The connection between gamma-ray bursts (GRBs) and their afterglows is currently not well understood. Afterglow models of synchrotron emission generated by external shocks in the GRB fireball model predict emission detectable in the gamma-ray regime (25 keV). In this paper, we present a temporal and spectral analysis of a subset of BATSE GRBs with smooth extended emission tails to search for signatures of the "early high-energy afterglow," i.e., afterglow emission that initially begins in the gamma-ray phase and subsequently evolves into X-ray, UV, optical, and radio emission as the blast wave is decelerated by the ambient medium. From a sample of 40 GRBs we find that the temporal decays are best described with a power law ~tβ rather than an exponential with a mean index β ≈ -2. Spectral analysis shows that ~20% of these events are consistent with fast-cooling synchrotron emission for an adiabatic blast wave, three of which are consistent with the blast-wave evolution of a jet with Fν ~ t-p. This behavior suggests that in some cases, the emission may originate from a narrow jet, possibly consisting of "nuggets" whose angular sizes are less than 1/Γ, where Γ is the bulk Lorentz factor.
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