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We calculate the afterglow emission for gamma-ray bursts (GRBs) going off in an extremely low density medium, referred to as naked bursts . Our results also apply to the case where the external medium density falls off sharply at some distance from the burst. The observed afterglow flux in this case originates at high latitudes, i.e., where the angle between the fluid velocity and the observer line of sight is greater than Γ -1 . The observed peak frequency of the spectrum for naked bursts decreases with observer time as t -1 , and the flux at the peak of the spectrum falls off as t -2 . The 2-10 keV X-ray flux from a naked burst of average fluence should be observable by the Swift satellite for time duration of about 10 3 longer than the burst variability timescale. The high-latitude emission contributes to the early X-ray afterglow flux for any GRB, not just naked bursts, and can be separated from the shocked interstellar medium emission by their different spectral and temporal properties. Measurements of the high-latitude emission could be used to map the angular structure of GRB-producing shells.
Kumar et al. (2000) studied this question.