SELF-SIMILAR EVOLUTION OF COSMIC-RAY MODIFIED SHOCKS: THE COSMIC-RAY SPECTRUM
- Department of Earth Sciences, Pusan National University, Pusan 609-735 (Korea, Republic of)
- Department of Astronomy and Space Science, Chungnam National University, Daejeon 305-764 (Korea, Republic of)
We use kinetic simulations of diffusive shock acceleration (DSA) to study the time-dependent evolution of plane, quasi-parallel, cosmic-ray (CR) modified shocks. Thermal leakage injection of low-energy CRs and finite Alfven wave propagation and dissipation are included. Bohm diffusion as well as the diffusion with the power-law momentum dependence are modeled. As long as the acceleration timescale to relativistic energies is much shorter than the dynamical evolution timescale of the shocks, the precursor and subshock transition approach the time-asymptotic state, which depends on the shock sonic and Alfvenic Mach numbers and the CR injection efficiency. For the diffusion models we employ, the shock precursor structure evolves in an approximately self-similar fashion, depending only on the similarity variable, x/(u{sub s}t). During this self-similar stage, the CR distribution at the subshock maintains a characteristic form as it evolves: the sum of two power laws with the slopes determined by the subshock and total compression ratios with an exponential cutoff at the highest accelerated momentum, p {sub max}(t). Based on the results of the DSA simulations spanning a range of Mach numbers, we suggest functional forms for the shock structure parameters, from which the aforementioned form of CR spectrum can be constructed. These analytic forms may represent approximate solutions to the DSA problem for astrophysical shocks during the self-similar evolutionary stage as well as during the steady state stage if p {sub max} is fixed.
- OSTI ID:
- 21296241
- Journal Information:
- Astrophysical Journal, Vol. 695, Issue 2; Other Information: DOI: 10.1088/0004-637X/695/2/1273; Country of input: International Atomic Energy Agency (IAEA); ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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