Echo emission from dust scattering and x-ray afterglows of gamma-ray bursts

We investigate the effect of X-ray echo emission in gamma-ray bursts (GRBs). We find that the echo emission can provide an alternative way of understanding X-ray shallow decays and jet breaks. In particular, a shallow decay followed by a "normal" decay and a further rapid decay of X-ray afterglows can together be explained as being due to the echo from prompt X-ray emission scattered by dust grains in a massive wind bubble around a GRB progenitor. We also introduce an extra temporal break in the X-ray echo emission. By fitting the afterglow light curves, we can measure the locations of the massive wind bubbles, which will bring us closer to finding the mass-loss rate, wind velocity, and age of the progenitors prior to the GRB explosions.