Analysis of the duration$-$hardness ratio plane of gamma-ray bursts with skewed distributions

TL;DR

This paper demonstrates that gamma-ray burst data from multiple space observatories can be effectively modeled with two skewed distribution components in the duration-hardness ratio plane, challenging the need for a third class.

Contribution

It extends previous findings by showing that various gamma-ray burst datasets are consistent with a two-class skewed distribution model, simplifying the classification scheme.

Findings

Gamma-ray burst data are well described by two skewed components.

The two-class model applies across multiple datasets from different observatories.

The intermediate class of gamma-ray bursts is unnecessary according to this analysis.

Abstract

It was recently shown that the $T_{90}-H_{32}$ distributions of gamma-ray bursts from CGRO/BATSE and Fermi/GBM are well described by a mixture of only two skewed components, making the presumed third, intermediate class unnecesary. The Swift/BAT, Konus-Wind, RHESSI and Suzaku/WAM data sets are found to be consistent with a two-class description as well.

Full text

gamma-ray burst: general – methods: data analysis – methods: statistical

1 Introduction

The two widely accepted classes of gamma-ray bursts (GRBs), short and long, are with confidence ascribed to mergers of compact objects and collapse of massive stars, respectively. 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 approach111Mukherjee et al. (1998) noted that ”the distributions often seem bimodal with asymmetrical non-Gaussian shapes”, but failed to employ skewed distributions in modeling and proceeded considering multinormal distributions. (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. In this work the $T_{90}-H_{32}$ plane is examined in case of data sets from four other satellites: Swift/BAT, Konus-Wind, RHESSI, and Suzaku/WAM.

2 Data

The following data sets are investigated: 1033 GRBs from the Swift/BAT catalogue (Lien et al., 2016), 1143 GRBs observed by Konus-Wind (Svinkin et al., 2016), 427 GRBs detected by RHESSI (Řípa et al., 2009), and 259 GRBs from Suzaku/WAM (Ohmori et al., 2016). The bivariate distributions of duration $T_{90}$ and hardness ratio $H_{32}$ in the log-log plane are examined. For each instrument, fluences $F$ in different energy bands are available, hence the definitions of $H_{32}$ are: $H_{32}=\frac{F_{50-100\,{\rm keV}}}{F_{25-50\,{\rm keV}}}$ for Swift; $H_{32}=\frac{F_{200-750\,{\rm keV}}}{F_{50-200\,{\rm keV}}}$ for Konus; $H_{32}=\frac{F_{120-1500\,{\rm keV}}}{F_{25-120\,{\rm keV}}}$ for RHESSI; and $H_{32}=\frac{F_{240-520\,{\rm keV}}}{F_{110-240\,{\rm keV}}}$ for Suzaku.

3 Methodology

The methodology is the same as in (Tarnopolski, 2019). Two- and three-component mixtures of the following bivariate distributions are fitted: regular Gaussian (2G and 3G), skew-normal (2SN and 3SN), Student $t$ (2T and 3T), and skew-Student (2ST and 3ST). The fits are compared using the small sample Akaike (Hurvich & Tsai, 1989) and Bayesian Information Criteria ($AIC_{c}$ and $BIC$). $AIC_{c}$ is liberal, and has a tendency to overfit. $BIC$ is much more stringent, and tends to underfit. Therefore, when the two $IC$ point at different models, the truth lies somewhere in between. (See Tarnopolski 2019 for details.) The fitting is performed using the R package mixsmsn222https://cran.r-project.org/web/packages/mixsmsn/index.html (Prates et al., 2013).

4 Results

The results are displayed in Figs. 1–4. For Swift and Konus no clear answer is obtained, however both $IC$ point at skewed distributions (see bottom panels of Figs. 1 and 2). For Swift, the $BIC$ yields 2ST and 2SN, while $AIC_{c}$ gives 3ST and 3SN. Henceforth, the lack of a third component in the data cannot be confidently ruled out; on the other hand, its presence is also not unambiguously supported. Konus gives remarkably similar results.

In case of RHESSI (see Fig. 3), both $IC$ point unequivocally at 2-component mixtures, however $BIC$ prefers symmetric distributions (2G and 2T), while $AIC_{c}$ hints at skewed ones (2ST and 2SN). Suzaku, the smallest data set examined, can be with no doubt well modeled with only 2 components, with 2G being the simplest model (see Fig. 4).

5 Discussion

GRBs from BATSE and Fermi can be confidently divided into only two classical groups, short and long; the elusive soft-intermediate class is not necessary to satisfactorily describe the data (Tarnopolski, 2015, 2016c, 2016a, 2019). In case of Swift and Konus, however, no firm conclusion can be formulated—the $IC$ point at either two or three classes. The smallest data sets—RHESSI and Suzaku—can be adequately construed as consisting of two groups, although due to the smallness of these samples, the more subtle structure in the $T_{90}-H_{32}$ plane can simply be not traced prominently enough.

The asymmetry of the data, manifested via skewed distributions, might come from a non-symmetric distribution of the envelope masses of the progenitors of the long GRBs or other inherently asymmetrical distributions of physical parameters governing the progenitors or GRBs themselves; from the impact of the redshift distribution on the observables; or a combination of the listed possibilities (Tarnopolski, 2015; Zitouni et al., 2015; Tarnopolski, 2016c, a, b, 2019).

6 Conclusions

No definite signs of the putative third GRB class are visible in the examined data. On the other hand, the Swift and Konus data yield inconclusive. It is desirable to have the exact shape of the observed distributions derived from a physical theory, or inferred on the grounds of statistics, which has not been convincingly realized thus far.

The author is grateful to Péter Veres for the Fermi data, Dmitry Svinkin for the Konus data, Norisuke Ohmori for the Suzaku data, Amy Lien for help with the Swift data, and Jakub Řípa and Natalia Żywucka for discussions. Support by the Polish National Science Center through an OPUS grant No. 2017/25/B/ST9/01208 is acknowledged.