Abstract
The external forward shock (EFS) models have been the standard paradigm to
interpret the broad-band afterglow data of gamma-ray bursts (GRBs). One
prediction of the models is that some afterglow temporal breaks at different
energy bands should be achromatic. Observations in the Swift era have revealed
chromatic afterglow behaviors at least in some GRBs, casting doubts on the EFS
origin of GRB afterglows. In this paper, we perform a systematic study to
address the question: how bad/good are the external forward shock models? Our
sample includes 85 GRBs well-monitored X-ray and optical lightcurves. Based on
how well the data abide by the EFS models, we categorize them as: Gold sample:
(Grade I and II) include 45/85 GRBs. They show evidence of, or are consistent
with having, an achromatic break. The temporal/spectral behaviors in each
afterglow segment are consistent with the predictions (closure relations) of
the EFS models. Silver sample: (Grade III and IV) include 37/85 GRBs. They are
also consistent with having an achromatic break, even though one or more
afterglow segments do not comply with the closure relations. Bad sample: (Grade
V), 3/85 shows direct evidence of chromatic behaviors, suggesting that the EFS
models are inconsistent with the data. These are included in the Bad sample. We
further perform statistical analyses of various observational properties
(\$\alpha\$, \$\beta\$, \$t\_b\$ and model parameters (energy injection index q, p,
\$þeta\_j\$, \$\eta\_\gamma\$, etc) of the GRBs in the Gold Sample, and derive
constraints on the magnetization parameter \$\epsilon\_B\$ in the EFS. Overall, we
conclude that the simplest EFS models can account for the multi-wavelength
afterglow data of at least half of the GRBs. When more advanced modeling (e.g.,
long-lasting reverse shock, structured jets) is invoked, up to \$>90 \%\$ of the
afterglows may be interpreted within the framework of the ESF models.
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