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A random forest of six galaxy and halo properties reproduces simulated halo gas density profiles to roughly 83–90% accuracy, and Sobol sensitivity analysis shows the central galaxy's gas mass and total halo mass dominate, while black hole a

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2026-08-03 17:30 UTC pith:UIUVUCU5

load-bearing objection Useful, well-executed proof of concept on the prediction side; the Sobol feature ranking is physically over-interpreted because the sensitivity analysis samples off the manifold real haloes occupy. the 2 major comments →

arxiv 2512.09021 v3 pith:UIUVUCU5 submitted 2025-12-09 astro-ph.GA astro-ph.COastro-ph.IMcs.LG

Interpretable machine learning of halo gas density profiles: a sensitivity analysis of cosmological hydrodynamical simulations

Daniele Sorini , Sownak Bose , Mathilda Denison , Romeel Dav\'e This is my paper
classification astro-ph.GA astro-ph.COastro-ph.IMcs.LG
keywords galaxy formationcircumgalactic mediumgas density profileshydrodynamical simulationsmachine learningrandom forestSobol sensitivity analysisAGN feedback
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 claims that a simple random forest trained on just six halo and galaxy properties — halo mass, central galaxy gas and stellar mass, star formation rate, and black hole mass and accretion rate — can reproduce the spherically averaged gas density profile of a halo as predicted by three different hydrodynamical simulation suites (EAGLE, IllustrisTNG, Simba) to roughly 83–90% accuracy across halo masses 10^9.5–10^15 Msun and redshifts 0–4. The authors then apply Sobol sensitivity analysis, apparently for the first time to full cosmological hydrodynamical simulations, to ask which of those features actually drives the predicted profile at each radius. The answer is consistent across simulations and redshifts: total halo mass and central galaxy gas mass dominate, while stellar mass and black hole properties are secondary and the instantaneous black hole accretion rate is essentially uninformative. The significance of the claim is practical as well as physical: a cheap, interpretable surrogate model could be embedded in semi-analytic galaxy formation models, and the feature rankings offer a route to connect observed gas distributions to specific feedback prescriptions.

Core claim

On the paper's own terms, the central discovery is a two-stage claim. First, a random forest regression trained on the logarithmic (or arcsinh-rescaled) values of six features recovers the simulated radial gas density profile with mean accuracy of roughly 80–90%, with performance best at z≥1 and slightly worse at z=0, and with the largest failures confined to the inner regions of the most massive Simba haloes. Second, the Sobol first-order and total-order indices computed from this surrogate show, in every simulation and at every redshift, that the gas mass of the central galaxy is the single most informative feature, followed by total halo mass, while star formation rate and BH accretion ra

What carries the argument

The argument rests on a random forest ensemble of decision trees (500 trees, depth 32) trained per simulation snapshot, with features and targets rescaled by a modified inverse hyperbolic sine that behaves linearly near zero and logarithmically at large values. Sensitivity is quantified with Sobol indices — first-order and total-order — computed on Saltelli-sequence samples of the six features drawn uniformly over each simulation's feature ranges; a significance threshold is derived from the intrinsic accuracy of the surrogate at each radial bin. The Sobol index of a feature at a given radius measures the fraction of predicted-profile variance attributable to varying that feature, with the d

Load-bearing premise

The Sobol rankings assume the six input features can be treated as independent, uniformly sampled variables over each simulation's range; because the real halo population has tightly correlated galaxy and halo properties, the importance hierarchy could be an artefact of that sampling rather than a physical discovery.

What would settle it

Compute the same Sobol indices after resampling the Saltelli sequence from the empirical joint distribution of the simulation features (or from observed scaling relations), and check whether halo mass and gas mass still dominate; if the ranking changes materially, the paper's physical ranking is an artefact of the independent-uniform sampling.

