Cosmological constraints from calibrated Yonetoku and Amati relation suggest fundamental plane of gamma-ray bursts

We consider two empirical relations using data only from the prompt emission of Gamma-Ray Bursts (GRBs), the peak energy (Ep)-peak luminosity (Lp) relation (so called Yonetoku relation) and the Ep-isotropic energy (Eiso) 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 Lp and Eiso from the best function, and found that a partial linear correlation degree is quite small of Delta *rLpEisoEp = 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 Ep, and similar quantities Lp and Eiso 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, Delta *Wm and Delta *W Delta *L, using the Yonetoku and the Amati relation calibrated by low-redshift GRBs with z < 1.8. We found that they are different in 1- Delta *s level, although they are still consistent in 2- Delta *s level. In this paper, we introduce a luminosity time TL defined by TL=Eiso/Lp as a hidden parameter to correct the large dispersion of the Yonetoku relation. A new relation is described as (Lp/1052 erg s-1) = 10-3.87+/-0.19(Ep/keV)1.82+/-0.08(TL/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 ( Delta *Wm, Delta *W Delta *L) = (0.17+0.15-0.08, 1.21+0.07-0.61), which is consistent with the concordance cosmological model.