X‐Ray Hardness Variations as an Internal/External Shock Diagnostic

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Abstract
The early, highly time-variable X-ray emission immediately following gamma-ray bursts (GRBs) exhibits strong spectral variations that are unlike the temporally smoother emission that dominates after t ~ 103 s. The ratio of hard-channel (1.3-10.0 keV) to soft-channel (0.3-1.3 keV) counts in the Swift X-ray telescope provides a new measure delineating the end time of this emission. We define TH as the time at which this transition takes place and measure for 59 events a range of transition times that spans 10 2 to 104 s, on average 5 times longer than the prompt T90 duration observed in the gamma-ray band. It is very likely that the mysterious light-curve plateau phase and the later power-law temporal evolution, both of which typically occur at times greater than TH and hence exhibit very little hardness ratio evolution, are both produced by external shocking of the surrounding medium and not by the internal shocks thought responsible for the earlier emission. We use the apparent lack of spectral evolution to discriminate among proposed models for the plateau phase emission. We favor energy injection scenarios with a roughly linearly increasing input energy versus time for six well-sampled events with nearly flat light curves at t ≈ 103-104 s. Also, using the transition time TH as the delineation between the GRB and afterglow emission, we calculate that the kinetic energy in the afterglow shock is typically a factor of 10 lower than that released in the GRB. Three very bright events suggest that this presents a missing X-ray flux problem rather than an efficiency problem for the conversion of kinetic energy into the GRB. Lack of hardness variations in these three events may be due to a very highly relativistic outflow or due to a very dense circumburst medium. There are a handful of rare cases of very late time t > 104 s hardness evolution, which may point to residual central engine activity at very late time.