Microlensing of collimated Gamma-Ray Burst afterglows

We investigate stellar microlensing of the collimated gamma-ray burst afterglows. A spherical afterglow appears on the sky as a superluminally expanding thin ring (“ring-like” image), which is maximally amplified as it crosses the lens. We find that the image of the collimated afterglow becomes quite uniform (“disk-like” image) after the jet break time (after the Lorentz factor of the jet drops below the inverse of the jet opening angle). Consequently, the amplification peak in the light curve after the break time is lower and broader, and even disappears at frequencies above the typical synchrotron frequency (optical and X-ray) but remains at low frequencies (radio). Therefore multi-band observations are important to constrain the cosmological density of the stellar mass objects. We also show that some proper motion and polarization is expected, peaking around the maximum amplification. A low peak in the optical light curve with the detection of the peak in the radio light curve, proper motion or polarization can test whether the afterglows are jets or not.