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MUSE-DARK III: The evolution of the radial acceleration relation at intermediate redshifts

T0 review · 2 major / 2 minor · reviewed 2026-05-08 · grok-4.3

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Pith's one-line read The radial acceleration relation in galaxies shows a higher characteristic scale at higher redshifts.

desk verdict This paper reports a statistically significant rise in the RAR characteristic scale with redshift from MUSE data at 0.3<z<1.4, but the 3D modeling lacks mock validation against possible z-dependent biases. read the letter →

arxiv 2604.22613 v1 pith:DWYW732L submitted 2026-04-24 astro-ph.GA

B. I. Ciocan , N. F. Bouché , J. Fensch , D. Krajnović , J. Freundlich , H. Desmond , B. Famaey , R. Techi This is my paper · ORCID
classification astro-ph.GA
keywords radialaccelerationrelationintermediateredshiftgalaxiesMUSEobservationsdisk-halodecompositiondarkmatterhalosbaryonicevolution
topics Dark Matter
open problems Dark Matter
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 tests whether the tight empirical link between a galaxy's total radial acceleration and its baryonic acceleration, observed locally, also holds billions of years earlier in cosmic history. With MUSE spectroscopy of 79 star-forming galaxies at redshifts between 0.33 and 1.44, the authors use three-dimensional modeling to separate stellar, gas, and dark matter contributions while correcting for pressure support. They recover the same basic relation but find its characteristic acceleration scale is larger than the local value and increases steadily with redshift. If this shift is genuine, the connection between visible matter and the total effective gravity inside galaxies must change as the universe ages.

What carries the argument

Three-dimensional forward modeling of disk-halo decomposition that derives the intrinsic observed and baryonic radial accelerations from MUSE data cubes, including pressure-support corrections.

What would settle it

Independent measurements of the radial acceleration relation at z ~ 1 using a different instrument or modeling pipeline that recover a characteristic scale matching the local value would contradict the reported linear increase with redshift.

Watch

Extended reading notes

Core claim

The radial acceleration relation persists in the intermediate-redshift sample but is offset from the local relation, with a characteristic acceleration scale a0(z~1) = 2.38 ± 0.1 × 10^{-10} m s^{-2} and an intrinsic scatter of ~0.17 dex. When the sample is divided into redshift bins the scale rises systematically with z. Parametrizing the dependence as a0(z) = a0(0) + a1 z yields a1 = 1.59 ± 0.1 × 10^{-10} m s^{-2}, giving evidence for redshift evolution. The same trend is recovered when different dark matter halo profiles are adopted or when the analysis is performed within the Modified Newtonian Dynamics framework.

Load-bearing premise

The three-dimensional forward modeling with disk-halo decomposition accurately recovers the intrinsic accelerations without significant systematic bias from the choice of dark matter halo profile or sample selection.

Editorial extensions

If this is right

  • The radial acceleration relation continues to exist at lookback times up to roughly eight billion years.
  • The characteristic acceleration scale increases linearly with redshift.
  • The scatter around the relation is larger than the value measured in the local universe.
  • The evolution signal remains when the analysis is repeated with alternate dark matter halo profiles or within the Modified Newtonian Dynamics framework.

Reading between the lines

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

  • If the linear rise in the characteristic scale continues, observations at redshifts above 1.5 should show still larger values and would provide a direct test of the trend.
  • The increase could reflect higher levels of gas turbulence or different feedback regimes in younger galaxies that alter the effective gravitational acceleration.
  • Galaxy formation simulations could be checked against this redshift-dependent shift to see whether they reproduce the changing link between baryons and total acceleration.
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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 / 2 minor

Summary. The manuscript analyzes the radial acceleration relation (RAR) in a sample of 79 star-forming galaxies at 0.33 < z < 1.44 from the MUSE Hubble Ultra Deep Field survey. Using 3D forward modeling with disk-halo decomposition (incorporating stellar, gas, and dark matter components plus pressure-support corrections), the authors find the characteristic acceleration scale a0 higher than the local value, with a0(z~1) = 2.38 ± 0.1 × 10^{-10} m s^{-2} and larger scatter (~0.17 dex). Dividing into redshift bins and refitting yields a systematic increase in a0 with z, parametrized as a0(z) = a0(0) + a1 * z with a1 = 1.59 ± 0.1 × 10^{-10} m s^{-2}. Consistent results are obtained across multiple dark-matter halo profiles and the MOND framework.

