2001ApJ...548..770B

We study the hardness-intensity correlation (HIC) in gamma-ray bursts (GRBs). In particular, we analyze the decay phase of pulse structures in their light curves. The study comprises a sample of 82 long pulses selected from 66 long bursts observed by the Burst and Transient Source Experiment (BATSE) on the Compton Gamma-Ray Observatory. We find that at least 57% of these pulses have HICs that can be well described by a power law. A number of the other cases can still be explained with the power-law model if various limitations of the observations are taken into account. The distribution of the power-law indices γ, obtained by modeling the HIC of pulses from different bursts, is broad, with a mean of 1.9 and a standard deviation of 0.7. We also compare indices among pulses from the same bursts and find that their distribution is significantly narrower. The probability p of a random coincidence is shown to be very small (<2x10^–5). In most cases, the indices are equal to within the uncertainties. These results demand a physical model to be able to reproduce multiple pulses with similar characteristics for an individual burst, but with a large diversity for pulses from an ensemble of bursts. This is particularly relevant when comparing the external versus the internal models. In our analysis, we also use a new method for studying the hardness-intensity correlation, in which the intensity is represented by the peak value of the EF_E spectrum, where E is the energy and F_E is the energy flux spectrum. We compare it to the traditional method in which the intensity over a finite energy range is used instead, which may be an incorrect measure of the bolometric intensity. This new method gives stronger correlations and is useful in the study of various aspects of the HIC. In particular, it produces a better agreement between indices of different pulses within the same burst. Also, we find that some pulses exhibit a track jump in their HICs, in which the correlation jumps between two power laws with the same index. We discuss the possibility that the track jump is caused by strongly overlapping pulses. Based on our findings, the constancy of the index is proposed to be used as a tool for pulse identification in overlapping pulses and examples of its application are given.