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Astrophysics > Cosmology and Nongalactic Astrophysics

arXiv:1311.4494 (astro-ph)
[Submitted on 18 Nov 2013 (v1), last revised 30 May 2014 (this version, v2)]

Title:Probability distribution for the relative velocity of colliding particles in a relativistic classical gas

Authors:M. Cannoni
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Abstract:We find the probability density function $\mathcal{P}(V_{\texttt{r}})$ of the relativistic relative velocity for two colliding particles in a non-degenerate relativistic gas. The distribution reduces to Maxwell distribution for the relative velocity in the non-relativistic limit. We find an exact formula for the mean value $\langle V_{\texttt{r}}\rangle$. The mean velocity tends to the Maxwell's value in the non-relativistic limit and to the velocity of light in the ultra-relativistic limit. At a given temperature $T$, when at least for one of the two particles the ratio of the rest energy over the thermal energy $m c^2/k_B T$ is smaller than 40 the Maxwell distribution is inadequate.
Comments: 5 pages, 2 figures. V2: text revised. Part of this material is published in Phys. Rev. D 89, 103533 (2014) in a merged version with arXiv:1311.4508
Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph); Mathematical Physics (math-ph); Nuclear Theory (nucl-th)
Cite as: arXiv:1311.4494 [astro-ph.CO]
  (or arXiv:1311.4494v2 [astro-ph.CO] for this version)
  https://doi.org/10.48550/arXiv.1311.4494
Journal reference: Phys. Rev. D 89, 103533 (2014)
Related DOI: https://doi.org/10.1103/PhysRevD.89.103533

Submission history

From: Mirco Cannoni [view email]
[v1] Mon, 18 Nov 2013 19:06:45 UTC (1,716 KB)
[v2] Fri, 30 May 2014 18:04:23 UTC (1,716 KB)
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