Three-Dimensional Stacking as a Line Intensity Mapping Statistic

Line-intensity mapping (LIM) is a growing technique that measures the integrated spectral-line emission from unresolved galaxies over a three-dimensional region of the Universe. Although LIM experiments ultimately aim to provide powerful cosmological constraints via auto-correlation, many LIM experiments are also designed to take advantage of overlapping galaxy surveys, enabling joint analyses of the two datasets. We introduce a flexible simulation pipeline that can generate mock galaxy surveys and mock LIM data simultaneously for the same population of simulated galaxies. Using this pipeline, we explore a simple joint analysis technique: three-dimensional co-addition (stacking) of LIM data on the positions of galaxies from a traditional galaxy catalogue. We test how the output of this technique reacts to changes in experimental design of both the LIM experiment and the galaxy survey, its sensitivity to various astrophysical parameters, and its susceptibility to common systematic errors. We find that an ideal catalogue for a stacking analysis targets as many high-mass dark matter halos as possible. We also find that the signal in a LIM stacking analysis originates almost entirely from the large-scale clustering of halos around the catalogue objects, rather than the catalogue objects themselves. While stacking is a sensitive and conceptually simple way to achieve a LIM detection, thus providing a valuable way to validate a LIM auto-correlation detection, it will likely require a full cross-correlation to achieve further characterization of the galaxy tracers involved, as the cosmological and astrophysical parameters we explore here have degenerate effects on the stack.

💡 Research Summary

This paper presents a comprehensive study of a simple joint‑analysis technique—three‑dimensional stacking (co‑addition) of line‑intensity‑mapping (LIM) data on the positions of galaxies from a traditional spectroscopic catalogue. The authors first develop a flexible simulation pipeline, called joint_limlam_mocker, that simultaneously produces mock LIM cubes and mock galaxy catalogues for the same underlying population of dark‑matter halos. The pipeline starts from peak‑patch N‑body simulations to generate a halo catalogue spanning 2.9 × 10¹⁰ M⊙ to 9.1 × 10¹³ M⊙. For each halo, two line luminosities are assigned: CO (1‑0) for the LIM map and Ly α for the galaxy catalogue. Three distinct CO‑halo mass relations are implemented (the COMAP fiducial model C22, the Padmanabhan 2018 model P18, and the Li et al. 2016 model L16), while three Ly α Schechter‑function parametrisations (“default”, “bright” quasar‑dominated, and “faint” low‑z) are used to explore a range of galaxy populations. A correlated log‑normal scatter is added to the two luminosities to mimic the astrophysical connection between the tracers at the halo level.

The stacking procedure consists of extracting a sub‑volume around each galaxy (typically a few Mpc h⁻¹ radius) from the LIM cube, averaging the intensity within that volume, and then averaging over all galaxies. The resulting stacked signal is shown to be dominated not by the intrinsic CO emission of the catalogued galaxies themselves, but by the large‑scale clustering of surrounding high‑mass halos. In effect, the stack measures the zero‑lag term of the galaxy‑LIM cross‑correlation function.

A systematic exploration of experimental design and astrophysical parameters follows. The authors vary LIM instrumental characteristics (spatial resolution, spectral channel width, noise level), catalogue depth and selection (minimum halo mass, number density), and astrophysical models (CO‑Ly α scatter amplitude, line broadening, duty cycle, interloper contamination). Key findings include:

1. Optimal catalogue – Stacking performance improves dramatically when the catalogue includes as many high‑mass halos (M > 10¹² M⊙) as possible. Low‑mass‑only samples yield a negligible stacked signal.
2. LIM design trade‑offs – Finer angular resolution and narrower spectral channels increase the stacked signal‑to‑noise, primarily because they reduce line‑broadening dilution. However, the stack is relatively robust to line‑broadening because it relies on large‑scale modes.
3. Systematics sensitivity – Spectral line broadening mainly affects high‑k modes and thus has limited impact on the stack. Interloper lines introduce a bias that can be mitigated with frequency masking and modelling. Redshift uncertainties in the galaxy catalogue smear the stack centre and reduce amplitude, highlighting the need for precise spectroscopic redshifts. Map noise and masking lower the stacked amplitude but can be compensated by larger sample sizes and appropriate weighting.
4. Parameter degeneracies – Variations in cosmological parameters (e.g., Ωₘ, σ₈) and astrophysical parameters (e.g., CO‑Ly α scatter, halo bias) produce very similar changes in the stacked amplitude. Consequently, the stack alone cannot disentangle these effects.

The authors conclude that three‑dimensional stacking is a powerful, conceptually simple tool for detecting LIM signals and for validating auto‑correlation measurements, especially in the early stages of an experiment. However, because the stacked amplitude conflates multiple physical effects, a full three‑dimensional cross‑power spectrum analysis remains essential for robust cosmological and astrophysical parameter inference. The paper thus positions stacking as a complementary, validation‑oriented technique that should be used alongside traditional cross‑correlation methods in future LIM‑galaxy joint analyses.