We present uniform, detailed spectral analyses of γ-ray burst (GRB) X-ray afterglows observed with ASCA, Beppo-SAX, Chandra, and XMM-Newton, and critically evaluate the statistical significances of X-ray emission and absorption features in these spectra. The sample consists of 21 X-ray afterglow observations up to and including that of GRB040106 with spectra of sufficient statistical quality to allow meaningful line searches, chosen here somewhat arbitrarily to be detections with more than 100 total (source plus background) counts. This sample includes all nine X-ray afterglows with published claims of line detections. Moderate resolution spectra are available for 16 of the 21 sources, and for the remaining five the Chandra transmission grating spectrometers obtained high-resolution data. All of the data are available from the public archive. We test a simple hypothesis in which the observed spectra are produced by a powerlaw continuum model modified by photoelectric absorption by neutral material both in our Galaxy and possibly also local to the burst. As a sample, these afterglow spectra are consistent with this relatively simple model. However, since the χ 2 statistic is not sensitive to weak and/or localized fluctuations, we have performed Monte Carlo simulations to search for discrete features and t
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