Time-dependent nonextensivity arising from the rotational evolution of solar-type stars

TL;DR

This study explores how the nonextensive entropic index q, derived from stellar rotation data, varies with age in solar-type stars, revealing a transition to extensive behavior around 170 million years and linking it to magnetic braking effects.

Contribution

It introduces a time-dependent analysis of the nonextensive parameter q in stellar rotation, connecting it to stellar age and magnetic braking, which was not previously studied.

Findings

q decreases with stellar age, indicating loss of initial angular momentum.

Distribution of stellar rotation becomes extensive after ~170 million years.

Proposes a physical link between q and magnetic braking in stars.

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, 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, Vsini, for a sample of 254 rotational data for solar-type stars from 11 open clusters aged between 35.5Myr and 2.6Gyr. 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 Vsini for these stars becomes extensive for an age greater than about 170Myr. 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.