Testing the external-shock model of gamma-ray bursts using the late-time simultaneous optical and X-ray afterglows

We study the "normal" decay phase of the X-ray afterglows of gamma-ray bursts (GRBs), which follows the shallow decay phase, using the events simultaneously observed in the R band. The classical external-shock model - in which neither the delayed energy injection nor time dependency of shock microphysics is consideredshows that the decay indices of the X-ray and R-band light curves, α_x and α_o, obey a certain relation, and that in particular, α_o - α_x should be larger than -1/4 unless the ambient density increases with the distance from the central engine. For our selected 14 samples, we have found that four events violate the limit at more than the 3 σ level, so that a fraction of events are outliers of the classical external-shock model at the "normal" decay phase.