The observation of GRB 080319B , with an isotropic energy E _ { iso } = 1.32 \times 10 ^ { 54 } erg , and GRB 050904 , with E _ { iso } = 1.04 \times 10 ^ { 54 } erg , offers the possibility of studying the spectral properties of the prompt radiation of two of the most energetic Gamma Ray Bursts ( GRBs ) .
This allows us to probe the validity of the fireshell model for GRBs beyond 10 ^ { 54 } erg , well outside the energy range where it has been successfully tested up to now ( 10 ^ { 49 } – 10 ^ { 53 } erg ) .
We find that in the low energy region , the prompt emission spectra observed by Swift BAT reveals more power than theoretically predicted .
The opportunities offered by these observations to improve the fireshell model are outlined in this paper .
One of the distinguishing features of the fireshell model is that it relates the observed GRB spectra to the spectrum in the comoving frame of the fireshell .
Originally , a fully radiative condition and a comoving thermal spectrum were adopted .
An additional power-law in the comoving thermal spectrum is required due to the discrepancy of the theoretical and observed light curves and spectra in the fireshell model for GRBs 080319B and 050904 .
A new phenomenological parameter \alpha is correspondingly introduced in the model .
We perform numerical simulations of the prompt emission in the Swift BAT bandpass by assuming different values of \alpha within the fireshell model .
We compare them with the GRB 080319B and GRB 050904 observed time-resolved spectra , as well as with their time-integrated spectra and light curves .
Although GRB 080319B and GRB 050904 are at very different redshifts ( z=0.937 and z=6.29 respectively ) , a value of \alpha = -1.8 leads for both of them to a good agreement between the numerical simulations and the observed BAT light curves , time-resolved and time-integrated spectra .
Such a modified spectrum is also consistent with the observations of previously analyzed less energetic GRBs and reasons for this additional agreement are given .
Perspectives for future low energy missions are outlined .