This paper discusses the X-ray halo around the Swift gamma-ray burst GRB 050724 (z=0.258), detected by the Swift X-Ray Telescope. The halo, which forms a ring around the fading X-ray source, expands to a radius of 200 within 8 ks of the burst exactly as expected for small-angle X-ray scattering by Galactic dust along the line of sight to a cosmologically distant GRB. The expansion curve and radial profile of the halo constrain the scattering dust to be concentrated at a distance of D = 139 +/- 9 pc (from Earth) in a cloud/sheet of thickness delta-D < 22 pc. The halo was observed only out to scattering angles of 200, for which the scattering is dominated by the largest grains, with a maximum size estimated to be a_max ~ 0.4-0.5 um. The scattering-to-extinction ratio was estimated to be tau_scat/A_V > 0.022; this is a lower limit to the true value because contribution from smaller grains, which scatter to larger angles, was not directly observed. The line-of-sight to the GRB passes close to the Ophiuchus molecular cloud complex, which provides a plausible site for the scattering dust.
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