Cosmological Microlensing Statistics: Variability rates for Quasars and GRB Afterglows, and implications for macrolensing magnification bias and flux ratios

Abstract

The fraction of quasar's and gamma-ray burst (GRB) afterglows that vary due to 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 1 in 3 multiply imaged quasars should vary by more than 0.5 magnitudes per decade due to microlensing, while 10% of macrolensed GRB afterglows should show a departure of more than 0.5 magnitudes from their intrinsic light-curve during the first 30 days. However microlensing by stars is rare in general, with only 1 source in ~500 varying by more than 0.5 magnitudes 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 magnitudes) images rises significantly to ~1 in 10 for quasars and ~1 in 5 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.