{
  "id": "1008.0429",
  "version": "v1",
  "published": "2010-08-03T00:33:44.000Z",
  "updated": "2010-08-03T00:33:44.000Z",
  "title": "Diffusive Shock Acceleration in Test-Particle Regime",
  "authors": [
    "Hyesung Kang",
    "Dongsu Ryu"
  ],
  "comment": "17 pages, 5 figures, to appear in ApJ",
  "categories": [
    "astro-ph.HE"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-03T00:33:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diffusive shock acceleration",
      "test-particle regime",
      "test-particle solution",
      "exponential cutoff",
      "cr spectrum"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0004-637X/721/1/886",
      "journal": "The Astrophysical Journal",
      "year": 2010,
      "month": "Sep",
      "volume": 721,
      "number": 1,
      "pages": 886
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 864287,
      "adsabs": "2010ApJ...721..886K"
    }
  }
}