Pop-III Star Formation Rate Inferred from Ep—Luminosity Relation of Gamma-Ray Bursts.

We estimate a GRB formation rate based on the relation between the spectral peak energy (Ep) and the peak luminosity. This relation is derived combining the data of Ep and the peak luminosities by BeppoSAX, BATSE, HETE-2, Integral, Konus, RHESSI and Swift, and it looks considerably tighter and more reliable than the relations suggested by the previous works. In this paper, we show the revised Ep–luminosity (Yonetoku) relation. Using the new Ep–luminosity relation, we estimate redshifts of the 689 GRBs without known distances in the BATSE catalog and derive a GRB formation rate as a function of the redshift. For the redshift range of 0<z<2, the GRB formation rate increases and is well correlated with the star formation rate while it keeps constant toward z = 12. [ABSTRACT FROM AUTHOR]