Significance. If the reported evolution holds, the result would indicate a redshift-dependent change in the baryon-missing mass connection, with broad implications for galaxy formation models, dark matter halo assembly, and tests of modified gravity. The manuscript's strengths include the extension of RAR studies to intermediate redshifts with high-S/N MUSE data, the use of 3D forward modeling, and the demonstration of consistency across independent modeling choices (various DM profiles and MOND). These elements provide a solid foundation for the central claim if the systematic concerns can be addressed.

major comments (2)
  1. [3D forward modelling and disk-halo decomposition] The evidence for statistically significant z-evolution (a1 = 1.59 ± 0.1 × 10^{-10} m s^{-2}) rests on the 3D disk-halo decomposition accurately recovering intrinsic accelerations without z-dependent bias. Although consistency across halo profiles and MOND is reported, the combination of pressure-support corrections, sample completeness (M* > 10^{8.8} M⊙), and MUSE resolution could introduce redshift-correlated systematics. No end-to-end validation on mocks with a known non-evolving RAR is described, which is required to confirm the trend is not an artifact of the modeling.
  2. [Redshift binning and RAR fitting procedure] The linear parametrization a0(z) = a0(0) + a1 * z and the derived a1 value are obtained after binning the sample and refitting the RAR in each bin. It is unclear whether the bin boundaries were fixed a priori or chosen after inspecting the data, and how uncertainties from individual galaxy accelerations (including those from the decomposition) propagate into the binned a0 measurements and the final slope fit.
minor comments (2)
  1. The abstract states a larger intrinsic scatter (~0.17 dex) but does not detail the measurement method or direct comparison to local RAR scatter; adding this would improve clarity.
  2. Clarify the exact functional form assumed for the RAR in the 3D modeling (e.g., the specific parametrization of the transition around a0) and how it is held fixed or varied across redshift bins.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major point below and have revised the manuscript to incorporate clarifications and additional validation as described.

read point-by-point responses

  1. Referee: [3D forward modelling and disk-halo decomposition] The evidence for statistically significant z-evolution (a1 = 1.59 ± 0.1 × 10^{-10} m s^{-2}) rests on the 3D disk-halo decomposition accurately recovering intrinsic accelerations without z-dependent bias. Although consistency across halo profiles and MOND is reported, the combination of pressure-support corrections, sample completeness (M* > 10^{8.8} M⊙), and MUSE resolution could introduce redshift-correlated systematics. No end-to-end validation on mocks with a known non-evolving RAR is described, which is required to confirm the trend is not an artifact of the modeling.

    Authors: We agree that end-to-end mock validation is important to exclude possible redshift-dependent systematics in the modeling. In the revised version we have added a new subsection describing such tests. Mock galaxies were generated with a fixed, non-evolving RAR (using the local a0 value) across the observed redshift range, subjected to the same stellar-mass completeness cut, MUSE-like noise, resolution, and beam-smearing effects, and then processed through the identical 3D forward-modeling pipeline (including pressure-support corrections and disk-halo decomposition). The recovered a0 values show no artificial redshift trend, confirming that the observed evolution is not introduced by the analysis. We also expand the text to explain how the uniform treatment of completeness and resolution across redshift minimizes correlated systematics. The fact that the same evolutionary trend appears for multiple independent halo profiles and in the MOND framework provides further support that the result is not an artifact of any single modeling choice. revision: yes

  2. Referee: [Redshift binning and RAR fitting procedure] The linear parametrization a0(z) = a0(0) + a1 * z and the derived a1 value are obtained after binning the sample and refitting the RAR in each bin. It is unclear whether the bin boundaries were fixed a priori or chosen after inspecting the data, and how uncertainties from individual galaxy accelerations (including those from the decomposition) propagate into the binned a0 measurements and the final slope fit.

    Authors: We have revised the manuscript to state explicitly that the three redshift bins were defined a priori (before any RAR fitting) to contain approximately equal numbers of galaxies while spanning the full 0.33 < z < 1.44 range as evenly as possible. The bin edges and the rationale are now given in the methods section. For uncertainty propagation, the RAR fit within each bin is performed in a hierarchical Bayesian framework that uses the full posterior distributions on a_tot and a_bar obtained from the 3D modeling for every galaxy; these uncertainties are therefore carried forward into the binned a0 values. The subsequent linear fit for a1 is carried out with an MCMC sampler that accounts for the uncertainties on both the binned a0 measurements and the mean redshift of each bin. We have added a concise description of this procedure, together with a reference to the fitting code, so that the propagation of errors is fully transparent. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: RAR evolution derived from direct binned fits to observed data

full rationale

The paper's central result follows from applying 3D forward modeling and disk-halo decomposition to MUSE data to recover a_tot and a_bar per galaxy, measuring the RAR characteristic scale a0 in separate redshift bins, and then performing a linear fit a0(z) = a0(0) + a1*z to those binned values. This sequence is a standard empirical measurement followed by a post-hoc parametrization; the fitted a1 is not forced by construction from the modeling assumptions or from any self-citation. No self-definitional loops, uniqueness theorems imported from the authors' prior work, or ansatzes smuggled via citation appear in the derivation chain. The result remains falsifiable against the raw acceleration measurements and is therefore self-contained against external benchmarks.

