FAST Drift Scan Survey for H <scp>i</scp> Intensity Mapping: Simulation of Bayesian-stacking-based H <scp>i</scp> Mass Function Estimation

Abstract This study investigates the estimation of the neutral hydrogen (H i ) mass function (H i MF) using a Bayesian stacking approach with simulated data for the Five-hundred-meter Aperture Spherical radio Telescope (FAST) H i intensity mapping (H i IM) drift-scan surveys. Using data from the IllustrisTNG simulation, we construct H i sky cubes at redshift z ∼ 0.1 and the corresponding optical galaxy catalogs, simulating FAST observations under various survey strategies, including pilot, deep-field, and ultradeep-field surveys. The H i MF is measured for distinct galaxy populations—classified by optical properties into red, blue, and bluer galaxies—and injected with systematic effects such as observational noise and flux confusion caused by the FAST beam. The results show that Bayesian stacking significantly enhances H i MF measurements. For red and blue galaxies, the H i MF can be well constrained with pilot surveys, while deeper surveys are required for the bluer galaxy population. Our analysis also reveals that sample variance dominates over observational noise, emphasizing the importance of wide-field surveys to improve constraints. Furthermore, flux confusion shifts the H i MF toward higher masses, which we address using a transfer function for correction. Finally, we explore the effects of intrinsic sample incompleteness and propose a framework to quantify its impact. This work lays the groundwork for future H i MF studies with FAST H i IM, addressing key challenges and enabling robust analyses of H i content across galaxy populations.