Ages of Stars and Planets in the Kepler Field Younger Than Four Billion Years

Recent analyses of FGK stars in open clusters have helped clarify the precision with which a star's rotation rate and lithium content can be used as empirical indicators for its age. Here we apply this knowledge to stars observed by Kepler. Rotation periods are drawn from previous work; lithium is measured from new and archival Keck/HIRES spectra. We report rotation-based ages for 23,813 stars (harboring 795 known planets) for which our method is applicable. We find that our rotational ages recover the ages of stars in open clusters spanning 0.04-2.5 Gyr; they also agree with over 90% of the independent lithium ages. The resulting yield includes 63 planets younger than 1 Gyr at 2$\sigma$, and 109 with median ages below 1 Gyr. This is about half the number expected under the classic assumption of a uniform star formation history. The age distribution that we observe, rather than being uniform, shows that the youngest stars in the Kepler field are 3-5 times rarer than stars 3 Gyr old. This trend holds for both known planet hosts and for the parent stellar sample. We attribute this "demographic cliff" to a combination of kinematic heating and a declining star formation rate in the Galaxy's thin disk, and highlight its impact on the age distribution of known transiting exoplanets.