2013ApJ...777...20S

Nonextensive formalism is a generalization of the Boltzmann-Gibbs statistics. In this formalism, the entropic index q is a quantity characterizing the degree of nonextensivity and is interpreted as a parameter of long-memory or long-range interactions between the components of the system. Since its proposition in 1988, this formalism has been applied to investigate a wide variety of natural phenomena. In stellar astrophysics, a theoretical distribution function based on nonextensive formalism (q distributions) has been successfully applied to reproduce the distribution of stellar radial and rotational velocity data. In this paper, we investigate the time variation of the entropic index q obtained from the distribution of rotation, Vsin i, for a sample of 254 rotational data for solar-type stars from 11 open clusters aged between 35.5 Myr and 2.6 Gyr. As a result, we have found an anti-correlation between the entropic index q and the age of clusters, and that the distribution of rotation Vsin i for these stars becomes extensive for an age greater than about 170 Myr. Assuming that the parameter q is associated with long-memory effects, we suggest that the memory of the initial angular momentum of solar-type stars can be scaled by the entropic index q. We also propose a physical link between the parameter q and the magnetic braking of stellar rotation.