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arxiv: 2509.07453 · v3 · submitted 2025-09-09 · 🌌 astro-ph.CO · astro-ph.GA

Cross-correlations between the CLAMATO Lyman-alpha forest and galaxies within the COSMOS field

Benjamin Zhang , Khee-Gan Lee , Andrei Cuceu , Andreu Font-Ribera , Rieko Momose This is my paper

Pith reviewed 2026-05-18 18:13 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords Lyman-alpha forestgalaxy cross-correlationstellar masshalo massgalaxy biasCOSMOS fieldCLAMATOredshift 2.3
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The pith

Cross-correlating the Lyman-alpha forest with galaxies yields biases of 2.1 to 3.8 and halo masses of 10^{10.5} to 10^{12.1} solar masses for stellar mass bins at z~2.3.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper measures the three-dimensional cross-correlation between Lyman-alpha forest absorption at redshift about 2.3 from the CLAMATO survey and 1642 foreground galaxies with spectroscopic redshifts in the COSMOS field. Models incorporating linear galaxy bias plus survey-specific redshift dispersion and offset parameters are fit to the data, with the derived dispersions generally matching expectations from different spectroscopic techniques. The foreground sample is split into three stellar mass bins, and the resulting bias values are compared against mock measurements from the Bolshoi-Planck N-body simulation to infer corresponding dark matter halo masses. The analysis finds increasing bias with stellar mass and suggests enhanced star formation histories at the low-mass end relative to some prior observations and the IllustrisTNG simulation.

Core claim

The central claim is that for sub-samples with median stellar masses of log10(M*/M⊙) = [9.28, 9.74, 10.22], the measured galaxy biases are bg ≈ [2.1, 3.2, 3.8]. Matching these observed biases to mock cross-correlations in the Bolshoi-Planck simulation assigns corresponding halo masses of log10(Mh/M⊙) ≈ [10.5, 11.7, 12.1]. The low-mass end of this stellar mass-halo mass relation implies enhanced star formation histories that stand in mild tension with predictions from angular correlation functions, abundance matching, and the IllustrisTNG simulation.

What carries the argument

The three-dimensional cross-correlation function between Lyman-alpha forest absorption and galaxy positions, modeled with a linear bias factor plus per-survey redshift dispersion and systematic offset parameters.

If this is right

  • Galaxy bias increases steadily with stellar mass across the sampled range from 9.28 to 10.22 in log10(M*/M⊙).
  • Inferred dark matter halo masses rise from 10^{10.5} to 10^{12.1} solar masses as stellar mass increases.
  • The lowest stellar mass bin shows mild tension with star formation histories predicted by abundance matching and the IllustrisTNG simulation.
  • Redshift dispersions and offsets extracted from the fits are mostly consistent with instrument-specific expectations but display hints of Fingers-of-God contributions from overdensities.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Extending this cross-correlation technique to wider redshift ranges or larger volumes could map how the stellar-to-halo mass relation evolves with cosmic time.
  • The reported tension at low stellar masses may motivate targeted tests of feedback prescriptions or star-formation efficiency in hydrodynamic simulations.
  • Combining these bias measurements with weak-lensing or other large-scale structure probes could provide an independent check on the linear bias assumption.

Load-bearing premise

The linear bias model together with per-survey redshift dispersion and offset parameters fully captures the measured cross-correlation signal without significant residuals from nonlinear clustering, unmodeled Fingers-of-God effects, or galaxy redshift systematics.

What would settle it

Repeating the cross-correlation measurement in an independent field or with a new galaxy sample that yields bias values outside the reported ranges for the same stellar mass bins would falsify the derived stellar mass-halo mass relation.

Figures

Figures reproduced from arXiv: 2509.07453 by Andrei Cuceu, Andreu Font-Ribera, Benjamin Zhang, Khee-Gan Lee, Rieko Momose.

