BATSE gamma-ray burst line search .5. Probability of detecting a line in a burst

The physical importance of the apparent discrepancy between the detections by pre-BATSE missions of absorption lines in gamma-ray burst spectra and the absence of a BATSE line detection necessitates a statistical analysis of this discrepancy. This analysis requires a calculation of the probability that a line, if present, will be detected in a given burst. However, the connection between the detectability of a line in a spectrum and in a burst requires a model for the occurrence of a line within a burst. We have developed the necessary weighting for the line detection probability for each spectrum spanning the burst. The resulting calculations require a description of each spectrum in the BATSE database. With these tools, we identify the bursts in which lines are most likely to be detected. Also, by assuming a small frequency with which lines occur, we calculate the approximate number of BATSE bursts in which lines of various types could be detected. Lines similar to the Ginga detections can be detected in relatively few BATSE bursts; for example, in only similar to 20 bursts are lines similar to the GB 880205 pair of lines detectable. Ginga reported lines at similar to 20 and similar to 40 keV, whereas the low-energy cutoff of the BATSE spectra is typically above 20 keV; hence BATSE's sensitivity to lines is less than that of Ginga below 40 keV, and greater above. Therefore, the probability that the GB 880205 lines would be detected in a Ginga burst rather than a BATSE burst is similar to 0.2. Finally, we adopt a more appropriate test of the significance of a line feature.