Images and Spectra from the Interior of a Relativistic Fireball

The detection of an afterglow, following a gamma-ray burst (GRB), can bedescribed reasonably well by synchrotron emission from a relativistic sphericalexpanding blast wave, driven by an expanding fireball. We perform detailedcalculations considering the emission from the whole region behind the shockfront. We use the Blandford McKee self similar adiabatic solution to describethe fluid behind the shock. Using this detailed model, we derive expressionsfor the peak flux, and the peak frequency at a given observed time. Theseexpressions provide important numerical corrections to previous, moresimplified models. We calculate the observed light curve and spectra forseveral magnetic field models. We show that both the light curve and thespectra are flat near the peak. This rules out the interpretation of theoptical peak of GRB970508 as the peak of the light curve, predicted by theexisting fireball models. We calculate the observed image of a GRB afterglow.The observed image is bright near the edge and dimmer at the center, thuscreating a ring. The contrast between the edge and the center is larger at highfrequencies and the width of the ring is smaller.Comment: 32 page latex file including 14 figures and 2 table