The present work is based on a description for the angular mometum loss rate due to magnetic braking for main-sequence stars on the relationship between stellar rotation and age. In general, this loss rate denoted by dJ/dt depends on angular velocity Ω in the form dJ/dt ∝ Ω q , where q is a parameter extracted from nonextensive statistical mechanics. Already, in context of stellar rotation, this parameter is greater than unity and it is directly related to the braking index. For q equal to unity, the scenario of saturation of the magnetic field is recovered, otherwise q indicates an unsaturated field. This new approach have been proposed and investigated by de Freitas & De Medeiros for unsaturated field stars. In present work, we propose a nonextensive approach for the stellar rotational evolution based on the Reiners & Mohanthy model. In this sense, we developed a nonextensive version of Reiners & Mohanthy torque and also compare this generalized version with the model proposed in de Freitas & De Medeiros based on the spin-down Kawaler torque for the main-sequence stars with F and G spectral types. We use the same sample of ∼ 16000 field stars with rotational velocity v sin i limited in age and mass. As a result, we show that the Kawaler and Reiners & Mohanthy models exhibit strong discrepancies, mainly in relation to the domain of validity of the entropic index q. These discrepancies are mainly due to sensitivity on the stellar radius. Finally, our results showed that modified Kawaler prescription is compatible with a wider mass range, while the Reiners & Mohanty model is restricted to masses less than G6 stars.

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 Kepler mission with well-defined mass, radius, and rotation period. As a result, Kepler stellar parameters provide rather precise values of q index limited in the range 1 q 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.