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

Abstract

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 star-spot 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-law fits 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 λ with 0.22 ± 0.03 < λ < 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 λ separated by variability bins, with the lower branch showing nearly constant star-spot coverage and the upper branch λ ∼ 0.35 ± 0.04. G-type stars with periods longer than 15 d exhibit a transition to steeper power law of λ ∼ 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.