Self-similar evolution of cosmic-ray-modified quasi-parallel plane shocks

2007/05/23 by Hyesung Kang, T. W. Jones · 68 citations
Physics and Astronomy · #Astronomy #Astrophysical Phenomena and Observations #Astrophysics #Astrophysics and Cosmic Phenomena #COSMIC cancer database #Cosmic ray #Gamma-ray bursts and supernovae #Geometry #Nuclear physics #Physics #Plane (geometry) #Ultra-high-energy cosmic ray #astro-ph

paper · pdf · doi:10.1016/j.astropartphys.2007.05.007

published in Astroparticle Physics 28(2), 232-246 (Elsevier BV) · 29 pages, 8 figures

arxiv created 2007/05/23 · openalex publication_date 2007/05/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Using an improved version of the previously introduced CRASH (Cosmic Ray Acceleration SHock) code, we have calculated the time evolution of cosmic-ray (CR) modified quasi-parallel plane shocks for Bohm-like diffusion, including self-consistent models of Alfven wave drift and dissipation, along with thermal leakage injection of CRs. The new simulations follow evolution of the CR distribution to much higher energies than our previous study, providing a better examination of evolutionary and asymptotic behaviors. The postshock CR pressure becomes constant after quick initial adjustment, since the evolution of the CR partial pressure expressed in terms of a momentum similarity variable is self-similar. The shock precursor, which scales as the diffusion length of the highest energy CRs, subsequently broadens approximately linearly with time, independent of diffusion model, so long as CRs continue to be accelerated to ever-higher energies. This means the nonlinear shock structure can be described approximately in terms of the similarity variable, x/(u_s t), where u_s is the shock speed once the postshock pressure reaches an approximate time asymptotic state. As before, the shock Mach number is the key parameter determining the evolution and the CR acceleration efficiency, although finite Alfven wave drift and wave energy dissipation in the shock precursor reduce the effective velocity change experienced by CRs, so reduce acceleration efficiency noticeably, thus, providing a second important parameter at low and moderate Mach numbers.

Citations

• A theory of the interstellar medium - Three components regulated by supernova explosions in an inhomogeneous substrate
• Nonlinear Diffusive Shock Acceleration with Magnetic Field Amplification
• Particle acceleration at astrophysical shocks: A theory of cosmic ray origin
• Cluster Magnetic Fields

Cited by

• Cosmological Shocks in Adaptive Mesh Refinement Simulations and the Acceleration of Cosmic Rays