Dependence of the GRB Lag-Luminosity Relation on Redshift in the Source Frame

Abstract

The lag-luminosity relation for gamma-ray bursts (GRBs) is an anti-correlation between the time lag, ?lag, which represents the delay between the arrival of hard and soft photons, and the isotropic peak luminosity, L. In this paper, we use a sample of 43 Swift bursts, which was taken from Ukwatta et al., to investigate whether this relation depends on redshift. Both the z-correction and the k-correction are taken into account. Our analysis consists of binning the data in redshift, z, then applying a fit of the form: for each bin, where ?lag0 is the time-lag in the burst’s source frame, and is the corresponding mean value for the entire sample. The goal is to see whether the two fitting parameters, A and B, evolve in a systematic way with z. Our results indicate that both the normalization, A, and the slope, B, seem to vary in a systematic way with redshift. We note that although good best-fits were obtained, with reasonable values for both the linear regression coefficient, r, and the reduced chi-squared, the data showed large scatter. Also, the number of GRBs in the sample studied is not large, and thus our conclusions are only tentative at this point. A flat universe with M = 0.27, ?? = 0.73, and a Hubble constant, H0 = 70 km.s -1 .Mpc -1 is assumed.