Formation rate, evolving luminosity function, jet structure, and progenitors for long gamma-ray bursts

We constrain the isotropic luminosity function (LF) and formation rate of long gamma-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)(delta), with an optimal delta of 1.0+/-0.2. For a single-power law LF, the best slope is approximately -1.57 with an upper luminosity of 10(53.3) 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 10(52.7) ergs s(-1). Our finding implies a jet model intermediate between the universal structured epsilon(theta)proportional to theta(-2) model and the quasi-universal Gaussian structured model. For the uniform-jet model our result is compatible with an angle distribution between 2degrees and 15degrees. Our best-constrained GRB formation rate histories increase from z=0 to 2 by a factor of similar to30 and then continue increasing slightly. We connect these histories to the cosmic star formation history and compare with observational inferences up to zsimilar to6. 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 similar to5x10(-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.