We reconsider correlations among the spectral peak energy ($E_p$), 1-second peak luminosity ($L_p$) and isotropic energy (Eiso), using the database constructed by citet{yonetoku10} which consists of 109 Gamma-Ray Bursts (GRBs) whose redshifts are known and $E_p$, $L_p$ and Eiso are well determined. We divide the events into two groups by their data quality. One (gold data set) consists of GRBs with peak energies determined by the Band model with four free parameters. On the other hand, GRBs in the other group (bronze data set) have relatively poor energy spectra so that their peak energies were determined by the Band model with fixed spectral index (i.e. three free parameters) or by the Cut-off power law (CPL) model with three free parameters. Using only the gold data set we found the intrinsic dispersion in $log L_p$ ($=sigma_{rm int}$) is 0.13 and 0.22 for tsutsui correlation ($T_L equiv E_{rm iso}/L_p$) and yonetoku correlation, respectively. We also find that GRBs in the bronze data set have systematically larger $E_p$ than expected by the correlations constructed with the gold data set. This means that the intrinsic dispersion of correlations among $E_p$, $L_p$, and Eiso of GRBs depends on the quality of data set. At present, using tsutsui correlation with gold data set, we would be able to determine the luminosity distance with $sim 16%$ error, which might be useful to determine the nature of the dark energy at high redshift $z > 3$.
تحميل البحث