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

We consider two empirical relations using data only from the prompt emission of Gamma-Ray Bursts (GRBs), the peak energy (E p ) -peak luminosity (L p ) relation (so called Yonetoku relation) and the E p -isotropic energy (E iso ) relation (so called Amati relation). Both relations show high correlation degree, but they also have larger dispersion around the best fit function rather than the statistical uncertainty. Then we first investigated the correlation between the residuals of L p and E iso from the best function, and found that a partial linear correlation degree is quite small of ρ Lp Eiso·Ep = 0.379. This fact indicates that some kinds of independence may exist between Amati and Yonetoku relation even if they are characterized by the same physical quantity E p , and similar quantities L p and E iso which mean the brightness of the prompt emission. Therefore we may have to recognize two relations as the independent distance indicators. From this point of view, we compare constraints on cosmological parameters, Ω m and Ω Λ , using the Yonetoku and the Amati relation calibrated by low-redshift GRBs with z < 1.8. We found that they are different in 1-σ level, although they are still consistent in 2-σ level. In this paper, we introduce a luminosity time T L defined by T L ≡ E iso /L p as a hidden parameter to correct the large dispersion of the Yonetoku relation. A new relation is described as (L p /10 52 erg s −1 ) = 10 −3.87±0.19 (E p /keV) 1.82±0.08 (T L /s) −0.34±0.09 . We succeeded in reducing the systematic error about 40% level, and might be regarded as "Fundamental plane" of GRBs. We show a possible radiation model for this new relation. Finally, applying the new relation to high-redshift GRBs with 1.8 < z < 5.6, we obtain (Ω m , Ω Λ ) = (0.17 +0.15 −0.08 , 1.21 +0.07 −0.61 ), which is consistent with the concordance cosmological model.

We extend the Hubble diagram up to z= 5.6 using 63 gamma‐ray bursts (GRBs) via peak energy–peak luminosity relation (so‐called Yonetoku relation), and obtain constraints on cosmological parameters including dynamical dark energy parametrized by P/ρ≡w(z) =w0+wa×z/(1 +z). It is found that the current GRB data are consistent with the concordance model (Ωm= 0.28, ΩΛ= 0.72, w0=−1, wa= 0) within 2σ level. Although constraints from GRBs themselves are not so strong, they can improve the conventional constraints from type Ia supernovae because GRBs have much higher redshifts. Further, we estimate the constraints on the dark energy parameters expected by future observations with Gamma‐ray Large Area Space Telescope and Swift by Monte Carlo simulation. Constraints would improve substantially with another 150 GRBs.

We argue for a new classification scheme of long gamma-ray bursts (LGRBs) using the morphology of the cumulative light curve of prompt emission. We parametrize the morphology by an absolute deviation from their constant luminosity (ADCL), and derive the value for 36 LGRBs that have spectropic redshifts, spectral parameters determined by the Band model, 1-s peak fluxes, fluences, and 64-ms resolution light curves whose peak counts are 10-times larger than background fluctuations. Based on a possible bimodal distribution of the value of ADCL, we divide the sample into two groups (ADCL$ &lt;$ 0.17 and ADCL$ &gt;$ 0.17), and for each group derive the spectral peak energy $ E_{\rm p}$ –peak luminosity $ L_{\rm p}$ correlation and the Fundamental Plane of LGRBs, which is a correlation between $ E_{\rm p}$ , the luminosity time $ T_{\rm L}$ ($ \equiv$$ E_{\rm iso}/L_{\rm p}$ where $ E_{\rm iso}$ is isotropic energy), and $ L_{\rm p}$ . We find that the Fundamental Plane at $ E_{\rm p}$$ =$ 10$ ^{2.71}$ keV and $ T_{\rm L}$$ =$ 10$ ^{0.86}$ s for large ADCL events are 2.8-times brighter than that for small ADCL events with 5-$ \sigma$ levels. The Fundamental Planes with small and large ADCL are given by $ L_{\rm p}$$ =$ 10$ ^{52.53\pm 0.01}$ ($ E_{\rm p}/$ 10$ ^{2.71}$ keV)$ ^{1.84\pm 0.03}$ ($ T_{\rm L}/$ 10$ ^{0.86}$ s)$ ^{0.29\pm0.08}$ with $ \chi^2_{\nu}$$ =$ 10.93$ /$ 14 and $ L_{\rm p}$$ =$ 10$ ^{52.98\pm0.08}$ ($ E_{\rm p}/$ 10$ ^{2.71}$ keV)$ ^{1.82\pm 0.09}$ ($ T_{\rm L}/$ 10$ ^{0.86}$ s)$ ^{0.85\pm 0.27}$ with $ \chi^2_{\nu}$$ =$ 7.58$ /$ 8, respectively. This fact implies the existence of subclasses of LGRBs characterized by the value of ADCL. The other significant difference between the relations for the two subclasses consists in the exponent of $ T_{\rm L}$ , which might provide a hint of the physics of the relations, but the significance is now only at 2-$ \sigma$ levels. Also, there is a hint for the existence of an intermediate-ADCL class, which deviates from both fundamental planes. Both relations are so tight that our result provides a new accurate distance measurement scheme up to the high-redshift universe.

We compared redshifts zY measured from the Yonetoku relation and zlag from the lag–luminosity relation for 565 BATSE gamma‐ray bursts (GRBs) and were surprised to find that the correlation between these two redshifts is very low. Assuming that the luminosity is a function of both zY and the intrinsic spectral lag τlag, we found a new redshift‐dependent lag–luminosity relation L= 7.5 × 1050 erg s−1 (1 +z)2.53τ−0.282lag with the correlation coefficient of 0.77 and the chance probability of 7.9 × 10−75. Although the spectral lag is computed from two channels of the Burst and Transient Source Experiment (BATSE), our new lag–luminosity relation suggests that a future lag–luminosity relation defined in the Swift data should also depend on the redshift.