On the residual missing mass of the Bullet Cluster

Using an updated JWST-based gravitational lens model, the paper confirms that the Bullet Cluster exhibits a residual missing mass discrepancy under Modified Newtonian Dynamics (MOND) that is centered on its collisionless galaxies, similar to other clusters of comparable mass.

The Gist

Imagine the universe as a giant cosmic dance floor. For decades, physicists have been trying to figure out why the dancers (galaxies) move the way they do. The standard explanation is that there's an invisible partner, called Dark Matter, holding hands with the visible dancers and pulling them along.

But there's a rival theory called MOND (Modified Newtonian Dynamics). It suggests there are no invisible partners at all. Instead, the rules of gravity itself change when things move very slowly or are very far apart. MOND works perfectly for individual galaxies, but it has a famous problem: it struggles to explain the behavior of massive groups of galaxies called clusters.

This paper, written by Benoit Famaey, takes a fresh look at the most famous "cosmic crash" in the sky: the Bullet Cluster.

The Cosmic Crash: The Bullet Cluster

Think of the Bullet Cluster as two massive galaxy clusters that slammed into each other.

• The Gas: Imagine the clusters are filled with a thick, sticky fog (hot gas). When they crashed, this fog got slowed down and stuck in the middle, like two cars crashing and their airbags getting stuck between them.
• The Galaxies: The actual galaxies are like the cars themselves. They are mostly empty space, so they zoomed right through the crash without slowing down.
• The Mystery: If you look at where the gravity is strongest (using a technique called gravitational lensing, which acts like a cosmic magnifying glass), the gravity is centered on the galaxies that zoomed through, not the sticky gas that got left behind.

In the standard "Dark Matter" view, this makes perfect sense: the invisible Dark Matter is like the cars, passing through the crash unaffected. But in the MOND view, gravity should be strongest where the most stuff (the gas) is. Since the gravity is actually with the galaxies, MOND usually has a hard time explaining this.

The New Investigation

Famaey decided to test MOND against the very latest, high-definition data from the James Webb Space Telescope (JWST). He built a digital simulation of the Bullet Cluster to see if MOND could explain the gravity map without needing invisible Dark Matter.

He created two versions of the simulation:

1. The "Smooth" Model: Treating the galaxies like a continuous cloud of dust.
2. The "Discrete" Model: Treating the galaxies as individual distinct points (which is more accurate for MOND).

The Findings: The "Missing" Weight

Here is what the simulation revealed, using a simple analogy:

Imagine you are trying to lift a heavy box.

• The Visible Stuff: You can see the box (the galaxies and gas).
• The MOND Boost: MOND says, "Gravity gets a little stronger when things are light," so it gives the box a slight boost, making it feel a bit heavier than it looks.
• The Reality: When Famaey calculated the weight, the "MOND boost" wasn't enough. The gravity map showed the cluster was much, much heavier than the visible galaxies and gas could possibly explain, even with MOND's special rules.

The Analogy:
It's like seeing a person walking down the street. You can see them (the visible matter). You know they are wearing a heavy backpack (the MOND boost). But when you try to lift them, they feel as heavy as a small car. Something is still missing.

The Conclusion: A "Residual" Ghost

Famaey found that even with the latest data and a very careful simulation, MOND still cannot explain the Bullet Cluster on its own.

• To make the math work, he had to add a "residual missing mass" to the simulation.
• Crucially, this missing mass had to be centered on the galaxies (the things that zoomed through the crash), not the gas.
• This means the missing mass acts like Dark Matter: it is "collisionless" (it doesn't get stuck in the crash) and it travels with the galaxies.

The Bottom Line

The paper concludes that while MOND is a great theory for explaining how single galaxies spin, it hits a wall when it comes to galaxy clusters like the Bullet Cluster. Even with the most advanced data available, the cluster still seems to contain a huge amount of invisible, collisionless mass that MOND cannot generate on its own.

In short: The Bullet Cluster still looks like it needs a "Dark Matter" partner, even if you try to change the rules of gravity. The invisible mass is still there, and it's still hanging out with the galaxies, not the gas.

