Measuring deviation from Skumanich braking index in active stars observed by Kepler mission

Abstract: The aim of this work is to determine the deviation of the value of magnetic braking index $q$ from Skumanich $q=3$ canonical value for giant and main-sequence stars. In this context, the present work attempts to analytically calculate the braking index based on the balance of gravitational and centrifugal forces, a determining factor for understanding the delicate mechanisms that control the spin-down of stars in these evolutionary phases. In the present study, we used a wide sample of stellar targets from the \textit{Kepler} mission with well-defined mass, radius, and rotation period. As a result, \textit{Kepler} stellar parameters provide rather precise values of $q$ index limited in the range $1\leq q\leq 3$, which is consistent with the predictions of the model of magnetic stellar wind. Our results show conclusively that, within the model used in this work, any significant deviation of the braking index away from the value $q=3$ occurs at masses higher than the Kraft break.