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REVIEW 5 major objections 6 minor 35 references

Where are all the dark galaxies? Predicting galaxy/halo locations from their bright neighbors

T0 review · 5 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper shows that dark galaxies and dark matter halos can be located from the distances to their two nearest bright neighbors.

desk verdict Interesting empirical fit to dark-object density from bright-neighbor distances, but the predictive claim is undermined by in-sample evaluation and an undefined baseline. read the letter →

arxiv 2507.01814 v1 pith:HHVPU2CB submitted 2025-07-02 astro-ph.CO astro-ph.GA

Alice Chen , Niayesh Afshordi This is my paper
classification astro-ph.COastro-ph.GA
keywords darkgalaxiesmatterhalossymbolicregressionnearestneighborstatisticsgalaxyclusteringhalobiasIllustris-TNGPoissonlikelihood
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 aims to establish that the probability of finding an otherwise-invisible astronomical object—a faint dwarf galaxy or a dark matter halo—is well described by an analytic function of just three distances: the distances from that object to its two closest bright (directly visible) neighbors, and the distance between those two neighbors. The authors fit this function with symbolic regression on the Illustris-TNG cosmological simulations, using a Poisson likelihood loss, and find a single functional form, Eq. (15), with parameters that differ for halo-halo, halo-galaxy, and galaxy-galaxy pairs. A sympathetic reader would care because the result offers a route to target searches: if the formula survives contact with real surveys, telescopes and gravitational-wave follow-up campaigns could point where dark objects are most likely to sit, instead of scanning blindly. The paper reports that this nearest-neighbor predictor substantially outperforms the standard linear scale-dependent halo bias at wavenumber $k \sim 1\,h\,\mathrm{Mpc}^{-1}$, the scale relevant to galaxy-sized structure.

What carries the argument

The load-bearing object is the conditional probability density $p(r_1,r_2,r_{12})$, defined in Eq. (3), where $r_1$ and $r_2$ are the distances from a candidate dark object to its first and second nearest bright neighbors and $r_{12}$ is the separation between those two neighbors. The paper models this density with symbolic regression—a machine learning method that searches over closed-form expressions—using a Poisson maximum-likelihood loss (Eq. 12) and a Poisson Information Criterion to select a parsimonious formula. The selected formula, Eq. (15), is the paper's central identity: it expresses the dark-object density as an exponential of a ratio built from the three distances, with mass-dependent dimensionless parameters.

What would settle it

Estimate the same p(r1,r2,r12) from an independent simulation with different resolution or from a complete observational galaxy sample with known completeness, and compare the dark-object density predicted by Eq. (15) with the measured one; if the residuals correlate significantly with large-scale density or tidal shear, the assumption that nearest-neighbor distances suffice is falsified.

Watch

Extended reading notes

Core claim

The central claim is that the conditional probability density $p(r_1,r_2,r_{12})$ of a dark object given its two closest bright neighbors is captured by Eq. (15), an exponential function of the rescaled dimensionless distances $\tilde{r}=r\,\bar{n}^{1/3}$: $p=\exp\!\left(\frac{1}{a\tilde{r}_2+b}\left(\frac{c}{2\tilde{r}_2+\tilde{r}_{12}}\right)^{d\tilde{r}_1}+e\right)$, with fitted constants $a,b,c,d,e$ given in Table I for each tracer combination. The same expression, with different parameters, fits the simulated density of dark halos around bright halos, faint galaxies around bright galaxies, and halos around bright galaxies. The paper interprets this as evidence that local gravitational clustering encodes the information needed to locate dark, faint, or otherwise undetectable objects, and shows that maps reconstructed this way correlate with the true dark-object map more strongly than the linear bias prediction at small scales.

Load-bearing premise

The model assumes that once the two distances to the nearest bright neighbors and the distance between them are fixed, the probability of a dark object is fully determined; if other environmental variables (large-scale density, tidal shear, or formation history) also matter, the fitted formula will not generalize to other simulations or to the real sky.

