We reconsider correlations among the spectral peak energy ( E _ { p } ) , 1-second peak luminosity ( L _ { p } ) and isotropic energy ( E _ { iso } ) , using the database constructed by Yonetoku et al .
( 41 ) which consists of 109 Gamma-Ray Bursts ( GRBs ) whose redshifts are known and E _ { p } , L _ { p } and E _ { iso } 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 _ { int } ) is 0.13 and 0.22 for E _ { p } – T _ { L } – L _ { p } correlation ( T _ { L } \equiv E _ { iso } / L _ { p } ) and E _ { p } – L _ { p } 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 E _ { iso } of GRBs depends on the quality of data set .
At present , using E _ { p } – T _ { L } – L _ { p } 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 .