The luminosity function and formation rate of gamma-ray bursts (GRBs) are two key properties to understand the nature of GRBs and to determine their progenitors. Several models have been proposed to account for these two properties: no evolution model, density evolution model, luminosity evolution model, and empirical density model. The authors considered a complete sample of long GRBs and adopted a MCMC method to estimate the parameters of these models. This is the first time this method was applied to a well-defined sample of GRBs that is complete in redshift.

By with LAN Guangxuan

Figure 1. Redshift (left-hand panel) and luminosity (right-hand panel) distributions of GRBs. Data points are the observed redshift distributions of 81 GRBs in the complete Swift sample. Curves show the expected distributions for different best-fitting models: no evolution model (yellow dot–dashed lines), luminosity evolution model (blue dashed lines), density evolution model (red solid lines), and empirical density model (green dotted lines). Shaded regions show the 1σ confidence regions of the corresponding models.

  They confirmed that the expectation from the no evolution model does not provide a good representation of the observed luminosity and redshift distributions of the complete GRB sample. A strong redshift evolution in luminosity (with an evolution index of ) or in density () is needed in order to reproduce the observations well. And in the empirical density model, the GRB formation rate rises like for and is proportional to for . The local formation rate of GRBs is .

See more details in: https://academic.oup.com/mnras/article/488/4/4607/5538809