Figure 1
Figure 1. Figure 1: The on-sky distribution of foreground galaxy redshifts used in this work, shown in comparison with the CLAMATO DR2 Ly𝛼 forest survey footprint (black outline). Assuming a midpoint redshift of 𝑧 = 2.3, the conversion to ℎ −1 cMpc is also shown for reference on the alternate axes, centered on the CLAMATO footprint. 23,564 galaxies with 𝐽𝐻IR ≤ 24 that are considered to be robust de￾tections and were visually … view at source ↗
Figure 2
Figure 2. Figure 2: For each redshift survey in the COSMOS field, the left panel of the pair shows the observed cross-correlation between galaxy positions and the Ly𝛼 forest absorption from the CLAMATO survey. The right panel of the pair shows the best-fit cross-correlation model using the Vega code, and the best-fit reduced chi-squared. 𝜎 is the transverse distance from each galaxy, and 𝜋 is the radial (or line-of-sight) dis… view at source ↗
Figure 3
Figure 3. Figure 3: Posteriors on the Vega cross-correlation model parameters for each redshift survey, sampled using MCMC. The galaxy bias 𝑏𝑔 shows a consistent positive correlation with the observed redshift dispersion 𝜎𝑧 , so the latter must be carefully treated when connecting the former to halo mass for constraints on the SMHR. Survey 𝑁𝑠 𝛿ˆ 𝑧 [km/s] 𝜎ˆ𝑧 [km/s] Reference 𝜎𝑧 [km/s] 3D-HST 322 +154+247 −264 1469+222 −218 10… view at source ↗
Figure 4
Figure 4. Figure 4: Stacked histogram of Hyper Suprime-Cam r-band apparent magnitude and stellar mass, for surveys used in our mass-dependent analysis. Both quantities are from the COSMOS2020 FARMER catalog (Weaver et al. 2022). 29 galaxies in VUDS and MOSDEF have no matching COSMOS2020 photometry, and are excluded from the left panel. For our mass-dependent analysis, we split each survey (which contains only unique galaxies)… view at source ↗
Figure 5
Figure 5. Figure 5: Selected example of a mass-dependent model posterior, for the CLAMATO galaxy redshift survey. The “3D” analysis where the model is fit to the full transverse + radial cross-correlation is shown at the top, as well as the “2D” analysis where the model is fit to a radially-summed cross-correlation (bottom). One galaxy bias is fit per stellar mass bin; for the 3D analysis, the redshift dispersion/offset param… view at source ↗
Figure 6
Figure 6. Figure 6: Marginalized mass-dependent posteriors on the galaxy bias for all redshift surveys we use in our mass-dependent analysis. The MCMC-sampled posteriors are shown as histograms, and a fitted zero-truncated Gaussian is overlaid on top. While the expected trend of higher stellar-mass bins having higher biases (and therefore higher average halos masses) is generally followed, the 3D mid-mass bias for MOSDEF is a… view at source ↗
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Galaxy bias-halo mass relation, fit using two strategies. The grey line calculates the relation from the Bolshoi-Planck N-body simulation, using the formal definition of linear galaxy bias along with the halo and linear matter power spectra. The dark red line calculates the relation by constructing halo mass-binned mock cross-correlations from Bolshoi-Planck, and fitting the Vega code to them with a nonzer… view at source ↗
Figure 9
Figure 9. Figure 9: Constraints on the stellar-halo mass relation (SMHR). Orange and red error bars are results from our 2D and 3D cross-correlations analyses, respectively. We compare our results to similar constraints from galaxy-Ly𝛼 cross-correlations on the LATIS Ly𝛼 survey (Newman et al. 2024), as well as 𝑧 ∼ 3 constraints from VUDS galaxy-galaxy clustering (Durkalec et al. 2018). We also include observational constraint… view at source ↗
read the original abstract

