Gamma-ray burst formation rate inferred from the spectral peak energy-peak luminosity relation

We estimate a gamma-ray burst (GRB) formation rate based on the new relation between the spectral peak energy (E_p) and the peak luminosity. The new relation is derived by combining the data of E_p and the peak luminosities by BeppoSAX and BATSE, and it looks considerably tighter and more reliable than the relations suggested by the previous works. Using the new E_p-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. We also discuss the luminosity function and the redshift dependence of the intrinsic luminosity (luminosity evolution).