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This paper claims that gas-rich galaxies selected by their atomic hydrogen content follow a single Schechter form for their stellar mass function, and that abundance matching this against the HI mass function yields a selection-free M_HI–M_

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2026-08-01 08:05 UTC pith:IW5NMW6P

load-bearing objection Useful alpha.100 HI-selected GSMF and an abundance-matched scaling relation, but the 'free from selection bias' claim leans on an untested transfer of V_eff weights to the optical-limited subsample. the 3 major comments →

arxiv 2607.21225 v1 pith:IW5NMW6P submitted 2026-07-23 astro-ph.GA astro-ph.CO

The Stellar Mass Function of Gas-Rich Galaxies and the Underlying M_(rm HI)-M_(rm star) Scaling Relation in the Local Universe

Tanya Tripty , Nishikanta Khandai , Saili Dutta , Khushi Sharma This is my paper
classification astro-ph.GA astro-ph.CO
keywords galaxy stellar mass functionHI mass functionALFALFA surveyM_HI–M_star scaling relationabundance matchingSchechter function1/V_eff method
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper sets out to measure the stellar mass function of galaxies selected by their atomic hydrogen (HI) content — rather than by their starlight — and to recover the relation between HI mass and stellar mass in a way that is not biased by how ALFALFA detects galaxies. Using the 100% ALFALFA catalog with optical counterparts from SDSS and UV/IR mass estimates from GSWLC-2, it finds that the HI-selected stellar mass function is consistent with a single Schechter function, and that red galaxies contribute about 54% of the stellar mass yet only ~18% of the number density. The main payoff is a M_HI–M_star relation obtained by abundance matching the HI mass function to the stellar mass function, which the authors argue is free from selection effects and agrees with a volume-limited sample and with the MIGHTEE-HI survey. If right, the result gives an unbiased view of how much atomic gas galaxies carry at a given stellar mass, and shows that gas-rich galaxies hold about a third of the local stellar mass density.

Core claim

The central claim is that once the ALFALFA selection function is corrected via a 1/V_eff weighting scheme, the stellar mass function of HI-selected galaxies is a single Schechter function with log10(M*/M⊙) = 10.83, α = −1.14, and φ* = 2.30×10^-3 h70^3 Mpc^-3 dex^-1 (GSWLC-calibrated masses). Red and blue populations are each also single Schechter functions, with red galaxies making up ~18% of the corrected number density but ~54% of the stellar mass density. Abundance matching the HI mass function against this GSMF yields an intrinsic M_HI–M_star relation that lies below the relation seen in the raw data — that is, the observed HI-selected relation is biased toward gas-rich galaxies at fixed

What carries the argument

The load-bearing machinery is the 1/V_eff method applied to the ALFALFA survey: a two-dimensional stepwise maximum likelihood fit to the HI mass–velocity width plane yields a normalized bivariate function, and each galaxy's effective maximum volume V_eff is then computed from it using the survey's 50% completeness relation for flux versus velocity width. These V_eff weights correct the HI-selected sample for selection effects and are reused to build the HI-selected stellar mass function by binning in stellar mass. The selection-free M_HI–M_star relation is then produced by abundance matching: the HI mass function and the stellar mass function are both normalized at the high-mass end, and mat

Load-bearing premise

The analysis assumes that applying the optical r-band magnitude cut (r < 17.77) and spectral-class cleaning does not bias the stellar-mass distribution relative to the full HI-selected sample, since the selection weights (V_eff) are computed from the larger HI sample and then transferred to the optical-limited subset without recomputation.

What would settle it

The paper's own volume-limited sample (0.0025 < z < 0.004) gives a direct, unbiased M_HI–M_star relation that agrees with the abundance-matched curve; the claim would be falsified if a larger volume-limited sample spanning a wider redshift range measured M_HI–M_star values that deviate from the abundance-matched curve by more than the combined uncertainties.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Gas-rich galaxies contribute about 33% of the local stellar mass density and 39% of galaxy number counts when compared with an optically selected SDSS sample in a shared volume.
  • Red galaxies in the HI-selected population dominate the stellar mass budget (~54%) despite being only ~18% of the galaxies by number.
  • The corrected M_HI–M_star relation lies below the directly observed one at fixed stellar mass, implying that naive HI-selected relations overestimate typical gas content.
  • Dust-corrected (GSWLC-calibrated) stellar masses raise the characteristic mass of the HI-selected GSMF by about 0.2 dex relative to uncorrected KCORRECT masses, shifting the inferred stellar mass density by more than 1σ.

