Lost in the FoG: Pitfalls of Models for Large-Scale Hydrogen Distributions

Large-scale HI surveys and their cross-correlations with galaxy distributions have immense potential as cosmological probes. Interpreting these measurements requires theoretical models that must incorporate redshift-space distortions (RSDs), such as the Kaiser and fingers-of-God (FoG) effect, and differences in the tracer and matter distributions via the tracer bias. These effects are commonly approximated with assumptions that should be tested on simulated distributions. In this work, we use the hydrodynamical simulation suite IllustrisTNG to assess the performance of models of $z \leq 1$ HI auto and HI-galaxy cross-power spectra, finding that the models employed by recent observations introduce errors comparable to or exceeding their measurement uncertainties. In particular, neglecting FoG causes $\gtrsim 10\%$ deviations between the modeled and simulated power spectra at $k \gtrsim 0.1$ $h$ / Mpc, larger than assuming a constant bias which reaches the same error threshold at slightly smaller scales. However, even without these assumptions, models can still err by $\sim 10\%$ on relevant scales. These remaining errors arise from multiple RSD damping sources on HI clustering, which are not sufficiently described with a single FoG term. Overall, our results highlight the need for an improved understanding of RSDs to harness the capabilities of future measurements of HI distributions.