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Analysis of Two Scenarios for the Early Optical Emission of the GRB Afterglows 990123 and 021211

The optical light-curves of GRB afterglows 990123 and 021211 exhibit a steep decay at 100--600 seconds after the burst, the decay becoming slower after about 10 minutes. We investigate two scenarios for the fast decaying early optical emission of these GRB afterglows. In the reverse-forward shock scenario, this emission arises in the reverse shock crossing the GRB ejecta, the mitigation of the light-curve decay occurring when the forward shock emission overtakes that from the reverse shock. Both a homogeneous and wind-like circumburst medium are considered. In the wind-bubble scenario, the steeply decaying, early optical emission arises from the forward shock interacting with a 1/r^2 bubble, with a negligible contribution from the reverse shock, the slower decay starting when the blast wave reaches the bubble termination shock and enters a homogeneous region of the circumburst medium. We determine the shock microphysical parameters, ejecta kinetic energy, and circumburst density which accommodate the radio and optical measurements of the GRB afterglows 990123 and 021211. We find that, for a homogeneous medium, the radio and optical emissions of the afterglow 990123 can be accommodated by the reverse-forward shock scenario if the microphysical parameters behind the two shocks differ substantially. A wind-like circumburst medium also allows the reverse-forward shocks scenario to account for the radio and optical properties of the afterglows 990123 and 021211, but the required wind densities are at least 10 times smaller than those of Galactic Wolf-Rayet stars. The wind-bubble scenario requires a variation of the microphysical parameters when the afterglow fireball reaches the wind termination shock, which seems a contrived feature.