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 produces 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 that is ∼3 pc in size with a density of n_H ∼ 10³ cm^-3, the echo spectrum peaks at ∼3.6 μm and ∼8.8 eV for the thermal and scattered components, respectively. Dust echoes should be detectable with the Very Large Telescope up to z ∼ 0.1, with IRAC, on board the Spitzer Space Telescope, up to z ∼ 0.2, and with NICMOS, on board 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, and 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.