arxiv: 2605.10022 · v1 · submitted 2026-05-11 · 🌌 astro-ph.CO · gr-qc

Recognition: 2 theorem links

· Lean Theorem

On the residual missing mass of the Bullet Cluster

Benoit Famaey

Pith reviewed 2026-05-12 03:05 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc

keywords Bullet ClusterMONDresidual missing massgravitational lensingJWSTgalaxy clusterscollisionless mass

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The pith

The Bullet Cluster exhibits the same residual missing mass discrepancy under MOND as other similar-mass clusters, with the missing mass being collisionless and centered on galaxies.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses an updated JWST-based gravitational lens model to verify that the Bullet Cluster displays a residual missing mass discrepancy in Modified Newtonian Dynamics that matches the discrepancy seen in other clusters of comparable mass. It further shows that this missing mass is centered on the galaxies rather than the hot gas, implying the extra mass is mostly collisionless. A reader would care because this replication strengthens the case that MOND accounts for galaxies but leaves a systematic shortfall at cluster scales that cannot be explained by the cluster's merger dynamics alone.

Core claim

This cluster exhibits the same residual missing mass discrepancy as other clusters of similar mass in the MOND context. Moreover, this missing mass should be mostly collisionless, since it is centred on the galaxies of the Bullet Cluster.

What carries the argument

The residual missing mass discrepancy, computed as the difference between the total mass inferred from gravitational lensing and the baryonic mass expected under MOND.

Load-bearing premise

The JWST-based gravitational lens model correctly captures the total mass distribution without significant systematic errors, and the MOND calculation for the expected baryonic contribution is accurate for this system.

What would settle it

A revised mass model from deeper observations showing that the lensing-inferred total mass matches the MOND-predicted baryonic mass within uncertainties, or showing that the residual mass is not centered on the galaxies, would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.10022 by Benoit Famaey.

**Figure 1.** Figure 1: The gas surface density of the Bullet Cluster Plummer model. 2.3. Discrete realisation There are only a few hundred to a thousand galaxies in a rich cluster such as the Bullet Cluster, hence a discrete representation of each galaxy is more accurate than a smooth distribution, especially in the non-linear context of MOND gravity. Therefore, in order to have a slightly better representation of the galaxies c… view at source ↗

**Figure 2.** Figure 2: The projected enclosed mass of the baryonic components of the model around the three BCGs [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: The projected enclosed mass of the baryonic and phantom components of the model around BCG1 and BCG3. the cluster, exactly as observed in other clusters of similar mass (e.g., B. Famaey et al. 2025). In this last model with additional residual missing mass, the ratio of baryonic+residual+phantom over baryonic mass at 300 kpc from BCG1 and BCG3 is 8 and 9, respectively, with total values close to those from… view at source ↗

**Figure 4.** Figure 4: The κ-map (colour-map and black isocontours) of the MOND model including two residual missing mass components centred around the galaxies’ regions. The κ-isocontours for the MOND model with only the observed baryons as sources are shown in orange [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

read the original abstract

Modified Newtonian Dynamics (MOND) is a paradigm that can do away with dark matter at galaxy scales, but displays a residual missing mass discrepancy in galaxy clusters. Prompted by the updated JWST-based gravitational lens model of the Bullet Cluster, I confirm here that this cluster exhibits the same residual missing mass discrepancy as other clusters of similar mass in the MOND context. Moreover, this missing mass should be mostly collisionless, since it is centred on the galaxies of the Bullet Cluster.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Famaey's note applies fresh JWST lensing to the Bullet Cluster and recovers the standard MOND residual mass, centered on the galaxies.

read the letter

The key point is that this short paper takes the new JWST gravitational lensing model for the Bullet Cluster and shows it has the same residual missing mass under MOND as other clusters, and that this mass lines up with the galaxies rather than the hot gas. What stands out is the use of the updated lens model to confirm the centering. In the Bullet Cluster the galaxies and gas are separated by the collision, so seeing the extra mass follow the galaxies strengthens the case that whatever is missing behaves like collisionless matter. The paper does not introduce a new calculation or fix for the MOND cluster problem. It is a straightforward application to one well-known system with newer data. The abstract gives no numbers or plots, so it is hard to judge how close the match is or what uncertainties are involved. A potential issue is whether the JWST model has any systematic offsets in mass or position that could mimic or hide the discrepancy. The MOND side also uses a standard setup without extra corrections for the high-speed merger. This is mainly for people already working on MOND at cluster scales or tracking Bullet Cluster observations. It is a useful data point but not a breakthrough. A reader looking for new ideas on the missing mass problem will not find them here. I would send it for peer review. The topic is important enough that even a confirmatory note with new data should get checked by referees who know the lensing and MOND literature.

Referee Report

2 major / 1 minor

Summary. The manuscript uses an updated JWST-based gravitational lens model of the Bullet Cluster to confirm that this system exhibits the same residual missing mass discrepancy as other clusters of similar mass in the MOND framework, and argues that the residual component is mostly collisionless because it is spatially centered on the galaxies rather than the X-ray gas.

