SIMBAD references

We compute the intrinsic isotropic peak luminosity function (LF) and formation rate of long gamma-ray bursts (LGRBs) using a novel approach. We complement a standard logN-logP brightness distribution and Vmax estimations with two observation-time relations: a redshift-observation-time relation (logz-logT) and a new luminosity-observation-time relation (logL-logT). We show that this approach reduces degeneracies that exist between the rate and LF of a brightness distribution. To account for the complex triggering algorithm employed by Swift, we use recent results of Lien et al. to produce a suite of efficiency functions. Using these functions with the above methods, we show that a logL-logT method can provide good constraints on the form of the LF, particularly the high end. Using a sample of 175 peak luminosities determined from redshifts with well-defined selection criteria, our results suggest that LGRBs occur at a local rate (without beaming corrections) of [0.7 < ρ0 < 0.8]/Gpc3/yr. Within this range, assuming a broken power-law LF, we find best estimates for the low- and high-energy indices of -0.95±0.09 and -2.59±0.93, respectively, separated by a break luminosity 0.80±0.43x10⁵² erg/s.