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arxiv: 2607.05326 · v1 · pith:U2ZVSWQE · submitted 2026-07-06 · astro-ph.GA · astro-ph.CO

Weak Evolution of Cosmic Atomic Hydrogen over the Past 4.5 Billion Years

Chuan-Peng Zhang , Hong Guo , Yizhou Gu , Am\'elie Saintonge , Xiaohu Yang , Dirk Scholte , Ming Zhu , Peng Jiang
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Hu Zou Manasvee Saraf Wenlin Ma Yirong Wang Y. P. Jing Zheng Zheng Zhejie Ding J. Aguilar S. Ahlen D. Bianchi D. Brooks T. Claybaugh A. de la Macorra P. Doel E. Gazta\~naga G. Gutierrez M. Ishak R. Joyce S. Juneau R. Kehoe D. Kirkby A. Kremin O. Lahav C. Lamman M. Landriau L. Le Guillou M. Manera A. Meisner R. Miquel J. Moustakas S. Nadathur W. J. Percival F. Prada I. P\'erez-R\`afols G. Rossi E. Sanchez D. Schlegel M. Schubnell H. Seo J. Silber D. Sprayberry G. Tarl\'e B. A. Weaver FASHI Collaboration
This is my paper

Reviewed by Pith2026-07-07 17:04 UTCglm-5.2pith:U2ZVSWQEopen to challenge →

classification astro-ph.GA astro-ph.CO
keywords cosmic hydrogen densityHI gas fractionstar formation rate density21-cm stackinggalaxy baryon cycleluminosity bias correctionFASTDESI
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The pith

Cosmic atomic hydrogen barely declined while star formation plummeted

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

The paper combines FAST 21-cm radio observations with DESI optical spectroscopy for roughly 2.5 million galaxies across 12,000 square degrees, measuring how the cosmic density of atomic hydrogen (Omega_HI) has changed over the past 4.5 billion years. The authors find that Omega_HI decreased by only a factor of 1.35±0.10 from z=0.41 to the present, and by just 1.12±0.10 after conservative systematic corrections. This is far weaker than the factor-of-2.46 decline in the cosmic star formation rate density over the same period. Crucially, the average HI gas fraction at fixed stellar mass evolves by less than 0.2 dex across the full galaxy population, showing that the weak evolution is not a cancellation between different galaxy types but a universal trend. The central mechanism the authors identify is that the late-time decline in cosmic gas supply does not deplete the atomic hydrogen reservoir directly; instead, its impact is mediated through the baryon cycle, affecting the conversion of atomic gas into molecular gas and stars rather than draining the atomic reservoir itself.

Core claim

The cosmic atomic hydrogen density has remained nearly constant over the past 4.5 billion years, declining by at most a factor of 1.35 (or 1.12 after systematic corrections), while the cosmic star formation rate density fell by a factor of 2.46 over the same interval. This mismatch, present at fixed stellar mass across the galaxy population, rules out rapid HI depletion as the cause of declining star formation and points to the HI-to-H2 phase conversion or gas accretion regulation as the operative bottleneck.

What carries the argument

The paper introduces a luminosity-bias correction method that models the HI gas fraction as a function of both r-band luminosity and stellar mass, f_HI(L_r|M_*), using an 8-parameter double-power-law fit. This correction accounts for the fact that flux-limited optical samples are biased toward more luminous (and gas-richer) galaxies at fixed mass. By measuring how f_HI depends on luminosity within each stellar-mass bin, the method reconstructs the intrinsic gas fraction that would be observed in a complete sample, without requiring mass-completeness cuts that would sacrifice the low-mass galaxy population.

If this is right

  • Galaxy formation models must reproduce a baryon cycle where the atomic hydrogen reservoir stays nearly invariant while molecular gas and star formation decline substantially — a tighter constraint than matching Omega_HI alone.
  • The bottleneck driving late-time cosmic star formation decline lies downstream of the atomic gas reservoir, in the atomic-to-molecular phase conversion or in the regulation of gas accretion onto galactic disks, not in the depletion of HI itself.
  • Future 21-cm intensity mapping surveys can use the measured Omega_HI(z) relation, Omega_HI proportional to (1+z)^0.9, as a benchmark over 0 < z < 0.41.
  • The f_HI(M_*) relation's near-invariance with redshift provides a stable calibration target for semi-analytic and hydrodynamical models aiming to predict gas partitioning across cosmic time.

