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Title: A late-time flattening of light curves in gamma-ray burst afterglows

The afterglow emission from gamma-ray bursts (GRBs) is usually interpreted as synchrotron radiation from relativistic electrons accelerated at the GRB external shock. We investigate the temporal decay of the afterglow emission at late times, when the bulk of the shock-accelerated electrons are non-relativistic (the 'deep Newtonian phase', as denoted by Huang and Cheng). We assume that the electron spectrum in the deep Newtonian phase is a power-law distribution in momentum with slope p, as dictated by the theory of Fermi acceleration in non-relativistic shocks. For a uniform circumburst medium, the deep Newtonian phase begins at t{sub DN}∼3 ϵ{sub e,−1}{sup 5/6}t{sub ST}, where t {sub ST} marks the transition of the blast wave to the non-relativistic, spherically symmetric Sedov-Taylor (ST) solution, and ε {sub e} = 0.1 ε {sub e,–1} quantifies the amount of shock energy transferred to the electrons. For typical parameters, the deep Newtonian stage starts ∼0.5 to several years after the GRB. The radio flux in this phase decays as F {sub ν}∝t {sup –3(p+1)/10}∝t {sup –(0.9÷1.2)}, for a power-law slope 2 < p < 3. This is shallower than the scaling F {sub ν}∝t {sup –3(5p–7)/10}∝t {sup –(0.9÷2.4)} derived by Frail et al., which only applies ifmore » the GRB shock is non-relativistic, but the electron distribution still peaks at ultra-relativistic energies (a regime that is relevant for a narrow time interval, and only if t {sub DN} ≳ t {sub ST}, namely, ε {sub e} ≳ 0.03). We discuss how the deep Newtonian phase can be reliably used for GRB calorimetry, and we comment on the good detection prospects of trans-relativistic blast waves at 0.1÷10 GHz with the Karl G. Jansky Very Large Array and LOw-Frequency ARray.« less
Authors:
 [1] ;  [2]
  1. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
  2. Department of Physics, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907 (United States)
Publication Date:
OSTI Identifier:
22341949
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 778; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AFTERGLOW; CALORIMETRY; COSMIC GAMMA BURSTS; DECAY; DETECTION; DISTRIBUTION; ELECTRON SPECTRA; ELECTRONS; EMISSION; EXPLOSIONS; GHZ RANGE; RELATIVISTIC RANGE; SHOCK WAVES; SPHERICAL CONFIGURATION; SYMMETRY; VISIBLE RADIATION