🔭 astrophysics

A consistent MOND modelling of the Bullet Cluster

This paper refutes the common misconception that the Bullet Cluster contradicts Modified Newtonian Dynamics (MOND) by demonstrating that, within the QUMOND framework, the gravitational potential generated by the concentrated galaxies produces a lensing signal closely matching observations, despite the system's baryonic mass being dominated by diffuse gas.

Original authors: X. Hernandez

Published 2026-04-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: X. Hernandez

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Bullet Cluster: A Cosmic Collision and a New Way to See Gravity

Imagine two massive cosmic trains colliding. One is a huge, heavy freight train (the big galaxy cluster), and the other is a smaller, faster commuter train (the "bullet" cluster). When they smash into each other at millions of miles per hour, something strange happens to their cargo.

The Setup: What We See
In this cosmic crash, there are two main types of "cargo":

The Stars (Galaxies): These are like the passengers on the trains. They are solid, distinct, and don't bump into each other much. They keep moving forward, passing right through the collision.
The Gas: This is like the air inside the trains or the smoke from the engines. It's a giant, diffuse cloud filling the space between the stars. When the trains collide, this gas slams into the gas from the other train, slows down, heats up, and glows brightly in X-rays.

The Mystery: The "Invisible" Weight
For decades, astronomers have looked at this crash and tried to figure out where the "weight" is.

The Standard View (Dark Matter): They see the glowing gas (the smoke) is huge and heavy, but the "gravity" (the invisible pull) seems to be centered on the passengers (the galaxies), which have moved far away from the gas. To explain this, they say there must be invisible "Dark Matter" passengers sitting with the galaxies, holding the gravity there.
The Old Criticism of MOND: Critics of Modified Newtonian Dynamics (MOND)—a theory that says gravity works differently at very low speeds—argued that this crash "falsified" MOND. Their logic was simple: "If there's no Dark Matter, and the gas is the heaviest thing there, the gravity must be strongest where the gas is. But the gravity is strongest where the galaxies are! So, MOND is wrong."

The New Paper: A Different Perspective
X. Hernandez, an astronomer from Mexico, says, "Hold on. You're looking at this the wrong way."

He uses a creative analogy to explain why the old criticism is flawed:

The Neutron Star vs. The Cloud: Imagine a tiny, incredibly dense neutron star (like a galaxy) sitting next to a giant, fluffy molecular cloud (like the gas) that has 10,000 times more mass. If you look at the gravitational pull, it won't be centered on the giant cloud. It will be centered on the tiny, dense star. Why? Because gravity cares about density (how packed the mass is), not just the total amount of mass.

Hernandez argues that MOND works exactly like this. Even though the gas is heavier overall, the galaxies are so dense and "point-like" that they create a much stronger gravitational signal in the MOND framework than the diffuse, spread-out gas does.

The Experiment: Running the Simulation
Hernandez didn't just talk about it; he built a massive 3D computer model of the Bullet Cluster.

He mapped out all the real galaxies and the X-ray gas.
He ran the numbers using the rules of MOND (specifically a version called QUMOND).
He asked the computer: "If we pretend this is a normal universe with standard gravity, what would we think the invisible mass distribution looks like?"

The Result: A Perfect Match
The computer generated a map of "phantom mass" (the fake dark matter MOND predicts we would see).

The Prediction: The map showed the strongest gravity centered exactly on the two groups of galaxies, just like the real observations. The gas contributed a little bit of "phantom" gravity, but it was spread out and weak compared to the sharp, strong signal from the galaxies.
The Comparison: When Hernandez compared his MOND-generated map to the actual maps made by astronomers using standard gravity and Dark Matter, they looked almost identical.

The Takeaway
This paper is like a detective solving a case by realizing the witness was looking at the wrong clue.

The Old View: "The gas is heavy, so gravity should be there. It's not, so MOND is wrong."
The New View: "Gravity depends on how packed the mass is. The galaxies are packed tight, so they win, even if the gas is heavier overall. When we calculate this correctly, MOND predicts the Bullet Cluster perfectly."

Why It Matters
This suggests that the Bullet Cluster isn't the "smoking gun" that kills Modified Gravity theories. Instead, it shows that if you understand how gravity behaves in these extreme conditions, you don't need to invent invisible Dark Matter to explain why the gravity is where the galaxies are. The "phantom" gravity predicted by MOND matches the real-world data just as well as the standard Dark Matter model does.

In short: The Bullet Cluster isn't a problem for MOND; it's actually a perfect example of how MOND works, provided you look at the density of the objects, not just their total weight.

1. Problem Statement

The Bullet Cluster (1E 0657-56) is widely considered a "smoking gun" against Modified Newtonian Dynamics (MOND) and in favor of the existence of collisionless Dark Matter (DM). The standard argument posits a contradiction:

Baryonic Distribution: The system consists of two colliding clusters. The dominant baryonic mass (approx. 90% of the total baryonic mass) is in the form of hot X-ray emitting gas, which has been stripped and lags behind the galaxies due to hydrodynamical drag.
Lensing Signal: Gravitational lensing observations under General Relativity (GR) show that the total mass distribution (required to explain the lensing) is centered on the collisionless galaxies, not the dominant gas.
The MOND Conflict: Critics argue that in MOND, where gravity is modified based on local acceleration, the gravitational potential (and thus the lensing signal) should be dominated by the largest mass concentration (the gas). The observed offset between the gas and the lensing peaks is interpreted as evidence that an invisible, collisionless component (Dark Matter) must exist.

Hernandez's Counter-Argument: The paper challenges the assumption that the gravitational potential in MOND depends solely on total mass. It argues that, similar to GR, the lensing signal in MOND depends critically on the volume density and spatial configuration of the baryons. The paper posits that the "phantom" dark matter (the effective mass inferred under GR when viewing a MOND reality) generated by point-like galaxies is significantly stronger and more concentrated than that generated by diffuse gas, even if the gas has a higher total mass.

