A New Window into the Baryon Cycle at Cosmic Noon with Line Intensity Mapping: Forecasts for auto- and cross-correlations in [CII]-158$μ$m, HI 21 cm, CO$_{J+1\rightarrow J}$, and H$α$ galaxies

Abstract

Across the peak of cosmic star formation at $z\sim1-2$, inflow, processing, and feedback drive rapid changes in the spatial distribution and chemical composition of baryons in galaxies and surrounding reservoirs; this baryon cycle can be tomographically mapped by line intensity mapping (LIM) of atomic hydrogen, ionized carbon, and carbon monoxide. We present a simulation-based forecasting framework for detecting auto- and cross-power spectra between spectroscopic surveys of four such tracers at $z\sim0.5-1.7$ mapping the same deep field - TIM, EoRSpec/FYST, MeerKAT, & Euclid. We forward-model 3-D distributions for these tracers from magnetohydrodynamic simulations, directly capturing the two-halo, one-halo, and shot statistics without relying on analytical decompositions. We further detail a signal-to-noise formalism, tailored to LIM surveys with highly anisotropic geometries and Fourier-space coverage. We demonstrate that galaxy cross-correlations will be the dominant discovery channel for current-generation surveys. These instruments will detect the auto-spectra for CO and HI 21 cm and the CO $\times$ 21 cm cross-spectrum at modest S/N $\sim 1-10$, while placing upper limits on the [CII]-158$μ$m signals. [CII], CO, and HI LIM will be $\sim3-30\times$ ($0.5-1.5$ dex) more sensitive to cross-correlation with the Euclid survey, however, than their respective auto-correlations, constraining all three models of line emission at high significance (S/N $\sim 10-40$) within this decade. Finally, we formulate a staged instrumental trajectory with planned or reasonable improvements, including the as-proposed SKA-Mid. We forecast advancing the per-$k$-mode sensitivities of each auto-, galaxy-line, and line-line spectrum by several orders of magnitude, enabling new percent- and sub-percent level constraints on cosmology and the redshift evolution of star formation and the baryon cycle.

Figures (8)

• Figure 1: Constructed three-dimensional distributions at $z\sim1.17$ of (clockwise from top left) line emission from [CII]-158$\mu$m, HI 21 cm, CO$_{5\rightarrow4}$, and galaxy densities from a Euclid-depth H$\alpha$ spectroscopic redshift survey. The entire TNG100 volume (with side length 75 Mpc/$h$) is shown; all species trace the same cosmic web at large scales, but exhibit variations at small scales dictated by the empirical emission models dependent on subhalo properties and relevant correlation coefficients (see Figure \ref{['fig:ccc']}). We made the visualizations with the yt Python toolkit 2011ApJS..192....9T.
• Figure 2: Cross-correlation coefficients, $r_{ij}(\bar{k}, z) = P_\text{cross, $i\times j$} / \sqrt{P_\text{auto, $i$} P_\text{auto, $j$}}$, for all six possible pairs for the four tracers ([CII]-158$\mu$m, HI 21 cm, CO, H$\alpha$-galaxies) considered, in our four $z$ bins. These coefficients encapsulate new information present in the cross-correlation, unavailable from measurements of just the two auto-correlations; the values start to deviate from unity as we progress from the two-halo to the one-halo and shot regimes at higher $k$'s. Different tracers have different cross-shot behaviors; these also evolve with $z$, indicating new astrophysical potential from tomographically measuring cross-power spectra. The cross correlation coefficients encode differences in scaling relations of line luminosities to galaxy properties, intrinsic scatter in line luminosities, and line-line covariance, and can inform models of galaxy evolution and the baryon cycle.
• Figure 3: We compare (clockwise from top left) star formation rate density, sky-averaged mean [CII]-158$\mu$m intensity, sky-averaged mean CO intensity, and neutral hydrogen density, obtained from our MHD simulation-based forward modeling methodology, against literature models and measurements. These are described in detail in Section \ref{['subsec:validation']}: SFR measurements from UV and IR data are from the compilation in Madau_2014, [CII]-158$\mu$m measurements are from Herschel data agrawal2025farinfraredlineshiddenarchival, HI density measurements from the compilation in Walter_2020, and CO mean intensities derived from decarli+20lenkic+20boogaard+23Keating_2020. The scatter in the MC sampling ($N=50$) is represented as violin plots between the extrema, with the median value marked. Our models are in general agreement with the literature.
• Figure 4: Key components in our calculation of a LIM survey's sensitivities to the power spectra. As a representative example, we present quantities for the Terahertz Intensity Mapper [CII]-158$\mu$m $1 \deg \times 1 \deg$ survey, in the third redshift bin at $z\sim 1.17$. (Top Left) Comparison of $k$-mode counting in our formalism to the fiducial analytical expressions, wherein $N_\text{modes}$ is proportional to the volume of thin isotropic shells in $k$-space, i.e., $N_\text{modes} \propto k^2 \Delta k$. Accounting for survey geometry anisotropy and potential contamination in zero-wavenumber modes ($k_{x, y, \text{or} z} = 0$), we conservatively directly bin and count modes from our $k$-space lattice and also exclude modes where any of the components $\bar{k}$ are zero ($k_x$, $k_y$, or $k_z$ = 0), resulting in lower values for $N_\text{modes}$, and a cutoff at lower $k$ magnitudes due to mismatch in the minimum modes measured in spatial and spectral directions. (Top Right) Two classes of window functions, $w_\text{beam}$ and $w_\text{hpf}$, due to the survey's non-zero resolution and finite coverage, attenuate high and low $k$ modes, respectively. We consider each class in all three Cartesian directions; the mismatch in the modes sampled in the spectral and spatial directions is apparent. (Bottom) Effect of applying the two main corrections (lattice-based mode counting with exclusion of modes with a vanishing Cartesian component, and window functions) in our analysis as per Eqn. \ref{['eqn:noisecross']} to the sensitivity of TIM to the [CII]-158$\mu$m auto-power spectrum.
• Figure 5: Forecasts for sensitivities to the line intensity auto-correlations, in four redshift bins over $z\sim0.5-1.7$, for [CII]-158$\mu$m, CO$_{J+1\rightarrow J}$ ($J=3, 4$), and HI 21 cm, for the three classes of surveys considered with coverage $1\deg^2$, $4\deg^2$, and $100\deg^2$. The scatters shown in the theoretical spectra (as well as the uncertainties on the signal-to-noise ratio S/N) are model uncertainties, marking 16th, 50th, and 84th percentiles. The A1 far-infrared spectrometer, TIM, will place upper-limits on the auto-power spectrum, assuming an SFR-tracing [CII]-158$\mu$m intensity history; note that certain other models for [CII] emission can predict up to two orders of magnitude brighter auto-correlation signal, allowing the current generation TIM survey to discriminate between these models. MeerKAT will be able to place integrated S/N $\sim10$ detections on the HI signal with the as-proposed LADUMA survey, with SKA-Mid approaching higher S/N in individual $k$ bins. Even with the $1\deg^2$ portion of the DSS, EoRSpec will place S/N $\sim3$ limits on the CO auto-spectrum, with each of the next two generations offering a $10-100\times$ improvement.