Significance. If the quantitative comparison holds, the result would add a key data point from a high-velocity merger to the existing pattern of residual discrepancies in MOND clusters, while the centering argument supplies dynamical evidence that the residual mass behaves as collisionless matter, which is a non-trivial test for any proposed resolution of the cluster-scale issue.

major comments (2)

[Main text] The central claim that the residual matches that of other clusters of similar mass is load-bearing but unsupported by any explicit numbers, MOND-predicted baryonic mass, lensing-inferred total mass, or direct comparison (e.g., no table or figure showing the discrepancy value for the Bullet Cluster versus prior clusters). Without these, the confirmation cannot be verified independently of the author's earlier work.
[Main text] The inference that the residual mass is collisionless rests on the JWST lens model accurately recovering both the amplitude and the galaxy-centered location of the mass peaks distinct from the gas. The manuscript provides no quantitative assessment of possible convergence biases, mis-centering, or systematics in the lens reconstruction at the scale of the observed galaxy-gas offset.

minor comments (1)

[Abstract] The abstract states the result clearly but would benefit from a brief mention of the specific mass range or reference clusters used for the comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting points that will improve its clarity and verifiability. We address each major comment below and describe the revisions that will be incorporated.

read point-by-point responses

Referee: [Main text] The central claim that the residual matches that of other clusters of similar mass is load-bearing but unsupported by any explicit numbers, MOND-predicted baryonic mass, lensing-inferred total mass, or direct comparison (e.g., no table or figure showing the discrepancy value for the Bullet Cluster versus prior clusters). Without these, the confirmation cannot be verified independently of the author's earlier work.

Authors: We agree that the manuscript would be strengthened by making the numerical comparison explicit and self-contained. In the revised version we will insert a dedicated table (and accompanying text) that reports the MOND-predicted baryonic mass, the lensing-inferred total mass, and the resulting residual discrepancy for the Bullet Cluster, together with the corresponding values drawn from the earlier cluster sample. This will include the precise references and calculation steps used for each entry, allowing independent verification without requiring the reader to consult prior work. revision: yes
Referee: [Main text] The inference that the residual mass is collisionless rests on the JWST lens model accurately recovering both the amplitude and the galaxy-centered location of the mass peaks distinct from the gas. The manuscript provides no quantitative assessment of possible convergence biases, mis-centering, or systematics in the lens reconstruction at the scale of the observed galaxy-gas offset.

Authors: The lens model is taken from a published JWST reconstruction that already supplies formal uncertainty maps and convergence diagnostics. Nevertheless, we accept that the manuscript does not explicitly propagate those uncertainties to the galaxy-gas offset scale. In the revision we will add a short subsection that (i) quotes the relevant error estimates from the lens-model paper, (ii) estimates the maximum plausible mis-centering or convergence bias at the observed offset, and (iii) shows that even under conservative assumptions the residual mass peak remains statistically closer to the galaxies than to the X-ray gas. A full re-derivation of the lens model lies outside the scope of the present work, but the added discussion will make the robustness argument quantitative within the limits of the published data. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper applies the standard MOND framework (with its established acceleration scale and interpolation function) to the new JWST-based lensing mass map of the Bullet Cluster, computing the residual discrepancy as the difference between total lensing mass and the baryonic mass contribution under MOND. This is a direct, independent calculation for the present system rather than a quantity fitted or defined from the same data. The claim that the residual matches other clusters of similar mass is a consistency comparison to prior independent measurements, not a load-bearing derivation that reduces to self-citation or redefinition. The inference that the residual mass is collisionless follows from its spatial centering on galaxies in the lens model, which is external to the MOND computation itself. No self-definitional loops, fitted inputs renamed as predictions, or ansatzes smuggled via self-citation are present.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the MOND framework and prior cluster analyses; limited details available from abstract only.

axioms (2)

domain assumption The JWST gravitational lens model accurately represents the total mass distribution in the Bullet Cluster.
The confirmation of the discrepancy and its location depends directly on this model being reliable.
domain assumption MOND predictions for the baryonic mass contribution are computed consistently with previous cluster studies.
The statement that the discrepancy is 'the same' as other clusters assumes identical application of the MOND formula.

invented entities (1)

residual missing mass component no independent evidence
purpose: To explain the shortfall between MOND-predicted and observed dynamics in clusters
The paper posits this component must be mostly collisionless and galaxy-centered to match the lensing data.

pith-pipeline@v0.9.0 · 5359 in / 1354 out tokens · 61610 ms · 2026-05-12T03:05:55.413628+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
I use the quasilinear MOND field equation … ν̃(g) ≡ (e^√g − 1)^−1 … a0 = 3700 km² s⁻² kpc⁻¹
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
The total Plummer masses of these two residual components … exactly as observed in other clusters of similar mass

Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages · 1 internal anchor

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