Energy spectra of cosmic rays accelerated at ultrarelativistic shock waves

Details Energy spectra of cosmic rays accelerated at ultrarelativistic shock waves Energy spectra of cosmic rays accelerated at ultrarelativistic shock waves

1998-06-12

arxiv.org/abs/astro-ph/9806181v1

Phys.Rev.Lett.80:3911,1998

Astronomy and Astrophysics

Astrophysics

4 pages, 6 figures

Scientific paper

10.1103/PhysRevLett.80.3911

Energy spectra of particles accelerated by the first-order Fermi mechanism are investigated at ultrarelativistic shock waves, outside the range of Lorentz factors considered previously. For particle transport near the shock a numerical method involving small amplitude pitch-angle scattering is applied for flows with Lorentz factors $\gamma$ from 3 to 243. For large $\gamma$ shocks a convergence of derived energy spectral indices up to the value $\sigma_\infty \approx 2.2$ is observed for all considered turbulence amplitudes and magnetic field configurations. Recently the same index was derived for $\gamma$-ray bursts by Waxman [Astrophys. J. Lett. 485, L5 (1997)].

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