Letter to the Editor

The Amati relation in the “fireshell” model

¹ ICRANet and ICRA, Piazzale della Repubblica 10, 65122 Pescara, Italy
² Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, 00185 Roma, Italy e-mail: [roberto.guida;maria.bernardini;bianco;letizia.caito;dainotti;ruffini]@icra.it
³ ICRANet, Université de Nice Sophia Antipolis, Grand Château, BP 2135, 28 avenue de Valrose, 06103 Nice Cedex 2, France

Received: 6 June 2008
Accepted: 23 June 2008

Abstract

Context. The cosmological origin of gamma-ray bursts (GRBs) has been firmly established, with redshifts up to . They are possible candidates for use as “distance indicators” for testing cosmological models in a redshift range hardly achievable by other cosmological probes. Asserting the validity of the empirical relations among GRB observables is now crucial for their calibration.

Aims. Motivated by the relation proposed by Amati and collaborators, we look within the “fireshell” model for a relation between the peak energy E_p of the total time-integrated spectrum of the afterglow and the total energy of the afterglow E_aft, which in our model encompasses and extends the prompt emission.

Methods. The fit within the fireshell model, as for the “canonical” GRB 050315, uses the complete arrival time coverage given by the Swift satellite. It is performed simultaneously, self-consistently, and recursively in the four BAT energy bands (15–25 keV, 25–50 keV, 50–100 keV, and 100–150 keV), as well as in the XRT one (0.2–10 keV). It uniquely determines the two free parameters characterizing the GRB source, the total energy of the e plasma and its baryon loading B, as well as the effective CircumBurst Medium (CBM) distribution. We can then build two sets of “gedanken” GRBs varying the total energy of the electron-positron plasma and keeping the same baryon loading B of GRB 050315. The first set assumes the one obtained in the fit of GRB 050315 for the effective CBM density. The second set assumes instead a constant CBM density equal to the average value of the GRB 050315 prompt phase.

Results. For the first set of “gedanken” GRBs we find a relation , with , whose slope strictly agrees with the Amati one. Such a relation, in the limit , coincides with the Amati one. Instead, no correlation is found in the second set of “gedanken” GRBs.

Conclusions. Our analysis excludes the proper GRB (P-GRB) from the prompt emission, extends all the way to the latest afterglow phases, and is independent of the assumed cosmological model, since all “gedanken” GRBs are at the same redshift. The Amati relation, on the other hand, includes the P-GRB, focuses only on the prompt emission, being therefore influenced by the instrumental threshold that fixes the end of the prompt emission, and depends on the assumed cosmology. This might explain the intrinsic scatter observed in the Amati relation.