Particle acceleration in ultra-relativistic parallel shock waves

Abstract

Monte-Carlo computations for highly relativistic parallel shock particle acceleration are presented for upstream flow gamma factors, $\Gamma =(1-V_1^2/c^2{)}^{-0.5}$ with values between 5 and $10^3$. The results show that the spectral shape at the shock depends on whether or not the particle scattering is small angle with $\delta \theta <{\Gamma }^{-1}$ or large angle, which is possible if $\lambda >2r_g{\Gamma }^2$ where $\lambda$ is the scattering mean free path along the field line and $r_g$ the gyroradius, these quantities being measured in the plasma flow frame. The large angle scattering case exhibits distinctive structure superimposed on the basic power-law spectrum, largely absent in the pitch angle case. Also, both cases yield an acceleration rate faster than estimated by the conventional, non-relativistic expression, $t_{acc}=[c/(V_1-V_2)][{\lambda }_1/V_1+{\lambda }_2/V_2]$ where '1' and '2' refer to upstream and downstream and $\lambda$ is the mean free path. A ${\Gamma }^2$ energy enhancement factor in the first shock crossing cycle and a significant energy multiplication in the subsequent shock cycles are also observed. The results may be important for our understanding of the production of very high energy cosmic rays and the high energy neutrino and gamma-ray output from Gamma Ray Bursts (GRB) and Active Galactic Nuclei (AGN).

16 pages, 16 figures, accepted for publication in Astroparticle Physics

References in corpus (1)

• Particle acceleration in ultra-relativistic oblique shock waves

Cited by in corpus (10)

• Diffusive Shock Acceleration in Unmodified Relativistic, Oblique Shocks
• The origin of cosmic rays: Explosions of massive stars with magnetic winds and their supernova mechanism
• Ultra High Energy Cosmic Rays
• On the generation of UHECRs in GRBs: a reappraisal
• Relativistic Fermi acceleration with shock compressed turbulence
• Self-Similar Collisionless Shocks
• Particle acceleration in ultra-relativistic oblique shock waves
• On the origin of ultra high energy cosmic rays: Subluminal and superluminal relativistic shocks
• Supernova explosions of massive stars and cosmic rays
• Active Galactic Nuclei Jets and Multiple Oblique Shock Acceleration: Starved Spectra