The Luminosity Function and Formation Rate History of GRBs

— The isotropic luminosity function (LF) and formation rate history (FRH) of long GRBs is by the first time constrained by using jointly both the observed GRB peak-flux and redshift distributions. Our results support an evolving LF and a FRH that keeps increasing after z = 2. We discuss some interesting implications related to these results. PACS 98.70.Rz – gamma ray bursts. The primordial and most extensive information on GRBs obtained directly from observations is the differential peak-flux, P , distribution, the so commonly called logN − logP diagram (NPD). The NPD is the convolution of basically three factors: the intrinsic LF, the FRH and the cosmic volume. In the past, several attempts were done to constrain the LF from fits to the NPD, assuming arbitrary GRB FRHs and cosmologies. The results were rather poor because the complicated mixing between the model LF and FRH introduces a high degeneracy among these factors in the NPD. The most direct way to infer both the LF and the FRH is based on the observational luminosity-redshift diagram [10, 6, 12]. Unfortunately, this strategy is so far limited by the small number of GRBs with known or inferred z, by the bias introduced by the given method to infer z, and by the sensitivity limit related to the z estimate. We propose [4] a new strategy for constraining the GRB LF and FRH based on the joint use of the NPD and the observed or inferred GRB differential z distribution (the N − z diagram, NZD). 2. – The Method and the Data The differential NPD and NZD are modelled by seeding at each z a large number of GRBs with a given rate, ˙ ρ GRB , and LF, f (L iso)dL iso , and then by propagating the flux of each source to z = 0. We use the popular ΛCDM cosmology with Ω m =0.29,