Where Pith is reading between the lines

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

  • If the HI reservoir is stable while H2 declines, the star formation efficiency per unit molecular gas may itself be evolving, or the molecular gas depletion timescale may be lengthening — a question the paper does not directly address but that follows from the decoupling it establishes.
  • The near-invariance of f_HI(M_*) suggests that gas accretion and gas loss are finely balanced across all stellar masses, which may point to a self-regulating equilibrium in the atomic gas phase that is insensitive to the processes driving the molecular phase decline.
  • Extending the same f_HI(L_r|M_*) correction framework to higher redshifts (z > 0.4) with deeper surveys would test whether the weak evolution breaks down at earlier epochs when cosmic gas accretion rates were higher.

Load-bearing premise

The luminosity bias correction assumes that the intrinsic distribution of r-band luminosity at fixed stellar mass does not evolve over 0 < z < 0.41, using the local (z < 0.05) sample as the reference for all redshifts. If this distribution actually evolves with redshift, the corrected HI gas fractions at z > 0.25 could be systematically offset.

What would settle it

If future independent measurements of Omega_HI at z ~ 0.3 (e.g., from deeper interferometric surveys or DLA absorbers) find a decline substantially larger than the factor of 1.35 reported here, the weak-evolution conclusion would be undermined.

Figures

Figures reproduced from arXiv: 2607.05326 by A. de la Macorra, A. Kremin, A. Meisner, Am\'elie Saintonge, B. A. Weaver, Chuan-Peng Zhang, C. Lamman, D. Bianchi, D. Brooks, Dirk Scholte, D. Kirkby, D. Schlegel, D. Sprayberry, E. Gazta\~naga, E. Sanchez, FASHI Collaboration, F. Prada, G. Gutierrez, G. Rossi, G. Tarl\'e, Hong Guo, H. Seo, Hu Zou, I. P\'erez-R\`afols, J. Aguilar, J. Moustakas, J. Silber, L. Le Guillou, Manasvee Saraf, Ming Zhu, M. Ishak, M. Landriau, M. Manera, M. Schubnell, O. Lahav, P. Doel, Peng Jiang, R. Joyce, R. Kehoe, R. Miquel, S. Ahlen, S. Juneau, S. Nadathur, T. Claybaugh, Wenlin Ma, W. J. Percival, Xiaohu Yang, Yirong Wang, Yizhou Gu, Y. P. Jing, Zhejie Ding, Zheng Zheng.

Figure 1
Figure 1. Figure 1: Atomic gas fraction as a function of stellar mass. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparisons with literature. Left: we compare our measurements of fH i at 0 < z < 0.05 with those of Refs.[26, 30] (blue symbols) using ALFALFA in the same redshift range. The model predictions from the hydrodynamical simulations of TNG and SIMBA are also shown as lines of different colours. Right: our measurements of fH i at 0.25 < z < 0.41 are compared with previous measurements at similar redshifts of R… view at source ↗
Figure 3
Figure 3. Figure 3: Cosmic HI gas density (ΩHI) as a function of redshift. Left: we compare our measurements of ΩH i (black filled circles) with previous results of 21-cm observations[6, 9–21] (brown open circles) and DLA absorption measurements[2] (gray stars; without contribution from helium). All measurements are corrected to the same cosmological parameters. Our measurement errors of ΩH i show 1σ statistical uncertainties… view at source ↗
read the original abstract

The cosmic star formation rate density (CSFRD) has declined sharply toward the present day, but the roles of the atomic and molecular gas reservoirs remain uncertain. We measure the cosmic HI density, $\Omega_{\mathrm{HI}}$, over $0<z<0.41$ by combining HI spectra from the Five-hundred-meter Aperture Spherical Telescope with optical spectroscopy from the Dark Energy Spectroscopic Instrument for $\sim2.5$ million galaxies across $\sim12,000\,{\rm deg}^2$. We measure a raw decrease in $\Omega_{\mathrm{HI}}$ by a factor of $1.35\pm0.10$ over the past 4.5 Gyr. Even after applying the conservative systematic corrections from our forward model, the inferred decline is only $1.12\pm0.10$ -- still far weaker than the CSFRD decline (a factor of 2.46). The molecular gas density, in contrast, is known to evolve more closely with star formation. At fixed stellar mass, the average HI gas fraction evolves by less than 0.2 dex, showing that the weak evolution is present across the galaxy population. These quantitative differences rule out rapid depletion of galaxy HI as the primary driver of the late-time CSFRD decline, and provide a stringent benchmark for models of gas accretion, phase conversion and star-formation regulation.

