2005ApJ...618..403B

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 400 for a flat Ω_Λ=0.7 cosmology, whereas one event was seen in about 30 afterglows. Assuming baryonic MACHOs making up one-half the baryons in the universe, the microlensing probability per burst can be roughly 5% for a gamma-ray burst 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 on the basis of fluxes at widely separated wave bands that 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 of the 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 3 above the simple estimates of the microlensing rate. We find that the probability of observing at least one microlensing event in the sample of 27 measured afterglows can be 3%-4% for stellar lenses, or as much as 25 Ω_lensfor baryonic MACHOs. We note that the probability of observing 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.