The cosmic rate, luminosity function, and intrinsic correlations of long gamma-ray bursts

We calculate durations and spectral parameters for 207 Swift bursts detected by the Burst Alert Telescope from 2007 April to 2009 August, including 67 events with measured redshifts. This is the first supplement to our catalog of 425 Swift gamma-ray bursts (GRBs; 147 with redshifts) starting from GRB 041220. This complete and extensive data set, analyzed with a unified methodology, allows us to conduct an accurate census of intrinsic GRB energetics, hardnesses, durations, and redshifts. The GRB world model we derive reproduces well the observables from both Swift and pre-Swift satellites. Comparing to the cosmic star formation rate, we estimate that only about 0.1% of massive stars explode as bright GRBs. There is strong evidence for evolution in the Swift population at intermediate and high-z, and we can rule out (at the 5σ level) that this is due to evolution in the luminosity function of GRBs. Instead, the Swift sample suggests a modest propensity for low metallicity, evidenced by an increase in the rate density with redshift. Treating the multivariate data and selection effects rigorously, we find a real, intrinsic correlation between E _iso and E _pk (and possibly also T _r45,z); however, the correlation is not a narrow log-log relation and its observed appearance is strongly detector-dependent. We also estimate the high-z rate (3%-9% of GRBs at z beyond 5) and discuss the extent of a large missing population of low-E _pk,obs X-ray flashes as well as a potentially large missing population of short-duration GRBs that will be probed by EXIST.