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 / 6 minor

Summary. This paper measures the cosmic HI density Omega_HI over 0<z<0.41 by combining FAST 21-cm spectral data (FASHI) with DESI optical spectroscopy for ~2.5 million galaxies across ~12,000 deg^2. The authors use HI spectral stacking in stellar mass bins to measure the average HI gas fraction f_HI(M*) at four redshift intervals. They find that Omega_HI decreases by only a factor of 1.35+/-0.10 (or 1.12+/-0.10 after systematic corrections from a TNG100-based forward model) from z=0.41 to the present, far weaker than the CSFRD decline of a factor of 2.46. They conclude that rapid HI depletion is not the primary driver of the late-time CSFRD decline. The analysis includes corrections for luminosity bias (validated against mass-complete and 1/Vmax methods), FAST beam confusion, and a detailed forward-modeling mock for systematic error estimation.

Significance. The paper provides a significant advance in 21-cm emission measurements at intermediate redshift, improving sample sizes by orders of magnitude over previous work (from hundreds to millions of galaxies) and providing the most precise Omega_HI constraints at z>0.25 to date. The f_HI(M*) relation is extended to ~10^6 M_sun at low redshift. The luminosity bias correction method (Eq. 8) is a useful methodological contribution, and its cross-validation against two independent methods (Extended Data Fig. 6) is a strength. The forward-modeling framework based on TNG100 is thorough in its treatment of selection effects, fibre assignment, and residual confusion. The central qualitative conclusion -- that Omega_HI evolves more weakly than the CSFRD -- is consistent with the existing consensus from DLA and stacking studies, but the precision and sample representativeness here represent a clear improvement.

major comments (3)
  1. Methods, Eq. (10) and Extended Data Table 2: At z>0.25, the f_HI(M*) relation is fit with Mcrit fixed at 10^7.73 (the z<0.05 value), and only f0 and gamma are free parameters. Extended Data Table 4 shows that direct measurements at z>0.25 only cover M*>10^9 M_sun. The integration for Omega_HI (Eq. 9) extends down to 10^6 M_sun, meaning a substantial fraction of Omega_HI at z>0.25 comes from extrapolation of the broken power-law into an unmeasured regime. The paper should explicitly quantify what fraction of Omega_HI at z>0.25 is contributed by M*<10^9 M_sun (it appears to be >50% based on the numbers: total Omega_HI ~0.6 vs. Omega_HI(M*>10^9) ~0.25 at z~0.3), and should discuss the sensitivity of the evolution factor to the assumed Mcrit. A simple test varying Mcrit by +/-0.3 dex at z>0.25 would demonstrate whether the evolution factor is robust to this extrapolation assumption.
  2. Methods, step 5 of mock construction: The forward model assigns HI masses using the fiducial Eq. (10) relation by construction. This means the mock can validate selection effects, confusion, and luminosity-bias corrections, but it cannot detect a systematic error arising from the functional-form extrapolation being wrong at low masses. The paper should explicitly acknowledge this limitation -- the systematic uncertainty budget does not include the possibility that the low-mass slope or characteristic mass of f_HI(M*) evolves with redshift. This is a load-bearing assumption for the total Omega_HI measurement, and the current text does not clearly flag that the forward model is circular with respect to this specific extrapolation assumption.
  3. Methods, Eq. (8): The luminosity bias correction assumes no redshift evolution in the intrinsic luminosity distribution phi(L_r|M*) over 0<z<0.41, using the z<0.05 sample as the reference. Extended Data Fig. 5 is cited as support, but the comparison shown is for massive galaxies where the sample is complete; the low-mass end at z>0.25 is precisely where the luminosity cut is most severe. The paper should discuss whether evolution in phi(L_r|M*) at low masses could systematically bias the corrected f_HI at z>0.25, and ideally provide a quantitative test (e.g., using the TNG mock to assess the magnitude of any such bias).
minor comments (6)
  1. Abstract: '1.12+/-0.10' after systematics -- clarify whether this is the factor of decrease or the residual evolution factor. The phrasing 'inferred decline is only 1.12' could be misread as Omega_HI declining by 1.12x rather than the evolution being nearly flat.
  2. Extended Data Table 4: the column header 'f_HI' for the 0.32<z<0.41 bin appears to be missing the 'log' prefix, inconsistent with the 0.25<z<0.32 column header 'log f_HI'.
  3. Figure 3 caption: 'rescaled by a constant factor of 30' -- clarify that this scaling is purely for visual comparison and has no physical meaning, to avoid confusion for readers skimming the figures.
  4. The RFI-driven redshift gaps between z~0.09 and z~0.25 mean the power-law fit Omega_HI ~ (1+z)^0.9 is fit to four points with a large gap. The paper should note that the fit is not well-constrained across this gap and is intended only as a summary, not for interpolation.
  5. Methods, Eq. (4)-(7): the parameterization of f_HI(L_r|M*) has 8 parameters but only 5 are listed in Eqs. (5)-(7). Clarify whether alpha and beta (Eq. 7) are the remaining parameters, and state the total count explicitly.
  6. The paper uses DESI DR2 data that is not yet public at the time of submission. A note on data availability timeline would help reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a thorough and constructive report. All three major comments identify legitimate limitations of the current analysis that we will address in revision. Specifically: (1) we will quantify the fraction of Omega_HI at z>0.25 contributed by M*<10^9 Msun (which is indeed >50%), perform the requested Mcrit variation test, and report the results; (2) we will explicitly acknowledge that the forward model is circular with respect to the low-mass extrapolation assumption and cannot detect systematics from an incorrect functional form at low masses; and (3) we will add a quantitative test using the TNG mock to assess potential bias from redshift evolution in phi(L_r|M*) at low masses. In all three cases, we expect the central conclusion (weak evolution of Omega_HI relative to CSFRD) to remain robust, but the revisions will make the systematic uncertainty budget more transparent and complete.

