**1. Introduction**

Gamma-Ray Bursts (GRBs) are traditionally classified based on their duration and hardness as short/hard or long/soft bursts. These classes are separated at T<sup>90</sup> ≈ 2 s, derived from the duration distribution of the Third BATSE catalogue [1]. T<sup>90</sup> is defined as the duration during which 5–95% of the counts above background are detected. The properties of these classes suggest different progenitors—long GRBs often lie in star-forming galaxies [2] and some long GRBs are associated with Type Ic supernovae [3–6] linking them to the deaths of massive stars [7]. Short GRBs are linked to compact object mergers [8,9], as some short GRBs have been identified near elliptical galaxies [10], and many are offset from their hosts [11,12]. The detection of GRB 170817A [13,14], associated with the neutron star merger GW170817, detected in gravitational waves by LIGO [15], lends further weight to this progenitor theory.

The classification of GRBs based on their duration is affected by the significant overlap between the duration distributions of the long and short groups, and is further complicated by a possible 'intermediate' class of GRBs, first identified through Gaussian fits to the duration distribution of GRBs in the third BATSE catalogue [16]. Clustering of the duration– hardness plane and multi-dimensional analyses of GRB samples from different satellites have also revealed evidence of more than two classes of bursts.

**Citation:** Salmon, L.; Hanlon, L.; Martin-Carrillo, A. Two Classes of Gamma-ray Bursts Distinguished within the First Second of Their Prompt Emission. *Galaxies* **2022**, *10*, 78. https://doi.org/10.3390/ galaxies10040078

Academic Editors: Elena Moretti and Francesco Longo

Received: 27 April 2022 Accepted: 23 June 2022 Published: 26 June 2022

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Salmon et al. [17] presents a review of previous studies and reports on an updated clustering analysis of *Swift*/BAT and *Fermi*/GBM bursts which finds that Gaussian models applied to *Swift*/BAT and *Fermi*/GBM GRB samples recover three clusters, including an intermediate-duration one. However, the latter is identified as an excess Gaussian component when an entropy criterion is used and the resulting best-fit solution contains two classes, which are broadly consistent with the typical short- and long-duration groups. A key conclusion of the analysis is that model-based methods may identify spurious components in one-, two- and multi-dimensional analyses of GRB samples and that modelindependent analyses of GRBs should be conducted, for example, using GRB light curves.

Short GRBs with extended emissions have been detected, which may form an additional sub-class [18–20] and are possibly associated with a magnetar central engine [21]. These episodes, combined with the late X-ray flares in some short GRBs, and the nondetection of supernovae associated with some long GRBs, led to the suggestion of a new classification scheme by Zhang et al. [22]. Type I (massive star/collapsar origin) and Type II (compact-object merger origin) bursts are defined by multiple observational criteria beyond duration and hardness [23]. Other classification methods, based on afterglow and host galaxy properties [24], minimum variability timescales [25] and prompt emission and energetics, have been defined [26–30]. The instrument, sample size and classification method used can lead to different results [31], and the collapsar/merger fractions for each instrument's sample cannot simply be defined by a T<sup>90</sup> = 2 s threshold [32].

Analysis of GRB light curves in several bands does not rely on summary statistics, such as parameters derived from spectral fits, which could be poorly fit or incorrect. Jespersen et al. [33] extracted features from 64 ms-resolution *Swift*/BAT light curves using Discrete Fourier Transforms and found two groups using t-distributed Stochastic Neighbourhood Embedding (t-SNE). This approach does not assume the underlying distribution of the variables, unlike model-based clustering and distribution fitting.

An alternative to Fourier analysis is wavelet analysis, which has been used to study non-stationary time-series [34]. Wavelet analysis has the advantage of extracting both frequency and temporal information, and for this reason it has been used to compress and de-noise GRB light curves for the study of their time evolution [35–37], to identify peaks [38–41], and to quantify the minimum variability timescale of GRBs [42–46]. Wavelet decomposition has been used to reduce the dimensionality of supernova light curves for classification [47], and has been combined with Principal Component Analysis (PCA) and t-SNE for classification [48,49]. Lochner et al. [48] found that classifiers performed better when supplied with wavelet coefficients of supernova light curves, in contrast to feature extraction using parametric models.

GRB pulses exhibit spectral evolution, including hard-to-soft [50] or intensity-tracking [51] behaviour. Other common features of all GRB pulses include longer-observed durations at lower energies [52] and asymmetric shapes [53,54]. These commonalities suggest that a similar emission mechanism creates GRB pulses, regardless of the progenitor [55,56].

However, pulses in short and long bursts also exhibit some differences. Long GRB pulses are observed to peak earlier at higher energies, but these spectral lags are not typically significant in short GRBs [18,54,57–63]. The minimum variability timescales [44–46] retrieved from wavelet analysis of long and short GRBs are ∼200 ms and ∼10 ms respectively. Hakkila and Preece [64] found that pulses in short GRBs are shorter and harder than long GRBs, and exhibit more spectral evolution. Coupled with the observation that shorter pulses have a higher peak flux and ∼90% of short GRBs consist of a single pulse, compared to 25–40% for long GRBs, the pulse properties are likely to be a distinguishing feature in the first seconds of a burst. In particular, spectral evolution is evident at early times in previous studies of bursts from BATSE [65–70], *Swift* [71] and *Fermi*/GBM [72–74].

Redshift effects have not been observed in GRB light curves, as the standard time dilation of GRB pulses is thought to be masked by a contrasting effect whereby only the shorter, brightest portion of the burst is observed [75]. Therefore, analysis of GRB light curves is unlikely to be strongly affected by cosmological effects [76].

In this work, the light curves of GRBs in four energy bands from three different instruments are analysed, using wavelets as a feature-extraction method. The T<sup>100</sup> burst intervals, during which 100% of the counts above background is recorded, are studied at 64-ms resolution, and the early phase of GRB emission (first few seconds) at 4-ms resolution. Wavelet coefficients are extracted and reduced and then visualised using PCA and t-SNE. Section 2 outlines the sample construction, while Section 3 provides details of the methods applied to perform feature extraction. Results are presented in Section 4 and consistency checks with other studies and between instrument samples are discussed in Section 5. The classification of notable GRBs is presented in Section 6. Possible signatures in the first second are discussed in Section 7, while conclusions are outlined in Section 8.
