The correlation between the cosmological rest–frame \nu F _ { \nu } spectrum peak energy , E _ { p,i } , and the isotropic equivalent radiated energy , E _ { iso } , discovered by Amati et al .
in 2002 and confirmed/extended by subsequent osbervations , is one of the most intriguing and debated observational evidences in Gamma–Ray Bursts ( GRB ) astrophysics .
In this paper I provide an update and a re–analysis of the E _ { p,i } – E _ { iso } correlation basing on an updated sample consisting of 41 long GRBs/XRFs with firm estimates of z and observed peak energy , E _ { p,obs } , 12 GRBs with uncertain valeus of z and/or E _ { p,obs } , 2 short GRBs with firm estimates of z and E _ { p,obs } and the peculiar sub–energetic events GRB980425/SN1998bw and GRB031203/SN2003lw .
In addition to standard correlation analysis and power–law fitting , the data analysis here reported includes a modelization which accounts for sample variance .
All 53 classical long GRBs and XRFs , including 11 Swift events with published spectral parameters and fluences , have E _ { p,i } and E _ { iso } values , or upper/lower limits , consistent with the correlation , which shows a chance probability as low as \sim 7 \times 10 ^ { -15 } , a slope of \sim 0.57 ( \sim 0.5 when fitting by accounting for sample variance ) and an extra–Poissonian logarithmic dispersion of \sim 0.15 , it extends over \sim 5 orders of magnitude in E _ { iso } and \sim 3 orders of magnitude in E _ { p,i } and holds from the closer to the higher z GRBs .
Sub–energetic GRBs ( 980425 and possibly 031203 ) and short GRBs are found to be inconsistent with the E _ { p,i } – E _ { iso } correlation , showing that it can be a powerful tool for discriminating different classes of GRBs and understanding their nature and differences .
I also discuss the main implications of the updated E _ { p,i } – E _ { iso } correlation for the models of the physics and geometry of GRB emission , its use as a pseudo–redshift estimator and the tests of possible selection effects with GRBs of unknown redshift .