Two dimensional classification of the Swift/BAT GRBs

Abstract

Using Gaussian Mixture Model and Expectation Maximization algorithm, we have performed a density estimation in the framework of T 90 versus hardness ratio for 296 Swift/BAT GRBs with known redshift. Here, Bayesian Information Criterion has been taken to compare different models. Our investigations show that two instead of three or more Gaussian components are favoured in both the observer and rest frames. Our key findings are consistent with some previous results.

Classification of gamma-ray burst durations using robust model-comparison techniques

“…The parameters of the GMM can be found by the Expectation-Maximization (EM) Algorithm (Ivezić et al 2014). The GMM and the corresponding parameter estimation using the EM algorithm have been also applied to GRB datasets using both T90 (Zhang et al 2016b) as well as using T90 vs hardness ratio (Yang et al 2016). Note however that Zhang et al (2016b) have included the covariances between the datasets.…”

“…Here, we use multiple analysis methods, such as the frequentist hypothesis testing (based on χ 2 probabilities) and information criterion based tests such as Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for model comparison. AIC and BIC have also been previously used for GRB classification by a number of authors (Mukherjee et al 1998;Tarnopolski 2016a,b;Yang et al 2016;Zhang et al 2016b). Frequentist model comparison after binning the data has been used by Zitouni et al (2015); Tarnopolski (2015).…”

“…An early analysis by Zhang & Choi (2008) showed that the T90 distribution (in both the observer and rest frame) for the first 95 Swift GRBs obeys a lognormal distribution with two components, instead of three. Yang et al (2016) have found after applying the Gaussian mixture model on T90 and hardness ratio on Swift GRBs with redshifts, two components are favored compared to three or more in both the observer and intrinsic frame. Another recent analysis of BATSE, Swift, and Fermi/GBM using application of Gaussian Mixture model on T90 finds that BATSE, Fermi and Swift data (for GRBs with measured redshifts in observer and rest frame) are better fitted by two components (Zhang et al 2016b).…”

Analysis of the Duration–Hardness Ratio Plane of Gamma-Ray Bursts Using Skewed Distributions

“…A third, intermediate class (Horváth 1998), remains putative. Its existence was claimed based on univariate and bivariate analyses of GRB observables modeled with Gaussian distributions (Mukherjee et al 1998;Horváth 2002;Horváth et al 2008;Zhang & Choi 2008;Huja et al 2009;Řípa et al 2009;Horváth et al 2010;Veres et al 2010;Zitouni et al 2015;Zhang et al 2016;Horváth et al 2018), but also has been put into doubt several times (Bystricky et al 2012;Řípa et al 2012;Tarnopolski 2015;Zitouni et al 2015;Narayana Bhat et al 2016;Tarnopolski 2016a,b;Ohmori et al 2016;Yang et al 2016;Kulkarni & Desai 2017;Zitouni et al 2018). Gaussian models, however, may not be the appropriate approach 1 (Koen & Bere 2012;Tarnopolski 2015;Koen & Bere 2017), as it has been already shown that the univariate distributions of T 90 (Tarnopolski 2016c,a;Kwong & Nadarajah 2018) and bivariate T 90 − H 32 ones (Tarnopolski 2019) are better described by mixtures of two skewed components rather than three Gaussian ones.…”

How does the shape of gamma-ray bursts' pulses affect the duration distribution?

“…This approach was undertaken in several subsequent analyses (Horváth 2002;Horváth et al 2008;Zhang & Choi 2008;Huja et al 2009;Horváth et al 2010;Zhang et al 2016), usually resulting in a conclusion that three Gaussian components are needed to describe the data accurately (Horváth et al 2006;Řípa et al 2009;Horváth et al 2010;Veres et al 2010;Horváth et al 2018), hence claiming the presence of three GRB classes. Some works, however, pointed at only two such components (Řípa et al 2012;Yang et al 2016;von Kienlin et al 2020).…”