X-ray lines from gamma-ray bursts

X-ray lines have been recently detected in the afterglows of a few gamma-ray bursts. We derive general constraints on the physical conditions in the line-emitting gas and illustrate our results using as an example the multiple Kalpha lines detected by Reeves et al. in GRB 011211. We argue that photoionization models previously discussed in the literature require either a very extreme geometry or too much mass in the line-emitting region. Shock-heated models also have a serious problem since they require the emitting region to have a large optical depth unless electrons in this region are shock-heated multiple times. We propose a new model in which gamma rays from the burst and hard X-rays from the early afterglow are backscattered by an electron-positron pair screen at a distance of about 10(14)-10(15) cm from the source and irradiate the expanding outer layers of the supernova ejecta, thereby producing X-ray lines. The model suers from fewer problems compared to previous models. It also has the advantage of requiring only a single explosion to produce both the gamma-ray burst (GRB) and the supernova ejecta, in contrast to most other models for the lines that require the supernova to go off days or weeks prior to the GRB. The model, however, has difficulty explaining the greater than 10(48) ergs of energy emitted in the X-ray lines, which requires somewhat extreme choices of model parameters. The difficulties associated with the various models are not particular to GRB 011211. They are likely to pose a problem for any GRB with X-ray lines.