Where Pith is reading between the lines

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

  • Editorial inference: the V_eff weights are computed from the full 19,838-galaxy HI sample and then applied to a subsample of 16,955 galaxies after optical magnitude and spectral-class cuts; recomputing the weights on the optical-limited subsample would test whether those cuts bias the stellar-mass distribution.
  • Editorial inference: the abundance-matched relation assumes monotonic rank correlation between HI mass and stellar mass; incorporating the full conditional distribution P(M_HI|M_star) (the paper itself adds scatter only through a σ=0.2 dex broadening) would provide a sturdier basis for the claimed unbiased relation.
  • Editorial inference: the ~33% and ~39% budget numbers rely on spectroscopic coverage that exists in only ~65% of the ALFALFA footprint; HI-selected galaxies outside that region could shift the global budget if their stellar masses differ systematically.
  • Editorial inference: the paper's machine-learning mass predictions reproduce the GSMF only in the well-sampled middle mass range; training the models to predict (M_star, V_eff) jointly, as the paper suggests, would be a direct test of whether low-mass-end distortions can be removed.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper uses the ALFALFA 100% catalog with SDSS optical counterparts to construct an HI-selected galaxy stellar mass function (GSMF), recalibrating KCORRECT stellar masses with GSWLC-2 masses via a linear relation. Applying 1/V_eff weights derived from the 2DSWML bivariate HI mass–velocity-width function, the authors find that the HI-selected GSMF is described by a single Schechter function with {phi* = 2.30e-3, log10(M*/M_sun) = 10.83, alpha = -1.14} (Table 1, KCORRECT+GSWLC), and that red galaxies contribute ~18% of the number density but ~54% of the stellar mass density. Comparison with an optically selected SDSS sample in a common sub-volume yields gas-rich fractions of ~33% in stellar mass and ~39% in number counts. Finally, the authors abundance-match the HI-selected GSMF and HIMF to obtain an M_HI-M_star relation, claiming it is free from selection bias, and validate it against a local volume-limited sample and MIGHTEE-HI results.

Significance. If the central claims hold, the paper provides the first ALFALFA 100%-based, selection-corrected stellar mass function of gas-rich galaxies and a corresponding M_HI-M_star relation, which would be valuable for galaxy evolution studies and for comparisons with simulations. The analysis is thorough in several respects: it cross-checks the HIMF against Oman (2022), uses three stellar mass estimators, tests consistency with machine-learning mass predictions, and compares with an external interferometric survey (MIGHTEE-HI). These checks are genuine strengths and demonstrate careful attention to systematics. However, the headline claim that the derived M_HI-M_star relation is 'free from selection bias' is not fully secured by the presented tests, for the reasons detailed below.

