GRB Formation Rates inferred from the Spectral Peak Energy – Luminosity Relation

We investigate the GRB formation rate based on the relation between the spectral peak energy (E p) and the isotropic luminosity. The E p –luminosity relation covers the energy range of 50 – 2000 keV and the luminosity range of 10 50 –10 54 erg s −1 , respectively. We find that the relation is considerably tighter than similar relations suggested previously. Using E p –luminosity relation, we estimate the luminosity and the redshift of 684 GRBs with the unknown distances and derive the GRB formation rate as a function of the redshift. For 0 ≤ z ≤ 2 , the GRB formation rate is well correlated with the star formation rate while it increases monotonously from z ∼ 2 out to z ∼ 12. This behavior is consistent with the results of previous works using the lag–luminosity relation or the variability–luminosity relation.