Strong Correlation between Galactic HI-to-stellar Mass Ratio And Halo Spin Explored by HI-rich Galaxies

Huijie Hu; Shihong Liu; Yu Rong; Zichen Hua

REVIEW 3 major objections 5 minor 1 cited by

Strong Correlation between Galactic HI-to-stellar Mass Ratio And Halo Spin Explored by HI-rich Galaxies

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper claims that the HI-to-stellar mass ratio rises with dark-matter halo spin in both low-mass and massive isolated galaxies, making halo spin a likely universal regulator of gas retention.

desk verdict The reported η–λ_h correlation is largely an artifact of the spin estimator's dependence on M_HI; the paper needs a null test or an independent spin proxy to be convincing. read the letter →

arxiv 2411.11446 v3 pith:JCDNALNZ submitted 2024-11-18 astro-ph.GA

Shihong Liu , Yu Rong , Zichen Hua , Huijie Hu This is my paper · ORCID

classification astro-ph.GA

keywords galaxyformationhalospinHI-to-stellarmassrationeutralhydrogendarkmatterhalosevolutionstarfeedback21-cmsurvey

topics Dark Matter

open problems Dark Matter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that the amount of neutral hydrogen a galaxy holds, relative to its stars, is set to a significant degree by how fast its dark-matter halo spins. Using a semi-analytic estimator of halo spin applied to thousands of isolated HI-rich galaxies, it reports a positive correlation between the HI-to-stellar mass ratio and the spin parameter in both low-mass and massive systems, with correlation coefficients of about 0.4 and 0.5. If the correlation is real, halo spin would be a universal regulator of gas retention: high-spin halos keep their gas from collapsing quickly, which slows star formation and weakens feedback, leaving more HI in place. A sympathetic reader would care because this would connect a readily observable gas fraction to a fundamental dark-matter property, giving a new handle on galaxy formation models.

What carries the argument

The object doing the work is the semi-analytic spin estimator $\lambda_h \simeq 21.8\,(R_{\rm HI,d}/{\rm kpc})\,(V_{\rm rot}/{\rm km\,s^{-1}})^{-3/2}$ from Hernandez et al. (2007), which assumes an isothermal dark-matter halo with negligible baryonic gravity and a thin, rotationally supported exponential HI disk. The disk scale length $R_{\rm HI,d}$ is not measured directly; it is computed from the total HI mass $M_{\rm HI}$ through the empirical $r_{\rm HI}$--$M_{\rm HI}$ relation, while the rotation velocity $V_{\rm rot}$ comes from the measured HI line width corrected by an optical inclination. This estimator converts large HI-survey data into halo spins, and the analysis then compares $\eta$ against $\lambda_h$ separately for the two mass regimes, restricting to isolated systems with double-horned HI profiles to remove environmental gas loss and dispersion-dominated kinematics.

What would settle it

Recompute halo spins for the same galaxies using an estimator that does not use $M_{\rm HI}$ as input--for example, one based on stellar disk scale lengths and rotation velocities only--and check whether the $\eta$--$\lambda_h$ correlation coefficients stay near 0.4 and 0.5. If the correlation largely disappears or drops below significance, the claimed universal spin--gas relation is not supported by the current method.

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Extended reading notes

Core claim

The central claim is that the HI-to-stellar mass ratio, defined as $\eta = \log M_{\rm HI} - \log M_{\star}$, increases with the halo spin parameter $\lambda_h$ for both low-mass ($M_\star < 10^9\,M_\odot$) and massive ($M_\star > 10^9\,M_\odot$) isolated galaxies in the sample. The paper reports correlation coefficients of $0.40$ and $0.50$ for the two subsamples and linear fits with positive slopes (steeper for massive galaxies), and interprets this as evidence for a universal formation scenario: a higher-spin halo receives high-angular-momentum gas that resists infall and condensation, so star formation proceeds gently and supernova feedback is too weak to expel the gas, leaving a high HI fraction. The same mechanism previously proposed for ultra-diffuse galaxies is thereby extended across a broad stellar mass range.

Load-bearing premise

The load-bearing assumption is that the semi-analytic halo spin estimate measures the dark-matter halo's true angular momentum and is not merely a re-expression of the galaxy's neutral-hydrogen mass, because the spin estimate is derived from that same gas mass, which also defines the ratio being tested.

