Non-Gaussian Statistics and Stellar Rotational Velocities of Main-Sequence Field Stars

Carvalho, J. C.; Nascimento, J. D. Do; Silva, R.; Medeiros, J. R. De

doi:10.1088/0004-637x/696/1/l48

Cited by 74 publications

(55 citation statements)

References 14 publications

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“…(8)), our method allows us to fit any known distribution. In this case, we reach the same conclusion as Carvalho et al (2009), but using a different algorithm, i.e., Tsallis or Kaniadakis distributions are in close agreement to the empirical CDF, although the two distributions show a slight discrepancy in their tails.…”

Section: Application To Main-sequence Field Starssupporting

confidence: 77%

“…On the other hand, Carvalho et al (2009) found a better agreement for two other probability distributions, namely: Tsallis and Kaniadakis. These distributions are based on the concept of maximum entropy.…”

Section: Discussionmentioning

confidence: 82%

“…In this catalog, 12 931 stars have values of v sin i. Furthermore, considering that the listed values of v sin i are rounded to the nearest km s −1 up to 30 km s −1 , and upwards of that value the survey lists v sin i to the nearest 5 or 10 km s −1 , and that about 91% of the sample have rotational speeds below 30 km s −1 , we only select (following Carvalho et al 2009) stars with v sin i ≤ 30 km s −1 , obtaining a sample of 11 818 stars.…”

Section: Application To Main-sequence Field Starsmentioning

confidence: 99%

“…This sample has been used by Carvalho et al (2009) distribution function of this sample cannot be fitted using a Maxwellian distribution (Deutsch 1970). They obtained a much better fit when the assumption of Gibbs entropy in standard statistical mechanics is released and distribution functions from nonextensive statistical mechanics are applied to the sample.…”

Section: Application To Main-sequence Field Starsmentioning

confidence: 99%

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A method to deconvolve stellar rotational velocities

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Rial

Christen

et al. 2014

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Aims. Rotational speed is an important physical parameter of stars, and knowing the distribution of stellar rotational velocities is essential for understanding stellar evolution. However, rotational speed cannot be measured directly and is instead the convolution between the rotational speed and the sine of the inclination angle v sin i. Methods. We developed a method to deconvolve this inverse problem and obtain the cumulative distribution function for stellar rotational velocities extending the work of Chandrasekhar & Münch (1950, ApJ, 111, 142) Results. This method is applied: a) to theoretical synthetic data recovering the original velocity distribution with a very small error; and b) to a sample of about 12.000 field main-sequence stars, corroborating that the velocity distribution function is non-Maxwellian, but is better described by distributions based on the concept of maximum entropy, such as Tsallis or Kaniadakis distribution functions. Conclusions. This is a very robust and novel method that deconvolves the rotational velocity cumulative distribution function from a sample of v sin i data in a single step without needing any convergence criteria.

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Section: Application To Main-sequence Field Starssupporting

confidence: 77%

Section: Discussionmentioning

confidence: 82%

Section: Application To Main-sequence Field Starsmentioning

confidence: 99%

Section: Application To Main-sequence Field Starsmentioning

confidence: 99%

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A method to deconvolve stellar rotational velocities

Curé

Rial

Christen

et al. 2014

A&A

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“…Kaniadakis statistics has been applied in astrophysics, e.g., relativistic plasmas [19] and stellar rotational velocities [20].…”

Section: Introductionmentioning

confidence: 99%

Third law of thermodynamics as a key test of generalized entropies

et al. 2015

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The laws of thermodynamics constrain the formulation of statistical mechanics at the microscopic level. The third law of thermodynamics states that the entropy must vanish at absolute zero temperature for systems with nondegenerate ground states in equilibrium. Conversely, the entropy can vanish only at absolute zero temperature. Here we ask whether or not generalized entropies satisfy this fundamental property. We propose a direct analytical procedure to test if a generalized entropy satisfies the third law, assuming only very general assumptions for the entropy S and energy U of an arbitrary N-level classical system. Mathematically, the method relies on exact calculation of β=dS/dU in terms of the microstate probabilities p(i). To illustrate this approach, we present exact results for the two best known generalizations of statistical mechanics. Specifically, we study the Kaniadakis entropy S(κ), which is additive, and the Tsallis entropy S(q), which is nonadditive. We show that the Kaniadakis entropy correctly satisfies the third law only for -1<κ<+1, thereby shedding light on why κ is conventionally restricted to this interval. Surprisingly, however, the Tsallis entropy violates the third law for q<1. Finally, we give a concrete example of the power of our proposed method by applying it to a paradigmatic system: the one-dimensional ferromagnetic Ising model with nearest-neighbor interactions.

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