A possible redshift evolution of the time-lag and variability luminosity relations for long gamma-ray bursts

The data we use are taken from Schaefer's literature (Schaefer et al., 2007) in which 69 long gamma-ray bursts were analyzed. The method consists of binning the data by redshift interval, then writing the time-lag relation in the form log(L)=A+Blog[τlag/(1+z)] and extracting the fit parameters A and B for each redshift bin; likewise, for the variability relation, which we write in the form log(L)=A+Blog[V(1+z)]. The objective is then to see whether the fitting parameters A and B evolve in any systematic way with the redshift. Our analysis indicates that both the A and B parameters do evolve with z in a systematic way for the lag-relation but not for the variability relation. A flat universe with ΩM=0.3,ΩΛ=0.7, and H0=70kms-1Mpc-1 is assumed.