A nonextensive view of the stellar braking indices

Abstract: 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 $\mathrm dJ/\mathrm dt$ depends on angular velocity $\Omega$ in the form $\mathrm dJ/\mathrm dt\propto\Omega^{q}$, 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 $\sim16 000$ 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.