Gyrochronology, the formula is empirical ?

Question

The formula used in Gyrochronology that relates a star's Period of Rotation-Mass-Age is empirical?

This news How to Learn a Star’s True Age

"“A star’s rotation slows down steadily with time, like a top spinning on a table, and can be used as a clock to determine its age,"

pointed to this paper THE KEPLER CLUSTER STUDY: STELLAR ROTATION IN NGC6811
and later I found this one (gyro_background) with original work.

But I couldnt find a justification for the formula. Is the Period proportional to $age^{{1/2}}$ only an empirical result?

It seems to me that the formula is a data fit and not a direct result of a calculation of the stellar intrinsic dynamics. The rate of mass loss by radiation must have a 'word to say' in the formula.
Any help is welcome.

Answer 1

Stars lose angular momentum via stellar winds, which because of the coupling of magnetic fields to the stellar surface exhibit a drag on the stars rotation. So we would expect them to slow over time, the real question is a what rate? Stellar magnetic activity which largely drives coronal activity is expected to be stronger with high rotation rates, but does anyone have any decent quantitative theory on this? In any case, another issue is the distribution of initial rotation rates.