The Statistics of Gamma Ray Burst Lensing

Possibly the only unambiguous verification that gamma-ray bursts (GRBs) are at cosmological distances would be the observation of multiple images of a gravitationally lensed burst. Each images would arrive at a different time, but exhibit identical light curves. We improve upon previous calculations of GRB lensing by using revised cosmological burst models based upon better knowledge of burst spectra, and we consider several sets of cosmological parameters. Only lensing by the known population of galaxies is considered, and we compute the lensing rate and amplification bias using three different lens models. Assuming that 800 bursts per year are above the detection threshold of the BATSE experiment on the Compton Gamma-Ray Observatory, we predict one lensing event every 1.5--25 years, with a median time delay between images of about 7 days. However, BATSE has an instrumental efficiency of about 12\% for detecting double bursts, decreasing the detection rate to fewer than one per century for some cosmological parameters. This inefficiency can be overcome partially if cases of quadruple imaging by elliptical potentials are common, but simulations show that lensing by elliptical potentials enhances the detection rate by only about 20\%. We conclude that it is unlikely that the BATSE experiment will detect a lensed burst, but that a future experiment, which is either much more sensitive or has a much more efficient duty cycle, could.