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.

We calibrated the peak energy-peak luminosity relation of gamma-ray bursts (GRBs; the so-called Yonetoku relation) using 33 events with redshift z < 1.62 without assuming any cosmological models. The luminosity distances to GRBs are estimated from those of large numbers of Type Ia supernovae with z < 1.755. This calibrated Yonetoku relation can be used as a new cosmic distance ladder towards higher redshifts. We determined the luminosity distances of 30 GRBs in 1.8 < z < 5.6 using the calibrated relation, and plotted the likelihood contour in the ( m , ) plane. We obtained ( m , ) = (0.37 +0.14 −0.11 , 0.63 +0.11 −0.14 ) for a flat universe. Because our method is free from the circularity problem, we can say that our universe in 1.8 < z < 5.6 is compatible with the so-called concordance cosmological model derived for z < 1.8. This suggests that the time variation of the dark energy is small or zero up to z ∼ 6.

We analyzed correlations among the rest frame spectral peak energy E p , the observed frame 64ms peak isotropic luminosity L p and the isotropic energy E iso for 13 Short Gamma Ray Burst (SGRB) candidates having the measured redshift z, T obs 90 /(1 + z) < 2 sec and well determined spectral parameters. A SGRB candidate is regarded as a misguided SGRB if it is located in the 3-σ int dispersion region from the best-fit function of the E p -E iso correlation for Long GRBs (LGRBs) while the others are regarded as secure SGRBs possibly from compact star mergers. Using 8 secure SGRBs out of 13 SGRB candidates, we tested whether E p -E iso and E p -L p correlations exist for SGRBs. We found that E p -E iso correlation for SGRBs(E iso = 10 51.42±0.15 erg s −1 (E p /774.5 keV) 1.58±0.28 ) seems to exist with the correlation coefficeint r = 0.91 and chance probability p = 1.5 × 10 −3 . We found also that the E p -L p correlation for SGRBs(L p = 10 52.29±0.066 erg s −1 (E p /774.5 keV) 1.59±0.11 ) is tighter than E p -E iso correlation since r = 0.98 and p = 1.5 × 10 −5 . Both correlations for SGRBs are dimmer than those of LGRBs for the same E p by factors ∼100 (E p -E iso ) and ∼ 5(E p -L p ). Applying the tighter E p -L p correlation for SGRBs to 71 bright BATSE SGRBs, we found that pseudo redshift z ranges from 0.097 to 2.258 with the mean < z > of 1.05. The redshifts of SGRBs apparently cluster at lower redshift than those of LGRBs (< z >∼ 2.2), which supports the merger scenario of SGRBs.

The accuracy and reliability of gamma-ray bursts (GRBs) as distance indicators are strongly restricted by their systematic errors which are larger than statistical errors. These systematic errors might come from either intrinsic variations of GRBs, or systematic errors in observations. In this paper, we consider the possible origins of systematic errors in the following observables, (i) the spectral peak energies (E p ) estimated by Cut-off power law (CPL) function, (ii) the peak luminosities (L p ) estimated by 1 second in observer time. Removing or correcting them, we reveal the true intrinsic variation of the E p -T