3 research outputs found
Particle Acceleration at Ultra-Relativistic Shocks and the Spectra of Relativistic Fireballs
We examine Fermi-type acceleration at relativistic shocks, and distinguish
between the initial boost of the first shock crossing cycle, where the energy
gain per particle can be very large, and the Fermi process proper with repeated
shock crossings, in which the typical energy gain is of order unity. We
calculate by means of numerical simulations the spectrum and angular
distribution of particles accelerated by this Fermi process, in particular in
the case where particle dynamics can be approximated as small-angle scattering.
We show that synchrotron emission from electrons or positrons accelerated by
this process can account remarkably well for the observed power-law spectra of
GRB afterglows and Crab-like supernova remnants. In the context of a
decelerating relativistic fireball, we calculate the maximum particle energy
attainable by acceleration at the external blast wave, and discuss the minimum
energy for this acceleration process and its consequences for the observed
spectrum.Comment: To appear in Proceedings of the 5th Huntsville Gamma-Ray Burst
Symposium. LaTeX, 6 pages, 2 figures, uses aipproc.sty and epsfi
An eigenfunction method for particle acceleration at ultra-relativistic shocks
We adapt and modify the eigenfunction method of computing the power-law
spectrum of particles accelerated at a relativistic shock front via the
first-order Fermi process (Kirk, J.G., Schneider, P., Astrophysical Journal
315, 425 (1987)) to apply to shocks of arbitrarily high Lorentz factor. The
power-law index of accelerated particles undergoing isotropic small-angle
scattering at an ultrarelativistic, unmagnetized shock is found to be s=4.23
+/- 0.2 (where s=d\ln f/ d\ln p, with f the Lorentz-invariant phase-space
density and p the momentum), in agreement with the results of Monte-Carlo
simulations. We present results for shocks in plasmas with different equations
of state and for Lorentz factors ranging from 5 to infinity.Comment: 4 pages, 2 figures, contribution to the Proceedings of the 5th
Huntsville GRB Symposiu