We present detailed calculations of nonthermal synchrotron and synchrotron self-Compton (SSC) spectra radiated by blast waves that are energized by interactions with a uniform surrounding medium. Radio, optical, X-ray and gamma-ray light curves and spectral indices are calculated for a standard parameter set that yields hard GRB spectra during the prompt emission phase. Because no lateral spreading of the blast-wave is assumed, the calculated temporal breaks represent the sharpest breaks possible from collimated outflows in a uniform surrounding medium. Absence of SSC hardenings in observed GRB X-ray afterglows indicates magnetic field generation toward equipartition as the blast wave evolves. EGRET detections of 100 MeV-GeV photons observed promptly and 90 minutes after GRB 940217 are attributed to nonthermal synchrotron radiation and SSC emission from a decelerating blast wave, respectively. The SSC process will produce prompt TeV emission that could be observed from GRBs with redshifts z < ∼ 0.1, provided γ-γ opacity in the source is small. Measurements of the time dependence of the 100 MeV-GeV spectral indices with the planned GLAST mission will chart the evolution of the SSC component and test the external shock scenario. Transient optical and X-ray emissions from misaligned GRBs are generally much weaker than on-axis emissions produced by dirty and clean fireballs that would themselves not trigger a GRB detector; thus detection of long wavelength transients not associated with GRBs will not unambiguously demonstrate GRB beaming.
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We wish to thank the editors John Taylor and Harald Uhlig, discussants of the chapter, Carlos Thomas, Claudio Michelacci, Tony Smith and Chris Tonetti, as well as seminar participants at several conferences and institutions for many useful comments and Simone Civale for outstanding research assistance. Krueger gratefully acknowledges financial support from the NSF under grants SES 1123547 and SES 1326781. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.
We have developed a computer model to calculate gamma ray burst (GRB) light curves and efficiencies from the interaction of a single, thin blast wave with clouds in the external medium. Large amplitude, short timescale variability occurs when the clouds have radii r ≪ R/Γ, where R is the mean distance of a cloud from the GRB source and Γ is the blast-wave Lorentz factor. Efficiencies ∼ > 10% require a large number of small clouds, each with sufficiently large column densities to extract most of the available blast-wave energy in the region of interaction. The number and duration of pulses in the simulated GRB light curves are compared with the respective properties found in GRB light curves. If GRB sources are surrounded by clouds with such properties, then short timescale variability of GRBs can be obtained in the external shock model.
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