2 Procedures

To determine the evolution of GRB spectral shapes, we examined High Energy Resolution data collected from the BATSE Large-Area Detectors (LADs) and Spectroscopy Detectors (SDs) We began with the 126 bursts from the catalog developed for Preece et al. (1998). We deconvolved the gamma-ray spectra of each time interval using the Band et al. (1993) GRB function. While LK96 assumed that the Band GRB parameters $\alpha$ and $\beta$ were constant during the course of each burst, this has since been shown to be untrue with a larger data set (Crider et al. 1997). We thus left $\alpha$ and $\beta$ as free parameters in our fits.

At this point, we needed to select pulses within our bursts that we could use to test Eq. (1). Unfortunately, by forcing our time bins to have a SNR $\sim45$ so that spectra may be fit to them, much time resolution is lost. Pulses which would be easily separable at a higher time resolution became blurred together. In Fig. 1, we show an example of what would likely be identified as two pulses in our coarse data. Below it, we plot 64-ms count rate data for this same burst, obtained from the Compton Observatory Science Support Center (COSSC). With higher time resolution, we see this burst is composed of at least 4 distinct pulses.

  

Figure 1: The count rate (plotted as a histogram) of BATSE trigger 543 seen both in a) the lower time resolution which allowed us to fit a spectrum to each bin and b) 64-ms resolution. $E_{\rm pk}$, as determined from the data in the upper plot, is marked on both plots for convenience. The fits of the Norris function to these pulses appear as dotted lines

We used the COSSC 64-ms data to determine where each of our pulses began and ended by developing an interactive IDL routine to fit the Norris et al. (1996) pulse profile to the individual pulses within our bursts. We found that in many bursts, pulses overlapped in a fashion making them too complex for us to fit individual pulses. Other bursts contained pulses which could be resolved, but none of their pulses lasted long enough to span at least 4 time bins with SNR $\sim45$. For 13 of the bursts, no processed 64-ms data was available. Discarding bursts which fell into any of these three categories, left us with 26 bursts. Within these, we identified 41 regions composed of at least 4 time bins dominated by a single pulse (at least $70\%$ of the counts from one pulse).