Feedback driven interactions between dark and luminous matter to explain tight galaxy scaling relations
Pith reviewed 2026-05-20 15:48 UTC · model grok-4.3
The pith
Stellar feedback in standard simulations naturally produces the tight observed link between galaxy disk sizes and dark matter halo radii.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Hydrodynamical simulations that include only gravitational interactions and stellar feedback reproduce both the normalization and small scatter of the observed relation between stellar disk scale length Rd and dark matter scale radius r0 at the present day. Galaxies follow three evolutionary paths but preferentially move along the relation while their stellar and dark components rebalance, resulting in mild changes to normalization and slope from redshift 2 to 0. Direct comparison to dark-matter-only runs isolates the role of baryons in reshaping the central potential.
What carries the argument
The Rd-r0 scaling relation, whose evolution is isolated by comparing full hydrodynamical runs to their dark-matter-only counterparts to reveal the structural impact of stellar feedback.
If this is right
- Galaxies evolve along the relation as stellar and dark matter scales adjust together over time.
- The relation's normalization decreases mildly and its slope flattens slightly from z=2 to z=0.
- Stellar feedback is sufficient to establish the observed coupling without additional dark-sector physics.
- Three distinct evolutionary classes appear: disk expansion, contraction, and quasi-static evolution.
Where Pith is reading between the lines
- Similar feedback-driven adjustments may underlie other tight galaxy scaling relations such as the Tully-Fisher or size-luminosity correlations.
- High-redshift surveys could test whether the relation's scatter decreases toward lower redshift as predicted.
- If the mechanism holds, models of galaxy formation can rely on standard feedback prescriptions rather than invoking direct dark matter-baryon couplings.
Load-bearing premise
The specific feedback implementation and numerical resolution used in the simulations correctly capture the dominant processes that set the relation between stellar disks and dark matter halos in real galaxies.
What would settle it
Precise measurements of the Rd-r0 relation at redshift 2 that show a normalization offset larger than 0.1 dex or a slope outside 0.8-1.2 would contradict the predicted mild evolution.
Figures
read the original abstract
The tight empirical correlation linking the stellar disk scale length $R_d$ to the dark matter scale radius $r_0$ has been proposed as possible evidence for a fundamental coupling between baryons and dark matter beyond gravity. We re-examine the physical origin of this relation using a sample of 31 galaxies from the NIHAO cosmological hydrodynamical simulations, which include no dark matter-baryon interactions beyond gravity and baryonic feedback processes. NIHAO naturally reproduces both the normalization and the small scatter of the observed $R_d-r_0$ relation at $z=0$, while yielding a slightly shallower slope. By tracking galaxies from $z=2$ to $z=0$, we identify three distinct evolutionary classes: systems undergoing disk expansion, contraction, and quasi-static evolution. Using a Bayesian hierarchical framework, we provide the first characterization of the cosmic evolution of the $R_d-r_0$ relation, tracing the evolution of its normalization, slope, and intrinsic scatter from $z=2$ to the present day. We find a mild decrease in normalization ($\sim0.07$ dex), a flattening of the slope from $\alpha \simeq 1.05$ to $\alpha \simeq 0.95$, and a weak decline in the intrinsic scatter toward lower redshift, suggesting that galaxies evolve preferentially along the relation while jointly re-balancing their stellar and dark matter scales. By comparing hydrodynamical simulations with their dark-matter-only counterparts, we isolate the impact of baryons and baryonic feedback on halo structure. Our results show that stellar feedback alone can reshape the central potential and naturally establish the observed coupling between luminous and dark matter, without requiring modifications to the dark sector.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript uses a sample of 31 galaxies from the NIHAO cosmological hydrodynamical simulations (no dark matter-baryon interactions beyond gravity) to argue that stellar feedback alone reshapes the central potential and reproduces the observed tight Rd-r0 scaling relation at z=0, including normalization and small scatter (with a slightly shallower slope). By tracking galaxies from z=2 to z=0, the authors identify three evolutionary classes and employ a Bayesian hierarchical framework to characterize the mild redshift evolution of normalization, slope, and scatter, concluding that galaxies evolve preferentially along the relation and that no modifications to the dark sector are required.
Significance. If robust, the result would be significant for galaxy formation studies: it supplies a concrete baryonic mechanism for the Rd-r0 coupling via feedback-driven potential reshaping, supported by forward simulation rather than post-hoc fitting and by direct hydro versus DM-only contrasts. The evolutionary tracking and first characterization of the relation's cosmic evolution add value, as does the isolation of baryonic effects on halo structure.
major comments (3)
- [Methods] Methods section: NIHAO feedback efficiencies were previously tuned to reproduce the stellar mass function and other z=0 properties. Without resolution convergence tests or explicit variations in feedback strength, it remains possible that the reproduction of the Rd-r0 normalization, slope, and scatter is a consequence of this calibration rather than a generic outcome of stellar feedback. This directly affects the central claim that the coupling arises naturally without dark-sector modifications.
- [Results] Results (hydro vs. DM-only comparison): The manuscript states that hydro runs reproduce the relation while matched DM-only runs do not, but does not quantify the changes in central potential or density profile (e.g., via explicit profiles or potential depth metrics) that would demonstrate how feedback sets r0 to track Rd. This step is load-bearing for isolating the baryonic mechanism.
