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Fig. 1

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The best-fit correlation between LX, Ta, and Eγ,iso for our “golden sample”. Y-axis is the X-ray luminosity at the end time of the plateau phase, i.e. LX, in units of 1047 erg/s. The X-axis is a combined quantity of Ta (in units of 103 s) and Eγ,iso (in units of 1053 erg), i.e. 1.17 − 0.87log Ta + 0.88log Eγ,iso. The filled points correspond to the observed data of 47 long GRBs and the hollow square points correspond to the eight intermediate-class GRBs. The solid line is plotted from Eq. (7), which is the best fit of the 55 observational data points.

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