Possible Origins of Dispersion of the Peak Energy–Brightness Correlations of Gamma-Ray Bursts

Abstract

Abstract We collected and reanalyzed about 200 GRB data of prompt-emission with known redshift observed until the end of 2009, and selected 101 GRBs that were well-observed to have good spectral parameters in order to determine the spectral peak energy ($E_{\rm p}$), 1-second peak luminosity ($L_{\rm p}$) and isotropic energy ($E_{\rm iso}$). Using our newly constructed database with 101 GRBs, we first revised the $E_{\rm p}$–$L_{\rm p}$ and $E_{\rm p}$–$E_{\rm iso}$ correlations. The correlation coefficients of the revised correlations were 0.889 for 99 degrees of freedom for the $E_{\rm p}$–$L_{\rm p}$ correlation and 0.867 for 96 degrees of freedom for the $E_{\rm p}$–$E_{\rm iso}$ correlation. These values correspond to a chance probability of 2.18 $\times$ 10$^{-35}$ and 4.27 $\times$ 10$^{-31}$, respectively. It is a very important issue whether these tight correlations are an intrinsic property of GRBs, or are caused by some selection effect of observations. In this paper, we examine how the truncation of the detector sensitivity affects the correlations, and conclude they are surely intrinsic properties of GRBs. Next we investigate origins of the dispersion of the correlations by studying their brightness and redshift dependence. Here, the brightness (flux or fluence) dependence would be regarded as being an estimator of the bias due to the detector threshold. We found a weak fluence-dependence in the $E_{\rm p}$–$E_{\rm iso}$ correlations and a redshift dependence in the $E_{\rm p}$–$L_{\rm p}$ correlation both at the 2$\ \sigma$ statistical level. These two effects may contribute to the dispersion of the correlations, which is larger than the statistical uncertainty. We discuss a possible reason of these dependences and give a future prospect to improve the correlations.