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

If this is right

  • The trained surrogate can be dropped into semi-analytic galaxy formation models to assign halo gas density profiles from galaxy properties, without rerunning hydrodynamics.
  • The feature rankings give a benchmark for what galaxy observables most tightly correlate with the CGM gas distribution, e.g., gas mass and halo mass rather than instantaneous BH activity.
  • The negligible Sobol index of BH accretion rate suggests that instantaneous AGN activity leaves a weak, volume-averaged imprint inside the virial radius, which can guide where to look for AGN feedback signatures.
  • The same random forest plus Sobol pipeline is transferable to other simulation suites and observables, subject to a minimum box size (~50 cMpc) for converged indices.
  • The accuracy relative to current X-ray profile measurements (~15%) suggests the surrogate is competitive for z≥1 comparisons.

Where Pith is reading between the lines

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

  • Because the Sobol sampling draws features independently and uniformly, the dominant status of gas mass may be inflated by its strong correlation with halo mass; reweighting the Saltelli samples to the joint halo-galaxy distribution (or conditioning on halo mass) would test whether gas mass remains first.
  • The BH accretion rate result may be a timescale and geometry artefact: instantaneous, spherically averaged density washes out short-lived, anisotropic jet/wind events; a time-integrated outflow-energy feature might rank higher.
  • A direct observational test: compare the predicted correlation between Mgas / M200c and the outer slope of the gas density profile against stacked CGM absorption/X-ray surveys; if the correlation is absent in data, the simulation-based ranking is model-dependent.
  • The method could be extended to phase-resolved profiles (cold/warm/hot) where the arcsinh transform was already chosen, and to include cosmology as an input feature using a simulation suite that varies cosmological parameters.

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

2 major / 6 minor

Summary. The paper trains random forest regressors on halo and galaxy properties from the EAGLE, IllustrisTNG, and Simba suites (including Simba feedback variants) to predict spherically averaged gas density profiles within 0.05-1 R200c over redshifts 0<z<4. The input features are M200c, central-galaxy gas mass, stellar mass, SFR, BH mass, and BH accretion rate. The authors report a mean test-set accuracy of about 80-90% depending on simulation and redshift, and then apply Sobol sensitivity analysis to the trained random forests, concluding that M200c and M_gas dominate the predicted gas distribution, while stellar and BH properties and especially BH accretion rate are subdominant. The paper frames this as a proof of concept for embedding simulation-informed gas profiles in semi-analytic models and for future observational constraints.

Significance. If the sensitivity ranking is robust, this would be a valuable contribution: it offers an interpretable, computationally cheap surrogate for gas density profiles across multiple feedback models, and the cross-simulation comparison is a useful way to expose model-dependent differences. The paper's strengths include a clearly defined and held-out test set, an explicit accuracy metric (Eqs. 5-6), a convergence test of the Sobol estimates (N_S = 2^14), and a volume/resolution robustness check in Appendix A. The authors are also transparent that the analysis is correlational, not causal. However, the central physical conclusion - the ranking of feature importance - rests on a Sobol analysis whose sampling distribution is uniform and independent over each feature's marginal range, whereas the actual halo population occupies a strongly correlated, lower-dimensional manifold. This concern is load-bearing: if the ranking is an artefact of out-of-distribution sampling, the headline results are not supported as stated. The paper is therefore promising but needs a major revision to establish the validity of the sensitivity measure.

