Testing the Standard Fireball Model of Gamma-Ray Bursts Using Late X-Ray Afterglows Measured by Swift

We show that all X-ray decay curves of γ-ray bursts (GRBs) measured by Swift can be fitted using one or two components, both of which have exactly the same functional form comprised of an early falling exponential phase followed by a power-law decay. The first component contains the prompt γ-ray emission and the initial X-ray decay. The second component appears later, has a much longer duration, and is present for ≈80% of GRBs. It most likely arises from the external shock that eventually develops into the X-ray afterglow. In the remaining ≈20% of GRBs the initial X-ray decay of the first component fades more slowly than the second and dominates at late times to form an afterglow. The temporal decay parameters and γ/X-ray spectral indices derived for 107 GRBs are compared to the expectations of the standard fireball model including a search for possible "jet breaks." For ~50% of GRBs the observed afterglow is in accord with the model, but for the rest the temporal and spectral indices do not conform to the expected closure relations and are suggestive of continued, late, energy injection. We identify a few possible jet breaks, but there are many examples where such breaks are predicted but are absent. The time T_a at which the exponential phase of the second component changes to a final power-law decay afterglow is correlated with the peak of the γ-ray spectrum, E_peak. This is analogous to the Ghirlanda relation, indicating that this time is in some way related to optically observed break times measured for pre-Swift bursts.