CLAMATO: Lyman‑α IGM Tomography in COSMOS

• CLAMATO is a pioneering high‑redshift survey that uses Lyman‑α forest absorption to reconstruct three-dimensional maps of the cosmic web at z between 2 and 3.
• The project employs advanced tomographic methods such as Wiener filtering and TARDIS-based forward modeling to resolve IGM structures on megaparsec scales.
• It integrates extensive spectroscopic data to correlate IGM features with galaxy distributions, providing new constraints on galaxy evolution during cosmic noon.

The COSMOS Lyman-Alpha Mapping And Tomography Observations (CLAMATO) project is a pioneering spectroscopic survey that uses the Lyman-α forest absorption in background galaxy and quasar spectra to reconstruct high-resolution three-dimensional maps of the intergalactic medium (IGM) and cosmic web at $2 < z < 3$. CLAMATO leverages the dense sampling capabilities of faint star-forming galaxies in the COSMOS field and advanced tomographic reconstruction methods to trace the IGM’s structure—voids, filaments, sheets, and nodes—on comoving scales of a few megaparsecs, providing new constraints on the relationship between galaxies and large-scale structure during the peak epoch of star formation.

1. Scientific Motivation and Survey Design

CLAMATO was conceived to overcome the sparse sightline limitations of traditional QSO-based Lyman-α forest studies by utilizing faint Lyman-break galaxies as alternative background sources. By doing so, CLAMATO achieves a differential sightline density exceeding $1000~\mathrm{deg}^{-2}$ at $g \sim 24.5$–25.0, resulting in mean transverse sightline separations of $d_\perp \sim 2$–$3~h^{-1}~\mathrm{Mpc}$ in the COSMOS field at $z \sim 2.3$ (Lee et al., 2013). This dense sightline distribution enables tomographic mapping of the IGM on megaparsec scales—small enough to resolve the cosmic web’s topology—across a contiguous area.

The survey strategy involves moderate-resolution ($R \sim 1000$–$1300$) spectroscopy targeting both star-forming galaxies and quasars at $2.05 < z < 3.0$, using the Keck-I/LRIS instrument. In the first and second public data releases, CLAMATO obtained spectra for 240 (DR1) and then 320 (DR2) background sources over $\sim 0.2~\deg^2$, covering a comoving volume of $4 \times 10^5~h^{-3}~\mathrm{Mpc}^3$ and achieving a spatial resolution of $\sim 2.5~h^{-1}~\mathrm{Mpc}$ (Horowitz et al., 2021, Lee et al., 2017).

2. tomographic Reconstruction: Methods and Algorithms

The core of CLAMATO’s data analysis is the tomographic reconstruction of the three-dimensional IGM absorption field, $\delta_F$, from noisy and irregularly spaced sightlines. The standard method employs a Wiener filter approach (Lee et al., 2014, Lee et al., 2017, Horowitz et al., 2021), modeling correlations through a Gaussian covariance:

$$C(\mathbf{r}_1,\mathbf{r}_2) = \sigma_F^2 \exp\left[-\frac{(\Delta r_\|)^2}{2L_\|^2}\right]\exp\left[-\frac{(\Delta r_\perp)^2}{2L_\perp^2}\right]$$

where $L_\|$ and $L_\perp$ are the line-of-sight and transverse correlation lengths, typically $L_\| \sim 2.0~h^{-1}~\mathrm{Mpc}$ and $L_\perp \sim 2.5~h^{-1}~\mathrm{Mpc}$; $\sigma_F$ is the variance of normalized flux fluctuations. The Wiener-reconstructed field is given by

$$\delta_F^\mathrm{(rec)} = C \cdot (C + N)^{-1} \cdot \delta_F$$

where $N$ is the diagonal noise covariance matrix.

