Gamma-Ray Burst Luminosity Functions Based On a Newly Discovered Correlation Between Peak Spectral Energy and V/Vmax

We have discovered a correlation between the observed peak spectral energy Epk,obs and the Euclidean value of < V/Vmax > of gamma-ray bursts (GRBs). We present the evidence for the correlation in the GUSBAD catalog and use it to derive the luminosity function of GRBs without using any redshifts. The procedure involves dividing GUSBAD GRBs into five spectral classes based on their Epk,obs. The overall luminosity function is derived assuming that each of the spectral classes contributes a gaussian luminosity function. Their central luminosity is derived from the observed Euclidean < V/Vmax >. We explore various forms for the GRB rate functionGR(z) in predicting redshift distributions of GRBs detected by Swift. We find that GR(z) peaks at a higher redshift than the typical star formation history currently favored in the literature. We consider two examples of GR(z) that sucessfully predict the observed redshift distribution of Swift GRBs. With the luminosity functions in hand, we convert the Epk,obs−V/Vmax correlation into an Epk,obs−Liso correlation and a rest frame Epk − Liso correlation. In comparing the Epk − Liso correlation with a published correlation based on GRBs with known Epk,obs and redshifts, we discuss the effect of Malmquist bias. Subject headings: gamma rays: bursts