major comments (2)
  1. [Section 3.2, Section 6.1] The Sobol indices are computed from a Saltelli sequence that samples each feature independently and uniformly over its marginal range. Standard Sobol theory (Eq. 10) requires independent inputs, but the six features are strongly correlated in the simulated halo population (e.g., M_star-M200c, M_BH-M_star). Consequently, most of the 2*N_S*(d+1) evaluation points lie outside the low-dimensional manifold occupied by the training data, and the reported S1 and ST indices measure the random forest's extrapolation behaviour under a uniform product measure rather than the sensitivity of gas profiles within the simulated population. This is not a minor technicality: the Abstract and Section 6.1 draw the paper's headline conclusions (M_gas and M200c dominate; Mdot_BH is negligible) directly from these indices. The caveat in Section 6 about strong correlations addresses causal wording, not the choi
  2. [Section 4, Eqs. (14)-(15)] The significance threshold S_th^(j) is computed using the training-set accuracy, while the paper elsewhere emphasizes the test-set accuracy (Fig. 5). At z=0 and for the Simba runs, the test-set accuracy is several percent lower than the training-set accuracy, so Eq. (15) underestimates the noise floor. Features with Sobol indices only slightly above the threshold could therefore be declared 'physically significant' when their contribution is actually below the model's true predictive error. Using a cross-validated or test-set accuracy in Eq. (14) would place the threshold on firmer ground.
minor comments (6)
  1. [Abstract, Section 4, Section 7] The accuracy numbers are quoted inconsistently: Abstract says 'about 83-90%', Section 4 reports '80-87% at z=0 and 84-90% at z>1', and Section 7 gives '78-87% at z=0 and 82-90% at z>1'. Please harmonize.
  2. [Eq. (1)] The notation in Eq. (1), with an arrow, is confusing; a standard equality would be clearer. Also, 'archsinh' in the text appears to be a typo for 'arcsinh'.
  3. [Section 5.1] The statement that the sum of all Sobol indices equals unity is only true for a proper ANOVA decomposition with independent inputs, which is the very assumption under question. Please add a caveat here, not only in Section 6.
  4. [Section 5.1] The claim that this is the first application of Sobol sensitivity analysis to full cosmological hydrodynamical simulations is somewhat overstated because the analysis is applied to a random forest trained on the simulations, not to the simulations themselves. Please soften the wording.
  5. [Figures 7 and 8] These figures are dense and difficult to parse with six features, four redshifts, and multiple simulations. A summary table or clearer highlighting of the leading features would aid the reader.
  6. [Data Availability] The paper mentions that derived data will be shared on request, but no code is released. Providing the feature-engineering and Sobol pipeline would significantly improve reproducibility.

Circularity Check

0 steps flagged

No significant circularity: the accuracy and sensitivity results are empirical outputs of a trained emulator, not reductions to the paper's own inputs.

full rationale

The paper's derivation chain is not circular at the level required by the rubric. The RF accuracy claim is validated on held-out test sets (20% of haloes) using Eq. (5)-(6), so the reported 80-90% accuracy is an empirical predictive performance measure, not a fitted quantity renamed as a prediction. The Sobol sensitivity analysis is applied to the trained RF, not directly to the simulation data, and the paper explicitly disclaims a causal reading: 'whenever we say that a certain feature has "high importance"... we do not mean that this is necessarily a cause-effect relationship. Rather, the implication is that the galaxy formation model embedded in the specific simulation considered generates strong correlations between the feature in question and the corresponding gas density profile' (Sec. 6). The headline ranking of M_gas and M_200c is therefore a statement about the emulator's response, which may or may not be physically robust, but it is not definitionally forced by the inputs. M_gas is a central-galaxy property, not the target radial profile itself; although it is naturally correlated with the halo gas content, the paper does not define M_gas as the target or set the target equal to a function of M_gas by construction. M_200c sets the radial normalization R_200c, but the gas density profile is not defined by M_200c alone. The possible concern that the Saltelli sequence samples features independently and uniformly, pushing evaluation points outside the correlated training manifold, is a statistical validity issue (relevant to correctness and interpretation), not a circularity: no equation or construction in the paper reduces the Sobol indices to the sampled ranges themselves, and the paper acknowledges limitations and tests robustness of rank ordering in Appendix A. Self-citations (e.g., Sorini et al. 2024b for universal profile fits, Scharré et al. 2024 for Simba correlations) are contextual and not load-bearing for the central derivation. No uniqueness theorem, no ansatz smuggled via citation, and no renaming of a known result as a new prediction are present. The honest finding is therefore no significant circularity, with the sensitivity-interpretation caveat assigned to correctness risk rather than circularity.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The key free choices are the RF hyperparameters, the uniform Saltelli sampling distribution, and the halo-resolution cut. The most consequential assumptions are that Sobol indices on a surrogate with independent uniform sampling reflect the physical drivers of gas profiles in the actual halo population, and that the feature set does not leak the target into the predictors. The paper states many of these choices explicitly but does not fully test their impact on the headline ranking.

