample (9257 stars). Implementing a broken power law for both the period and radius distributions, we find an overall planet occurrence of-+ 1.00 0.51 1.07 planets per star within a period range of 0.5-38 days. Making similar cuts and running a comparable analysis on the Kepler sample (2318 planets; 94,222 stars), we find an overall occurrence of 1.10±0.05 planets per star. Since the Campaign 5 field is nearly 120 angular degrees away from the Kepler field, this occurrence similarity offers evidence that the Kepler sample may provide a good baseline for Galactic inferences. Furthermore, the Kepler stellar sample is metal-rich compared to the K2 Campaign 5 sample, so a finding of occurrence parity may reduce the role of metallicity in planet formation. However, a weak (1.5σ) difference, in agreement with metal-driven formation, is found when assuming the Kepler model power laws for the K2 Campaign 5 sample and optimizing only the planet occurrence factor. This weak trend indicates that further investigation of metallicity-dependent occurrence is warranted once a larger sample of uniformly vetted K2 planet candidates is made available.

Using the updated exoplanet population parameters of our previous study, which includes the planetary radius updates from Gaia DR2 and an inferred multiplicity distribution, we provide a revised η ⊕ calculation. This is achieved by sampling planets from our derived population model and determining which planets meet our criterion for habitability. To ensure robust results, we provide probabilities calculated over a range of upper radius limits. Our most optimistic criterion for habitability provides an η ⊕ value of 0.34±0.02 planets star . We also consider the effects of multiplicity and the number of habitable planets each system may contain. Our calculation indicates that 6.4 ± 0.5% of GK dwarfs have more than one planet within their habitable zone. This optimistic habitability criterion also suggests that 0.036 ± 0.009% of solar-like stars will harbor 5 or more habitable planets. These tightly packed highly habitable system should be extremely rare, but still possible. Even with our most pessimistic criterion we still expect that 1.8 ± 0.2% of solar-like stars harbor more than one habitable planet.

We demonstrate that tidal evolution of the inner planet ('e') of the system orbiting the star ρ 55 Cancri could have led to passage through two secular resonances with other planets in the system. The consequence of this evolution is excitation of both the planetary eccentricity and inclination relative to the original orbital plane. The large mass ratio between the innermost planet and the others means that these excitations can be of substantial amplitude and can have dramatic consequences for the system organisation. Such evolution can potentially explain the large observed mutual inclination between the innermost and outermost planets in the system, and implies that tidal heating could have substantially modified the structure of planet e, and possibly reduced its mass by Roche lobe overflow. Similar inner secular resonances may be found in many multiple planet systems and suggest that many of the innermost planets in these systems could have suffered similar evolutions.

We provide the first full K2 transiting exoplanet sample, using photometry from Campaigns 1–8 and 10–18, derived through an entirely automated procedure. This homogeneous planet candidate catalog is crucial to perform a robust demographic analysis of transiting exoplanets with K2. We identify 747 unique planet candidates and 57 multiplanet systems. Of these candidates, 366 have not been previously identified, including one resonant multiplanet system and one system with two short-period gas giants. By automating the construction of this list, measurements of sample biases (completeness and reliability) can be quantified. We carried out a light-curve-level injection/recovery test of artificial transit signals and found a maximum completeness of 61%, a consequence of the significant detrending required for K2 data analysis. Through this operation we attained measurements of the detection efficiency as a function of signal strength, enabling future population analysis using this sample. We assessed the reliability of our planet sample by testing our vetting software EDI-Vetter against inverted transit-free light curves. We estimate that 91% of our planet candidates are real astrophysical signals, increasing up to 94% when limited to the FGKM dwarf stellar population. We also constrain the contamination rate from background eclipsing binaries to less than 5%. The presented catalog, along with the completeness and reliability measurements, enable robust exoplanet demographic studies to be carried out across the fields observed by the K2 mission for the first time.

In this study, we performed a homogeneous analysis of the planets around FGK dwarf stars observed by the Kepler and K2 missions, providing spectroscopic parameters for 310 K2 targets —including 239 Scaling K2 hosts—observed with Keck/HIRES. For orbital periods less than 40 days, we found that the distribution of planets as a function of orbital period, stellar effective temperature, and metallicity was consistent between K2 and Kepler, reflecting consistent planet formation efficiency across numerous ∼1 kpc sight-lines in the local Milky Way. Additionally, we detected a 3× excess of sub-Saturns relative to warm Jupiters beyond 10 days, suggesting a closer association between sub-Saturn and sub-Neptune formation than between sub-Saturn and Jovian formation. Performing a joint analysis of Kepler and K2 demographics, we observed diminishing super-Earth, sub-Neptune, and sub-Saturn populations at higher stellar effective temperatures, implying an inverse relationship between formation and disk mass. In contrast, no apparent host-star spectral-type dependence was identified for our population of Jupiters, which indicates gas-giant formation saturates within the FGK mass regimes. We present support for stellar metallicity trends reported by previous Kepler analyses. Using Gaia DR3 proper motion and radial velocity measurements, we discovered a galactic location trend; stars that make large vertical excursions from the plane of the Milky Way host fewer super-Earths and sub-Neptunes. While oscillation amplitude is associated with metallicity, metallicity alone cannot explain the observed trend, demonstrating that galactic influences are imprinted on the planet population. Overall, our results provide new insights into the distribution of planets around FGK dwarf stars and the factors that influence their formation and evolution.