Dust Echoes from the Ambient Medium of Gamma-Ray Bursts

Long gamma-ray bursts (GRBs) are likely associated with the collapse of massive stars, which produce dust and are born in dusty environments. Absorption and scattering of ultraviolet/X-ray photons from the prompt, optical flash and afterglow emission of the GRB produce dust echoes. We perform time-dependent calculations of these echoes, accounting for the evolution of the dust grain distribution due to selective grain destruction by the GRB radiation, and for off-axis beaming. We explore cloud configurations of differing density and size -- the echo light curve and spectrum depend on the cloud radius, with larger clouds peaking at longer wavelengths. For a region ~ 3 pc in size with hydrogen density ~ 1000 per cubic centimeter, the echo spectrum peaks at ~ 3.6 microns and ~ 8.8 eV for thermal and scattered components, respectively. Dust echoes should be detectable with the Very Large Telescope up to z ~ 0.1, IRAC onboard the Spitzer Space Telescope up to z ~ 0.2, and NICMOS onboard the Hubble Space Telescope up to z ~ 0.3. Furthermore, the shape of the echo light curve allows one to infer: the jet opening angle; the inclination of the jet axis with respect to the line of sight; the size of the dust-emitting region. For sources with symmetric, bipolar jets, dust echoes exhibit two bumps in the light curve, making them easily distinguishable from the rebrightening due to an underlying supernova.