1301.0291 (Z. Lucas Uhm et al.)

Non-existence of a Sharp Cooling Break in GRB Afterglow Spectra    [PDF]

Z. Lucas Uhm, Bing Zhang

Although the widely-used analytical afterglow model of gamma-ray bursts (GRBs) predicts a sharp cooling break $\nu_c$ in its afterglow spectrum, the GRB observations so far do not indicate a 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 $\nu_c$. 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 $\nu_c$ of each mini-shell requires an integration of its cooling rate over the time elapsed since its creation. This is in contrast to the un-justified analytical method, which takes the current $B$ as a constant value over the cooling history. 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.

View original: http://arxiv.org/abs/1301.0291