The redshift evolution of the luminosity function of type II GRBs

As of December 2023, the Swift satellite has detected more than 1600 gamma-ray bursts (GRBs). We select 307 Type II GRBs for constructing the luminosity function (LF) based on the following criteria: (1) duration $T_{90} \geq 2 s$; (2) conformity with the Amati relation for Type II GRBs; and (3) peak flux $P \geq 1 \, \text{ph} \, \text{cm}^{-2} \, \text{s}^{-1}$. We explore two general forms of the GRB LF: a broken power-law (BPL) LF and a triple power-law (TPL) LF. We consider three evolutionary scenarios: no evolution, luminosity evolution, and density evolution. We find that the no evolution model can be excluded, while both luminosity and density evolution models effectively account for the observations. This result is consistent with previous studies on long GRBs (LGRBs). However, our Type II GRB sample favors a BPL LF, in contrast to the preference for a TPL function discovered in Long GRBs.