Determination of the star-spot covering fraction as a function of stellar age from observational data

The association of star-spots with magnetic fields leads to an expectation that quantities which correlate with magnetic field strength may also correlate with star-spot 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 analyse the star-spot 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 Kepler main-sequence stars. We determine the correlation between age and variability using single and dual power-law best fits. We find that star-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-lawfits emerge for each stellar type. Using bin averages, we then find that the star-spot covering fraction scales with the X-ray to bolometric ratio to the power. with 0.22 +/- 0.03<.< 0.32 +/- 0.09 for G-type stars of rotation period below 15 d and for the full range of F- and M-type stars. For K-type stars, we find two branches of. separated by variability bins, with the lower branch showing nearly constant star-spot coverage and the upper branch lambda similar to 0.35 +/- 0.04. G-type stars with periods longer than 15 d exhibit a transition to steeper power law of lambda similar to 2.4 +/- 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.