Abstract
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, V sin 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 V sin 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.
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