All 6 Subsets of BATSE Gamma-Ray Burst, Trigger 551
A comparison of the curves resulting from interpreting six separate subsets of the data provides a clear indication of both the precision and limitations of using derivative reconstruction to identify underlying physical processes. There were 16,554 photons recorded by detectors 0,2 &6 in energy channels 3 &4, the selected main data set (displayed on the referring page). Six subsets were made by selecting every 6th point starting from the 1st, 2nd, 3rd, 4th, 5th & 6th points, representing six independent data sets of the same event for comparison. Each point in the graphs represents an average rate (6/t) based on the difference in arrival time of each 6th photon. .Subset 1, Subset 2, Subset 3, Subset 4, Subset 5, Subset 6, These scatter charts all show very similar patterns. Subset 1 is the only one with extreme value points, suggesting that the decision to treat these as accidental outliers to exclude from the analysis was valid.
Each of these were interpreted with the same procedure discussed for Subset 1 on the referring page. A large scale overlay of the results provides a revealing display of both the consistency and limitations of this method of analysis. (Fine Detail Overlay).
As simple statistical comparison and test of congruence is provided by the number of minima found in the fine detail (Figure 3, Curves 2) constructed by derivative smoothing of 0.5 millisecond periods. The number of minima found in each subset were 140, 142, 139, 139, 139, & 142 respectively, with mean values of 140.2 minima, in 490.7 milliseconds, for a rate of 3.53 milliseconds each. The standard deviations (1.47, 4.32 and .05 respectively) are about 1% of the means.
The consistency, and inconsistency are shown by the usually tight grouping of vertical lines indicating the reconstructed timing of minima in the rates of photon detection. One can also see that the great majority of shapes in each curve have corresponding concurrent shapes of similar scale in each of the others, indicating a strong invariance of the technique due to statistical components in the data, and conversely, an indication of a lack of statistical components. There are also sections where the results are inconsistent, clearly displaying the kind and level of uncertainty produced by this kind of analysis.
There are a number of concurrent shapes in the curves that are of particular interest. The detail box highlights a shape that appears to be a near background level scale micro-burst, but having a consistently interpreted form so similar to the large scale events to be associated with the same kind of process. This shape appears in all six subsets, and shows the characteristic steep rise and irregular decline of the others, with largely consistent identification of the maxima and minima for all six subsets of the data during its period of irregularity.
P. F. Henshaw 4/98
Derivative Reconstruction, Referring Page