Astronomy and Astrophysics – Astrophysics
Scientific paper
2005-03-09
Astrophys.J. 626 (2005) 877-886
Astronomy and Astrophysics
Astrophysics
23 pages, 9 figures. To appear in The Astrophysical Journal
Scientific paper
10.1086/430164
The probability that a particle, crossing the shock along a given direction, be reflected backwards along another direction, was shown to be the key element in determining the spectrum of non--thermal particles accelerated via the Fermi mechanism around a plane--parallel shock in the test--particle limit. Here an explicit equation for this probability distribution is given, for both the upstream and downstream sections. Though analytically intractable, this equation is solved numerically, allowing the determination of the spectrum in full generality, without limitation to shock speed or scattering properties. A number of cases is then computed, making contact with previous numerical work, in all regimes: Newtonian, trans--relativistic, and fully relativistic.
Blasi Pasquale
Vietri Mario
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