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

TL;DR

This paper assesses the reliability of large-scale HI distribution models by comparing common modeling prescriptions to hydrodynamical simulations from IllustrisTNG at z ≤ 1. It systematically decomposes the modeling into nonlinearities, tracer bias, and redshift-space distortions, then tests auto and HI–galaxy cross-spectra against the simulation, revealing substantial errors—often exceeding current observational uncertainties—when FoG is neglected or biases are assumed constant. The results show that even the best-case models yield ≳10% discrepancies on scales relevant to observations, and that Ω_HI inferences from HI power spectra can be biased by 15–30% if model errors are not properly accounted for. The authors advocate a more nuanced treatment of RSDs, including possibly a two-term FoG model to capture intra-halo and intra-galactic dispersion, to realize the full potential of upcoming HI surveys for precision cosmology.

Abstract

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.

Figures (16)

• Figure 1: A deconstructed example ${\rm H}$i-galaxy cross-power spectrum, providing insight into the contribution of each model ingredient. The linear matter power spectrum is shown with the black dashed line in the top panel, with the wiggles at $k \sim 0.05$h cMpc$^{-1}$ corresponding to baryonic acoustic oscillations. We then add each ingredient from Equation \ref{['eq:cross_full']} to the linear power spectrum sequentially, lightening the color as each is added (see text for ingredient descriptions). The $z = 1$ matter power spectrum (black) and ${\rm H}$i-galaxy cross-power spectrum (salmon) for TNG300 are shown in dotted lines, in fair agreement with the corresponding model values. The bottom panel shows the ratio of the power spectra with and without that component in order to more easily visualize its individual contribution.
• Figure 2: Top: Bias with respect to matter for various baryonic tracers. Blue (blue), red (red), and all-galaxies (gray) are shown with ${\rm H}$i (brown) at $z = 0$ (left), $z = 0.5$ (center), and $z = 1$ (right). Large-scale bias values provided in Table \ref{['tab:bias']}. Bottom: The percentage error caused by assuming a constant bias with gray dotted lines at $\pm 10\%$. The bias for all baryonic tracers at most redshifts differ from the assumed constant value by $\geq 10\%$ by $k \sim 0.2-0.3$h cMpc$^{-1}$. The exceptions are the $z = 0$ blue galaxy bias and $z = 1$${\rm H}$i bias, which arise from their low occupation of massive halos offsetting nonlinearities.
• Figure 3: The redshift evolution of the bias for each baryonic tracer, with linear fits (dashed lines) to the data points to help visualize the trends. The precise values presented in these fits should be taken with caution with only three data points. Dotted lines show the expected bias evolution of a population only subject to gravitational effects fry_evolution_1996. Tracers associated with star-formation (red, blue, ${\rm H}$i) deviate from the passive evolution more than the all-galaxy bias, suggesting that quenching processes play a significant role in how they trace the matter distribution.
• Figure 4: Correlation coefficients of ${\rm H}$i$\times$ Blue, ${\rm H}$i$\times$ Red, and ${\rm H}$i$\times$ Galaxy for $z = 0$ (left), $z = 0.5$ (center), and $z = 1$ (right). Large-scale values are presented in Table \ref{['tab:cc']}. ${\rm H}$i correlates more strongly with blue galaxies than red, leading to a larger amplitude and less scale-independence in ${\rm H}$i$\times$ Blue. ${\rm H}$i$\times$ Galaxy lies between ${\rm H}$i$\times$ Blue and ${\rm H}$i$\times$ Red, representing an effective average of its two subpopulations. The slope of each correlation coefficient becomes steeper with time as more galaxies quench.
• Figure 5: The 2D auto power spectra of all matter (top center), ${\rm H}$i (top right), and blue (bottom left), red (bottom center), and all-galaxies (bottom right) at $z=1$. Black dotted lines are concentric circles to help visualize the FoG effect, which vertically warps the isopower contours. This warping is strongest in red galaxies as compared to the other galaxy types, agreeing with observations madgwick_2df_2003. We find that ${\rm H}$iappears to have stronger FoG suppression than matter, as found in villaescusa-navarro_ingredients_2018, although their relative strengths depend on scale (see text). Power spectra are slightly smoothed by a Gaussian filter ($\sigma = 0.5$) to see the contour lines more clearly, but the smoothed values are not used for the determination of the pairwise velocity dispersion and do not otherwise impact our conclusions.