Scaling K2. III. Comparable Planet Occurrence in the FGK Samples of Campaign 5 and Kepler

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.