Graph-based clustering of gamma-ray bursts

Mariusz Tarnopolski

doi:10.1051/0004-6361/202038645

Abstract

Aims. An attempt to classify gamma-ray bursts (GRBs) with a low level of supervision using the state-of-the-start approaches stemming from graph theory was undertaken. Methods. Graph-based classification methods, relying on different variants of the k-nearest neighbour graph, were applied to various GRB samples in the duration–hardness ratio parameter space to infer the optimal partitioning. Results. In most cases it is found that both two and three groups are feasible, with the outcome being more ambiguous with an increasing sample size. Conclusions. There is no clear indication of the presence of a third GRB class; however, such a possibility cannot be ruled out with the employed methodology. There are no hints at more than three classes though.

Highlights

Gamma-ray bursts (GRBs, Klebesadel et al 1973) are confidently divided into two classes: short and long
The continuous kNN graph (CkNN) algorithm was applied with k = 8 and δ = 2.4, as recommended by Liu & Barahona (2020), for Markov times
In case of BATSE, the number of communities exhibits a prolonged plateau for K = 3, during which the variation of information (V I) drops to zero

Summary

Introduction

Gamma-ray bursts (GRBs, Klebesadel et al 1973) are confidently divided into two classes: short (attributed to compactobject mergers) and long (massive-star collapsars). The dichotomy is apparent in the bimodal distribution of durations T90 (i.e. the time during which 90% of the GRB’s fluence is detected), and it occurs at T90 2 s (Kouveliotou et al 1993) This is not a sharp separation due to significant overlap (Bromberg et al 2013; Tarnopolski 2015b; see Ahumada et al 2021 for the shortest confirmed GRB from a collapsar). Horváth 2002; Horváth et al 2008; Zhang & Choi 2008; Huja et al 2009; Horváth et al 2010; Zhang et al 2016), which have often concluded that a third Gaussian component is required to fit the data appropriately and have attributed physical meaning to it This third component is not necessarily evidence of a physically motivated group. It follows that when modelling with skewed distributions, instead of symmetric ones (e.g. Gaussian or Student), only two components are required to model the data appropriately (Tarnopolski 2016a,b; Kwong & Nadarajah 2018), implying the third one is spurious, and it appears because of modelling an intrinsically skewed distribution with symmetric ones

Methods

Results

Discussion

Conclusion