Can gyrochronological ages be affected by the variation of the magnetic braking index

The present work attempts to analytically explain the effects on the moment of inertia, $I$, caused by the evolution of stellar velocity in main-sequence stars. We have found that the effects linked to stellar oblateness can be estimated from the variation of the magnetic braking index denoted by $\Delta q$. We have also found that the effect of $\dot{I}$ is here a determining factor for understanding the delicate mechanisms that control the spin-down of stars in this evolutionary phase. We note that our models predict that the behaviour of the variations of the braking index is distinct when the star density decreases. In the present study, we used three sample stellar targets from the archives of the different satellites, such as CoRoT and \textit{Kepler}, to estimate the possible correlations among the parameters extracted from our model and the stellar age. As a result, we find that $\Delta q$ is strongly correlated to the age of stars. In conclusion, we suggest that the variations of the magnetic braking index due to oblateness can be an interesting way to estimate stellar ages.