Editorial extensions

If this is right

If the correlation is genuine, halo spin becomes a primary observable predictor of a galaxy's HI-to-stellar mass ratio, comparable in importance to halo mass and environment.
The positive $\eta$--$\lambda_h$ relation should hold across the full stellar mass range, implying that spin-driven gas retention is a universal rather than dwarf-specific process.
Simulations and semi-analytic models of galaxy formation would need to reproduce a stronger HI fraction in high-spin halos; a model that predicts the opposite or a flat relation would conflict with these data.
Large HI surveys can be used statistically to estimate halo spins for thousands of galaxies without resolved 21-cm mapping, opening a cheap way to study angular momentum in the field.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The reported correlation may be inflated by construction: $\lambda_h$ depends on $M_{\rm HI}$ through $R_{\rm HI,d}$, whereas $\eta$ is defined from $M_{\rm HI}$, so part of the correlation could reflect the same quantity appearing on both sides; testing with a spin estimator that uses only stellar sizes or rotation velocities would separate the physical relation from this arithmetic coupling.
If confirmed, the spin--gas connection could sharpen quenching models: at fixed halo mass, high-spin halos should host galaxies with lower current star formation rates per stellar mass and more gas-rich disks, a prediction testable with resolved HI and star-formation maps.
The sample selection (isolated, double-horned, high-SNR galaxies) may bias toward regular rotators; extending the same analysis to interacting or dispersion-dominated systems could reveal whether the spin--HI link persists in populations whose gas is most easily disturbed.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The punchline is straightforward: the central correlation in this paper is largely built into the estimators. The authors estimate halo spin λ_h from Eq. (1) using R_HI,d, which they solve from M_HI through the empirical r_HI–M_HI relation in Eqs. (2)–(4). Since the dependent variable is η = log M_HI – log M_*, within a fixed stellar-mass bin any galaxy with higher η automatically gets a larger λ_h before any halo physics is invoked. The Spearman coefficients 0.40 and 0.50 are about what you'd expect from that constructional coupling alone.

Credit where it's due: the paper extends the UDG-specific result from Rong et al. (2024a) to the full ALFALFA sample, split at 10^9 M_sun, with careful isolation criteria and environmental controls. The sample selection, inclination corrections, and profile-shape filtering are handled thoughtfully. The writing is clear.

The soft spot is load-bearing. The authors' response to inclination uncertainty misses the point—the coupling enters through M_HI, not through inclination. They never present a null test, a partial correlation controlling for M_HI, or a permutation analysis. Without breaking the M_HI dependence of λ_h, the observed trend is not evidence that halo spin regulates HI fraction. Their physical scenario may be correct, but this analysis does not demonstrate it.

If I'm being fair, this is a useful cautionary example of semi-analytic estimators sharing variables with the response. I'd encourage the authors to redo the analysis with a spin estimate that does not rely on M_HI (e.g., from resolved kinematics or a stellar-mass-based scaling) or at least to show that the correlation survives partial correlation tests. As it stands, I would not publish it.

Would I send it to peer review? Yes—the question is significant and the flaw is subtle enough that a good referee can help the authors see it. But I'd expect the referee to catch this, and the authors will need to do more than cite inclination uncertainty. For my own work, I wouldn't cite this result until the coupling is addressed.

Referee Report

3 major / 5 minor

Summary. The paper estimates dark matter halo spin parameters λ_h for a large sample of HI-rich galaxies from the ALFALFA survey using the semi-analytic approach of Hernandez et al. (2007), in which the HI disk scale length is derived from the empirical r_HI-M_HI relation. It then reports a positive correlation between the HI-to-stellar mass ratio η and λ_h in both low-mass (M* < 10^9 Msun) and massive (M* > 10^9 Msun) subsamples, with Spearman coefficients of 0.40 and 0.50, respectively. The authors interpret this as evidence for a universal formation scenario in which higher halo spin reduces angular momentum loss, suppresses star formation and feedback, and thus helps retain HI gas.