2. Methodology

The author employs the QUMOND (Quasi-Linear formulation of MOND) framework (Milgrom 2010) to perform a rigorous numerical simulation.

Theoretical Framework:
- QUMOND calculates the total gravitational potential $\Phi$ as the sum of the Newtonian potential ( $\Phi_N$ ) and an auxiliary "phantom" potential ( $\Phi_p$ ).
- The phantom density ( $\rho_p$ ) is derived from the baryonic density ( $\rho_b$ ) via the equation:
  $\rho_p = \frac{1}{4\pi G} \nabla \cdot \left[ \left( \nu \left( \frac{|\nabla \Phi_N|}{a_0} \right) - 1 \right) \nabla \Phi_N \right]$
  where $a_0$ is the MOND acceleration scale and $\nu(x)$ is a transition function.
- Under this framework, if a MOND reality is interpreted through standard GR, the "phantom" density represents the apparent Dark Matter halo.
Numerical Setup:
- Domain: A simulation box of $1500 \times 1100 \times 36,000$ kpc (covering 18 Mpc front and back of the cluster plane) with a resolution of 2 kpc on the sky plane and 12 kpc along the line of sight.
- Baryonic Components:
  1. Galaxies: Utilized the latest member catalogue from Rihtaršic et al. (2026) (R26), including 219 galaxies with JWST data. Galaxies were modeled as purely stellar distributions using a PIEMD profile in the limit of a cusp ( $r_c \to 0$ ), scaled by luminosity.
  2. X-ray Gas: Modeled using an effective $\beta$ -profile ( $\beta=1$ ) based on Halverson et al. (2009), with a scale length of 550 kpc.
- Exclusions: No hypothetical Dark Matter halos were added to the baryonic input; the simulation relied only on the observed baryonic matter.
Procedure:
1. Calculate the Newtonian force vector for the full baryonic distribution.
2. Compute the QUMOND transition function $\nu(x)$ and the resulting phantom density $\rho_p$ at every grid point.
3. Project the sum of baryonic density ( $\rho_b$ ) and phantom density ( $\rho_p$ ) onto the sky plane to generate a total surface density map ( $\kappa$ ).
4. Compare this QUMOND-predicted $\kappa$ map directly with the GR-inferred $\kappa$ map from R26.

3. Key Contributions

Analytical Insight: The paper provides an analytical derivation showing that for a point mass (galaxy), the phantom mass ratio grows linearly with radius ( $M_p/M_b \propto r$ ), creating a strong, peaked signal. Conversely, for shallow, extended density profiles (like the X-ray gas), the phantom-to-baryon ratio remains low and constant. This explains why the lensing signal peaks at the galaxies despite the gas being more massive.
First Full QUMOND Simulation: This is the first detailed numerical modeling of the Bullet Cluster using QUMOND with the latest observational data (R26), moving beyond simplified analytical estimates.
Direct Comparison: It provides a quantitative comparison between the surface density maps predicted by MOND (interpreted as GR) and the actual GR lensing reconstructions, rather than just qualitative arguments.

4. Results

Mass Budget:
- The X-ray gas mass ( $2.226 \times 10^{14} M_\odot$ ) is $\sim 13$ times larger than the total stellar mass of the galaxies ( $1.696 \times 10^{13} M_\odot$ ).
- However, the phantom mass generated by the galaxies alone accounts for 48% of the total phantom mass required.
- The total mass inferred by the QUMOND model ( $1.1 \times 10^{15} M_\odot$ ) matches recent GR lensing estimates.
Surface Density Maps ( $\kappa$ ):
- QUMOND Prediction: The resulting $\kappa$ map shows two distinct, high-density peaks centered precisely on the galaxy distributions. The contribution from the gas is broad and diffuse, adding a constant background but not shifting the peaks.
- Comparison with R26: The QUMOND-predicted map (Figure 1, Left) is qualitatively and quantitatively consistent with the GR lensing map from R26 (Figure 1, Right).
- Difference Map: The difference between the QUMOND prediction and the R26 GR reconstruction is consistently below 0.15 in $\kappa$ units. This level of discrepancy is comparable to, or smaller than, the differences found between independent GR studies using different Dark Matter halo assumptions.
Robustness: The results hold even when varying numerical schemes and transition functions, confirming that the dominance of the galaxy signal is a robust feature of the QUMOND formalism for this specific baryonic configuration.

5. Significance

Refutation of the "Bullet Cluster Objection": The paper demonstrates that the Bullet Cluster is not inconsistent with MOND. The common objection—that the lensing peak must follow the dominant gas mass—relies on a naive assumption that ignores the density dependence of the MOND potential.
Reinterpretation of Dark Matter: The study shows that the "Dark Matter" signal observed in the Bullet Cluster can be fully explained as the "phantom" density arising from the specific distribution of baryonic matter (point-like galaxies vs. diffuse gas) under MOND laws, without invoking any collisionless particle.
Implications for Cosmology: The paper suggests that the Bullet Cluster's configuration (high-velocity collision) is actually more consistent with MOND formation scenarios than with standard $\Lambda$ CDM, where such high-velocity encounters are statistically rare.
Methodological Shift: It establishes that to test MOND against lensing data, one must calculate the effective surface density (baryons + phantom) rather than assuming the potential follows the baryonic mass distribution directly.

In conclusion, Hernandez argues that when the full QUMOND formalism is applied to the latest data, the Bullet Cluster's lensing signal is naturally reproduced by the baryonic matter distribution alone, rendering the system consistent with Modified Gravity.