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We have conducted a thorough and blind search for emission lines in >70 SwiftX-ray afterglows of total exposure ~10^7s. We find that most afterglows areconsistent with pure power-laws plus extinction. Significant outliers to thepopulation exist at the 5-10% level and have anomalously soft, possibly thermalspectra. Four bursts are singled out via possible detections of 2-5 lines: GRBs060218, 060202, 050822, and 050714B. Alternatively, a blackbody model withkT~0.1-0.5 keV can describe the soft emission in each afterglow. The mostsignificant soft component detections in the full data set of ~2000 spectracorrespond to GRB060218/SN2006aj, with line significances ranging up to\~20-sigma. A thermal plasma model fit to the data indicates that the flux isprimarily due to L-shell transitions of Fe at ~ solar abundance. We associate(>4-sigma significant) line triggers in the 3 other events with K-shelltransitions in light metals. We favor a model where the possible line emissionin these afterglows arises from the mildly relativistic cocoon of mattersurrounding the GRB jet as it penetrates and exits the surface of theprogenitor star. The emitting material in each burst is at a similar distance\~10^12--10^13 cm, a similar density ~10^17 cm^-3, and subject to a similarflux of ionizing radiation. The lines may correlate with the X-ray flaring. Forthe blackbody interpretation, the soft flux may arise from break out of the GRBshock or plasma cocoon from the progenitor stellar wind, as recently suggestedfor GRB060218 (Campana et al. 2006). Due to the low z of GRB060218, burstsfaint in Gamma-rays with fluxes dominated by this soft X-ray component couldoutnumber classical GRBs 100-1.Comment: 32 pages, 10 tables, 17 figures, To Appear in ApJ v656, February 20,  200

On the Early‐Time X‐Ray Spectra ofSwiftAfterglows. I. Evidence for Anomalous Soft X‐Ray Emission