A cosmographic calibration of the E^p,i – E_iso (Amati) relation for GRBs

¹ Dipartimento di Scienze Fisiche, Università di Napoli “Federico II”, Compl. Univ. Monte S. Angelo, Ed. N, via Cinthia, 80126 Napoli, Italy e-mail: capozziello@na.infn.it
² INFN Sez. di Napoli, Compl. Univ. Monte S. Angelo, Ed. N, via Cinthia, 80126 Napoli, Italy
³ ICRANet and ICRA, Piazzale della Repubblica 10, 65122 Pescara, Italy
⁴ Dip. di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, 00185 Roma, Italy

Received: 27 March 2010
Accepted: 4 June 2010

Abstract

Aims. The Amati relation, which connects the isotropic energy emitted and the rest-frame peak energy of the νFν spectra of GRBs, is cosmology-dependent, so we need a method to obtain an independent calibration of the Amati relation.

Methods. Using the Union Supernovae Ia catalog, we obtain a cosmographic luminosity distance in the y-redshift and verify that this parameterization very well approximates the fiducial standard cosmological model ΛCDM. Using this cosmographic luminosity distance d_l, we compute the Amati relation considering this cosmology-independent definition of d_l.

Results. The cosmographic Amati relation we obtain agrees in the errors with other cosmology-independent calibrations proposed in the literature.