*4.3. Properties of GRB Clusters Identified in the First Second Post-Trigger*

2D t-SNE representation of the extracted wavelet and PCA features from the first second (T<sup>0</sup> to T<sup>0</sup> + 1.004 s) of GRB light curves, coloured by burst duration T<sup>90</sup> and hardness ratio HR<sup>32</sup> for BATSE, *Swift*/BAT and *Fermi*/GBM, are shown in Figure 5. The projections indicate the presence of two groups of bursts, which can be seen clearly in Figure 5b for *Swift*/BAT. For BATSE (Figure 5a) and *Fermi*/GBM (Figure 5c), this separation is less well-defined.

**Figure 5.** 2D t-SNE representation of the extracted wavelet and PCA features from the first second (T<sup>0</sup> to T<sup>0</sup> + 1.004 s) of burst light curves, coloured by burst duration T<sup>90</sup> (top row) and hardness ratio HR<sup>32</sup> (bottom row) for (**a**) BATSE, (**b**) *Swift*/BAT and (**c**) *Fermi*/GBM. Hardness ratios (HR32) for *Swift*/BAT and BATSE are calculated as the ratio of fluence in Band 3 and Band 2. The hardness ratio of *Fermi*/GBM bursts is defined as the ratio of fluence in the 50–300 keV and 10–50 keV bands, calculated using the best-fit spectral parameters.

GMM clustering applied to the *Swift*/BAT projection identifies two separate groups, shown in Figure 6a. The group consisting of mostly short/hard bursts is labelled Group 1, and the larger, longer-duration group is denoted Group 2. The groups are shown projected onto the duration-hardness plane in Figure 6b.

**Figure 6.** *Cont*.

**Figure 6.** (**a**) The t-SNE map of *Swift*/BAT bursts derived from the T<sup>0</sup> to T<sup>0</sup> + 1.004 s interval at 4 ms resolution showing 2 clearly separated groups and (**b**) their projection onto the duration-hardness plane. Histograms indicate the distribution of duration and hardness for each group.

Two-dimensional Kolmogorov–Smirnov (KS) tests applied to Group 1 and Group 2 verify that there are statistically significant differences in GRB properties such as the duration (T90), hardness (HR32), peak energy (*E*peak) and fluence (S) of the two clusters. Table 1 presents the results of the KS test. The probability (*p*-value) presented in Table 1 indicates the probability that Groups 1 and 2 are drawn from the same distribution. This hypothesis is rejected, as all probabilities are below 1%. Figure 7 demonstrates the distribution of the GRB properties for Group 1 and Group 2.

**Table 1.** Results of the 2D KS test comparing Group 1 and Group 2 identified within the first second of prompt emission of *Swift*/BAT bursts.

**Figure 7.** Violin plots showing the distribution of GRB properties for Group 1 (red) and Group 2 (blue) *Swift*/BAT bursts identified in the T<sup>0</sup> to T<sup>0</sup> + 1.004 s light curve interval. The white box plots represent the 1*σ* interval (i.e., the 16th to 84th percentile), with the median of each parameter marked as a black line.

Table 2 lists the cluster memberships of a subset of the *Swift* GRBs for both the analysis of the T<sup>100</sup> interval at 64 ms resolution, and the interval from T<sup>0</sup> to T<sup>0</sup> + 1.004 s at 4 ms resolution. The full table is available to download from the Supplementary Materials. When the first 1 s of prompt emission is considered, Group 1 contains 107 bursts, 73 of

which are short-duration (T<sup>90</sup> < 2 s). There are 1144 bursts in Group 2, containing 1112 long-duration bursts (T<sup>90</sup> > 2 s). The composition of each group and the properties of GRBs in Groups 1 and 2 are further discussed in Section 5.

**Table 2.** Group membership of *Swift* GRBs, based on the analysis of the first second of prompt emission at 4 ms resolution (T<sup>1</sup> ) and the T<sup>100</sup> interval at 64 ms resolution. The full table is provided in the Supplementary Materials.


<sup>1</sup> No 4 ms light-curve file available.

As with the T<sup>100</sup> analysis (Section 4.1), the results obtained for the T<sup>0</sup> to T<sup>0</sup> + 1.004 s interval at 4 ms resolution for BATSE and *Fermi*/GBM GRBs are not as clear-cut as they are for *Swift*/BAT. In the case of BATSE, GMM clustering with MCLUST identifies six clusters within the t-SNE projection in Figure 5a. However, we can tentatively identify two clusters of bursts for BATSE by eye. These two groups resemble the short/hard and long/soft groups identified for *Swift*/BAT. Similarly to *Swift*/BAT, a KS test applied to the two BATSE groups reveals significant differences in their duration, hardness, peak energy and peak flux. BATSE has a harder energy range than *Swift*/BAT; thus, the BATSE population contains more short/hard bursts. Therefore for BATSE, the short-duration Group 1 contains a larger proportion of bursts compared to *Swift*/BAT.

For *Fermi*/GBM, the projection in Figure 5c indicates two groups, primarily consisting of short/hard and long/soft bursts, but their clustering is not dense enough to allow for a clean separation between them. MCLUST identifies five clusters. This may indicate that the application of a Gaussian model does not adequately represent the underlying complex distributions [17].
