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The Kepler Mission revolutionized exoplanet science and stellar astrophysicsby obtaining highly precise photometry of over 200,000 stars over 4 years. Acritical piece of information to exploit Kepler data is its selection function,since all targets had to be selected from a sample of half a million stars onthe Kepler CCDs using limited information. Here we use Gaia DR2 to reconstructthe Kepler selection function and explore possible biases with respect toevolutionary state, stellar multiplicity, and kinematics. We find that theKepler target selection is nearly complete for stars brighter than $Kp < 14$mag and was effective at selecting main-sequence stars, with the fraction ofobserved stars decreasing from 95% to 60% between $14 < Kp < 16$ mag. We findthat the observed fraction for subgiant stars is only 10% lower, confirmingthat a significant number of subgiants selected for observation were believedto be main-sequence stars. Conversely we find a strong selection bias againstlow-luminosity red giant stars ($R \approx 3-5 R_\odot$, $T_{eff} \approx5500$K), dropping from 90% at $Kp = 14$ mag to below 30% at $Kp = 16$ mag,confirming that the target selection was efficient at distinguishing dwarfsfrom giants. We compare the Gaia Re-normalized Unit Weight Error (RUWE) valuesof the observed and non-observed main sequence stars and find a difference inelevated ($>$ 1.2) RUWE values at $\sim\,5\,\sigma$ significance, suggestingthat the Kepler target selection shows some bias against either close or widebinaries. We furthermore use the Gaia proper motions to show that the Keplerselection function was unbiased with respect to kinematics.

The Stars Kepler Missed: Investigating the Kepler Target Selection Function Using Gaia DR2