On the probability of microlensing in gamma-ray burst afterglows

The declining light curve of the optical afterglow of gamma-ray burst (GRB) GRB000301C showed rapid variability with one particularly bright feature a t about t - t(0) = 3.8 d. This event was interpreted as gravitational micro lensing by Garnavich, Loeb & Stanek and subsequently used to derive constra ints on the structure of the GRB optical afterglow. In this paper, we use t hese structural parameters to calculate the probability of such a microlens ing event in a realistic scenario, where all compact objects in the univers e are associated with observable galaxies. For GRB000301C at a redshift of z = 2.04, the a posteriori probability for a microlensing event with an amp litude of Deltam greater than or equal to 0.95 mag (as observed) is 0.7 per cent (2.7 per cent) for the most plausible scenario of a flat A-dominated Friedmann-Robertson-Walker (FRW) universe with Ohm (m) = 0.3 and a fraction f* = 0.2 (1.0) of dark matter in the form of compact objects. If we lower the magnification threshold to Deltam greater than or equal to 0.10 mag, th e probabilities for microlensing events of GRB afterglows increase to 17 pe r cent (57 per cent). We emphasize that this low probability for a microlen sing signature of almost I mag does not exclude that the observed event in the afterglow light curve of GRB000301C was caused by microlensing, especia lly in light of the fact that a galaxy was found within 2 arcsec from the G RB. In that case, however, a more robust upper limit on the a posteriori pr obability of approximate to5 per cent is found. It does show, however, that it will not be easy to create a large sample of strong GRB afterglow micro lensing events for statistical studies of their physical conditions on micr oarcsec scales.