The Amati relation within the fireshell model

Abstract

In this work we show the existence of a spectral‐energy correlation within our “fireshell” model for GRBs. The free parameters of the model are the total energy Etote± of the e± plasma and its baryon loading B≡MBc2/Etote±, characterizing the source, and the parameters describing the effective Circum Burst medium (CBM) distribution, namely its particle number density ρ and its effective emitting area R. We build a sample of pseudo‐GRBs, i.e. a set of theoretically simulated light curves, varying the total energy of the electron‐positron plasma Etote± and keeping the same baryon loading; the parametrization used to describe the distribution of the Circum Burst medium is the same as well for all the pseudo‐GRBs. The values of these parameters (B, ρ and R) used in this work are equal to the ones assumed to fit GRB050315, a Swift burst representing a good example of what in the literature has been addressed as “canonical light curve”. For each GRB of the sample we calculate the νFν spectrum integrating the theoretically computed light curve over the total time, namely from our T0, the end of the Proper‐GRB (P‐GRB), up to the end of our afterglow phase, when the fireshell Lorentz gamma factor is close to unity; we exclude the P‐GRB from this spectral computation because, following our “canonical” GRB scenario, this component of the GRB emission is physically different from the other component, that is our afterglow component, so one should take care in no mixing them. We find that the maximum of this spectrum, that is the observed peak energy Ep,tot, correlates with the initial electron‐positron plasma energy Etote± in a way very similar to the Amati one: Ep,tot∝(Etote±)0.5.