New probability distributions in astrophysics: III. The truncated Maxwell-Boltzmann distribution

TL;DR

This paper introduces a double truncated Maxwell-Boltzmann distribution, deriving its properties and demonstrating its applications in astrophysics, including a relation between speed and temperature and a modified escape flux formula.

Contribution

It presents the first detailed formulation of a double truncated Maxwell-Boltzmann distribution and explores its practical applications in astrophysical contexts.

Findings

Derived probability density and distribution functions for the truncated distribution

Established a numerical relation between root-mean-square speed and temperature

Modified the Jeans escape flux formula using the truncated distribution

Abstract

The Maxwell-Boltzmann (MB) distribution for velocities in ideal gases is usually defined between zero and infinity. A double truncated MB distribution is here introduced and the probability density function, the distribution function, the average value, the rth moment about the origin, the root-mean-square speed and the variance are evaluated. Two applications are presented: (i) a numerical relationship between root-mean-square speed and temperature, and (ii) a modification of the formula for the Jeans escape flux of molecules from an atmosphere.