Abstract
In nonextensive formalism (NF) the index q can be interpreted as a parameter of long-memory. When q→ 1 the system becomes extensive and the memory effects are negligible. We found that for solar-type stars in open clusters the index q of the distribution of Vsin i decreases with the cluster age. The extensivity of the distributions (q = 1) is not present until about an age range of 100-700 Myr. A possible explanation for the anti-correlation can be the memory of the initial stellar angular momentum vanishing, considering q as a memory parameter (q=1 corresponding to no memory). In fact, these stars retain the memory of their initial angular momentum until an age > 100 Myr (e.g., Bouvier et al. 1997, A&A, 326, 1023). de Freitas & De Medeiros (2013, MNRAS, 433, 1789) shown that the rotation-age relationship can be reproduced using a model from NF. In this model the index q_{K} is derived from the Kawalers parameterization, where q_{K}=1 indicates the saturated magnetic field regime, and the unsaturated one is given by q_{K}=1 + 4aN/3. The parameters a and N are related to the dynamo and magnetic field geometry, respectively. We used the de Freitas & De Medeiros' model to derive an empirical relationship between q, a and N as the equation q≈ q_0(1 - Δ t/q_{K}), where Δ t = t - t_{0} is the age range, and q_{0} is the index q for the cluster with age t_{0}. This equation constitutes a bridge between q and the theory of magnetic braking of stellar rotation.
