The luminosity function of Swift long gamma-ray bursts

The accumulation of Swift observed gamma-ray bursts (GRBs) has gradually made it possible to directly derive a GRB luminosity function (LF) from the observational luminosity distribution. However, two complexities are involved: (i) the evolving connection between GRB rate and cosmic star formation rate; and (ii) observational selection effects due to telescope thresholds and redshift measurements. With a phenomenological investigation of these two complexities, we constrain and discriminate two popular competing LF models (i.e. the broken-power-law LF and the single-power-law LF with an exponential cut-off at low luminosities). As a result, we find that the broken-power-law LF may be more favoured by observations, with a break luminosity L b= 2.5 × 1052 erg s−1 and prior- and post-break indices ν1= 1.72 and ν2= 1.98. Regarding an extra evolution effect expressed by a factor (1 +z)δ, if the metallicity of GRB progenitors is lower than ∼0.1 Z⊙ as expected by some collapsar models, then there may be no extra evolution effect other than the metallicity evolution (i.e. δ approaches zero). Alternatively, if we remove the theoretical metallicity requirement, then a relationship between the degenerate parameters δ and Z max can be found, very roughly, δ∼ 2.4(Z max /Z⊙− 0.06). This indicates that extra evolution could become necessary for relatively high metallicities.