A comprehensive analysis of Swift/XRT data: I. Apparent spectral evolution of GRB X-ray tails

An early steep decay component following the prompt GRBs is commonly observed in {\em Swift} XRT light curves, which is regarded as the tail emission of the prompt gamma-rays. Prompted by the observed strong spectral evolution in the tails of GRBs 060218 and 060614, we present a systematic time-resolved spectral analysis for the {\em Swift} GRB tails detected between 2005 February and 2007 January. We select a sample of 44 tails that are bright enough to perform time-resolved spectral analyses. Among them 11 tails are smooth and without superimposing significant flares, and their spectra have no significant temporal evolution. We suggest that these tails are dominated by the curvature effect of the prompt gamma-rays due to delay of propagation of photons from large angles with respect to the line of sight . More interestingly, 33 tails show clear hard-to-soft spectral evolution, with 16 of them being smooth tails directly following the prompt GRBs,while the others being superimposed with large flares. We focus on the 16 clean, smooth tails and consider three toy models to interpret the spectral evolution. The curvature effect of a structured jet and a model invoking superposition of the curvature effect tail and a putative underlying soft emission component cannot explain all the data. The third model, which invokes an evolving exponential spectrum, seems to reproduce both the lightcurve and the spectral evolution of all the bursts, including GRBs 060218 and 060614. More detailed physical models are called for to understand the apparent evolution effect.Comment: 13 pages in emulateapj style,6 figures, 1 table, expanded version, matched to published version, ApJ, 2007, in press. This is the first paper of a series. Paper II see arXiv:0705.1373 (ApJ,2007, in press

The gain and carrier density in semiconductor lasers under steady-state and transient conditions

The carrier distribution functions in a semiconductor crystal in the presence of a strong optical field are obtained. These are used to derive expressions for the gain dependence on the carrier density and on the optical intensity-the gain suppression effect. A general expression for high-order nonlinear gain coefficients is obtained. This formalism is used to describe the carrier and power dynamics in semiconductor lasers above and below threshold in the static and transient regimes