major comments (3)
  1. [Sec. 2.1 / Sec. 3.3] The 1/V_eff weights used for the HI-selected GSMF are computed from the 19,838-galaxy sample (Sec. 3.1) and then applied to the 16,955 galaxies that pass the r_petro<17.77 and spectral-class cuts (Sec. 2.1). The manuscript does not demonstrate that these cuts are independent of M_star at fixed (M_HI, W50). The 2,298 excluded galaxies are likely to be preferentially faint, low-mass, or optically incomplete; if so, the weighted GSMF, the red/blue fractions (Table 2), and the abundance-matched relation in Fig. 9 are all biased. Appendix C concedes that the ML algorithms are 'trained to predict M_star rather than predicting both M_star and V_eff simultaneously' and therefore do not test the weight transfer. A direct test comparing M_HI, W50, and z distributions, or a re-estimation of V_eff on the optical-limited sample, is required to support the claim that the relation is 'free from selecti
  2. [Sec. 5 / Fig. 9] The 'underlying' M_HI-M_star relation is obtained by abundance matching the HIMF and GSMF derived from the same survey with the same 1/V_eff weights. It is therefore a restatement of those two mass functions rather than an independent measurement. The zero-scatter line is a rank-matching; the sigma=0.2 dex line is an assumed value, not constrained by the data. The uncertainty band shown in Fig. 9 includes only propagation from the mass-function fits, not the uncertainty in sigma or in the transfer of weights. The volume-limited check uses a very small sample (no N quoted) and the MIGHTEE comparison is encouraging, but the matching line is constructed with the same assumed sigma. To claim an unbiased relation, sigma should be fitted or explicitly marginalized, and the relation should be tested on an external sample, e.g. xGASS or the MIGHTEE data themselves.
  3. [Sec. 2.1 / Fig. 2] The KCORRECT-to-GSWLC linear calibration (Fig. 2, M_kcorrect = 0.917 M_GSWLC + 0.740) is fitted to the 8,280 galaxies with GSWLC masses and applied to the 8,677 without. The text states that only 49% of the sample has GSWLC estimates and that no suitable selection criteria were found, but no test is given that the GSWLC subset is representative in M_HI, W50, color, or redshift. The ML checks (Sec. 5, Appendix C) are trained and tested on GSWLC galaxies, so they do not validate extrapolation to the no-GSWLC population. A systematic difference would shift the M* and alpha values in Table 1 and the fractions in Table 2. A binned comparison of the two subsets, or a calibration stability test on random subsamples, would strengthen the analysis.
minor comments (6)
  1. [Sec. 2.2] The sentence 'We therefore removed these galaxies from our analysis. Finally, we are left with 45,609 galaxies' is contradictory; please clarify how many galaxies were removed and the selection criteria for the final optical sample.
  2. [Sec. 3.3 / Appendix B] The statement 'the GSMF for the total population is complete above the mass 6.2> M_HI>7.3' appears to contain a typo; it should presumably refer to M_star. Also, the completeness statement is not self-consistent with the adopted M_star>7.0 threshold.
  3. [Fig. 9 / Sec. 5] Please provide the number of galaxies in the volume-limited sample and the mass range they span; this is important for assessing the strength of the consistency check.
  4. [Appendix C] The statement that the algorithms 'had (wrongly) originally anticipated' is informal; please rephrase. Also, the ML cross-check is not a full validation of the calibration, as acknowledged.
  5. [Table 1] The chi^2_red values are reported without degrees of freedom or the fit range; please specify.
  6. [Figures] The name 'Schecter' appears in some figure captions; it should be 'Schechter' throughout.

Circularity Check

0 steps flagged

No significant circularity: the HI-selected GSMF, HIMF, and abundance-matched scaling relation are derived from data with explicit weights and validated against independent volume-limited and MIGHTEE-HI samples.

full rationale

The paper's central derivation chain is: (i) measure the HIMF via 2DSWML/V_eff; (ii) compute the HI-selected GSMF by binning stellar masses with the same V_eff weights; (iii) abundance-match the HIMF and GSMF to obtain the M_HI-M_star relation; and (iv) validate with a volume-limited sample and compare with MIGHTEE-HI. Each step is a standard estimator applied to data, not a reduction of the conclusion to its inputs. The V_eff weights are determined self-consistently from Eqs. (3)-(7), with normalization fixed at the complete high-mass end, and the resulting HIMF is explicitly checked against the independent Oman (2022) measurement. The abundance-matched relation is transparently a transformation of the two measured mass functions, not an independent prediction; but this is the stated method, not a hidden circularity. The volume-limited sample (z in [0.0025,0.004]) provides an external check that does not use 1/V_eff weighting, and the agreement with MIGHTEE-HI (Pan et al. 2023) is an independent benchmark. Self-citations to Dutta et al. (2020) concern the 2DSWML implementation and normalization convention; these are methodological, not load-bearing uniqueness claims, and the method is also standard (Loveday 2000; Zwaan et al. 2003). The sigma=0.2 dex scatter curve is an assumed illustrative value, explicitly deferred to future work, not a fitted prediction. The main residual concern is the transfer of V_eff weights from the 19,838-galaxy HI sample to the 16,955-galaxy r_petro<17.77 optical-limited subsample; if the optical cuts are correlated with stellar mass at fixed HI properties, the GSMF and derived scaling relation could be biased. This is a selection-bias/correctness risk, not circularity, because the paper does not define the GSMF in terms of the scaling relation or vice versa, and the volume-limited comparison provides partial external support.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The analysis rests on an empirical completeness relation, a linear mass calibration fitted to a 49% subset, and an adopted 0.2 dex scatter. These are the main inputs the reader must accept on faith; the remaining machinery is standard survey analysis.

