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 _ { \mathrm { 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 _ { 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 _ { \mathrm { brk } } .
We also present the L _ { X } - T _ { \mathrm { 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 _ { \mathrm { iso } } - \tau and \rho = -0.88 for the L _ { X } - T _ { \mathrm { brk } } relation ) and have surprisingly similar best-fit power law indices ( -1.19 \pm 0.17 for L _ { \mathrm { iso } } - \tau and -1.10 \pm 0.03 for L _ { X } - T _ { \mathrm { brk } } ) .
Even more surprisingly , we noted that although \tau and T _ { \mathrm { brk } } represent different GRB time variables , it appears that the first relation ( L _ { \mathrm { iso } } - \tau ) extrapolates into the second one for timescales \tau \simeq T _ { \mathrm { 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 .