Efficiency Crisis of Swift Gamma-Ray Bursts with Shallow X-ray Afterglows : Prior Activity or Time-Dependent Microphysics?

Context. Most X-ray afterglows of gamma-ray bursts (GRBs) observed by the Swift satellite have a shallow decay phase $\propto$$t^{-1/2}$ in the first few hours. Aims. This is not predicted by the standard afterglow model and needs an explanation. Methods. We discuss that the shallow decay requires an unreasonably high gamma-ray efficiency, $\ga$$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 ~$10^3{-}10^6$ s prior to the main burst or if the microphysical parameter of the electron energy increases during the shallow decay, $\epsilon_{\rm e} \propto t^{1/2}$. 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, $\epsilon_B \propto t^{-0.6}$.