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New Probability Distributions in Astrophysics: IV. The Relativistic Maxwell-Boltzmann Distribution
Physics Department, via P.Giuria 1, Turin, Italy
- 1 Physics Department, via P.Giuria 1, Turin, Italy
International Journal of Astronomy and Astrophysics·Volume 10 (2020)·Pages 302–318·Published 16 October 2020·DOI10.4236/ijaa.2020.104016
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Abstract
Two relativistic distributions which generalize the Maxwell Boltzman (MB) distribution are analyzed: the relativistic MB and the Maxwell-Jüttner (MJ) distribution. For the two distributions, we derived in terms of special functions the constant of normalization, the average value, the second moment about the origin, the variance, the mode, the asymptotic behavior, approximate expressions for the average value as function of the temperature and the connected inverted expressions for the temperature as function of the average value. Two astrophysical applications to the synchrotron emission in presence of the magnetic field and the relativistic electrons are presented.
Keywords05.20.-y Classical Statistical Mechanics05.20.Dd Kinetic Theory
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