- [Evolutionary analysis] Evolutionary analysis (§ on tracking from z=2 to z=0): The Bayesian hierarchical fit reports a mild normalization decrease (~0.07 dex), slope flattening from α ≃ 1.05 to α ≃ 0.95, and weak scatter decline. The priors, likelihood construction, and robustness to sample selection within the 31-galaxy suite should be shown explicitly, as the evolutionary classes (expansion, contraction, quasi-static) rely on internal tracking that could be sensitive to the specific sub-grid implementation.
minor comments (2)
- [Abstract] Abstract and main text: The slope parameter α is introduced without an explicit equation (e.g., whether log Rd = α log r0 + const); adding this definition would improve clarity for readers.
- [Figures] Figures: Captions for the Rd-r0 plots should explicitly reference the observational sample used for comparison and indicate which points correspond to the three evolutionary classes.
Simulated Author's Rebuttal
We thank the referee for their constructive and detailed comments, which have helped clarify several aspects of our analysis. We address each major comment point by point below. Revisions have been made to improve methodological transparency, add quantitative comparisons, and expand the evolutionary analysis where feasible. These changes strengthen the manuscript without altering its core conclusions regarding stellar feedback's role in the Rd-r0 relation.
read point-by-point responses
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Referee: [Methods] Methods section: NIHAO feedback efficiencies were previously tuned to reproduce the stellar mass function and other z=0 properties. Without resolution convergence tests or explicit variations in feedback strength, it remains possible that the reproduction of the Rd-r0 normalization, slope, and scatter is a consequence of this calibration rather than a generic outcome of stellar feedback. This directly affects the central claim that the coupling arises naturally without dark-sector modifications.
Authors: We acknowledge that the NIHAO feedback parameters were calibrated to match the stellar mass function and other z=0 global properties, as detailed in the original NIHAO papers. However, the Rd-r0 relation was not a target of this calibration and emerges as an independent prediction. In the revised manuscript, we have added a dedicated paragraph in the Methods section emphasizing this distinction and noting that the relation holds across the diverse galaxy sample. We also reference prior NIHAO studies that performed resolution convergence tests for structural properties. While we cannot introduce new feedback variations or resolution tests in this work, the reproduction of the observed normalization and scatter with the standard setup supports our conclusion that stellar feedback can establish the coupling without dark-sector modifications. revision: partial
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Referee: [Results] Results (hydro vs. DM-only comparison): The manuscript states that hydro runs reproduce the relation while matched DM-only runs do not, but does not quantify the changes in central potential or density profile (e.g., via explicit profiles or potential depth metrics) that would demonstrate how feedback sets r0 to track Rd. This step is load-bearing for isolating the baryonic mechanism.
Authors: We agree that explicit quantification of the central potential and density profile changes would strengthen the isolation of the baryonic mechanism. In the revised Results section, we now include direct comparisons of dark matter density profiles for matched hydrodynamical and DM-only runs at z=0. We additionally report metrics such as the central potential depth (evaluated at 0.1 r_vir) and show that feedback induces a shallower inner density slope, enabling r0 to adjust in tandem with Rd. These additions demonstrate how stellar feedback reshapes the halo to produce the observed coupling. revision: yes
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Referee: [Evolutionary analysis] Evolutionary analysis (§ on tracking from z=2 to z=0): The Bayesian hierarchical fit reports a mild normalization decrease (~0.07 dex), slope flattening from α ≃ 1.05 to α ≃ 0.95, and weak scatter decline. The priors, likelihood construction, and robustness to sample selection within the 31-galaxy suite should be shown explicitly, as the evolutionary classes (expansion, contraction, quasi-static) rely on internal tracking that could be sensitive to the specific sub-grid implementation.
Authors: We have expanded the Evolutionary analysis section to explicitly document the Bayesian hierarchical model. This includes the priors (wide normal distributions for normalization and slope, half-normal for intrinsic scatter), the likelihood formulation (linear relation with redshift-dependent parameters and Gaussian scatter), and robustness checks via jackknife resampling of the 31-galaxy sample, which yields consistent evolutionary trends. The three evolutionary classes are now defined quantitatively based on the sign and magnitude of ΔRd and Δr0 from z=2 to z=0, with a supplementary table listing classifications for each galaxy. While some sensitivity to sub-grid physics is inherent to any simulation suite, our results are presented as specific to the NIHAO model. revision: yes
- New simulations with explicit variations in feedback strength or additional resolution convergence tests tailored to the Rd-r0 relation cannot be performed within the scope of this revision, as they would require rerunning the full NIHAO suite.
Circularity Check
No circularity: forward simulations compared to external observations
full rationale
The paper performs forward cosmological hydrodynamical simulations in the NIHAO suite, evolves galaxies from z=2 to z=0, and directly compares the resulting Rd-r0 distribution to independent observational data. The central claim that stellar feedback reshapes the central potential is supported by the difference between hydro runs and matched DM-only runs, plus the match to external galaxy scaling relations. The Bayesian hierarchical fit is applied only to characterize evolution inside the simulated sample and does not redefine or fit the target relation parameters to the same data used to claim success. No step reduces the reported outcome to a fitted input or self-citation by construction.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption NIHAO simulations include standard baryonic feedback processes without additional dark-matter-baryon interactions beyond gravity
Lean theorems connected to this paper
-
IndisputableMonolith/Foundation/RealityFromDistinction.leanreality_from_one_distinction unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
stellar feedback alone can reshape the central potential and naturally establish the observed coupling between luminous and dark matter, without requiring modifications to the dark sector
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Reference graph
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