Time-Dependent Nonextensivity Arising From the Rotational Evolution of Solar-Type 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, 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.

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

“…In this paper we present a nonextensive insight to investigate the behavior of rotational evolution from a sample of 548 rotation period data items for solar-type stars from 11 young OCs aged between 35 and 794 Myr. In particular, we revisit the connection q-q K proposed by Silva et al [17] and compare our results with those obtained using V sin i data. The structure of the present study is as follows: in the next section we explain our working sample and best-fit parameters; the third section presents results and discussion based on the physical implications of nonextensive indices and; finally, conclusions are given in the last section.…”

“…As such, the meaning of these parameters should not be taken too literally. In this context, the work by Silva et al [17] suggests that the memory of initial angular momentum can be scaled by the entropic index q derived from rotational velocities. The authors proposes a connection between q and the parameter q K from the nonextensive model created by de Freitas & De Medeiros [15].…”

A method to deconvolve stellar rotational velocities

“…If the distribution of inclination angles is uniform, then independent of the rotational velocity distribution, there must be a nonnegligible portion of the sample with lower values of the projected rotational velocity due to low values of i. There are some studies of open clusters where this assumption no longer seems reasonable, see Silva et al (2013) and Rees y Zijlstra (2013). We want to develop a "completeness" test for the uniform distribution of angles of a sample of v sin i.…”

Can gyrochronological ages be affected by the variation of the magnetic braking index?

“…By using a nonextensive framework (Tsallis, Mendes & Plastino 1988;Tsallis et al 1999;Tsallis 2004;de Freitas and De Medeiros 2012;Silva et al 2013), de Freitas & De Medeiros (2013 proposed the following equation to describe the behaviour of the rotational velocity of the main-sequence stars: Ω ∝ Ω q ; (q 1).…”