Redshift distribution and luminosity function of long gamma-ray bursts from cosmological simulations

We study the luminosity function (LF), the comoving rate and the detection rate of long gamma-ray bursts (LGRBs) to high redshift, using galaxy catalogues constructed by combining high-resolution N-body simulations with semi-analytic models of galaxy formation. We assume the collapsar model and different metallicity thresholds and conclude that LGRBs are not good tracers of the star formation history in the Universe. By using the log N-log P diagram for Burst And Transient Source Experiment (BATSE) bursts, we then determine the LF (with and without evolution with redshift) and the formation rate of LGRBs, obtaining constraints on the slope of the power law. We check the resulting redshift distribution with Swift data updated to 2009 August, finding that models where LGRBs have as progenitors stars with Z < 0.3 Z_⊙ and without evolution of the LF are in agreement with the data. We also predict that there are about ∼1 per cent of GRBs at redshift z > 6.