Determination of Starspot Covering Fraction as a function of Stellar Age from Observational Data.

The association of starspotswith magnetic fields leads to an expectation that quantities which correlate with magnetic field strength may also correlate with spot coverage. Since younger stars spin faster and are more magnetically active, assessing whether spot coverage correlates with shorter rotation periodsand stellar youth tests these principles. Here we analyze the spot covering fraction versus stellar age for M, G, K, and F type stars based on previously determined variability and rotation periodsof over 30,000 Keplermain-sequence stars. We determine the correlation between age and variability using single and dual power law best fits. We find that spot 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. Then we find that the spot covering fraction scales with the x-ray to bolometric ratio to the power $\lambda$ with $0.21\pm 0.03 < \lambda < 0.35\pm 0.12$ for G stars of rotation periodbelow 15 days and for the full range of F and M stars. For K type stars, we find two branches of $\lambda$ separatedby variabilitybins, with the lower branch showing nearly constant spot coverage and the upper branch $\lambda \sim 0.36\pm 0.04$. G type stars with periods longer than $15$ days exhibit a transition to steeper power law of $ \lambda \sim 3.4 \pm 1.3$. 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.