Images and Spectra from the Interior of a Relativistic Fireball

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Abstract
The power-law decay of gamma-ray burst (GRB) afterglow can be well described by synchrotron emission from a relativistic spherical blast wave, driven by an expanding fireball. We calculate the spectrum and the light curve expected from an adiabatic blast wave which is described by the Blandford-McKee self-similar solution. These calculations include emission from the whole blast wave and not just from the shock front. We provide numerical corrections that can be used to modify simple analytic estimates of such emission. We find that the expected light curve and spectra are flat near the peak. This rules out the interpretation of the sharp optical peak observed in GRB 970508 as the peak of the light curve. We also calculate the observed image of an afterglow. This image could be resolved in future VLBI observations, and its structure could influence microlensing and scintillation. The observed image is ringlike: brighter near the edge and dimmer at the center. The image depends on the observed frequency. The contrast between the edge and the center increases and the ring becomes narrower at higher frequencies.
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