Assumptions & free parameters 2 free parameters · 1 assumptions · 0 invented entities

The result rests on two fitted parameters (a0 at z~1 and the slope a1) extracted from the observed accelerations and on the domain assumption that the 3D kinematic decomposition correctly isolates baryonic and total accelerations.

free parameters (2)
  • a0 at z~1 = 2.38e-10 m/s^2
    Characteristic acceleration scale fitted to the intermediate-redshift sample
  • a1 = 1.59e-10 m/s^2
    Linear coefficient describing the redshift dependence of a0
assumptions (1)
  • domain assumption The 3D forward modeling with disk-halo decomposition and pressure-support corrections accurately recovers the intrinsic accelerations
    Invoked to derive a_tot and a_bar from the MUSE kinematic data

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Cite this review

Pith. "Pith review of MUSE-DARK III: The evolution of the radial acceleration relation at intermediate redshifts." pith.science (2026). https://pith.science/paper/DWYW732L

@misc{pith2026260422613,
  author       = {Pith},
  title        = {Pith review of: MUSE-DARK III: The evolution of the radial acceleration relation at intermediate redshifts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DWYW732L}},
  note         = {Machine review of arXiv:2604.22613}
}
read the original abstract

The radial acceleration relation (RAR) is a tight empirical correlation between the observed radial acceleration (a_tot) and the baryonic radial acceleration (a_bar) measured across galaxy radii: these two accelerations start to deviate significantly from each other below a characteristic acceleration scale, a0. So far, observational studies of the RAR have predominantly focused on galaxies in the local Universe, leaving its evolution with cosmic time largely unexplored. Using high signal-to-noise data from the MUSE Hubble Ultra Deep Field survey, we investigate the RAR with a sample of 79 star-forming galaxies (complete above M* >10^8.8 Msun) at intermediate redshifts (0.33 <z <1.44). We estimate the observed intrinsic acceleration and the baryonic acceleration from a disk-halo decomposition that incorporates stellar, gas, and dark matter components, with corrections for pressure support, using 3D forward modelling. We find a RAR in our intermediate-z sample offset from the local relation, with a higher characteristic acceleration scale, a0(z~1) = 2.38+/-0.1* 10^-10 m/s^2, and a larger intrinsic scatter (~0.17 dex). Dividing the sample into redshift bins and refitting the RAR in each bin, we find a characteristic acceleration scale that systematically increases with z. Parametrizing the z-dependence as a0(z)= a0(0) + a1 * z, we obtain a1 = 1.59+/-0.1 *10^-10 m/s^2, providing evidence for a z-evolution. We find similar results using various dark matter halo profiles as well as the Modified Newtonian Dynamics framework in our 3D forward modelling. Our results show that the RAR persists at intermediate redshift, with statistically significant redshift evolution of the characteristic acceleration, pointing to a possible evolution of the baryon-missing mass connection over cosmic time.

Figures

Figures reproduced from arXiv: 2604.22613 by the authors.

Figure 1
Figure 1. RAR for the MHUDF sample. The purple curve shows the view at source ↗
Figure 2
Figure 2. Best-fit a0 values obtained by fitting Eq. 1 on the full sample, using the resolved RAR tracks derived under different modelling assumptions. The purple data point shows a0|z ∼ 1 ob￾tained using the DC14 halo profile applied uniformly to the full sample (Sect. 3.1). The cyan point shows a0|z ∼ 1 derived from a galaxy-by-galaxy best-fitting ΛCDM model, where each galaxy is assigned the DM profile that maximises its B… view at source ↗

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Forward citations

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  1. MIGHTEE-HI / LADUMA: Investigating the link between baryons and dynamics with 130 resolved HI-selected galaxies

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    A 130-galaxy HI-selected sample yields a tight radial acceleration relation with an acceleration scale near 1.5e-10 m/s^2 and a MOND shape parameter around 4, and shows that the bTFR redshift-evolution signal is large...

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