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Luminosity Correlations for Gamma-Ray Bursts and Implications for Their Prompt and Afterglow Emission Mechanisms

We present the relation between the (z- and k-corrected) spectral lags, tau, for the standard Swift energy bands 50 - 100 keV and 100 - 200 keV and the peak isotropic luminosity, L(sub iso) (a relation reported first by Norris et al.), for a subset of 12 long Swift GRBs taken from a recent study of this relation by Ukwatta et al. The chosen GRBs are also a subset of the Dainotti et al. sample, a set of Swift GRBs of known redshift, employed in establishing a relation between the (GRB frame) luminosity, L(sub x), of the shallow (or constant) flux portion of the typical XRT GRB-afterglow light curve and the (GRB frame) time of transition to the normal decay rate, T(sub brk). We also present the L(sub x) - T(sub brk) relation using only the bursts common in the two samples. The two relations exhibit a significant degree of correlation (rho = -0.65 for the L(sub iso) - tao and rho = -0.88 for the L(sub x) -T(sub brk) relation) and have surprisingly similar best-fit power law indices (-1.19 +/- 0.17 for L(sub iso) - tau and -1.10 +/- 0.03 for L(sub x) - T(sub brk)). Even more surprisingly, we noted that although tau and T(sub brk) represent different GRB time variables, it appears that the first relation (L(sub iso) - tao) extrapolates into the second one for timescales tau similar to T(sub brk) 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.

Sultana, J.↗