free parameters (4)
  • RF hyperparameters (min_samples_leaf=2, max_depth=32, n_estimators=500) = 2, 32, 500
    Chosen by maximizing training-set accuracy across the stated ranges (§3.3.3); no held-out validation for hyperparameter selection. All predictions and Sobol indices depend on this choice.
  • Saltelli sampling boundaries for each input feature = min/max of each feature in each simulation dataset
    The Sobol indices are computed by sampling uniformly over these ranges (§5.2). The resulting rankings reflect sensitivity over the full range, not over the actual distribution of haloes in the simulation.
  • Well-resolved halo criterion = ≥5000 FoF resolution elements
    This cut defines which haloes enter the training/test sets (§3.1). The Appendix itself shows that changing resolution/volume changes the magnitude of Sobol indices for EAGLE and Simba.
  • Arcsinh rescaling constant X0 = 1 Msun, 1 Msun/yr, or critical density
    Hand-chosen unit scales in Eq. (1) to make the arcsinh argument dimensionless; asymptotically the transformation is a log, so the specific value has minor effect.
axioms (5)
  • domain assumption The simulation snapshots and halo/galaxy catalogues are treated as ground truth for gas density profiles and galaxy properties.
    The entire model is trained on EAGLE/IllustrisTNG/Simba outputs; no independent observational or analytic validation is attempted. Invoked throughout §2-§3.
  • domain assumption Sobol indices computed on a random forest surrogate meaningfully represent how input features drive the gas density profile.
    The random forest is an approximation of the simulation mapping; Sobol analysis is applied to the surrogate, not to the simulation itself (§5). Any RF approximation error propagates into the indices.
  • ad hoc to paper Input features are treated as independent in the Sobol decomposition even though they are correlated in the data.
    The Saltelli sequence draws each feature independently (§5.2). Standard Sobol indices require independent inputs; the paper notes correlations (e.g., M_BH-M_star) and interprets differences between first-order and total-order indices as interactions, but does not correct for dependence.
  • ad hoc to paper Uniform sampling over the full feature range is an appropriate distribution p(X) for the sensitivity analysis.
    Section 5.2 chooses Saltelli uniform sampling over boundaries defined by each simulation. This is not the actual joint distribution of haloes, so the resulting 'importance' is not the importance for the halo population.
  • standard math The convergence radius criterion of Power et al. (2003) places the numerically robust radial range at 0.05 R_200c.
    Used in §3.3 to restrict predictions to 0.05 < r/R_200c < 1.

pith-pipeline@v1.3.0-alltime-deepseek · 35479 in / 10287 out tokens · 105321 ms · 2026-08-03T17:30:37.947281+00:00 · methodology

0 comments
read the original abstract

Stellar and AGN-driven feedback processes affect the distribution of gas on a wide range of scales, from within galaxies well into the intergalactic medium. Yet, it remains unclear how feedback, through its connection to key galaxy properties, shapes the radial gas density profile in the host halo. We tackle this question using suites of the EAGLE, IllustrisTNG, and Simba cosmological hydrodynamical simulations, which span a variety of feedback models. We develop a random forest algorithm that predicts the radial gas density profile within haloes from the total halo mass and five global properties of the central galaxy: gas and stellar mass; star formation rate; mass and accretion rate of the central black hole (BH). The algorithm reproduces the simulated gas density profiles with an average accuracy of $\sim$83-90% over the halo mass range $10^{9.5} \, \mathrm{M}_{\odot} < M_{\rm 200c} < 10^{15} \, \mathrm{M}_{\odot}$ and redshift interval $0<z<4$. For the first time, we apply Sobol statistical sensitivity analysis to full cosmological hydrodynamical simulations, quantifying how each feature affects the gas density as a function of distance from the halo centre. Across all simulations and redshifts, the total halo mass and the gas mass of the central galaxy are the most strongly tied to the halo gas distribution, while stellar and BH properties are generally less informative. The exact relative importance of the different features depends on the feedback scenario and redshift. Our framework can be readily embedded in semi-analytic models of galaxy formation to incorporate halo gas density profiles consistent with different hydrodynamical simulations. Our work also provides a proof of concept for constraining feedback models with future observations of galaxy properties and of the surrounding gas distribution.

