Fast Simulation of Cosmological Neutral Hydrogen based on the Halo Model

Cosmological neutral hydrogen (HI) surveys provide a promising tomographic probe of the post-reionization era and of the standard model of cosmology. Simulations of this signal are crucial for maximizing the utility of these surveys. We present a fast method for simulating the cosmological distribution of HI based on a halo model approach. Employing the approximate $\texttt{PINOCCHIO}$ code, we generate the past light cone of dark matter halos. Subsequently, the halos are populated with HI according to a HI-halo mass relation. The nature of 21 cm intensity mapping demands large-volume simulations with a high halo mass resolution. To fulfill both requirements, we simulate a past light cone for declinations between -15{\deg} and -35{\deg} in the frequency range from 700 to 800 MHz, matching HIRAX, the Hydrogen Intensity and Real-time Analysis eXperiment. We run $\texttt{PINOCCHIO}$ for a 1 h$^{-3}$Gpc$^3$ box with 6700$^3$ simulation particles. With this configuration, halos with masses as low as M$_\text{min}$ = 4.3 $\times$ 10$^{9}$M$_{\odot}$ are simulated, resulting in the recovery of more than 97% of the expected HI density. From the dark matter and HI past light cone, maps with a width of 5 MHz are created. To validate the simulations, we have implemented and present here an analytical dark matter and HI halo model in $\texttt{PyCosmo}$, a Python package tailored for theoretical cosmological predictions. We perform extensive comparisons between analytical predictions and the simulations for the mass function, mass density, power spectrum, and angular power spectrum for dark matter and HI. We find close agreement in the mass function and mass densities, with discrepancies within a few percent. For the three-dimensional power spectra and angular power spectra, we observe an agreement better than 10%.