The 1-m telescope at Lulin Observatory and the 0.76-m Katzman Automatic Imaging Telescope at Lick Observatory were used to observe the optical afterglow of the short-duration (1.2--1.5 s) gamma-ray burst (GRB) 040924. This object has a soft high-energy spectrum, thus making it an exceptional case, perhaps actually belonging to the short-duration tail of the long-duration GRBs. Our data, combined with other reported measurements, show that the early R-band light curve can be described by two power laws with index alpha = -0.7 (at t = 16-50 min) and alpha = -1.06 (at later times). The rather small difference in the spectral indices can be more easily explained by an afterglow model invoking a cooling break rather than a jet break.
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