We present a time-resolved spectral analysis of 51 long and 11 short bright gamma-ray bursts (GRBs) observed with the Fermi/Gamma-Ray Burst Monitor, paying special attention to E p evolution within each burst. Among eight single-pulse long GRBs, five show an evolution from hard to soft, while three show intensity tracking. The multi-pulse long GRBs have more complicated patterns. Statistically, the hard-to-soft evolution pulses tend to be more asymmetric than the intensity-tracking ones, with a steeper rising wing than the falling wing. Short GRBs have E p tracking intensity exclusively with the 16 ms time-resolution analysis. We performed a simulation analysis and suggest that for at least some bursts, the late intensity-tracking pulses could be a consequence of overlapping hard-to-soft pulses. However, the fact that the intensity-tracking pattern exists in the first pulse of the multi-pulse long GRBs and some single-pulse GRBs, suggests that intensity tracking is an independent component, which may operate in some late pulses as well. For the GRBs with measured redshifts, we present a time-resolved E p −L γ,iso correlation analysis and show that the scatter of the correlation is comparable to that of the global Amati/Yonetoku relation. We discuss the predictions of various radiation models regarding E p evolution, as well as the possibility of a precessing jet in GRBs. The data pose a great challenge to each of these models, and hold the key to unveiling the physics behind GRB prompt emission.
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