Strong evidences for a nonextensive behavior of the rotation period in open clusters

Time-dependent nonextensivity in a stellar astrophysical scenario combines nonextensive entropic indices qK derived from the modified Kawaler's parametrization, and q, obtained from rotational velocity distribution. These q's are related through a heuristic single relation given by , where t is the cluster age. In a nonextensive scenario, these indices are quantities that measure the degree of nonextensivity present in the system. Recent studies reveal that the index q is correlated to the formation rate of high-energy tails present in the distribution of rotation velocity. On the other hand, the index qK is determined by the stellar rotation-age relationship. This depends on the magnetic-field configuration through the expression , where a and N denote the saturation level of the star magnetic field and its topology, respectively. In the present study, we show that the connection is also consistent with 548 rotation period data for single main-sequence stars in 11 open clusters aged less than 1 Gyr. The value of qK ∼ 2.5 from our unsaturated model shows that the mean magnetic-field topology of these stars is slightly more complex than a purely radial field. Our results also suggest that stellar rotational braking behavior affects the degree of anti-correlation between q and cluster age t. Finally, we suggest that stellar magnetic braking can be scaled by the entropic index q.