Microlensing of $γ$-Ray Burst Afterglows

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Abstract
The afterglow of a cosmological Gamma-Ray Burst (GRB) should appear on the sky as a narrow emission ring of radius 3x10^{16}cm(t/day)^{5/8} which 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 modify significantly the lightcurve and polarization signal from a GRB afterglow. 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 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 due to 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 which 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.

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