To reveal and understand astrophysical processes responsible for the Gamma Ray Burst ( GRB ) phenomenon , it is crucial to discover and understand relations between their observational properties .
The presented study is performed in the GRB rest frames and it uses a sample of 62 long GRBs from our sample of 77 Swift GRBs with known redshifts .
Following the earlier analysis of the afterglow characteristic luminosity L ^ { * } _ { a } – break time T ^ { * } _ { a } correlation for a sample of long GRBs ( 12 ) we extend it to correlations between the afterglow and the prompt emission GRB physical parameters .
We reveal a tight physical scaling between the mentioned afterglow luminosity L ^ { * } _ { a } and the prompt emission mean luminosity < L ^ { * } _ { p } > _ { 45 } \equiv E _ { iso } / T ^ { * } _ { 45 } .
The distribution , with the Spearman correlation coefficient reaching 0.95 for the data subsample with most regular light curves , can be fitted with approximately L ^ { * } _ { a } \propto { < L ^ { * } _ { p } > _ { 45 } } ^ { 0.7 } .
We also analyzed correlations of L ^ { * } _ { a } with several other prompt emission parameters , including the isotropic energy E _ { iso } , the peak energy in the \nu F _ { \nu } spectrum , E _ { peak } , and the variability parameter , V , defined by ( 32 ) .
As a result , we reveal significant correlations also between these quantities , with an exception of the variability parameter .
The main result of the present study is the discovery that the highest correlated GRB subsample in the Dainotti et al .
( 12 ) afterglow analysis , for the GRBs with canonical X - ray light curves , leads also to the highest prompt-afterglow correlations and such events can be considered to form a sample of standard GRBs for astrophysics and cosmology .