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We have investigated the gamma-ray bursts pulses assumed to arise fromrelativistically expending fireballs. We find, due to the curvature effect, theevolutionary curve of the raw hardness ratio (when the background count isincluded) varies significantly, depending on the hardness of a burst. For asoft burst, an upside-down pulse of its raw hardness ratio curve (HRC) would beobserved; for a hard burst, its raw HRC shows a pulse-like profile with asinkage in its decaying phase; for a very hard burst, the raw HRC possesses apulse-like profile without a sinkage in its decaying phase. For a pulse-likeraw HRC as shown in the case of the hard and very hard bursts, its peak wouldappear in advance of that of the corresponding light curve. We have studiedhere the HRC of GRB 920216, GRB 920830 and GRB 990816 in detail. The featuresof the raw HRC expected in the hard burst are observed in these bursts. A fitto the three bursts shows that the curvature effect alone could indeed accountfor the predicted characteristics of HRCs. In addition, we find that theobserved hardness ratio tends to be harder at the beginning of the pulses thanwhat the curvature effect could predict and be softer at the late time of thepulses. We believe this is an evidence showing the existence of intrinsichard-to-soft radiation.Comment: 26 pages, 8 figures, 1 tabl

Hardness ratio evolutionary curves of gamma-ray bursts expected by the curvature effect