Yan-Kun Qu, Zhong-Xiao Man, Shuang-Xi Yi, Yu-Peng Yang

Gamma-ray bursts (GRBs) are powerful probes of the high-redshift universe. However, the proportion of collapsar GRBs among long GRBs and their event rate relative to the star formation rate (SFR) remain contentious issues. We assume that long GRBs with $z\geq 2$ are all collapsar GRBs and construct the luminosity function using a high-redshift sample from the Swift satellite spanning 2004 to 2019. We model the luminosity function with a broken power-law form and consider three scenarios: no evolution, luminosity evolution, and density evolution. Our results are as follows: 1) The no-evolution model can be ruled out. 2) The fitting results indicate that to adequately explain the observations, a significant redshift evolution in either luminosity (evolution index $\delta = 1.54^{+0.21}_{-0.22}$) or density ($\delta = 2.09^{+0.29}_{-0.26}$) is required. This excludes the possibility that the evolution of long GRBs with redshift is due to contamination from non-collapsar GRBs. 3) The luminosity evolution model predicts that the number of collapsar GRBs with $z<2$ and $P \geq 1 \, \text{ph} \, \text{cm}^{-2} \, \text{s}^{-1}$ is 138.6, accounting for 82.5% of the observed long GRBs with $z<2$ and $P \geq 1 \, \text{ph} \, \text{cm}^{-2} \, \text{s}^{-1}$. The density evolution model predicts that the number of collapsar GRBs with $z<2$ and $P \geq 1 \, \text{ph} \, \text{cm}^{-2} \, \text{s}^{-1}$ is 80.2, accounting for 47.7% of the observation. Regardless of the model, a substantial portion of the long GRBs are not collapsar GRBs.