Fast cooling synchrotron radiation in a decaying magnetic field and γ\gamma-ray burst emission mechanism

Synchrotron radiation of relativistic electrons is an important radiation mechanism in many astrophysical sources. In the sources where the synchrotron cooling time scale $t_c$ is shorter than the dynamical time scale $t_{dyn}$, electrons are cooled down below the minimum injection energy. It has been believed that such "fast cooling" electrons have an energy distribution $dN_e /d\gamma_e \propto \gamma_e^{-2}$, and their synchrotron radiation flux density has a spectral shape $F_\nu \propto \nu^{-1/2}$. On the other hand, in a transient expanding astrophysical source, such as a gamma-ray burst (GRB), the magnetic field strength in the emission region continuously decreases with radius. Here we study such a system, and find that in a certain parameter regime, the fast cooling electrons can have a harder energy spectrum, and the standard $d N_e / d \gamma_e \propto \gamma_e^{-2}$ spectrum is achieved only in the deep fast cooling regime when $t_c \ll t_{dyn}$. We apply this new physical regime to GRBs, and suggest that the GRB prompt emission spectra whose low-energy photon index $\alpha$ has a typical value -1 could be due to synchrotron radiation in this moderately fast cooling regime.Comment: Accepted for publication in Nature Physics. This version is the original submitted version. A refereed version (with minor revision) will appear in Nature Physic

Mechanical Model for Relativistic Blast Waves

Relativistic blast waves can be described by a mechanical model. In this model, the "blast" -- the compressed gas between the forward and reverse shocks -- is viewed as one hot body. Equations governing its dynamics are derived from conservation of mass, energy, and momentum. Simple analytical solutions are obtained in the two limiting cases of ultra-relativistic and non-relativistic reverse shock. Equations are derived for the general explosion problem.Comment: 8 pages, accepted to ApJ Letter

Evidence of Bulk Acceleration of the GRB X-ray Flare Emission Region

Applying our recently-developed generalized version of the high-latitude emission theory to the observations of X-ray flares in gamma-ray bursts (GRBs), we present here clear observational evidence that the X-ray flare emission region is undergoing rapid bulk acceleration as the photons are emitted. We show that both the observed X-ray flare light curves and the photon index evolution curves can be simultaneously reproduced within a simple physical model invoking synchrotron radiation in an accelerating emission region far from the GRB central engine. Such an acceleration process demands an additional energy dissipation source other than kinetic energy, which points towards a significant Poynting-flux in the emission region of X-ray flares. As the X-ray flares are believed to share a similar physical mechanism as the GRB prompt emission, our finding here hints that the GRB prompt emission jets may also carry a significant Poynting-flux in their emitting region.Comment: 2 figures, accepted for publication in ApJ Letter

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

United States and Canadian Free Trade Agreement: Economic Implications

International Relations/Trade,

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