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REVIEW 3 major objections 4 minor 105 references

Relationship between 2D and 3D Galaxy Stellar Mass and Correlations with Halo Mass

T0 review · 3 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read A projected, 2D measurement of the outer stellar mass of massive galaxies matches, and sometimes beats, the same quantity measured in full 3D as a tracer of dark matter halo mass, and it introduces no bias in galaxy-galaxy lensing profiles.

desk verdict Solid simulation study of 2D vs 3D outer stellar mass as a halo proxy; the geometric conversion has an error that, if anything, makes the 2D result conservative. read the letter →

arxiv 2502.05158 v1 pith:QENSK6XA submitted 2025-02-07 astro-ph.CO astro-ph.GA

Conghao Zhou , Alexie Leauthaud , Shuo Xu , Benedikt Diemer , Song Huang , Katya Leidig , Tesla Jeltema , Marco Gatti
show 3 more authors
Yifei Luo Carlo Cannarozzo Sven Heydenreich
This is my paper · ORCID
classification astro-ph.COastro-ph.GA
keywords outerstellarmassstellar-to-halorelationgalaxy-galaxylensingprojectioneffectsIllustrisTNGex-situgalaxyclusterselectionhaloproxy
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

The paper asks whether the outer stellar mass of massive galaxies, which can only be measured in projection on the sky, is as good a proxy for dark matter halo mass as the same quantity measured in full 3D using simulated galaxies. Working with 2713 massive central galaxies from the IllustrisTNG300-1 simulation, it finds that the stellar mass in a 2D elliptical annulus between 50 and 100 kpc has a scatter in the stellar-to-halo mass relation comparable to, and sometimes marginally smaller than, the corresponding 3D ellipsoidal shell between 79 and 158 kpc. The explanation is geometric: a projected annulus acts as a cylinder along the line of sight, which excludes the galaxy core, preferentially samples the major-axis direction where accreted (ex-situ) stars concentrate, and collects stars from ellipsoidal radii beyond the 3D outer limit. The paper also computes mock galaxy-galaxy lensing profiles and finds that samples selected by 2D and 3D outer stellar mass have nearly identical mean lensing signals, indicating that the projection does not create a bias. These results matter because outer stellar mass is a promising, simple cluster selector for cosmology.

What carries the argument

The central objects are the 2D elliptical annulus stellar mass, defined as the integrated stellar mass between two elliptical isophotes with semi-major axes 50 and 100 kpc fitted to projected stellar maps, and the 3D ellipsoidal shell stellar mass, defined as the sum of stellar particles between concentric ellipsoids with semi-major axes 79 and 158 kpc fitted with a reduced inertia tensor. The argument is carried by the projection geometry of prolate galaxies: a 2D elliptical annulus is a cylinder along the line of sight, so the minimal 3D ellipsoidal radius of selected particles is at least the 2D inner radius for a prolate galaxy, the selection keeps more particles along the major axis where the ex-situ fraction is higher, and it has no upper bound on ellipsoidal radius. The authors justify this with a 'line approximation' that treats galaxies as needles and with an exact Schur-complement mapping between 2D elliptical and 3D ellipsoidal distances derived in an appendix.

What would settle it

Repeat the same 2D-versus-3D comparison in a second independent cosmological hydrodynamical simulation with a different feedback treatment, or in real imaging data by measuring 2D outer stellar mass and stacked lensing: if the 2D selection's SHMR scatter is not comparable to the 3D shell, or if the mean lensing profile of 2D-selected samples differs from 3D-selected samples at fixed stellar mass, the claim of no projection bias fails. A sharper internal test would be to split TNG galaxies selected in 2D by the orientation of their major axis relative to the line of sight; if the mean lensing amplitude varies systematically with orientation at fixed 2D outer stellar mass, the 2D selection does create orientation-dependent bias.

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Extended reading notes

Core claim

In IllustrisTNG300-1, for massive central galaxies at z=0.4 with stellar mass above $10^{11.2}\,M_\odot$, the 2D elliptical annulus stellar mass $M_*^{2D,[50,100]\,\mathrm{kpc}}$ is as good a halo mass proxy as the 3D ellipsoidal shell stellar mass $M_*^{3D,[79,158]\,\mathrm{kpc}}$, with comparable or marginally smaller SHMR scatter. The mean excess surface density profiles around 2D- and 3D-selected samples agree within $1\sigma$, so the 2D selection does not induce a projection bias in galaxy-galaxy lensing. The paper explains the counterintuitive success of the 2D selection by showing that the 2D elliptical annulus is a cylindrical selection along the line of sight: for the predominantly prolate galaxies in the sample, it always excludes the galaxy core, includes more particles along the major axis where the ex-situ fraction is higher, and has no upper bound on the 3D ellipsoidal radius of included particles, pulling in outer stellar-halo material that correlates most tightly with halo mass.

