Gamma-ray burst (GRB) dust echoes were first proposed as an alternative
explanation for the supernova-like (SN-like) components to the afterglows of
GRB 980326 and GRB 970228. However, the spectroscopic identification of Type Ic
SN 2003dh associated with GRB 030329, as well as the identification of SN-like
components to the afterglows of other GRBs, appears to have confirmed the
GRB/SN paradigm. However, the likely progenitors of Type Ic SNe are Wolf-Rayet
WC stars, and late-type WC stars have been observed to be surrounded by dust,
at a distance of 10^14 -- 10^15 cm from the star. Consequently, we revisit the
possibility of GRB dust echoes, not on a timescale of weeks after the burst but
on a timescale of minutes to hours. We find that if the optical flash is
sufficiently bright and the jet sufficiently wide, GRB afterglows may be
accompanied by chromatic variations on this timescale. From these signatures,
such model parameters as the inner radius of the dust distribution, the initial
opening angle of the jet, etc., may be deduced. With rapid and regular
localizations of GRBs by HETE-2, Integral, and now Swift, and new and improved
robotic telescope systems, these early-time GRB dust echoes may soon be
detected. We describe one such robotic telescope system, called PROMPT, that
the University of North Carolina at Chapel Hill is building at the Cerro Tololo
Inter-American Observatory in greater detail.Comment: Accepted to The Astrophysical Journal, 15 pages, 5 figures, LaTe