CSST Cosmological Emulator II: Generalized Accurate Halo Mass Function Emulation

Accurate theoretical prediction for halo mass function across a broad cosmological space is crucial for the forthcoming China Space Station Telescope (CSST) observations, which will capture cosmological information from multiple probes, e.g., cluster abundance, and weak lensing. In this work, we quantify the percent-level impact of different mass binning schemes when measuring the differential halo mass function from simulations, and demonstrate that the cumulative form of the halo mass function is independent of the binning scheme. Through the recently finished Kun simulation suite, we propose a generalized framework to construct multiple accurate halo mass function emulators for different halo mass definitions, including $M_{200m}$, $M_{vir}$, and $M_{200c}$. This extends our CSST Emulator to provide fast and accurate halo mass function predictions for halo mass $M\geq 10^{12}\,h^{-1}M_{\odot}$ up to $z=3.0$. For redshifts $z\leq 1.0$, the accuracy is within $2\%$ for $M\leq 10^{13}\,h^{-1}M_{\odot}$, $5\%$ for $M\leq 10^{14}\,h^{-1}M_{\odot}$, and $10\%$ for $M\leq 10^{15}\,h^{-1}M_{\odot}$, which is comparable with the statistical errors of training simulations. This tool is integrated in CSST Emulator and publicly available at https://github.com/czymh/csstemu, providing a fast and accurate theoretical tool to obtain unbiased cosmological constraints of the upcoming CSST survey.