Pseudo Redshifts of Gamma-Ray Bursts Derived from the L-T-E Correlation

The X-ray afterglow of many gamma-ray bursts (GRBs) exhibits a plateau phase before the normal power-law decay stage, which may be related to continued activities of the central engine. Tang et al. 2019 collected 174 such GRBs and confirmed the so called $L-T-E$ correlation which involves three key parameters, i.e., the isotropic $\gamma$-ray energy $E_{\gamma ,\mathrm{i}\mathrm{s}\mathrm{o}}$ of the prompt phase, the end time $T_a$ of the plateau phase and the corresponding X-ray luminosity $L_X$. In this study, the $L-T-E$ correlation is confirmed and updated as $L_X\propto T_a^{-0.99}{E}_{\gamma ,\mathrm{i}\mathrm{s}\mathrm{o}}^{0.86}$ with a large sample consisting of 210 plateau GRBs with known redshifts. The tight correlation is then applied to derive the pseudo redshift of other 130 plateau GRBs whose redshifts are not directly measured. Statistical analysis is also carried out on this pseudo redshift sample.