Load-bearing premise

The whole comparison assumes that the simulated galaxies in IllustrisTNG300-1 have the same 3D shapes, stellar-halo density profiles, and halo-orientation relations as real massive galaxies, and that observational effects such as the point-spread function, background subtraction errors, and blended satellites would not change the ranking.

Editorial extensions

If this is right

  • The 2D outer stellar mass measured in real surveys can be used as a cluster mass proxy without needing a full 3D shape correction, because the 2D selection is not biased relative to the 3D selection.
  • The mapping between the 2D annulus [50,100] kpc and the 3D shell [79,158] kpc lets observers interpret projected measurements in terms of physical 3D radii.
  • The absence of projection bias in the lensing profiles means stacked weak-lensing calibrations of outer-stellar-mass-selected clusters are not systematically offset by triaxiality or orientation effects.
  • Going to larger 2D annuli beyond 100 kpc may further reduce SHMR scatter, with the caveat that background subtraction becomes more difficult.
  • Outer stellar mass can be combined with richness-based cluster selection to provide an independent halo mass proxy with different systematics.

Reading between the lines

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

  • Beyond the paper: because the 2D selection is a cylinder with no upper ellipsoidal-radius bound, the result suggests that any projected aperture enclosing a radially increasing, halo-correlated tracer may outperform a 3D shell of the same nominal radius; the same logic could be tested on projected X-ray or Sunyaev-Zeldovich signals.
  • Beyond the paper: the analytic Schur-complement mapping between 2D elliptical and 3D ellipsoidal radii could be inverted to infer the intrinsic 3D shape distribution of observed massive galaxies from their projected isophotal shapes and outer stellar masses.
  • Beyond the paper: a direct observational test would measure 2D outer stellar mass in real imaging data and compare the scatter in lensing-calibrated halo mass with the simulation prediction; a discrepancy would flag simulation-specific shape or stellar-halo assumptions.
  • Beyond the paper: splitting a real 2D-selected sample by inferred orientation (for example, by alignment with large-scale structure) and checking whether the mean lensing amplitude is orientation-independent would provide a sharper test of the claimed absence of projection bias.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper uses IllustrisTNG300-1 to study whether projected, two-dimensional outer stellar mass (measured in elliptical annuli) can match the performance of three-dimensional ellipsoidal-shell stellar mass as a halo mass proxy. The authors first characterize the shapes of massive central galaxies and the spatial distribution of ex-situ stars, then fit the scatter of the stellar-to-halo mass relation for many 2D and 3D selections, and finally compare stacked weak lensing profiles of samples selected by 2D and 3D outer stellar mass. Their central claims are that the 2D [50,100] kpc annulus selection has SHMR scatter comparable to, and sometimes marginally better than, the corresponding 3D [79,158] kpc ellipsoidal shell, and that the lensing profiles of the 2D- and 3D-selected samples are nearly identical, implying that the 2D selection does not introduce a projection bias.

Significance. If the main claims hold, the results support the use of outer stellar mass as a practical cluster selection tool in wide-field surveys, where only projected stellar light is available. The paper's strengths are its direct comparison of 2D and 3D definitions within a state-of-the-art cosmological simulation, its use of realistic isophote fitting, and its lensing test with bootstrap errors. It also provides a physically motivated explanation for why the 2D selection works well: it excludes the galaxy core and preferentially includes particles along the major axis and at large radii. However, the quantitative mapping between 2D and 3D radii contains a technical error (Eq. 3.7), and the headline comparison of SHMR scatters is presented without uncertainties, so the main quantitative claims need revision before the paper can be accepted.