Advanced techniques, such as the Optimized Reconstruction with Constraints on Absorption (ORCA) (Li et al., 2021), replace the global matrix inversion by a multiscale, annealed optimization of a physically-motivated loss function:

$$\mathcal{L}(s) = k_1 \|S_m(s)-s\|^2 + (R(s)-d)^\top N^{-1} (R(s)-d) + k_2 \sum \mathrm{clip}(s,1,+\infty) + k_3 \sum \mathrm{clip}(s,0,\alpha)$$

Here, the physical clipping terms ensure the reconstructed transmission is bounded within physically allowed ranges, yielding improved recovery of extremal features such as voids and proto-clusters relative to Wiener filtering.

For dark matter field inference, CLAMATO utilizes a forward-modeling approach based on the TARDIS algorithm (Horowitz et al., 2019, Byrohl et al., 27 Sep 2024). This method reconstructs the initial density field by maximizing the joint likelihood of galaxy and Lyα forest data, then evolves the field using fast approximate gravity solvers, yielding models that—after calibration through the fluctuating Gunn-Peterson approximation (FGPA)—constrain the three-dimensional matter distribution and cosmic web classification (via the Hessian of the gravitational potential).

3. High-Redshift Cosmic Web: Mapping and Characterization

The dense CLAMATO data enable Mpc-scale mapping of the cosmic web at $z \sim 2.3$. The reconstructed IGM field at this epoch exhibits all canonical cosmic web elements: voids, sheets, filaments, and nodes (Horowitz et al., 2021, Krolewski et al., 2017). Cosmic web classification utilizes the eigenvalues of the deformation (tidal) tensor:

$$D_{ij} = \frac{\partial^2 \Phi}{\partial x_i \partial x_j}$$

where $\Phi$ is the gravitational potential sourced from the reconstructed density. Each spatial location is classified by the number of positive eigenvalues above a threshold, with nodes (+++), filaments (++–), sheets (+––), and voids (–––).

Quantitative cosmic web statistics—such as volume fractions, object counts, and eigenvector alignments—are validated against cosmological hydrodynamical (e.g., Nyx) and $N$-body simulations. TARDIS-based reconstructions recover eigenvalues with correlations $r \approx 0.95$ (for ELT-like quality), and ORCA improves structure recovery by $\sim$6% in void volume overlap relative to Wiener filtering.

CLAMATO also provides the first detection of cosmic voids at $z \sim 2.3$ (Krolewski et al., 2017). Voids are identified using a spherical underdensity algorithm tuned to the Lyα transmission field, with selection thresholds calibrated on simulations to yield consistent volume fractions ($\sim$18–19.5%). Stacked void profiles, radius functions, and redshift-space distortions are in close agreement with simulated predictions, enabling Alcock-Paczynski cosmological tests and investigation of modified gravity (Stark et al., 2015).

Protoclusters—overdense regions destined to evolve into massive galaxy clusters—are identified as large-scale absorption decrements spanning $\sim10~h^{-1}~\mathrm{Mpc}$, robustly recovered at $\sim$90% purity and $\sim$75% completeness in idealized and mock reconstructions at CLAMATO’s sightline density (Stark et al., 2014).

4. Relationship to Galaxy Distributions and Galaxy Evolution

A key strength of CLAMATO is the ability to correlate 3D IGM structures with extensive galaxy redshift samples in COSMOS. Extensive cross-correlation analysis between CLAMATO’s Lyα forest maps and 1642 foreground galaxies (from CLAMATO, zCOSMOS-Deep, MOSDEF, VUDS, 3D-HST) measures the 3D cross-correlation function and constrains the galaxy bias as a function of stellar mass (Zhang et al., 9 Sep 2025). The estimator for the cross-correlation $\hat{\xi}_A$ is:

$$\hat{\xi}_A = \frac{\sum_{i \in A} w_i \delta_{F,i}}{\sum_{i \in A} w_i}$$

Modeling the observed cross-power spectrum employs a redshift-space distortion formalism, accounting for line-of-sight velocity dispersion and systematic redshift offsets (notably, $+150~\mathrm{km~s}^{-1}$ for UV absorption line-based redshifts). The observed "fingers-of-god" effect in MOSDEF (dispersions above $100~\mathrm{km~s}^{-1}$) reflects expected intra-halo velocity dispersions within overdense regions.

