Confirming known planetary trends using a photometrically selected Kepler sample

Statistical studies of exoplanets and the properties of their host stars have been critical to informing models of planet formation. Numerous trends have arisen in particular from the rich Kepler dataset, including that exoplanets are more likely to be found around stars with a high metallicity and the presence of a "gap" in the distribution of planetary radii at 1.9$R_\oplus$. Here we present a new analysis on the Kepler field, using the APOGEE spectroscopic survey to build a metallicity calibration based on Gaia, 2MASS and Stromgren photometry. This calibration, along with masses and radii derived from a Bayesian isochrone fitting algorithm, is used to test a number of these trends with unbiased, photometrically derived parameters, albeit with a smaller sample size in comparison to recent studies. We recover that planets are more frequently found around higher metallicity stars; over the entire sample, planetary frequencies are $0.88\pm0.12$ percent for [Fe/H]<0 and $1.37\pm0.16$ percent for [Fe/H]$\geq$0 but at two sigma we find that the size of exoplanets influences the strength of this trend. We also recover the planet radius gap, along with a slight positive correlation with stellar mass. We conclude that this method shows promise to derive robust statistics of exoplanets. We also remark that spectrophotometry from Gaia DR3 will have an effective resolution similar to narrow band filters and allow to overcome the small sample size inherent in this study.