We have developed a functional fit which can be used to represent the entire temporal decay of the X-ray afterglow of gamma-ray bursts (GRBs). The fit delineates and parameterizes well-defined phases for the decay: the prompt emission; an initial steep decay; a shallow plateau phase; and finally, a powerlaw afterglow. For 20% of GRBs, the plateau phase is weak, or not seen, and the initial powerlaw decay becomes the final afterglow.
We compare the temporal decay parameters and X-ray spectral indices for 107 GRBs discovered by Swift with the expectations of the standard fireball model including a search for possible jet breaks. For approximately 50% of GRBs, the observed afterglow is in accord with the model, but for the rest the temporal and spectral properties are not as expected. We identify a few possible jet breaks, but there are many examples where such breaks are predicted but are absent. We also find that the start time of the final afterglow decay,
T
a
, is associated with the peak of the prompt
γ
-ray emission spectrum,
E
peak
, just as optical
jet-break
times,
t
j
, are associated with
E
peak
in the Ghirlanda relation.