New probability distributions in astrophysics: IV. The relativistic Maxwell-Boltzmann distribution

Autor:	Zaninetti, Lorenzo
Rok vydání:	2020
Předmět:	Condensed Matter - Statistical Mechanics Astrophysics - High Energy Astrophysical Phenomena
Zdroj:	The International Journal of Astronomy and Astrophysics, 2020, 10, 302-318
Druh dokumentu:	Working Paper
DOI:	10.4236/ijaa.2020.104016
Popis:	Two relativistic distributions which generalizes the Maxwell Boltzman (MB) distribution are analyzed: the relativistic MB and the Maxwell-J{\"u}ttner (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. Comment: 15 pages and 17 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.05797 Zobrazit plný text záznamu View this record from Arxiv