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

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 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 $\nu_c$. 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. 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.Comment: 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 unchange

A Statistical Study of GRB X-ray Flares: Evidence of Ubiquitous Bulk Acceleration in the Emission Region

When emission in a conical relativistic jet ceases abruptly (or decays sharply), the observed decay light curve is controlled by the high-latitude "curvature effect". Recently, Uhm & Zhang found that the decay slopes of three GRB X-ray flares are steeper than what the standard model predicts. This requires bulk acceleration of the emission region, which is consistent with a Poynting-flux-dominated outflow. In this paper, we systematically analyze a sample of 85 bright X-ray flares detected in 63 Swift GRBs, and investigate the relationship between the temporal decay index $\alpha$ and spectral index $\beta$ during the steep decay phase of these flares. The $\alpha$ value depends on the choice of the zero time point $t_0$. We adopt two methods. "Method I" takes $t_0^I$ as the first rising data point of each flare, and is the most conservative approach. We find that at 99.9% condifence level 56/85 flares have decay slopes steeper than the simplest curvature effect prediction, and therefore, are in the acceleration regime. "Method II" extrapolates the rising light curve of each flare backwards until the flux density is three orders of magnitude lower than the peak flux density, and defines the corresponding time as the time zero point (t_0^II). We find that 74/85 flares fall into the acceleration regime at 99.9% condifence level. This suggests that bulk acceleration is common, may be even ubiquitous among X-ray flares, pointing towards a Poynting-flux-dominated jet composition for these events.Comment: 68 pages, 6 figures, 2 tables, ApJS, in pres

On the Mechanism of Gamma-Ray Burst Afterglows

The standard model of afterglow production by the forward shock wave is not supported by recent observations. We propose a model in which the forward shock is invisible and afterglow is emitted by a long-lived reverse shock in the burst ejecta. It explains observed optical and X-ray light curves, including the plateau at 10^3-10^4 s with a peculiar chromatic break, and the second break that was previously associated with a beaming angle of the explosion. The plateau forms following a temporary drop of the reverse-shock pressure much below the forward-shock pressure. A simplest formalism that can describe such blast waves is the ``mechanical'' model (Beloborodov, Uhm 2006); we use it in our calculations.Comment: 11 pages, 3 figures, accepted to ApJ Letter

A Semi-analytic Formulation for Relativistic Blast Waves with a Long-lived Reverse Shock

This paper performs a semi-analytic study of relativistic blast waves in the context of gamma-ray bursts (GRBs). Although commonly used in a wide range of analytical and numerical studies, the equation of state (EOS) with a constant adiabatic index is a poor approximation for relativistic hydrodynamics. Adopting a more realistic EOS with a variable adiabatic index, we present a simple form of jump conditions for relativistic hydrodynamical shocks. Then we describe in detail our technique of modeling a very general class of GRB blast waves with a long-lived reverse shock. Our technique admits an arbitrary radial stratification of the ejecta and ambient medium. We use two different methods to find dynamics of the blast wave: (1) customary pressure balance across the blast wave and (2) the "mechanical model". Using a simple example model, we demonstrate that the two methods yield significantly different dynamical evolutions of the blast wave. We show that the pressure balance does not satisfy the energy conservation for an adiabatic blast wave while the mechanical model does. We also compare two sets of afterglow light curves obtained with the two different methods.Comment: 33 pages, 9 figures, published in Ap