New Probability Distributions in Astrophysics: IV. The Relativistic Maxwell-Boltzmann Distribution
Lorenzo Zaninetti
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.
Topics & Concepts
PhysicsRelativistic particleDistribution functionDistribution (mathematics)ElectronFunction (biology)Moment (physics)Field (mathematics)Probability distributionMaxwell–Boltzmann distributionConstant (computer programming)Magnetic fieldQuantum electrodynamicsProbability density functionStatistical physicsRelativistic plasmaMagnetic momentAnomalous magnetic dipole momentValue (mathematics)Quantum mechanicsClassical mechanicsRelativistic quantum chemistryGenerating functionMathematical physicsSymmetric probability distributionSynchrotronQuantum and Classical ElectrodynamicsLaser-Plasma Interactions and DiagnosticsDust and Plasma Wave Phenomena