Formation Rate, Evolving Luminosity Function, Jet Structure, and Progenitors for Long Gamma‐Ray Bursts

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Abstract
We constrain the isotropic luminosity function (LF) and formation rate of long γ-ray bursts (GRBs) by fitting models jointly to both the observed differential peak-flux and redshift distributions. We find evidence supporting an evolving LF, where the luminosity scales as (1 + z)δ, with an optimal δ of 1.0 ± 0.2. For a single-power law LF, the best slope is approximately -1.57 with an upper luminosity of 1053.3 ergs s-1, while the best slopes for a double-power law LF are approximately -1.6 and -2.6, with a break luminosity of 1052.7 ergs s-1. Our finding implies a jet model intermediate between the universal structured (θ) ∝ θ-2 model and the quasi-universal Gaussian structured model. For the uniform-jet model our result is compatible with an angle distribution between 2° and 15°. Our best-constrained GRB formation rate histories increase from z = 0 to 2 by a factor of ~30 and then continue increasing slightly. We connect these histories to the cosmic star formation history and compare with observational inferences up to z ~ 6. GRBs could be tracing the cosmic rates of both the normal and obscured star formation regimes. We estimate a current GRB event rate in the Milky Way of ~5 × 10-5 yr-1 and compare it with the birthrate of massive close Wolf-Rayet + black hole binaries with orbital periods of hours. The agreement is rather good, suggesting that these systems could be the progenitors of the long GRBs.