Editorial extensions

If this is right

  • Telescope surveys can be pointed at predicted high-probability regions around bright galaxies, increasing the chance of detecting faint dwarf and satellite galaxies.
  • Dark sirens—compact-object mergers without electromagnetic counterparts—can be localized better by weighting their sky positions with the predicted halo map, which the paper suggests could sharpen Hubble-constant measurements.
  • The same bright-galaxy sample can be used to infer host halo centers, which then predicts where other halos sit, informing weak-lensing searches for dark structure.
  • The formula's parameters are specific to tracer type but its form is stable across Illustris-2 and TNG-100, so it may serve as an empirical, simulation-calibrated replacement for scale-dependent bias at quasi-linear scales.
  • Future work could extend the k=2 nearest-neighbor statistic to higher k, potentially capturing even more environmental information.

Reading between the lines

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

  • Editorial inference: if Eq. (15) holds for real surveys, it would provide a testable, non-parametric check on ΛCDM structure formation, since the fitted parameters could be compared between simulation and observation without assuming a halo model.
  • Editorial inference: because the paper never tests whether adding large-scale density or tidal anisotropy improves the fit, a natural extension is to feed those features to the same regression and see whether the nearest-neighbor variables remain sufficient; this would identify what environmental information is truly encoded.
  • Editorial inference: the approach may extend beyond galaxies and halos to any tracers of the same underlying density field, such as X-ray clusters, quasars, or cosmic voids, as long as a 'bright' reference population and a 'dark' target population share clustering physics.
  • Editorial inference: the k=2 limitation is imposed by the simplicity of the chosen geometry; allowing k>2 neighbors, or including neighbor luminosities, could break degeneracies in Eq. (15) and might be required when applying the formula to observational data with incompleteness.
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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

5 major / 6 minor

Summary. The paper uses the PySR symbolic regression package on Illustris-TNG simulations to fit an analytic expression, Eq. (15), for the probability density of finding a 'dark' object (halo or faint galaxy) as a function of the distances to its two nearest 'bright' neighbors and the separation between those neighbors. The authors report that this expression predicts the dark-object number-density map significantly better than a 'linear scale-dependent biasing prediction' at k ~ 1 h/Mpc, and they demonstrate the same functional form across halo-halo, galaxy-galaxy, and halo-galaxy cases, including a cross-check with TNG-100.

Significance. If the predictive claim were properly validated, the paper would provide an interpretable, low-cost mapping from bright galaxy catalogues to dark-matter and faint-galaxy density fields, with potential applications to missing-satellite searches, dark-siren localization, and weak-lensing mass maps. The use of symbolic regression to produce a closed-form expression is a genuine strength: it is human-readable, reproducible, and may transfer across simulations. However, the present evidence does not yet support the core claim of predictive superiority over the stated baseline.

major comments (5)
  1. [Section III, Fig. 9] The correlation coefficients in Fig. 9 are computed on the same Illustris-2 volume used to fit the parameters a, b, c, d, e of Eq. (15) in Table I. This is an in-sample measure of goodness of fit, not a predictive test. The abstract's claim that Eq. (15) can 'predict' dark-object density is therefore not supported by this figure. The authors should provide a train/test split (e.g., fit on one half of the box and test on the other half, or use cross-validation) and report the test-set correlations.
  2. [Fig. 9 and abstract] The baseline labeled 'linear' in Figs. 9, 11, and 12 is never defined in the text. The abstract calls it a 'linear scale-dependent biasing prediction', but the caption of Fig. 9 refers to 'bright/visible object raw number counts'. No equation, bias parameter, or power-spectrum construction is given. The comparison is not meaningful unless the baseline is specified precisely (for instance, a linear bias model b(k) times the bright-galaxy overdensity, or a linear regression of dark counts on bright counts) and the correlation coefficients are computed for that model.
  3. [Section III, Fig. 11 and Table II] The TNG-100 check is presented as independent support, but Table II shows that all five parameters are refitted on TNG-100. This tests only whether the functional form of Eq. (15) is flexible enough to fit a second simulation; it does not test the predictive power of the parameters derived from Illustris-2. A more informative test would be to apply the Illustris-2 parameters to TNG-100 without refitting, or to fit on TNG-100 and test on Illustris-2, and report the resulting correlations.
  4. [Fig. 9, Fig. 10, Fig. 12] The correlation coefficients in Figs. 9 and 11 have no error bars, and the significance of the difference between the PySR model and the linear baseline is not quantified. Since Fig. 12 shows that the results depend strongly on voxel size, bootstrap or jackknife uncertainties over the 3D density field should be provided before claiming 'significantly better' performance.
  5. [Section II.A, Eq. (3)] The model assumes that the conditional probability density of a dark object is fully determined by (r1, r2, r12). This assumption is stated but never tested against alternative environmental variables such as large-scale density, tidal anisotropy, or assembly history. The random-forest importance test in Fig. 5 compares the three distances only to random numbers, not to other physical covariates, so it does not validate the completeness of the chosen descriptor set. If the fitted expression is intended as a predictive tool for real surveys, this missing test weakens the claim of generality.
minor comments (6)
  1. [Eq. (12)] In Eq. (12), the softening parameter epsilon appears inside the logarithm, so it has a small numerical effect even though the authors state it 'has no effect'; please rephrase to 'negligible effect'.
  2. [Section II.A] The text says the number of halos in each distance bin is divided by the total number of halos 'to obtain the probability.' Eq. (3) defines a probability density. Please clarify the normalization (per bin width in r1, r2, r12) and state whether the plotted quantities are densities or probabilities.
  3. [Table I] The fitted parameters in Table I are given without uncertainties. Given the small number of bins and the Poisson noise, reporting uncertainties would help the reader assess the stability of the fit.
  4. [Fig. 10] The Heaviside threshold applied to the predicted number densities (≤1 object per voxel) is not described in the Methods. Its effect on the correlation coefficients in Fig. 9 should be documented or justified.
  5. [Figs. 9 and 11] The baseline is called 'linear' in Fig. 9 and 'linear theory' in Fig. 11; please use consistent terminology and explicitly define the model in both captions.
  6. [Section III, text before Fig. 6] The sentence 'We use the subhalo galaxies as our training set and host halos as our testing set' is unclear, since the subsequent figures show halo-halo and galaxy-galaxy fits without an explicit train/test split; please clarify the intended meaning.