Significance. If the reported correlation were physically real, it would provide an interesting observational constraint on the role of halo spin in regulating the HI content of galaxies across a large sample. The paper has some positive features: it uses a large homogeneous sample from ALFALFA, selects isolated galaxies to minimize environmental effects, and uses the kurtosis of HI line profiles to exclude dispersion-dominated systems. However, the significance of the result is critically undermined by the likelihood that the correlation is built into the spin estimator itself, as detailed in the major comments. The central claim cannot be accepted on the present evidence.

major comments (3)

[Section 2.3, Eqs. (1)-(4)] In Eqs. (2)-(4), R_HI,d is solved from M_HI using the empirical relation log r_HI = 0.51 log M_HI - 3.59. Combining these equations gives R_HI,d ∝ M_HI^0.51 to a very good approximation, since the exponent in the M_HI dependence of the central surface density is only 2α−1 = 0.02. Substituting into Eq. (1), log λ_h ≈ 0.51 log M_HI - 1.5 log V_rot + const. Within a fixed stellar-mass bin, variation in M_HI is exactly variation in η, so a positive η-λ_h trend is partly generated by the estimator itself. The paper does not address this constructional coupling.
[Section 3, Figure 1] The reported Spearman coefficients (0.40 and 0.50) and the linear fits in Section 3 are presented as evidence for a physical correlation. Because λ_h is an increasing function of M_HI by construction, the authors must show that the correlation is not an artifact. A null test (e.g., permuting M_HI values among galaxies with the same V_rot and M_*, or correlating residuals of λ_h after subtracting the best-fit M_HI dependence) is required. No such control is provided, so the central claim is not supported.
[Section 3, inclination discussion] The discussion of inclination misalignment in Section 3 only addresses scatter in V_rot and does not affect the M_HI-based coupling via R_HI,d. Even if inclinations are perfectly known, galaxies with larger M_HI would still have systematically larger λ_h through the r_HI-M_HI relation. Thus the robustness argument is insufficient to address the main concern.

minor comments (5)

[Section 2.3] The phrase 'Total HI masMHI' is a typo; it should read 'Total HI mass M_HI'.
[Section 2.3] The parameter q0 is introduced without a clear definition; please state that it is the intrinsic axial ratio of the HI disk and provide the reference for the adopted values.
[Section 3, Figure 1] The figure caption should report the number of galaxies in each bin and the method used to compute the 1σ error bars.
[Section 4] The word 'universal' overstates the conclusion because the sample is limited to isolated, HI-rich, double-horned galaxies; this caveat should be stated in the abstract or conclusions.
[References] The reference list contains formatting errors (e.g., 'Guo, Q. et al. 2020, NewA, 4, 246' appears to have an incorrect volume/journal format); please check the bibliography.

Circularity Check

1 steps flagged · score 7.0 of 10

The spin estimator λ_h is constructed from M_HI, the same quantity that defines η, so the reported η–λ_h correlation is partly built into the estimator.

self definitional [Section 2.2, Eq. (1); Section 2.3, Eqs. (2)-(4)]
"λh ≃ 21.8 RHI,d/kpc / (Vrot/kms−1)3/2 . (1) ... log rHI = 0.51 logMHI − 3.59 ... R∞ 0 ΣHI(R)2πRdR = 2πΣHI,0R2 HI,d = MHI. ... Using equations above, we compute RHI,d for each galaxy, allowing halo spin estimation."

Equations (2)-(4) make R_HI,d a deterministic function of M_HI. With log r_HI = 0.51 log M_HI − 3.59 and Σ_HI,0 = M_HI/(2π R_HI,d^2), the condition Σ_HI,0 exp(−r_HI/R_HI,d) = 1 gives R_HI,d ∝ M_HI^0.51 up to a slowly varying factor. Inserting this into Eq. (1), log λ_h ≈ 0.51 log M_HI − 1.5 log V_rot + const. But η is defined in Sec. 2.2 as η = log M_HI − log M_*, so within each fixed stellar-mass bin the dependent variable is just log M_HI plus a constant. Every galaxy with higher HI mass therefore automatically receives a larger λ_h through R_HI,d, before any halo-spin physics is invoked.

full rationale

The central claim—that η increases with halo spin—rests on a spin estimator that is not independent of the quantity being correlated. λ_h in Eq. (1) uses R_HI,d, which is solved from M_HI via Eqs. (2)-(4) and the empirical r_HI–M_HI relation. Since η = log M_HI − log M_*, the correlation is substantially a correlation between log M_HI and a monotonic function of log M_HI and V_rot within fixed stellar-mass bins. This is a structural circularity in the estimator, not simply an interpretation issue. The self-citations to Rong et al. (2024a) supply the physical narrative but are secondary; the main reduction is the definitional dependence of λ_h on M_HI. Because V_rot is an independent input and could in principle weaken or reverse the mechanical trend, the correlation is not fully forced by definition, but it is partially built into the construction. Hence a score of 7 rather than 8 or 10.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The central result rests on a chain of literature-based modeling choices (isothermal halo, exponential disk, r_HI-M_HI relation, axis-ratio inclinations, isolation and profile cuts). The most consequential is the r_HI-M_HI scaling, because it injects the dependent variable's numerator into the spin estimate. No new entities are postulated.

