Since the observed gamma-ray burst spectrum reflects the energy content and particle distributions within the source's emitting region, spectral variations during a burst are an important diagnostic of the nature of this region. Early studies of spectral evolution reached apparently contradictory conclusions: Golenetskii et al. (1983) reported that the intensity and spectral hardness were correlated, while Norris et al. (1986) found a hard-to-soft trend. Subsequent studies using SIGNE (Kargatis et al. 1994) and BATSE (Ford 1995) spectra showed that both trends hold in general: the spectrum does indeed harden during intensity spikes, but there is a hard-to-soft trend during these spikes, and the hardness tends to peak at successively lower values from spike to spike.
This characterization of spectral evolution resulted from fitting a sequence of spectra accumulated during a burst, and comparing the time series of a hardness measure such as Ep to the intensity lightcurve. Many counts are required for a good fit to a spectrum, and therefore fitting sequences of spectra is feasible only for bright, long duration bursts. Even for the brightest bursts the time necessary to accumulate a spectrum with a sufficient signal-to-noise ratio (typically more than a second) is usually longer than the time structure evident to the eye (the separation between intensity spikes is typically a second). Therefore I have been developing other techniques of studying spectral evolution.
To characterize the spectral evolution of a large sample of bursts I used the auto- and crosscorrelation functions (ACF and CCFs, respectively) of burst lightcurves in different energy channels (Band 1997b). BATSE provides discriminator rates in 4 energy bands (Ch. 1: 25--50, Ch. 2: 50--100, Ch. 3: 100--300, and Ch. 4: 300--2000 keV) on a 64 ms timescale during a burst. I calculated the CCFs of a fiducial energy channel, Ch. 3 (100--300 keV), with each of the 4 energy channels (the CCF of the fiducial channel with itself is that channel's ACF). By comparing the time lags of the peaks of each curve and their relative values at different lags, I characterized the type of spectral evolution.
I calculated the ACFs and CCFs for 209 strong, mostly long bursts (Band 1997b). The order of the CCF peaks shows that in general high energy emission precedes low energy emission. As was known previously from comparing the ACFs of the different channels (Fenimore and Bloom 1995) the CCF widths indicate that high energy temporal structure is narrower than low energy structure (i.e., spikes last longer at low energy than at high). The relative order of the CCFs at different lags shows there is hard-to-soft evolution within and among spikes in ~80--90% of the bursts, and there are only a few cases of soft-to-hard evolution. The peaks of the CCFs for the high energy channels typically lead those of the low energy channels by 0.1-0.2 s. Thus this study showed that hard-to-soft spectral evolution is ubiquitous but counterexamples exist.
Liang and Kargatis (1996) found that when the logarithm of Ep is plotted as a function of the cumulative photon fluence (i.e., the photon fluence from the beginning of the burst to the time Ep is measured), the datapoints fall on a series of straight lines with the same slope for a given burst. This can be explained by an emission region with a fixed number of radiating particles which is re-energized for each intensity spike.