Multivariate $t$-Mixtures-Model-based Cluster Analysis of BATSE Catalog Establishes Importance of All Observed Parameters, Confirms Five Distinct Ellipsoidal Sub-populations of Gamma Ray Bursts

Abstract

Determining the kinds of gamma-ray bursts (GRBs) has been of interest to astronomers for many years. We analyzed 1599 GRBs from the Burst and Transient Source Experiment (BATSE) 4Br catalogue using $t$-mixtures-model-based clustering on all nine observed parameters ($T_{50}$, $T_{90}$, $F_1$, $F_2$, $F_3$, $F_4$, $P_{64}$, $P_{256}$, $P_{1024}$) and found evidence of five types of GRBs. Our results further refine the findings of Chattopadhyay and Maitra (2017) by providing groups that are more distinct. Using the Mukherjee et al. (1998) classification scheme, also used by Chattopadhyay and Maitra (2017), of duration, total fluence ($F_t = F_1 + F_2 + F_3 + F_4$)) and spectrum (using Hardness Ratio $H_{321} = F_3/(F_1 + F_2)$) our five groups are classified as long-intermediate-intermediate, short-faint-intermediate, short-faint-soft, long-bright-hard, and long-intermediate-hard. We also classify 374 GRBs in the BATSE catalogue that have incomplete information in some of the observed variables (mainly the four time integrated fluences $F_1$, $F_2$, $F_3$ and $F_4$) to the five groups obtained, using the 1599 GRBs having complete information in all the observed variables. Our classification scheme puts 138 GRBs in the first group, 52 GRBs in the second group, 33 GRBs in the third group, 127 GRBs in the fourth group and 24 GRBs in the fifth group.