On the Non-existence of a Sharp Cooling Break in GRB Afterglow Spectra

Z. Lucas Uhm; Bing Zhang

doi:10.1088/0004-637X/780/1/82

paper

On the Non-existence of a Sharp Cooling Break in GRB Afterglow Spectra

arXiv:1301.0291 · doi:10.1088/0004-637X/780/1/82

Abstract

Although the widely-used analytical afterglow model of gamma-ray bursts (GRBs) predicts a sharp cooling break $ν_{c}$ in its afterglow spectrum, the GRB observations so far rarely show clear evidence for a cooling break in their spectra or its corresponding temporal break in their light curves. Employing a Lagrangian description of the blast wave, we conduct a sophisticated calculation of the afterglow emission. We precisely follow the cooling history of non-thermal electrons accelerated into each Lagrangian shell. We show that a detailed calculation of afterglow spectra does not in fact give rise to a sharp cooling break at $ν_{c}$ . Instead, it displays a very mild and smooth transition, which occurs gradually over a few orders of magnitude in energy or frequency. The main source of this slow transition is that different mini-shells have different evolution histories of the comoving magnetic field strength $B$ , so that deriving the current value of $ν_{c}$ of each mini-shell requires an integration of its cooling rate over the time elapsed since its creation. We present the time evolution of optical and X-ray spectral indices to demonstrate the slow transition of spectral regimes, and discuss the implications of our result in interpreting GRB afterglow data.

Accepted for publication in ApJ, 17 pages, 5 figures; significantly expanded to address the referee's reports, new section (2.2) and three more figures added, conclusion unchanged

On the Non-existence of a Sharp Cooling Break in GRB Afterglow Spectra

Abstract

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