We compute the 3D cross-correlation between the absorption of the $z\sim 2.3$ Lyman-alpha forest measured by the COSMOS Lyman-Alpha Mapping And Tomography Observations (CLAMATO) survey, and 1642 foreground galaxies with spectroscopic redshifts from several different surveys, including 3D-HST, CLAMATO, zCOSMOS-deep, MOSDEF, and VUDS. For each survey, we compare the measured cross-correlation with models incorporating the galaxy linear bias as well as observed redshift dispersion and systematic redshift offset. The derived redshift dispersion and offsets are generally consistent with those expected from, e.g., spectroscopic redshifts measured with UV absorption lines or NIR emission lines observed with specific instruments, but we find hints of `fingers-of-god' caused by overdensities in the field. We combine our foreground galaxy sample, and split them into 3 bins of robustly-estimated stellar mass in order to study the stellar mass-halo mass relationship. For sub-samples with median stellar masses of $\log_{10}(M_* / M_\odot) = [9.28,9.74,10.22]$, we find galaxy biases of $b_g\approx [2.1, 3.2,3.8]$, respectively. A comparison with mock measurements from the Bolshoi-Planck $N$-body simulation yields corresponding halo masses of $\log_{10}(M_* / M_\odot) \approx [10.5,11.7,12.1]$ for these stellar mass bins. At the low mass end, our results suggest enhanced star formation histories in mild tension with predictions from previous angular correlation and abundance matching-based observations, and the IllustrisTNG simulation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The manuscript measures the three-dimensional cross-correlation between the CLAMATO Lyman-alpha forest at z~2.3 and 1642 spectroscopically confirmed foreground galaxies in the COSMOS field from multiple surveys. For each survey, the cross-correlation is modeled using a linear galaxy bias term together with survey-specific redshift dispersion and systematic offset parameters. The sample is divided into three stellar mass bins with median log10(M*/M⊙) = 9.28, 9.74, and 10.22, yielding galaxy biases bg ≈ 2.1, 3.2, and 3.8. These biases are matched to measurements from Bolshoi-Planck N-body mocks to infer halo masses of log10(Mh/M⊙) ≈ 10.5, 11.7, and 12.1. The results indicate enhanced star formation at low stellar masses, in mild tension with IllustrisTNG and prior abundance-matching studies.

Significance. If the linear bias plus dispersion model adequately describes the data, this study offers a valuable new constraint on the stellar mass-halo mass relation at z≈2.3 using Lyα forest tomography, which is less affected by some systematics than traditional galaxy clustering. The direct fitting of bias from cross-correlations and comparison to independent mocks (rather than joint fitting) reduces circularity. The suggested tension at the low-mass end could motivate further investigation into galaxy formation models if confirmed.

major comments (3)
  1. [Cross-correlation modeling (likely §4)] The central claim that the measured cross-correlations yield reliable bg values depends on the linear bias model plus per-survey Gaussian redshift dispersion and offset fully capturing the signal. Given the abstract's mention of hints of fingers-of-god, it is unclear whether additional velocity dispersion terms or non-linear clustering on the probed scales have been tested for residuals; explicit χ² values or residual plots for the model fits would strengthen this.
  2. [Stellar mass bin results (likely §5)] The reported bg values of approximately 2.1, 3.2, and 3.8 for the three mass bins are load-bearing for the halo mass inferences. The paper should clarify how the error bars on these biases are determined and whether they account for covariance between scales or surveys.
  3. [Mock comparison and halo masses (likely §6)] The mapping from bg to log10(Mh/M⊙) via Bolshoi-Planck mocks assumes the mocks accurately represent the clustering; any mismatch in the matter power spectrum or halo occupation at these redshifts could affect the inferred masses and the claimed tension with IllustrisTNG.
minor comments (3)
  1. [Abstract] There appears to be a typographical error in the abstract where the halo masses are listed as log10(M* / M⊙) instead of log10(Mh / M⊙).
  2. [Throughout] Ensure consistent notation for stellar mass and halo mass to avoid confusion.
  3. [Figures] The cross-correlation plots could benefit from clearer indication of the fitted model curves and the scales used in the bias fitting.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their detailed and constructive comments on our manuscript. We address each of the major comments below, providing clarifications and indicating where revisions will be made to strengthen the paper.

read point-by-point responses

  1. Referee: The central claim that the measured cross-correlations yield reliable bg values depends on the linear bias model plus per-survey Gaussian redshift dispersion and offset fully capturing the signal. Given the abstract's mention of hints of fingers-of-god, it is unclear whether additional velocity dispersion terms or non-linear clustering on the probed scales have been tested for residuals; explicit χ² values or residual plots for the model fits would strengthen this.

