The correlations between hardness ratios and fitting parameters in GRB spectrum

Abstract

In this paper, besides general definition of hardness ratio of gamma-ray bursts (GRBs), HR ₃₂, we also presented new definitions of hardness ratios, HR _hl and HR _ll, then presented the results of correlation studies, examining the association between the hardness ratios and the spectral fitting parameters (E ₀ or E _peak, α, β) by using the GRB data observed by BATSE. The HR _hl is defined as the fluence of channel 4 divided by the sum of the fluences of channels 1 to 3,and the HR _ll is defined as the fluence of channel 3 divided by the sum of the fluences of channel 1 and 2. We found that E ₀ and E _peak are correlated with hardness ratios, and β is only correlated with log (HR _hl). The α is not correlated with any hardness ratios in the total sample of GRBs, while it correlated with log (HR _ll) and log (HR ₃₂) in the two subsets seperated at log (HR _ll) = 0.34 ×α +0.66, respectively. These results show that a harder spectra tends to be steeper and has a higher E _peak or E ₀; HR _hl describes the spectral behaviors in high energy, while both of HR _ll and HR ₃₂ reflect the spectral characteristics in low energy; the spectral behaviors in low energy are different for the two subsets. We also presented a brief qualitative analysis discussion to the correlations and suggested that the correlations are caused by both of intrinsic and cosmological effects, but intrinsic effects are dominant.