New Probability Distributions in Astrophysics: IV. The Relativistic Maxwell-Boltzmann Distribution

• 作者: Lorenzo Zaninetti
• 来源期刊: 天文学与天体物理学国际期刊(英文)
• 学科: 物理学
• 关键词: 05.20.-y Classical Statistical Mechanics 05.20.Dd Kinetic Theory
• 年，卷（期）: 2020,（4）
• 页码范围: 302-318
• 页数: 17页
• 分类号: O57

摘要

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.