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

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