Small-Angle Scattering of X-Rays from Extragalactic Sources by Dust in Intervening Galaxies

Gamma-ray bursts are now known to be a cosmological population of objects, which are often accompanied by X-ray and optical afterglows. The total energy emitted in the afterglow can be similar to the energy radiated in the gamma-ray burst itself. If a galaxy containing a large column density of dust is near the line of sight to a gamma-ray burst, small-angle scattering of the X-rays due to diffraction by the dust grains will give rise to an X-ray echo of the afterglow. A measurement of the angular size of the echo at a certain time after the afterglow is observed yields a combination of the angular diameter distances to the scattering galaxy and the gamma-ray burst that can be used to constrain cosmological models in the same way as a time delay in a gravitational lens. The scattering galaxy will generally cause gravitational lensing as well, and this should modify the shape of the X-ray echo from a circular ring. The main difficulty in detecting this phenomenon is the very low flux expected for the echo. The flux can be increased when the gamma-ray burst is highly magnified by gravitational lensing, or when the deflecting galaxy is at low redshift. X-ray echos of continuous (but variable) sources, such as quasars, may also be detectable with high-resolution instruments and would allow similar measurements.