A Possible New Distance Indicator -Correlation between the duration and the X-ray luminosity of the shallow decay phase of Gamma Ray Bursts-

We investigated the characteristics of the shallow decay phase in the early Xray afterglows of GRBs observed by Swift X-Ray Telescope (XRT) during the period of January 2005 to December 2006. We found that the intrinsic break time at the shallow-to-normal decay transition in the X-ray light curve Tbrk^0 is moderately well correlated with the isotropic X-ray luminosity in the end of the shallow decay phase (LX,end) as Tbrk^0 = (9.39+/-0.64)*10^3s(LX,end/10^47 ergs/s)^(-0.71+/-0.03), while Tbrk^0 is weakly correlated with the isotropic gamma-ray energy of the prompt emission Egamma,iso. Using Tbrk^0 - LX,end relation we have determined the pseudo redshifts of 33 GRBs. We compared the pseudo redshifts of 11 GRBs with measured redshifts and found the rms error to be 0.17 in log z. From this pseudo redshift, we estimate that ~15% of the Swift GRBs have z > 5. The advantages of this distance indicator is that (1) it requires only X-ray afterglow data while other methods such as Amati and Yonetoku correlations require the peak energy (Ep) of the prompt emission, (2) the redshift is uniquely determined without redshift degeneracies unlike the Amati correlation, and (3) the redshift is estimated in advance of deep follow-ups so that possible high redshift GRBs might be selected for detailed observations.