{
  "id": "1411.0118",
  "version": "v1",
  "published": "2014-11-01T13:59:44.000Z",
  "updated": "2014-11-01T13:59:44.000Z",
  "title": "On the Curvature Effect of a Relativistic Spherical Shell",
  "authors": [
    "Z. Lucas Uhm",
    "Bing Zhang"
  ],
  "comment": "7 pages, 4 figures, submitted to ApJ",
  "categories": [
    "astro-ph.HE"
  ],
  "abstract": "We consider a relativistic spherical shell and calculate its spectral flux as received by a distant observer. Using two different methods, we derive a simple analytical expression of the observed spectral flux and show that the well-known relation $\\hat \\alpha = 2+\\hat \\beta$ (between temporal index $\\hat \\alpha$ and spectral index $\\hat \\beta$) of the high-latitude emission is achieved naturally in our derivation but holds only when the shell moves with a constant Lorentz factor $\\Gamma$. Presenting numerical models where the shell is under acceleration or deceleration, we show that the simple $\\hat \\alpha = 2+\\hat \\beta$ relation is indeed deviated as long as $\\Gamma$ is not constant. For the models under acceleration, we find that the light curves produced purely by the high-latitude emission decay initially much steeper than the constant $\\Gamma$ case and gradually resume the $\\hat \\alpha = 2+\\hat \\beta$ relation in about one and half orders magnitude in observer time. For the models under deceleration, the trend is opposite. The light curves made purely by the high-latitude emission decay initially shallower than the constant $\\Gamma$ case and gradually resume the relation $\\hat \\alpha = 2+\\hat \\beta$ in a similar time scale. We also show that how fast the Lorentz factor $\\Gamma$ of the shell increases or decreases is the main ingredient determining the initial steepness or shallowness of the light curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-01T13:59:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "relativistic spherical shell",
      "curvature effect",
      "light curves",
      "spectral flux",
      "high-latitude emission decay initially shallower"
    ],
    "publication": {
      "doi": "10.1088/0004-637X/808/1/33",
      "journal": "The Astrophysical Journal",
      "year": 2015,
      "month": "Jul",
      "volume": 808,
      "number": 1,
      "pages": 33
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1325744,
      "adsabs": "2015ApJ...808...33U"
    }
  }
}