read point-by-point responses

  1. Referee: At z>0.25, the f_HI(M*) relation is fit with Mcrit fixed at 10^7.73, and direct measurements only cover M*>10^9. The integration for Omega_HI extends to 10^6, so a substantial fraction comes from extrapolation. The paper should quantify this fraction and test sensitivity to Mcrit.

    Authors: The referee is correct on both points. We will add explicit quantification of the Omega_HI contribution from M*<10^9 Msun at z>0.25. The referee's estimate is accurate: at z~0.3, Omega_HI(M*>10^9) ~0.25e-3 while total Omega_HI ~0.6e-3, so approximately 55-60% comes from the extrapolated low-mass regime. We will state this clearly in the revised manuscript. We will also perform the requested test varying Mcrit by +/-0.3 dex at z>0.25 and report the resulting change in the evolution factor. We expect the evolution factor to be robust because the extrapolation applies similarly at both high-z bins and the low-z reference, so changes in Mcrit largely cancel in the ratio, but we will verify this quantitatively and report the result. We note that the right panel of Figure 3 already shows Omega_HI(M*>10^9) evolving weakly (from ~0.215 to ~0.274e-3, a factor of ~1.27), confirming that the weak evolution conclusion holds even in the directly measured regime. revision: yes

  2. Referee: The forward model assigns HI masses using the fiducial Eq. (10) relation by construction, so it cannot detect systematic error from the functional-form extrapolation being wrong at low masses. The paper should acknowledge this limitation.

    Authors: This is a fair and important point. The forward model is designed to validate selection effects, confusion, and luminosity-bias corrections, but by construction it assigns HI masses using the fiducial f_HI(M*) relation and therefore cannot detect a systematic error arising from the assumed functional form being incorrect in the unmeasured low-mass regime at z>0.25. We will explicitly acknowledge this limitation in the revised Methods section. The systematic uncertainty budget quoted in the current manuscript does not include the possibility that the low-mass slope or Mcrit evolves with redshift, and we will state this clearly. We note that the assumption of fixed Mcrit is partially supported by the consistency of the best-fitting Mcrit between the two low-redshift bins (7.730 +/- 0.004 and 7.724 +/- 0.015), but this does not constitute a proof that Mcrit is unchanged at z>0.25 where it cannot be directly constrained. The Mcrit variation test requested in the first comment will provide a partial assessment of this sensitivity. revision: yes

  3. Referee: The luminosity bias correction assumes no redshift evolution in phi(L_r|M*) over 0<z<0.41, using z<0.05 as reference. Extended Data Fig. 5 supports this for massive galaxies where the sample is complete, but the low-mass end at z>0.25 is where the luminosity cut is most severe. The paper should discuss whether evolution in phi(L_r|M*) at low masses could bias the corrected f_HI at z>0.25, and ideally provide a quantitative test using the TNG mock.

