Correlation between the isotropic energy and the peak energy at zero fluence for the individual pulses of GRBs: towards an universal physical correlation for the prompt emission

We find a strong correlation between the peak energy at zero fluence ($\rm E_{peak,0}$) and the isotropic energy ($\rm E_{\gamma,iso}$) 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 $\rm E_{peak}$ (in place of $\rm E_{peak,0}$) 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 $\rm E_{peak}$ - $\rm E_{\gamma,iso}$ 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 $\rm E_{peak,0}$, rather than $\rm E_{peak}$, is intrinsic to a GRB pulse and a natural choice as the parameter in the pulse-wise correlation studies.