major comments (3)
  1. [Eq. (3.7) in Section 3.5] The conversion factor A is defined as A = (2/pi) ∫_0^{π/2} cos θ dθ ≈ 0.63, which the text calls the mean projected length of a randomly oriented 3D unit vector. For a vector at angle θ from the line of sight, the projected length onto the sky plane is sin θ, not cos θ, and random orientation on the sphere has probability density (1/2) sin θ. The correct orientation-averaged projected length is ∫_0^π (1/2) sin^2 θ dθ = π/4 ≈ 0.785. The formula in Eq. 3.7 averages cos θ over a uniform θ interval, which is neither the mean projection onto the sky plane nor the mean over a random orientation. Consequently, the mapping l3D = l2D/A overestimates 3D lengths by a factor of about π^2/8 ≈ 1.23, so the 3D counterpart of the 2D [50,100] kpc annulus should be roughly [64,127] kpc, not [79,158] kpc. Because the SHMR scatter decreases monotonically with radius (Fig. 7), all comparisons in Fig. 8 and the lensing comparison in Section 4.4 are made between a 2D selection and a 3D selection that is not its true projected counterpart. The authors should correct the factor, propagate the corrected radii through Figures 8 and 9 and the summary bullet, and verify that the qualitative conclusions persist. This is a load-bearing error in the central quantitative comparison.
  2. [Section 3.3 and Figure 8] The main quantitative claim—that the 2D outer stellar mass selection has SHMR scatter comparable to, or marginally better than, the 3D ellipsoidal shell—is based on point estimates of σ_Mh|M* without any quoted uncertainties. The sample contains about 2700 galaxies, and the differences between the 2D and 3D scatter shown in the highlighted panel of Figure 8 are small (of order 0.01–0.02 dex). Without bootstrap or jackknife errors, the reader cannot tell whether the 'marginally better' statement is statistically significant or consistent with being equal. The authors should provide uncertainties on the fitted scatter values for the selections in Figure 8 and state explicitly whether the differences are significant.
  3. [Section 5 (Summary and Conclusions)] The lensing comparison in Section 4.4 is used to argue that 2D selection does not create a bias. However, the comparison uses the 3D [79,158] kpc shell, which, as discussed in the first major comment, is not the correct projected counterpart of the 2D [50,100] kpc annulus. Even after the conversion factor is fixed, the lensing test should be repeated with the corrected 3D shell, or with several 3D shells bracketing the expected projection, to demonstrate that the conclusion is not sensitive to the mapping. In addition, the conclusions in Section 5 should be qualified by the idealized nature of the mock stellar maps (no PSF, no background subtraction, no satellite blends), as the authors themselves note in Section 5; the abstract's statement that 'the 2D selection does not create a bias' should be explicitly scoped to these idealized conditions.
minor comments (4)
  1. [Section 3.5] The phrase 'mean length of a randomly projected 3D unit vector' in Eq. (3.7) is ambiguous: it should state whether the projection is onto the sky plane or along the line of sight, and the averaging should be over the sphere with the correct solid-angle measure.
  2. [Footnotes and cross-references] Footnote 2 on page 12 says the 79 kpc and 159 kpc radii are obtained 'following the conversion in Section 3.2', but the conversion is defined in Section 3.5; the cross-reference should be corrected.
  3. [Figure 4 caption] The caption refers to 'the area covered by the white hatch', but hatching is not described in the printed figure; the authors should either show the hatch in the figure or rephrase the text.
  4. [Section 4.4] The text says 'The shaped regions around the solid lines are the 1 σ uncertainties'; this should read 'shaded regions'.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the 2D-versus-3D comparison is measured from TNG rather than fitted, and the self-citations are methodological or contextual rather than load-bearing.

full rationale

The central derivation chain is self-contained. The SHMR scatter values in Figs. 7-9 are measurements from IllustrisTNG300-1 stellar particles, not parameters fitted to the 2D-versus-3D difference. The length conversion A in Eq. 3.7 is defined as a fixed geometric integral and Eq. 3.8 then chooses the 3D shell radii; A is not calibrated to the SHMR outcomes, so the comparison is an empirical measurement rather than a prediction forced by construction. The lensing test in Sec. 4.4 compares stacked DeltaSigma profiles of independently selected 2D and 3D samples, and the near-equality of the profiles is an output, not an input. The paper does contain self-citations from overlapping author groups: Sec. 3.1 adopts the isophote-fitting methodology of Ref. [47], and the introduction cites Refs. [43,45] for the prior result that outer stellar mass traces halo mass. These are methodological and motivational citations, not uniqueness theorems or unverified premises on which the present derivation depends. The paper also explicitly states its own limitations (single TNG300-1 box, neglect of PSF, background subtraction, and satellite blends), which reduces any concern that a hidden external benchmark is being imported as evidence. A possible issue with the orientation averaging in Eq. 3.7 would be a physical or statistical correctness concern about the chosen mapping, not a circularity problem, because the 2D and 3D stellar masses remain independently measured once the shell radii are fixed.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the fidelity of one hydrodynamical simulation, the merger-tree assignment of stellar origin, the assumed Gaussian SHMR form, and several hand-chosen cuts and radii. No new physical entities are introduced; the 2D-to-3D mapping uses a fixed geometric projection factor rather than a fitted constant. The main free parameters are the SHMR fit parameters and the sample/aperture choices.