Figures

Figures reproduced from arXiv: 2512.09021 by Daniele Sorini, Mathilda Denison, Romeel Dav\'e, Sownak Bose.

Figure 1
Figure 1. Figure 1: — Spherically averaged radial profiles of the total gas density around haloes in the test sets extracted from the EAGLE-100, IllustrisTNG, and Simba-100 simulations (top, middle, and bottom panels, respectively) at redshift 𝑧 = 0. The solid lines show the mean gas density profile of haloes in the 𝑀200c bin indicated on top of every panel. The corresponding number of haloes is reported in the upper-right co… view at source ↗
Figure 2
Figure 2. Figure 2: — Modified inverse hyperbolic sine function (solid line) as defined in equation (1), which we applied to a subset of the input features (𝑀¤ ★, 𝑀¤ BH, 𝑀BH) to improve the performance of the RF algorithm (see § 3.2 for details). For masses above ∼ 7 M⊙ (or accretion rates above ∼ 7 M⊙ yr−1 ), the function asymptotes to the decimal logarithm. As the property in question approaches zero, the function is well a… view at source ↗
Figure 3
Figure 3. Figure 3: — Spherically averaged comoving radial profiles of the total gas density around haloes in the test set extracted from IllustrisTNG simulations at redshift 𝑧 = 0. Each panel refers to the gas density profiles of haloes within the 𝑀200c bin indicated in the top of the column, hosting a central galaxy with total gas mass in the range annotated within the panel itself. The number of haloes falling within the 2… view at source ↗
Figure 4
Figure 4. Figure 4: — Average accuracy of the RF algorithm, as defined in § 4, at reproducing the gas density profiles in the test sets of the EAGLE-100, IllustrisTNG, and Simba-100 simulations at redshift 𝑧 = 0, as a function of the radial distance from the centre of the halo. The error bars indicate the 16th − 84th percentile spread of the accuracy within each 2D-bin of 𝑀200c and 𝑀gas, the bounds of which are indicated in t… view at source ↗
Figure 5
Figure 5. Figure 5: — Overall accuracy of the RF algorithm at reproducing the gas density profiles in all simulations considered, averaged over all radial bins and all haloes, as a function of redshift (see § 4 for details). The left panel shows the results for the training set: the accuracy is above 92% for all simulations, highlighting the self-consistency of the algorithm. The right panel shows the results for the test set… view at source ↗
Figure 6
Figure 6. Figure 6: — Sampling of the parameter space of the input features obtained from generating a Saltelli sequence (Saltelli et al. 2010) This technique, combined with the modified inverse hyperbolic sine function applied to certain features (𝑀¤ ★, 𝑀¤ BH, 𝑀BH; see § 3.2 and [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: — Results of the Sobol sensitivity analysis applied to our RF algorithm. Each row of panels refers to a different flagship simulation, as indicated in the left part of the figure. Every column corresponds to a different redshift, as reported in the top of the figure. Within each panel, the data points represent the 𝑆1 Sobol coefficients representing the importance of a certain input feature in predicting t… view at source ↗
Figure 8
Figure 8. Figure 8: — Results of the Sobol sensitivity analysis for the variants of the Simba simulation. Every row of panels corresponds to a different input feature, as indicated in the left part of the figure. Each column of panels is associated with a different redshift, as reported in the top part of the figure. The data points and solid lines represent the 𝑆1 and 𝑆T Sobol coefficients, as a function of the radial distan… view at source ↗
Figure 9
Figure 9. Figure 9: — [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗

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