We find a strong correlation between the peak energy at zero fluence ( E _ { peak, 0 } ) and the isotropic energy ( E _ { \gamma,iso } ) of the 22 pulses of 9 Gamma Ray Bursts ( GRB ) detected by the Fermi satellite .
The correlation holds for the individual pulses of each GRB , which shows the reality of the correlation .
The derived correlation ( Spearman correlation coefficient , r , is 0.96 ) is much stronger compared to the correlations using E _ { peak } ( in place of E _ { peak, 0 } ) determined from the time-integrated spectrum ( r = 0.8 ) , or the time-resolved spectrum not accounting for broad pulse structures ( r = 0.37 ) , or the pulse-wise spectrum ( r = 0.89 ) .
Though the improvement in the E _ { peak } - E _ { \gamma,iso } relation ( the Amati relation ) for a pulse-wise analysis is known earlier , this is the first time a parameter derived from a joint spectral and timing fit to the data is shown to improve the correlation .
We suggest that E _ { peak, 0 } , rather than E _ { peak } , is intrinsic to a GRB pulse and a natural choice as the parameter in the pulse-wise correlation studies .