Cosmological microlensing statistics: Variability rates for quasars and gamma-ray burst afterglows and implications for macrolensing magnification bias and flux ratios

The fraction of quasars and gamma-ray burst (GRB) afterglows that vary because of microlensing by the stellar populations of intervening elliptical/S0 galaxies is computed by combining the joint distribution of effective microlensing convergence (kappa) and shear (gamma) with microlensing magnification patterns. Microlensing is common in multiply imaged sources. We find that one in three multiply imaged quasars should vary by more than 0.5 mag decade(-1) because of microlensing while 10% of macrolensed GRB afterglows should show a departure of more than 0.5 mag from their intrinsic light curve during the first 30 days. However, microlensing by stars is rare in general, with only one source in 500 varying by more than 0.5 mag during the same periods. We find that most microlensing by stars will be observed in a regime where gamma > 0.1. Thus, point-mass lenses do not provide an adequate description for most microlensing events. If dark matter halos contain a large fraction of mass in compact objects, the fraction of microlensed ( by 0.5 mag) images rises significantly to about one in 10 for quasars and about one in five for GRB afterglows. Comparison of variability between macrolensed and normal quasar images and a moderate number of well-sampled GRB afterglow light curves should therefore discover or refute the existence of stellar mass compact objects in galaxy halos. While microlensing results in departures of the distribution of magnifications from that of a smooth model, the effect on the macrolensing magnification bias for the discovery of lenses in quasar surveys is small. On the other hand, microlensing significantly broadens the distribution of macrolensed image flux ratios.