Circularity Check

1 steps flagged · score 6.0 of 10

The headline 'prediction' is an in-sample fit: Eq. 15 is trained on the same Illustris-2 dark-object counts used to compute the Fig. 9 correlations, so the claimed improvement is not an out-of-sample test.

  1. fitted input called prediction [Section III, Eq. 15 and Fig. 9; fitting set up in Section II.C, Eq. 12]
    "To calculate the probability of finding a halo or galaxy object in a certain volume element, we model simulation data points by using symbolic regression and the Poisson error function in Eq. 12 as the loss function to be minimized. ... The correlation coefficients between the true 3D dark halo/galaxy map and our machine learning model based on 3D bright objects."

    The five parameters of Eq. 15 are fit to Illustris-2 dark-object counts (Section II.C maximizes the Poisson likelihood against per-voxel counts; Table I obtains a-e with curve_fit), and Fig. 9 then correlates the resulting dark-object map with those same true dark-object counts from the same simulation volume. No held-out split separating the fitted dark-object counts from the correlated counts is described for the Illustris-2 curves. The 'prediction' of dark-object density is therefore the fitted density of the training data; its correlation coefficient is an in-sample goodness-of-fit measure, not a predictive test. The abstract's 'significantly better' claim compares this in-sample fit to a raw bright-count map, so the advertised predictive improvement reduces to the fit by construction.

full rationale

The derivation of Eq. 15 is an ordinary symbolic-regression fit: PySR minimizes the Poisson loss (Eq. 12) against Illustris-2 voxel counts and Table I parameters are found by curve_fit. The paper calls this a prediction, but the Fig. 9 correlations use the same Illustris-2 data used for the fit, so the central quantitative claim is a training-set correlation rather than an out-of-sample prediction. The TNG-100 appendix provides some independent grounding, but it refits the five parameters on TNG-100 before evaluating, so it validates the functional form's robustness rather than the predictive power of fixed Table I parameters. A separate correctness issue, not itself circularity: the 'linear' baseline in Fig. 9 is the raw bright-object number-count map, not the 'linear scale-dependent biasing prediction' invoked in the abstract. No load-bearing self-citation or imported uniqueness theorem is present. Because the main claim partially reduces to an in-sample fit, score 6.

