Microlensing of gamma-ray burst afterglows

The afterglow of a cosmological gamma-ray burst (GRB) should appear on the sky as a narrow emission ring of radius ∼ 3 × 10¹⁶ cm (t/day)^5/8 that expands faster than light. After a day, the ring radius is comparable to the Einstein radius of a solar mass lens at a cosmological distance. Thus, microlensing by an intervening star can significantly modify the light curve and polarization signal from a GRB after-glow. We show that the achromatic amplification signal of the afterglow flux can be used to determine the impact parameter and expansion rate of the source in units of the Einstein radius of the lens, and we probe the superluminal nature of the expansion. If the synchrotron emission from the afterglow photosphere originates from a set of coherent magnetic field patches, microlensing would induce polarization variability as a result of the transient magnification of the patches behind the lens. The microlensing interpretation of the flux and polarization data can be confirmed by a parallax experiment that would probe the amplification peak at different times. The fraction of microlensed afterglows can be used to calibrate the density parameter of stellar-mass objects in the universe.