Luminosity correlations for gamma-ray bursts and implications for their prompt and afterglow emission mechanisms

Abstract

We present the relation between the (z- and k-corrected) spectral lags, τ, for the standard Swift energy bands 50-100keV and 100-200keV and the peak isotropic luminosity, Liso (a relation reported first by Norris etal.), for a subset of 12 long Swift gamma-ray bursts (GRBs) taken from a recent study of this relation by Ukwatta etal. The chosen GRBs are also a subset of the Dainotti etal. sample, a set of Swift GRBs of known redshift, employed in establishing a relation between the (GRB frame) luminosity, LX , of the shallow (or constant) flux portion of the typical X-Ray Telescope GRB-afterglow light curve and the (GRB frame) time of transition to the normal decay rate, Tbrk. We also present the LX-Tbrk relation using only the bursts common in the two samples. The two relations exhibit a significant degree of correlation (ρ = -0.65 for the L iso-τ and ρ = -0.88 for the LX -Tbrk relation) and have surprisingly similar best-fit power-law indices (-1.19 ± 0.17 for Liso-τ and -1.10 ± 0.03 for L X -Tbrk). Even more surprisingly, we noted that although τ and Tbrk represent different GRB time variables, it appears that the first relation (Liso-τ) extrapolates into the second one for timescales τ ≃ Tbrk. This fact suggests that these two relations have a common origin, which we conjecture to be kinematic. This relation adds to the recently discovered relations between properties of the prompt and afterglow GRB phases, indicating a much more intimate relation between these two phases than hitherto considered.