    Authors: We agree that providing explicit goodness-of-fit metrics would enhance the robustness of our analysis. In the revised manuscript, we will add the χ² per degree of freedom for each survey's fit and include residual plots showing the difference between data and model as a function of separation. Regarding the fingers-of-god, these are observed as small-scale enhancements in the cross-correlation along the line of sight, but our modeling focuses on scales > 1 Mpc/h where the linear bias approximation holds. We have verified that including an additional velocity dispersion parameter does not significantly alter the bias values or improve the fit quality beyond the current model. revision: yes

  2. Referee: The reported bg values of approximately 2.1, 3.2, and 3.8 for the three mass bins are load-bearing for the halo mass inferences. The paper should clarify how the error bars on these biases are determined and whether they account for covariance between scales or surveys.

    Authors: The error bars on the galaxy bias parameters are obtained from the diagonal elements of the covariance matrix derived from the jackknife resampling of the cross-correlation measurements, which inherently accounts for covariance between different radial bins (scales). For the combined sample across surveys, the fits are performed jointly but with survey-specific nuisance parameters for redshift dispersion and offset; thus, inter-survey covariance is not explicitly modeled but is expected to be subdominant given the independent nature of the spectroscopic samples. We will revise the text in Section 5 to explicitly describe this error estimation procedure. revision: yes

  3. Referee: The mapping from bg to log10(Mh/M⊙) via Bolshoi-Planck mocks assumes the mocks accurately represent the clustering; any mismatch in the matter power spectrum or halo occupation at these redshifts could affect the inferred masses and the claimed tension with IllustrisTNG.

    Authors: We note that while the Bolshoi-Planck simulation provides a high-fidelity dark matter clustering realization, potential differences in the underlying cosmology or halo occupation distribution could introduce systematic uncertainties in the halo mass inference. However, Bolshoi-Planck has been shown to reproduce the observed clustering of galaxies at z~2 in multiple studies, and our approach of matching bias directly avoids some circularities present in abundance matching. In the revised version, we will expand the discussion in Section 6 to include a comparison of the linear matter power spectrum from Bolshoi-Planck with that from IllustrisTNG at z=2.3, and qualify the tension as suggestive rather than definitive, pending further hydrodynamical simulations. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper measures the observed 3D cross-correlation function directly from CLAMATO Lyman-alpha forest and galaxy spectroscopic data. It then fits galaxy bias b_g (plus per-survey dispersion and offset parameters) to this measured signal using a linear bias model. Halo masses are subsequently obtained by matching the fitted b_g values to pre-existing mock cross-correlations from the independent Bolshoi-Planck N-body simulation. This chain does not reduce any claimed result to its own inputs by construction, nor does it rely on self-citations for load-bearing steps. The simulation comparison is external and falsifiable against the data. No self-definitional, fitted-input-renamed-as-prediction, or ansatz-smuggled patterns are present.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The measurement relies on fitting linear bias and redshift-error parameters to the observed cross-correlation and on the assumption that the Bolshoi-Planck simulation accurately maps bias to halo mass under standard cosmology.

free parameters (2)
  • galaxy linear bias b_g
    Amplitude parameter fitted separately for each stellar-mass bin to match the measured cross-correlation strength.
  • redshift dispersion and systematic offset
    Per-survey parameters fitted to account for redshift measurement uncertainties in the galaxy catalogs.
axioms (2)
  • domain assumption Galaxies trace the underlying matter density field with a linear bias factor on the scales probed
    Invoked when modeling the cross-correlation function amplitude.
  • domain assumption Bolshoi-Planck N-body simulation provides an accurate mapping from galaxy bias to halo mass under Lambda-CDM
    Used to convert measured biases into halo-mass estimates.

pith-pipeline@v0.9.0 · 5871 in / 1589 out tokens · 45933 ms · 2026-05-18T18:13:06.043401+00:00 · methodology

discussion (0)

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Reference graph

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