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

Abstract

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.

10 Pages, 7 figures, accepted by MNRAS