We compared redshifts z _ { Y } from Yonetoku relation and z _ { lag } from the lag-luminosity relation for 565 BASTE GRBs and were surprised to find that the correlation is very low .
Assuming that the luminosity is a function of both z _ { Y } and the intrinsic spectral lag \tau _ { lag } , we found a new redshift dependent lag-luminosity relation as L = 7.5 \times 10 ^ { 50 } { erg / s } ( 1 + z ) ^ { 2.53 } \tau _ { lag } ^ { -0.282 } with the correlation coefficient of 0.77 and the chance probability of 7.9 \times 10 ^ { -75 } .
To check the validity of this method , we examined the other luminosity indicator , Amati relation , using z _ { Y } and the observed fluence and found the correlation coefficient of 0.92 and the chance probability of 5.2 \times 10 ^ { -106 } .
Although the spectral lag is computed from two channels of BATSE , our new lag-luminosity relation suggests that a possible lag-luminosity relation in the Swift era should also depend on redshift .