Microlensing of Gamma Ray Bursts by Stars and MACHOs

The microlensing interpretation of the optical afterglow of GRB 000301C seems naively surprising, since a simple estimate of the stellar microlensing rate gives less than one in four hundred for a flat ΩΛ = 0.7 cosmology, whereas one event was seen in about thirty afterglows. Considering baryonic MACHOs making up half of the baryons in the universe, the microlensing probability per burst can be roughly 5 % for a GRB at redshift z = 2. We explore two effects that may enhance the probability of observing microlensed gamma-ray burst afterglows: binary lenses and double magnification bias. We find that the consideration of binary lenses can increase the rate only at the ∼ 15% level. On the other hand, because gamma-ray bursts for which afterglow observations exist are typically selected based on fluxes at widely separated wavebands which are not necessarily well correlated (e.g. localization in X-ray, afterglow in optical/infrared), magnification bias can operate at an enhanced level compared to the usual single– bias case. Using a simple model for the selection process in two bands, we compute the enhancement to microlensing rate due to magnification bias in two cases: perfect correlation and complete independence of the flux in the two bands. We find that existing estimates of the slope of the luminosity function of gamma-ray bursts, while as yet quite uncertain, point to enhancement factors of more than three above the simple estimates of the microlensing rate. We find that the probability to observe at least one microlensing event in the sample of 27 measured afterglows can be 3 − 4 % for stellar lenses, or as much as 25Ωlens for baryonic MACHOs. We note that the probability to observe at least one event over the available sample of afterglows is significant only if a large fraction of the baryons in the universe are condensed in stellar–mass objects. Subject headings: gamma rays:bursts — gravitational lensing – binaries: general 1