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An accurate and precise $Kepler$ Stellar Properties Catalog is essential for the interpretation of the $Kepler$ exoplanet survey results. Previous $Kepler$ Stellar Properties Catalogs have focused on reporting the best-available parameters for each star, but this has required combining data from a variety of heterogeneous sources. We present the $Gaia$-$Kepler$ Stellar Properties Catalog, a set of stellar properties of 186,301 $Kepler$ stars, homogeneously derived from isochrones and broadband photometry, $Gaia$ Data Release 2 parallaxes, and spectroscopic metallicities, where available. Our photometric effective temperatures, derived from $g-K_s$ colors, are calibrated on stars with interferometric angular diameters. Median catalog uncertainties are 112 K for $T_{\mathrm{eff}}$, 0.05 dex for $\log g$, 4% for $R_\star$, 7% for $M_\star$, 13% for $\rho_\star$, 10% for $L_\star$, and 56% for stellar age. These precise constraints on stellar properties for this sample of stars will allow unprecedented investigations into trends in stellar and exoplanet properties as a function of stellar mass and age. In addition, our homogeneous parameter determinations will permit more accurate calculations of planet occurrence and trends with stellar properties.

The Gaia–Kepler Stellar Properties Catalog. I. Homogeneous Fundamental Properties for 186,301 Kepler Stars