Context. Most X-ray afterglows of gamma-ray bursts (GRBs) observed by the Swift satellite have a shallow decay phase ∝1/2 in the first few hours. Aims. This is not predicted by the standard afterglow model and needs an explanation. Methods. We discuss that the shallow decay requires an unreasonably high gamma-ray efficiency, ≳75-90%, within current models, which is difficult to produce by internal shocks. Such a crisis may be avoided if a weak relativistic explosion occurs ∼103-106 s prior to the main burst or if the microphysical parameter of the electron energy increases during the shallow decay, εeoc ∝ t1/2 The former explanation predicts a very long precursor, while both prefer dim optical flashes from the reverse shock, as was recently reported. We also calculate the multi-wavelength afterglows and compare them with observations. Results. No optical break at the end of the shallow X-ray decay indicates a preference for the time-dependent microphysics model with additionally decaying magnetic fields, εB ∝ t-0.6.
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