Light Curves and Spectra of Dust Echoes from Gamma-Ray Bursts and Their Afterglows: Continued Evidence That GRB 970228 Is Associated with a Supernova

The relative brightening and reddening of the optical afterglows of GRB 970228 and GRB 980326 around 20-30 days after these bursts have been attributed to supernovae, which are red (blueward of their spectral peak) and which peak in time after ≈20(1 + z) days. However, this direct evidence for a gamma-ray burst/supernova (GRB/SN) connection has recently been challenged. It has been suggested that the late afterglows of these bursts can be explained by dust echoes, of which we consider two cases: (1) the scattering of light from the afterglow (the forward shock), the optical flash (the reverse shock), and/or the optical light from the burst itself by a shell of dust at a radius R from the progenitor and (2) the absorption and thermal reemission of this light by this shell of dust. In this paper, we model and compute dust echo light curves and spectra for both cases. Although the late-time afterglow of GRB 980326 was not sufficiently well sampled to rule out a dust echo description, we find that the late-time afterglow of GRB 970228 cannot be explained by a dust echo.