Astronomy and Astrophysics – Astrophysics – High Energy Astrophysical Phenomena
Scientific paper
2010-08-03
Astronomy and Astrophysics
Astrophysics
High Energy Astrophysical Phenomena
17 pages, 5 figures, to appear in ApJ
Scientific paper
We examine the test-particle solution for diffusive shock acceleration, based on simple models for thermal leakage injection and Alfv'enic drift. The critical injection rate, \xi_c, above which the cosmic ray (CR) pressure becomes dynamically significant, depends mainly on the sonic shock Mach number, M, and preshock gas temperature, T_1. In the hot-phase interstellar medium (ISM) and intracluster medium, \xi_c < 10^{-3} for shocks with M < 5, while \xi_c ~ 10^{-4}(T_1/10^6 K)^{1/2} for shocks with M > 10. For T_1=10^6 K, for example, the test-particle solution would be valid if the injection momentum, p_{inj} > 3.8 p_{th}. This leads to the postshock CR pressure less than 10% of the shock ram pressure. If the Alfv'en speed is comparable to the sound speed in the preshock flow, as in the hot-phase ISM, the power-law slope of CR spectrum can be significantly softer than the canonical test-particle slope. Then the CR spectrum at the shock can be approximated by the revised test-particle power-law with an exponential cutoff at the highest accelerated momentum, p_{max}(t). An analytic form of the exponential cutoff is also suggested.
Kang Hyesung
Ryu Dongsu
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