    Authors: We agree that this assumption needs more careful justification, particularly at low masses and high redshift where the luminosity cut is most severe. Extended Data Figure 5 does show consistency of the L_r-M* distribution for massive galaxies across redshift bins, but as the referee notes, this comparison is limited to the regime where the sample is complete and does not directly test the assumption at low masses. We will add a quantitative test using the TNG mock: specifically, we will measure the intrinsic phi(L_r|M*) at z~0.3 directly from the mock galaxy population (which includes realistic redshift evolution in the luminosity-stellar mass relation) and compare the luminosity bias correction obtained using the z~0.3 intrinsic distribution versus the z<0.05 reference distribution. This will directly quantify any systematic bias from the assumed non-evolution of phi(L_r|M*). We will report the magnitude of any such bias and, if significant, include it in the systematic uncertainty budget. We expect the effect to be small because the correction factor C_HI(M*) depends on the shape of f_HI(L_r|M*) rather than its absolute amplitude, and Extended Data Figure 7 shows that this shape is consistent across redshift bins, but a direct mock-based test is the right way to verify this. revision: yes

Circularity Check

0 steps flagged

No significant circularity: Ω_HI is derived from observed f_HI(M*) and an external stellar mass function; the forward-model mock is constructed to isolate observational systematics, not to define the result.

full rationale

The paper's central claim — that Ω_HI decreases by only a factor of 1.35±0.10 (1.12±0.10 after systematics) from z=0.41 to z=0 — is derived from directly observed stacked f_HI(M*) measurements (Extended Data Tables 3–4) integrated over the external UniverseMachine stellar mass function (Eq. 9). The power-law fit Ω_HI ∝ (1+z)^0.9 is explicitly described as a summary of four data points, not a prediction. The forward-model mock (Methods, step 5) assigns HI masses using the fiducial Eq. 10 relation 'so that the mock preserves the observed correlation,' and the paper states the mock's purpose is 'to isolate observational systematics rather than to test the physical HI prediction of the simulation.' The mock recovers systematic offsets (e.g., +0.082×10⁻³ at z=0.32–0.41) that are then applied as corrections. This is a standard forward-modeling procedure: the mock validates selection effects and confusion, and by construction cannot detect errors from the functional-form extrapolation to M*<10⁹ at z>0.25. However, the paper is transparent about this limitation — it presents Ω_HI(M*>10⁹) separately (Fig. 3, right panel) showing similarly weak evolution, and the low-mass extrapolation uses Mcrit fixed at 10^7.73 justified by the consistent best-fit at 0.05<z<0.09 (7.724±0.015). The skeptic's concern about the low-mass extrapolation is a correctness/model-assumption risk, not a circularity: the result is not defined by its own inputs. Self-citations (FASHI survey [23,44], HiFAST pipeline [48]) are standard survey/pipeline references and are not load-bearing for the derivation. No step in the derivation chain reduces to its inputs by construction.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The paper introduces no new physical entities or particles. The free parameters are standard fitting parameters for scaling relations. The key ad hoc assumption is the lack of redshift evolution in the luminosity distribution, which is tested but is a load-bearing simplification.

free parameters (5)
  • f0 (Eq. 10) = 1.102-1.297 (varies by z bin)
    Amplitude of the broken power-law f_HI(M∗) relation, fitted to stacked data in each redshift bin.
  • Mcrit (Eq. 10) = 10^7.73 M_sun
    Characteristic mass for the f_HI(M∗) relation, fitted at low-z and fixed at high-z.
  • γ (Eq. 10) = 0.744-0.787
    Slope at the massive end of the f_HI(M∗) relation, fitted to data.
  • Eq. 4 parameters (κ, L∗, α, β) = 8 parameters total
    Parameters of the f_HI(Lr|M∗) relation used for luminosity bias correction, fitted with MULTINEST.
  • Qe (evolution correction) = 1.03
    Luminosity evolution parameter from Ref. [75], adopted as input.
axioms (5)
  • domain assumption Flat ΛCDM cosmology with Ωm=0.3, ΩΛ=0.7, H0=70 km/s/Mpc
    Standard cosmological framework adopted throughout for distance and volume calculations (Methods).
  • ad hoc to paper No redshift evolution in the intrinsic luminosity distribution ϕ(Lr|M∗) over 0<z<0.41
    Used in the luminosity bias correction (Methods, Eq. 8) to apply the z<0.05 distribution to all redshifts.
  • domain assumption f_HI(M∗) has the same functional shape (broken power-law) across all redshift bins
    Assumed to extrapolate f_HI to stellar mass ranges not probed at high-z (Methods, Eq. 10).
  • domain assumption UniverseMachine stellar mass function accurately represents the true ϕ(M∗,z)
    Used as the weighting function for integrating Ω_HI (Methods, Eq. 9).
  • domain assumption TNG100 simulation provides a realistic galaxy distribution for forward-modelling systematics
    Used to construct the mock catalogue for estimating observational biases.

pith-pipeline@v1.1.0-glm · 35329 in / 2468 out tokens · 135401 ms · 2026-07-07T17:04:10.170341+00:00 · methodology

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