The association of starspots with magnetic fields leads to an expectation that quantities which correlate with magnetic field strength may also correlate with { starspot} coverage. Since younger stars spin faster and are more magnetically active, assessing whether { starspot} coverage correlates with shorter rotation periods and stellar youth tests these principles. Here we analyze the { starspot} covering fraction versus stellar age for M{ -}, G{ -}, K{ -}, and F{ -}type stars based on previously determined variability and rotation periods of over 30,000 { \textit{ Kepler}} main-sequence stars. We determine the correlation between age and variability using single and dual power law best fits. We find that { starspot} coverage does indeed decrease with age. Only when the data { are} binned in an effort to remove the effects of activity cycles of individual stars, do statistically significant power law fits emerge for each stellar type. { Using bin averages,} we then find that the { starspot} covering fraction scales with the { X}-ray to bolometric ratio to the power $\lambda$ with { $0.22\pm 0.03 < \lambda < 0.32\pm 0.09$} for { G-type} stars of rotation period below 15 days and for the full range of F{ -} and M{ -type} stars. For K{ -}type stars, we find two branches of $\lambda$ separated by variability bins, with the lower branch showing nearly constant starspot coverage and the upper branch { $\lambda \sim 0.35\pm 0.04$.} G{ -}type stars with periods longer than $15$ days exhibit a transition to steeper power law of { $ \lambda \sim 2.4 \pm 1.0$.} The potential connection to previous rotation-age measurements suggesting a magnetic breaking transition at the solar age, corresponding to period of $24.5$ is also of interest.
Categories: astro-ph.SR astro-ph.EP