Relation between the hardness ratio and time in the first two seconds for compatible samples of short and long gamma-ray bursts

Abstract

In this paper, we randomly selected a sample ( sample 1) of long gamma-ray bursts, with its size being the same as that of the short-burst group ( sample 2) ( N = 500), from the Current BATSE Bursts Catalog. We randomly selected a short burst and assigned its T-90 to each of these long bursts. We thus constructed a long-burst sample with both the sample size and the distribution of T-90 being the same as those of the short-burst sample obtained from the Current BATSE Bursts Catalog. Then we calculated the hardness ratio (hr(t)) over the assigned T-90 for the long bursts and over their own T90 for the short bursts, and studied the relation between the hardness ratio and the corresponding T90 for these two samples. We also calculated the hardness ratio ( hrt) over the randomly selected 64-ms time intervals within the T-90, and investigated the relation between this hardness ratio and the selected 64-ms time interval. In addition, the hr(T) within and beyond the first two seconds for all the long bursts ( sample 3; N = 1541) were also investigated. We found that the Kolmogorov - Smirnov (KS) probabilities of the distributions of hr(T) (7.15337E- 15) and hr(t) (9.54833E- 10) for samples 1 and 2 are very small, and the average values of hrT and hrt for short bursts are obviously larger than those of the long bursts. The correlations between log hr(T) and log T-90, and between log hrt and log t, are different for samples 1 and 2. These show that short and long bursts in the first two seconds have different characters and they probably originate from different progenitors. For sample 3, for the two time intervals, the KS probability is 5.35828E-5, which suggests that the hardness ratios in different time intervals for long bursts are also different.