free parameters (2)

Intrinsic HI disk axis ratio q0 = 0.2 (massive), 0.4 (low-mass)
Adopted from Tully et al. 2009 and Rong et al. 2024b; used to convert optical b/a into inclination, which sets V_rot and therefore λ_h. Results are sensitive to this choice.
r_HI-M_HI scaling relation coefficients = slope 0.51, intercept -3.59
Empirical fit from Wang et al. 2016; this relation is the channel through which M_HI enters R_HI,d and hence λ_h, creating the definitional dependence on the dependent variable.

assumptions (7)

domain assumption The dark matter halo is an isothermal sphere and baryonic gravity is negligible when estimating spin
Invoked before Eq. (1); this may be inaccurate for HI-rich low-mass galaxies where gas can dominate the inner potential.
domain assumption The HI disk has an exponential surface density profile with scale length R_HI,d
Equations (2) and (3); standard but not directly tested for each galaxy.
domain assumption The empirical r_HI-M_HI relation (Wang et al. 2016) applies to the selected ALFALFA sample
Used in Eq. (4) to determine R_HI,d; if the relation is biased for isolated HI-rich galaxies, all spin estimates shift.
domain assumption Optical axis ratio traces the HI disk inclination with negligible misalignment
Section 2.3; the paper acknowledges small misalignments but assumes they only add scatter, not bias.
domain assumption The kurtosis cut k4 > -1.0 cleanly separates rotation-dominated from dispersion-dominated galaxies
Section 2.3, following Hua et al. 2024; a wrong classification would bias the rotation velocity and spin sample.
domain assumption Isolation beyond 3 virial radii removes environmental effects on HI content
Section 2.4; the threshold is heuristic and could still admit galaxies with recent interactions.
domain assumption M_* = 10^9 M_sun marks a physical transition between feedback- and angular momentum-dominated regimes
Section 3, from Di Cintio et al. 2019; the division of the sample relies on this threshold.

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Cite this review

Pith. "Pith review of Strong Correlation between Galactic HI-to-stellar Mass Ratio And Halo Spin Explored by HI-rich Galaxies." pith.science (2026). https://pith.science/paper/JCDNALNZ

@misc{pith2026241111446,
  author       = {Pith},
  title        = {Pith review of: Strong Correlation between Galactic HI-to-stellar Mass Ratio And Halo Spin Explored by HI-rich Galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JCDNALNZ}},
  note         = {Machine review of arXiv:2411.11446}
}

read the original abstract

Using a semi-analytic approach, we estimate halo spins for a large sample of HI-rich galaxies from the Arecibo Legacy Fast Alfa Survey and examine the correlation between HI mass fractions and halo spins. Our analysis reveals a strong correlation between halo spin and the HI-to-stellar mass ratio in both low-mass and massive galaxy samples. This finding suggests a universal formation scenario: higher halo spin reduces angular momentum loss and gas condensation, leading to lower star formation rates and weaker feedback, which in turn helps retain gas within dark matter halos.

Figures

Figures reproduced from arXiv: 2411.11446 by the authors.

**Figure 1.** The η-λh relationships for low-mass (panel a) and massive (panel b) galaxies. Median η values with 1σ error bars are shown in blue and red for bins in log λh. The best linear fitting results are highlighted by the corresponding lines. Benavides, J. A., Sales, L. V., Abadi, M. G., Marinacci, F., Vogelsberger, M., Hernquist, L. 2023, MNRAS, 522, 1033 Cappellari, Michele; Bacon, R.; Bureau, M., et al. 2006, MNRAS, 366,… view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Moderate Influence of Halo Spin on Stellar Mass Distributions in Dwarf and Massive Galaxies
astro-ph.GA 2024-11 conditional novelty 4.0 of 10

An analysis of ALFALFA galaxies finds a weak to moderate inverse correlation between estimated halo spin and stellar surface density, with slopes consistent with zero at about 1 sigma.

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