THE COSMIC RATE, LUMINOSITY FUNCTION, AND INTRINSIC CORRELATIONS OF LONG GAMMA-RAY BURSTS

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Abstract
We calculate durations and spectral parameters for 207 Swift bursts detected by the BAT instrument from April 2007 to August 2009, including 67 events with measured redshifts. This is the first supplement to our catalog of 425 Swift GRBs (147 with redshifts) starting from GRB041220. 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 5-sigma 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 duration); however, the correlation {\it 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 XRFs as well as a potentially large missing population of short-duration GRBs that will be probed by EXIST.

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