Assumptions & free parameters 8 free parameters · 4 assumptions · 0 invented entities

The model uses five fitted coefficients plus hand-chosen thresholds and voxel sizes. No new physical entities are introduced. The main assumption is that nearest-neighbor distances are sufficient statistics for dark object density, which is not independently validated.

free parameters (8)
  • a = 0.28 (halo-galaxy), 10.0 (halo-halo), 180 (galaxy-galaxy)
    Coefficient in Eq. 15, fitted to simulation counts via curve fitting; part of the dimensionless parameter set.
  • b = 0.057 (halo-galaxy), 28.0 (halo-halo), 210 (galaxy-galaxy)
    Coefficient in Eq. 15, fitted to simulation counts.
  • c = 0.1 (halo-galaxy), 0.5 (halo-halo), 1.0 (galaxy-galaxy)
    Coefficient in Eq. 15, fitted to simulation counts.
  • d = 0.1 (halo-galaxy), 2.7 (halo-halo), 8.0 (galaxy-galaxy)
    Coefficient in Eq. 15, fitted to simulation counts.
  • e = 0.01 (halo-galaxy), 1.7 (halo-halo), 0.7 (galaxy-galaxy)
    Coefficient in Eq. 15, fitted to simulation counts.
  • Bright/dark mass thresholds = halo bright >= 1e12 Msun; galaxy bright >= 1e10 Msun; galaxy dark 2e9 to 1e10 Msun
    Hand-chosen classification criteria that define the samples; changing them changes the fitted function and results.
  • Voxel size = 3 Mpc/h (default; 1 to 5 Mpc/h tested)
    Used for correlation coefficient comparison in Fig. 9-12; Fig. 12 shows results depend on voxel size.
  • Heaviside density threshold = Predictions <= 1 object per voxel set to zero
    Ad hoc post-processing threshold applied to predicted densities in Section III.
assumptions (4)
  • domain assumption Illustris-TNG simulations faithfully represent the spatial distribution of dark matter halos and galaxies in the real universe.
    The entire analysis is based on simulation output; if the simulations are inaccurate, the fitted relation will not transfer to observations.
  • domain assumption The probability density of dark objects depends only on r1, r2, and r12 (the nearest two bright neighbors and their separation).
    Section II.A defines the modeling target as p(r1,r2,r12); this sufficiency assumption is never tested against other environmental features.
  • domain assumption One-to-one baryon mass-luminosity dependence for galaxies and an unknown mass-luminosity dependence for halos.
    Stated in the Discussion; necessary to connect simulation masses to observable luminosities.
  • standard math Poisson statistics for counts in voxels and Bayes theorem for the null distribution.
    Used to derive the null distribution in Eq. 4 and the loss function in Eq. 11.

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Cite this review

Pith. "Pith review of Where are all the dark galaxies? Predicting galaxy/halo locations from their bright neighbors." pith.science (2026). https://pith.science/paper/HHVPU2CB

@misc{pith2026250701814,
  author       = {Pith},
  title        = {Pith review of: Where are all the dark galaxies? Predicting galaxy/halo locations from their bright neighbors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HHVPU2CB}},
  note         = {Machine review of arXiv:2507.01814}
}
abstract

Astronomical objects in our universe that are too faint to be directly detectable exist and are important - an obvious example being dark matter. The same can also apply to very faint baryonic objects, such as low luminosity dwarf galaxies and gravitationally compact objects (e.g., rogue planets, white dwarfs, neutron stars, black holes, dark sirens). While they are very difficult to observe directly, they have locations that are highly important when studying astrophysical phenomena. Here, we use a machine learning algorithm known as symbolic regression to model the probability of a dark object's existence as a function of their separation distances to their closest two ``bright" (directly observable) neighbors, and the distances of these bright objects to each other. An advantage of this algorithm is that it is interpretable by humans and can be used to make reproducible predictions. Galaxies with masses above $10^9 M_{\odot}$ and halos above $10^{12} M_{\odot} $ are the objects that we separate into ``bright" and ``dark" to be used in our analysis. We find that it is possible to predict the density of dark objects using an analytic expression that depends on their distances to their closest bright neighbors in Illustris-TNG galaxy formation simulations, which is significantly better than the (linear) scale-dependent biasing prediction for $k \sim 1.0~ h$Mpc$^{-1}$ (and potentially beyond, if allowed by the resolution). This could potentially open the avenue for finding dark objects based on their vicinity to directly observable bright sources and make future surveys more targeted and efficient.

Figures

Figures reproduced from arXiv: 2507.01814 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
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Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
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Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]

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    2024

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.