free parameters (5)
  • SHMR slope alpha = 0.96 (all), 0.92 (ex-situ), 1.01 (in-situ) in Figure 2
    Free parameter in the Gaussian fit of log halo mass versus log stellar mass; used to characterize each stellar mass definition as a halo mass proxy.
  • SHMR intercept beta = not reported in text
    Second free parameter of the same linear SHMR fit; not central to the conclusions but part of the model.
  • SHMR scatter sigma_Mh|M* = 0.18 (all), 0.19 (ex-situ), 0.24 (in-situ) in Figure 2; grid values in Figures 7 and 8
    The key performance metric; the central claim that 2D and 3D selections have comparable scatter rests on these fitted values.
  • Sample stellar mass threshold = 10^11.2 Msun
    Hand-chosen cut to select massive central galaxies; the completeness cut at M*,peak follows Xu et al. 2024 and affects which galaxies enter the SHMR fit.
  • Outer stellar mass aperture radii = 2D [50,100] kpc, 3D [79,158] kpc
    Chosen following Huang et al. 2021 and the projection factor A=0.63; the paper scans nearby radii, but the headline comparison uses these apertures.
assumptions (6)
  • domain assumption IllustrisTNG300-1 is representative of massive central galaxies and their stellar halos at z=0.4.
    Section 2.1 states the paper uses only TNG300-1 and Section 5 notes it expects conclusions to hold in other simulations.
  • domain assumption In-situ and ex-situ stellar labels from the sublink merger tree are correct.
    Section 2.2 defines ex-situ via the main progenitor branch; the ex-situ fraction trends are central to the interpretation.
  • domain assumption Halo mass is the Friends-of-Friends group mass.
    Section 2.1 defines the halo mass used in all SHMR fits.
  • domain assumption The conditional distribution of halo mass at fixed stellar mass is log-normal with constant scatter.
    Equation 3.3 adopts a Gaussian model; the scatter comparison is meaningful only if this model is adequate.
  • ad hoc to paper Projected stellar maps without PSF, background subtraction, or satellite blending are sufficient for comparing intrinsic 2D and 3D selections.
    Section 2.3 explicitly excludes observational effects to isolate intrinsic correlations; this limits the direct applicability to real data.
  • domain assumption Massive galaxies can be approximated as prolate ellipsoids with axis ratios near zero for interpreting the 2D selection.
    Section 4.5 uses the line approximation; the authors show 67% of galaxies are prolate but acknowledge deviations.

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Pith. "Pith review of Relationship between 2D and 3D Galaxy Stellar Mass and Correlations with Halo Mass." pith.science (2026). https://pith.science/paper/QENSK6XA

@misc{pith2026250205158,
  author       = {Pith},
  title        = {Pith review of: Relationship between 2D and 3D Galaxy Stellar Mass and Correlations with Halo Mass},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QENSK6XA}},
  note         = {Machine review of arXiv:2502.05158}
}
read the original abstract

Recent studies suggest that the stars in the outer regions of massive galaxies trace halo mass better than the inner regions and that an annular stellar mass provides a low scatter method of selecting galaxy clusters. However, we can only observe galaxies as projected two-dimensional objects on the sky. In this paper, we use a sample of simulated galaxies to study how well galaxy stellar mass profiles in three dimensions correlate with halo mass, and what effects arise when observationally projecting stellar profiles into two dimensions. We compare 2D and 3D outer stellar mass selections and find that they have similar performance as halo mass proxies and that, surprisingly, a 2D selection sometimes has marginally better performance. We also investigate whether the weak lensing profiles around galaxies selected by 2D outer stellar mass suffer from projection effects. We find that the lensing profiles of samples selected by 2D and 3D definitions are nearly identical, suggesting that the 2D selection does not create a bias. These findings underscore the promise of using outer stellar mass as a tool for identifying galaxy clusters.

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.