free parameters (3)
  • KCORRECT-to-GSWLC linear calibration coefficients = slope=0.917, intercept=0.740
    Fit to 8,280 GSWLC galaxies in Sec. 2.1 and applied to all non-GSWLC galaxies in the final sample; this drives the stellar mass scale, phi*, and M* of every GSMF.
  • GSWLC mass-error relation coefficients = sigma_GSWLC = -0.021 * M_GSWLC + 0.250
    Fitted relation used to assign errors to calibrated masses; affects the quoted uncertainties and the Schechter fit chi-squared.
  • Intrinsic scatter sigma in abundance-matched M_HI-M_star relation = 0.2 dex
    Introduced by hand in Sec. 5 to align the abundance-matched relation with the observed data and MIGHTEE-HI mock; no fitting procedure or uncertainty is quoted for this value.
axioms (5)
  • domain assumption ALFALFA 50% completeness relation Eq. 1 (Oman 2022)
    Used to compute V_eff and every HIMF/GSMF weight. If this empirical completeness curve is wrong, the claimed selection corrections shift.
  • domain assumption Optical r_petro<17.77 and spectral-class cuts do not bias the stellar-mass sample relative to the full HI sample
    V_eff weights are computed from the 19,838-galaxy HI sample and then applied to the 16,955-galaxy optical-limited stellar-mass sample without recomputation (Sec 2.1 and 3.3).
  • domain assumption GSWLC linear calibration extrapolates to galaxies without GSWLC masses
    Only 49% of ALFALFA galaxies have GSWLC masses; the linear relation is applied to the rest with no external validation of the extrapolation (Sec 2.1).
  • domain assumption Abundance matching assumes a monotonic M_HI-M_star relation with symmetric scatter
    The cumulative matching of HIMF and GSMF in Sec. 5 defines the relation; if the relation is non-monotonic or scatter is asymmetric, the inferred mapping is not the underlying relation.
  • domain assumption Red/blue split follows the Baldry et al. (2004) color-magnitude divider (Eq. 2)
    All red/blue fractions and population mass functions depend on this boundary.

pith-pipeline@v1.3.0-alltime-deepseek · 34982 in / 16323 out tokens · 172981 ms · 2026-08-01T08:05:40.511041+00:00 · methodology

0 comments
read the original abstract

We estimate the Galaxy Stellar Mass Function (GSMF) of HI gas-rich galaxies using the 100\% ALFALFA ($\alpha$) catalog, $\sim 98\%$ of which have optical counterparts in the Sloan Digital Sky Survey (SDSS) and a subset of them have counterparts in GALEX SDSS WISE Legacy Catalogue-2(GSWLC-2). We use the mass estimates from this subset which combines UV, optical and IR bands with individual dust corrections to recalibrate optical stellar mass estimates. We use a non-parametric method to estimate the GSMF of these gas-rich galaxies. The resulting, HI-selected GSMF is consistent with a single Schechter function with best-fit parameters $\left\{\phi_* (10^{-3}\, h_{70}^{3}\,\mathrm{Mpc}^{-3}\,\mathrm{dex}^{-1}), \log_{10} (M_*/M_{\odot}) + 2\log_{10} h_{70}, \alpha \right\} = \left\{2.30^{+0.12}_{-0.12}, \,10.83^{+0.01}_{-0.01},\, -1.14^{+0.02}_{-0.02}\right\} $. Additionally, the red and blue populations are each well described by a single Schechter function. After correcting for selection effects, we find that the red population accounts for only $\sim18\%$ of gas-rich galaxies by number, yet contributes $\sim54\%$ of the total stellar mass, with the blue population accounting for the rest. Using an optically selected sample and a joint optical-HI sample, we find gas-rich galaxies represent $\sim 33\%$ of the total stellar mass density and $\sim 39\%$ of the total galaxy number counts in the local Universe. We use the GSMF and the HI mass function (HIMF) of the HI-selected sample to obtain the $M_{\rm HI}-M_{\rm star}$ relation, which is free from selection bias.

Figures

Figures reproduced from arXiv: 2607.21225 by Khushi Sharma, Nishikanta Khandai, Saili Dutta, Tanya Tripty.