Splitting the galaxy sample by stellar mass, direct constraints on the stellar mass–halo mass relation (SHMR) at $z\sim2.3$ are achieved:

Median $\log_{10}(M_*/M_\odot)$	Galaxy Bias $b_\mathrm{g}$	Typical $\log_{10}(M_h/M_\odot)$
9.23	2.85	10.27
9.71	3.32	11.55
10.21	4.71	12.06

Comparison with Bolshoi-Planck simulations and IllustrisTNG finds good consistency for mid-/high-mass bins, but the low-mass bin indicates that low-mass galaxies may reside in halos $\sim$2 orders of magnitude less massive than some empirical models predict, suggesting elevated star formation efficiency in these halos at "cosmic noon".

Quantitative comparison of IGM voids and galaxy redshifts demonstrates that CLAMATO-identified voids are underdense in galaxies at $5.95\sigma$ significance compared to random regions (Krolewski et al., 2017). Visual and quantitative correlation of absorption peaks and known protoclusters further validates CLAMATO's ability to trace the environments of large-scale structure and galaxy evolution (Lee et al., 2017).

5. Synergy with Simulation and Modeling: TARDIS and cosmosTNG

The initial density fields reconstructed by CLAMATO have been used to set constrained initial conditions for the cosmosTNG hydrodynamical simulation suite (Byrohl et al., 27 Sep 2024). Using the TARDIS algorithm, the reconstructed density field from CLAMATO and zCOSMOS is evolved forward in AREPO with IllustrisTNG physics and baryonic mass resolution $10^6~M_\odot$. Eight constrained realizations are simulated to sample stochasticity on small scales.

This approach allows for detailed environmental studies of the COSMOS field at $z\sim2$:

• The simulated region exhibits an overabundance of massive halos and galaxies, especially in the zFIRE protocluster.
• The cosmic star formation rate density and the abundance of high-mass galaxies are higher and peak earlier relative to random-field simulations.
• The simulated galaxies display a lower quenched fraction at fixed mass by $\sim$20% for $10^{10.5}$–$10^{11.5}~M_\odot$ compared to field expectations.
• Supermassive black holes are systematically overmassive by $\sim$0.5 dex at fixed stellar mass, consistent with JWST observations.
• Strong radial gradients in sSFR, gas fraction, and galaxy sizes with distance from protocluster centers reveal gas depletion and quenching consistent with environmental effects.

This demonstrates CLAMATO’s ability not only to map cosmic structure but also to supply physically-constrained environments for forward modeling of galaxy formation and feedback.

6. Data Releases, Community Resources, and Future Prospects

CLAMATO has released all reduced spectra, Lyα forest pixel data, and tomographic maps to the public (Lee et al., 2017, Horowitz et al., 2021). These releases include traditional figures, interactive 3D HTML visualizations, and VR panoramic explorations, enabling the community to analyze, validate, and extend the survey’s scientific reach.

Future directions indicated by the CLAMATO methodology and results include:

• Larger-area tomography (e.g., with Subaru-PFS or Maunakea Spectroscopic Explorer) to increase the void and protocluster sample sizes, improving cosmological constraints (AP test, growth rate, modified gravity).
• Cross-correlation with 21 cm experiments and intensity mapping surveys to jointly probe the ionized and neutral components of the high-$z$ IGM (Silva et al., 2012, Pullen et al., 2013).
• Application of improved inversion algorithms (TARDIS, ORCA) and denser background source sampling (with ELTs or high-multiplex facilities) to reduce systematics and allow physically richer IGM–galaxy studies.
• Synergistic use of simulations (e.g., cosmosTNG with CLAMATO initial conditions) to interpret multi-wavelength galaxy surveys and directly model the environmental impact on galaxy formation at cosmic noon.

CLAMATO thus stands as a template for IGM tomography, establishing both the methodology and empirical foundation for the next generation of cosmic web, IGM, and galaxy surveys at high redshift.