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We examine how the fraction $f$ of stars for which rotational modulation hasbeen detected in Kepler light curves depends on the stellar mass $M_\star$ andage $t_\star$. Our sample consists of $\approx 850$ FGK stars hostingtransiting planet candidates detected from the prime Kepler mission. For thesestars, atmospheric parameters have been derived using high-resolution spectrafrom the California-Kepler survey, and rotational modulation has been searchedin Kepler light curves homogeneously. We fit stellar models to the atmosphericparameters, Gaia parallax, and 2MASS magnitude of these stars and obtainsamples drawn from the posterior probability distributions for their masses andages under a given, uninformative prior. We combine them with the result ofrotational modulation search to simultaneously infer the mass-age distributionof the sample as well as $f(M_\star, t_\star)$, in a manner that fully takesinto account mass and age uncertainties of individual stars. We find that $f$remains near unity up to $t_\star \sim 3\,\mathrm{Gyr}$ and drops to almostzero by $t_\star \sim 5\,\mathrm{Gyr}$, although the trend is less clearlydetected for stars with $\lesssim 0.9\,M_\odot$ due to weaker age constraints.This finding is consistent with a view that the detection of rotationalmodulation is limited by photometric precision to younger stars that exhibithigher-amplitude modulation, and suggests that the detectability of rotationalmodulation in Kepler light curves is insensitive to metallicity and activitycycles for stars younger than the Sun.

Detectability of Rotational Modulation in Kepler Sun-like Stars as a Function of Age