Context. Most X-ray afterglows of gamma-ray bursts (GRBs) observed by the Swift satellite have a shallow decay phase proportional to t(-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, greater than or similar to 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 similar to 10(3)-10(6) s prior to the main burst or if the microphysical parameter of the electron energy increases during the shallow decay, epsilon(e) proportional to t(1/2). 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, epsilon(B) proportional to t(-0.6).