Constraining the rate and luminosity function of swift gamma-ray bursts

© 2014 The Authors. 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-log P brightness distribution and Vmax estimations with two observation-time relations: a redshift- observation-time relation (log z-log T ) and a new luminosity-observation-time relation (logL-log T ). 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. (2014) to produce a suite of efficiency functions. Using these functions with the above methods, we show that a logL-log T 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 <?0 <0.8] Gpc-3 yr-1. 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 ± 0.43 × 1052 erg s-1.