Nonthermal Synchrotron Radiation from Gamma‐Ray Burst External Shocks and the X‐Ray Flares Observed withSwift

Abstract

An analysis of the interaction between a spherical relativistic blast-wave shell and a stationary cloud with a spherical cap geometry is performed assuming that the cloud width ∆ cl ≪ x, where x is the distance of the cloud from the GRB explosion center. The interaction is divided into three phases:(1) a collision phase with both forward and reverse shocks; (2) a penetration phase when either the reverse shock has crossed the shell while the forward shock continues to cross the cloud, or vice versa; and (3) an expansion phase when, both shocks having crossed the cloud and shell, the shocked fluid expands. Temporally evolving spectral energy distributions (SEDs) are calculated for the problem of the interaction of a blast-wave shell with clouds that subtend large and small angles compared with the Doppler(-cone) angle θ 0 = 1/Γ 0 , where Γ 0 is the coasting Lorentz factor. The Lorentz factor evolution of the shell/cloud collision is treated in the adiabatic limit. Behavior of the light curves and SEDs on, e.g., Γ 0 , shell-width parameter η, where ∆ 0 + ηx/Γ 2 0 is the blast-wave shell width, and properties and locations of the cloud is examined. Short timescale variability (STV) in GRB light curves, including ∼ 100 keV γ-ray pulses observed with BATSE and delayed ∼ 1 keV X-ray flares found with Swift, can be explained by emissions from an external shock formed by the GRB blast wave colliding with small density inhomogeneities in the "frozen pulse" approximation (η → 0), and perhaps in the thin-shell approximation (η ≈ 1/Γ 0 ), but not when η ≈ 1. If the frozen-pulse approximation is valid, then external shock processes could make the dominant prompt and afterglow emissions in GRB light curves, consistent with short delay two-step collapse models for GRBs.

Analysis of GRB 080319b and GRB 050904 Within the Fireshell Model: Evidence for a Broader Spectral Energy Distribution

“…It is emphasized that, from the correct computations of the equations of motion of the shell and of the Lorentz γ factor, the short-timescale variability of GRB light curves occurs in regimes with the largest values of the Lorentz gamma factor, when the total visible area of the emission region is very small and the "dispersion" in arrival time of the luminosity peaks is negligible. Therefore, under this condition, the short-timescale variability of GRB light curves can be produced by inhomogeneities in the CBM, as found also by Dermer & Mitman (1999) and Dermer (2006Dermer ( , 2008. The application of the fireshell model leads to a direct evaluation of the filamentary and clumpy structure of the CBM, which was already predicted in pioneering works by Enrico Fermi in the theoretical study of interstellar matter (ISM) in our galaxy (Fermi 1949(Fermi , 1954, and is much in line with the knowledge obtained from various studies of the ISM in galaxies (see, for example, Kim et al 1998;Lockman 2002;Finkelstein et al 2009).…”

A Comparison of the Afterglows of Short- And Long-Duration Gamma-Ray Bursts

“…A potentially simple explanation of the results presented here is that both the afterglow and the prompt emission are due to an external interaction (e.g., Dermer 2008). In this case, both the afterglow and prompt emission might be expected to scale similarly.…”

Where are the prompt emitting regions of long GRBs?

“…Part of the kinetic energy is dissipated into prompt γ -ray radiation energy by internal processes, e.g., internal shocks and/or magnetic reconnection (Piran 2005a). Alternatively, the external shock model (Mészáros and Rees 1993;Sari and Piran 1996;Dermer et al 1999;Dermer 2004Dermer , 2008Ramirez-Ruiz and Granot 2007) or the electromagnetic model (Lyutikov and Blandford 2003;Lyutikov 2006a) had also been invoked in interpreting GRBs. Recently, Narayan and Kumar (2009) proposed another interesting turbulent model in which they pointed out that all pulses in the γ -ray light-curve are roughly produced from the same site, compatible with the requirement of electromagnetic model in Lyutikov and Blandford (2003).…”

“…Recently, Narayan and Kumar (2009) proposed another interesting turbulent model in which they pointed out that all pulses in the γ -ray light-curve are roughly produced from the same site, compatible with the requirement of electromagnetic model in Lyutikov and Blandford (2003). Furthermore, all above models can reproduce fast variability in their resulting GRB light-curves (Dermer 2008;Lyutikov 2006b;Narayan and Kumar 2009;Kumar 2007).…”

“…The typical internal shock radius is about R ∼ 10 12 -10 13 cm (Rees and Mészáros 1994;Lazzati et al 1999;Piran 2005b), while GRB pulses from an external shock are thought to originate at a representative distance of 10 15 -10 17 cm from their central engine (Dermer 2008). Similarly, the emitting regions in the frames of electromagnetic model and turbulence model are at least three orders larger than the internal shock radius.…”