We present X-ray light curves (1.5-12 keV) for fifteen gamma-ray bursts
(GRBs) detected by the All-Sky Monitor on the Rossi X-ray Timing Explorer. We
compare these soft X-ray light curves with count rate histories obtained by the
high-energy (>12 keV) experiments BATSE, Konus-Wind, the BeppoSAX Gamma-Ray
Burst Monitor, and the burst monitor on Ulysses. We discuss these light curves
within the context of a simple relativistic fireball and synchrotron shock
paradigm, and we address the possibility of having observed the transition
between a GRB and its afterglow. The light curves show diverse morphologies,
with striking differences between energy bands. In several bursts, intervals of
significant emission are evident in the ASM energy range with little or no
corresponding emission apparent in the high-energy light curves. For example,
the final peak of GRB 970815 as recorded by the ASM is only detected in the
softest BATSE energy bands. We also study the duration of bursts as a function
of energy. Simple, singly-peaked bursts seem consistent with the E^{-0.5} power
law expected from an origin in synchrotron radiation, but durations of bursts
that exhibit complex temporal structure are not consistent with this
prediction. Bursts such as GRB 970828 that show many short spikes of emission
at high energies last significantly longer at low energies than the synchrotron
cooling law would predict.Comment: 15 pages with 20 figures and 2 tables. In emulateapj format. Accepted
by ApJ