Luminosity function of Type II GRBs:differences from long GRBs

Gamma-ray bursts (GRBs) are generally categorized into long and short bursts based on their duration ($T_{90}$). Recently, it has been proposed that GRBs can also be classified into type I (merger) and type II (collapsar) bursts based on the different origin. From a sample of \textit{Swift} long GRBs~(LGRBs) with a redshift completeness of 60\% and $P \geq 2.6 \, \text{ph} \, \text{cm}^{-2} \, \text{s}^{-1}$, collected through the end of 2023, we identify a pure sample of 146 Type II GRBs. With this sample, we construct the luminosity function (LF) using both the Broken Power Law (BPL) and Triple Power Law (TPL) models. Our results indicate that, similar to LGRBs, a strong redshift evolution in either luminosity or density is necessary to accurately account for the observations, regardless of the specific form of the LF assumed. The LF of LGRBs remains a topic of debate, with some studies suggesting it follows a BPL form, while others advocate for a TPL form. In our study, we find that the LF of Type II GRBs tends to favor a BPL model.