2007ApJ...668L..95U

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 considered–shows that the decay indices of the X-ray and R-band light curves, α<sub>X</sub> and α<sub>o</sub>, obey a certain relation, and that in particular, α<sub>o</sub>-α<sub>X</sub> 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.