Technical Summary

Technical Summary: On the residual missing mass of the Bullet Cluster

Problem Statement
Modified Newtonian Dynamics (MOND) successfully explains galaxy rotation curves without invoking dark matter but has historically struggled to account for the gravitational fields observed in galaxy clusters. While the Bullet Cluster (1E 0657-56) is often cited as strong evidence for collisionless dark matter due to the spatial offset between its X-ray gas and gravitational lensing peaks, MOND proponents have argued that the theory might still hold if a residual "missing mass" component exists. However, previous assessments suggested MOND underpredicts the central gravitational field of such clusters. This paper investigates whether the Bullet Cluster, utilizing updated gravitational lensing models based on JWST data, exhibits the same residual missing mass discrepancy found in other clusters within the MOND framework, and whether this missing mass aligns with the collisionless galaxy components rather than the baryonic gas.

Methodology
The author employs a relativistic MOND framework where the gravitational potential $\Phi$ and relativistic potential $\Psi$ satisfy $\Phi - \Psi = 2\Phi$. The dynamics are governed by the quasilinear MOND field equation using the "Radial Acceleration Relation" (RAR) interpolating function.

To model the Bullet Cluster, two distinct realizations of the baryonic mass distribution were constructed:

1. Smooth Realization: The cluster is modeled as a sum of Plummer spheres representing the main galaxy component, a subcluster, and four gas components (including a negative mass component to taper surface density). The total baryonic mass is $\sim 2.4 \times 10^{14} M_\odot$.
2. Discrete Realization: To better capture the non-linear nature of MOND gravity, the model represents the three Brightest Cluster Galaxies (BCGs) and 216 other galaxies as individual Plummer spheres (totaling 219 galaxies). Their positions are sampled from a flattened Plummer distribution to match the observed on-sky geometry, including specific targets from recent lensing maps.

The study computes the gravitational convergence ($\kappa$) map in two stages:

• Analytic/Numerical Hybrid: The Newtonian potential is computed analytically as a sum of Plummer contributions plus a weak external field ($g_{ext} = a_0/1000$) to avoid infinite phantom mass. The "phantom" density (the MOND equivalent of dark matter) is derived numerically via second-order finite differences on a $10^9$ bin grid, with adaptive resolution ranging from $\sim 1$ kpc near BCGs to $\sim 600$ kpc at the box edges.
• Residual Mass Addition: To test the necessity of additional mass, two large Plummer spheres representing "residual missing mass" were added to the model, centered on the galaxy concentrations.

Key Results

• Insufficiency of Baryons and Phantom Mass: Back-of-the-envelope estimates and rigorous numerical computations confirm that the combination of baryonic matter and the MOND-induced phantom mass is insufficient to explain the observed lensing. At 300 kpc from the main BCG (BCG1) and the subcluster BCG (BCG3), the ratio of total (baryonic + phantom) projected mass to baryonic mass is approximately 2.8 and 3.4, respectively. This falls significantly short of the observed lensing mass-to-baryonic mass ratios of $\sim 7.5$ and $\sim 9$.
• Convergence Map Discrepancy: The MOND-only model fails to reproduce the observed convergence map. While observations (Rihtaršič et al. 2026) show a region between the two main clusters with $\kappa \ge 1$, the baryon-only MOND model barely reaches $\kappa \approx 0.5$ in limited regions around the BCGs. Even doubling the total galaxy mass in the model failed to reproduce the observed $\kappa \ge 1$ region between the clusters.
• Necessity and Nature of Residual Mass: When two large Plummer spheres of residual mass (totaling $\sim 6.8 \times 10^{14} M_\odot$) are added, centered on the galaxy concentrations, the resulting $\kappa$-map closely matches the observational data. The projected residual missing mass within the relevant radii is $\sim 3.4 \times 10^{14} M_\odot$, comparable to the total baryonic mass of the cluster.

Significance and Claims
The paper confirms that, even with updated JWST-based lensing models, the Bullet Cluster exhibits a residual missing mass problem within the MOND paradigm, similar to other galaxy clusters of comparable mass. The study concludes that this missing mass cannot be explained by the MOND "phantom" effect alone. Crucially, the analysis demonstrates that this residual mass must be collisionless and centered on the galaxies, as it aligns with the offset galaxy peaks rather than the slowed-down X-ray gas. This finding suggests that if MOND is to remain a viable alternative to dark matter on cluster scales, it requires an additional, collisionless mass component (potentially small gas clouds or other baryonic forms) that behaves similarly to dark matter in its distribution. The author provides the code used for these computations to ensure reproducibility.