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

We examine how the fraction $f$ of stars for which rotational modulation has been detected in Kepler light curves depends on the stellar mass $M_\star$ and age $t_\star$. Our sample consists of $\approx 850$ FGK stars hosting transiting planet candidates detected from the prime Kepler mission. For these stars, atmospheric parameters have been derived using high-resolution spectra from the California-Kepler survey, and rotational modulation has been searched in Kepler light curves homogeneously. We fit stellar models to the atmospheric parameters, Gaia parallax, and 2MASS magnitude of these stars and obtain samples drawn from the posterior probability distributions for their masses and ages under a given, uninformative prior. We combine them with the result of rotational modulation search to simultaneously infer the mass-age distribution of the sample as well as $f(M_\star, t_\star)$, in a manner that fully takes into 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 almost zero by $t_\star \sim 5\,\mathrm{Gyr}$, although the trend is less clearly detected for stars with $\lesssim 0.9\,M_\odot$ due to weaker age constraints. This finding is consistent with a view that the detection of rotational modulation is limited by photometric precision to younger stars that exhibit higher-amplitude modulation, and suggests that the detectability of rotational modulation in Kepler light curves is insensitive to metallicity and activity cycles for stars younger than the Sun.