Figure 1
Figure 1. Figure 1: The H I sample used in this work plotted in the RA-Dec plane. Each point is a galaxy with an H I detection. Galaxies inside the solid black boundary (regions 1 and 2) are used to construct H Iselected sample described in Sec. 2.1. The blue points represent galaxies outside the SDSS footprint. The yellow (green) points are galaxies which have (do not have) an OC. All yellow points have photometric detection… view at source ↗
Figure 2
Figure 2. Figure 2: Left: The scaling relation between GSWLC and Taylor stellar mass estimates for each galaxy (points). Right: The scaling relation between GSWLC and KCORRECT stellar mass estimates. The blue line with error bars is the mean relation in mass bins and their variance in each bin. The black dotted line is the 𝑦 = 𝑥 curve. The solid maroon line in the right panel shows the best fit linear relation 𝑀kcorrect = 0.9… view at source ↗
Figure 3
Figure 3. Figure 3: Left: The 𝛼.100 HIMF for our sample (data points with errors) is estimated based on the the 1/𝑉eff method. The solid line and the shaded region are the best-fit Schechter function and its uncertainty respectively. Comparison is made with the HIMF derived from the 𝛼.100 sample, based on similar quality cuts, survey volume, and completeness relation 1 of Oman (2022) (dotted line) Right: The HIMF for the tota… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of H I selected GSMFs derived using different stellar mass estimates.Top left: GSMF estimated using 𝑀Taylor. Top right: GSMF using 𝑀kcorrect. Bottom left: GSMF using 𝑀kcorrect+GSWLC. In each panel, the total (grey squares), blue (blue circles), and red (red triangles) populations are shown with their error bars, along with their corresponding best-fit Schechter functions (solid lines) and associ… view at source ↗
Figure 5
Figure 5. Figure 5: The stellar mass function of the H I-selected sample derived using 𝑀kcorrect+GSWLC mass estimates (open squares, with the best-fit Schechter function and its 1𝜎 uncertainty shown as the black curve and grey shaded band) compared with Machine Learning models: Random Forest (Breiman 2001) (filled circle) and LightGBM (Ke et al. 2017) (filled triangle) pre￾dicted mass estimates trained on 𝑀GSWLC mass estimate… view at source ↗
Figure 6
Figure 6. Figure 6: Optically selected GSMF: comparison between this work (filled squares) using SDSS DR15 in the redshift range 0.0025 < 𝑧 < 0.05 with the 𝑀kcorrect+GSWLC stellar mass estimate and previous measurements in the local Universe. These measurements are Baldry et al. (2012) (open circles) and Driver et al. (2022) (open triangles) with the GAMA survey and Bernardi et al. (2013) (open tilted square) and Weigel et al… view at source ↗
Figure 7
Figure 7. Figure 7: Left: optically selected GSMF for the total(black), red(red) and blue(blue) populations (data points with error bars) and their corresponding double Schecter function (equation 10 fits and uncertainties, solid lines and shaded regions. The data points corresponding to blue (red) galaxies are shifted to the right (left) by 0.02 dex with respect to the total population for a better comparison. The dashed (do… view at source ↗
Figure 8
Figure 8. Figure 8: Optically and joint optical-H I selected GSMF for the total(Left), blue(Middle), and red(Right) galaxy populations. In the upper panel, solid and dashed curves show the best-fit optical and H I Schecter function, respectively, with shaded bands denoting 1𝜎 uncertainties. Filled and open markers indicate optical and H I selected measurements. The lower panel shows residuals with respect to the optical-selec… view at source ↗
Figure 9
Figure 9. Figure 9: Left: log10 (𝑀HI/𝑀⊙ ) as a function of redshift for ALFALFA galaxies (black points). Purple diamonds denote galaxies from the volume-limited sample in the redshift range 0.0025 ≤ 𝑧 ≤ 0.004. Middle: Comparison of stellar mass and H I mass scaling relations for ALFALFA galaxies. The solid black line(Φ 𝑀HI 𝜎=0.0 (𝑀star))is the H I selected 𝑀star − 𝑀HI relation obtained by abundance matching the H I selected 𝜙… view at source ↗
Figure 10
Figure 10. Figure 10: The H I selected 𝑀star − 𝑀HI scaling relations and uncertainties (shaded regions) for the total(black), red(red) and blue(blue) populations. The solid (dashed) line corresponds to the H I (joint optical-H I) selected sample. The solid line segments with numbers denote the local slope of the scaling relations. , whereas it is negative for the total and blue populations and it is negative for the three popu… view at source ↗

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