The Bullet Cluster Supports Modified Gravity Theories

The initial reaction to the Bullet Cluster was that it resolved the modified gravity v. particle dark matter debate unequivocally in favor in particle dark matter. But, in fact, the opposite is true. Modified gravity theories can explain the Bullet Cluster, while the Bullet Cluster is deeply problematic for particle dark matter theories.

[C]urious scientists had to tell apart their two hypotheses: Modified gravity or particle dark matter? They needed an observation able to rule out one of these ideas, a smoking gun signal – the Bullet Cluster. 

The theory of particle dark matter had become known as the “concordance model” (also: ΛCDM). It heavily relied on computer simulations which were optimized so as to match the observed structures in the universe. From these simulations, the scientists could tell the frequency by which galaxy clusters should collide and the typical relative speed at which that should happen.

From the X-ray observations, the scientists inferred that the collision speed of the galaxies in the Bullet Cluster must have taken place at approximately 3000 km/s. But such high collision speeds almost never occurred in the computer simulations based on particle dark matter. The scientists estimated the probability for a Bullet-Cluster-like collision to be about one in ten billion, and concluded: that we see such a collision is incompatible with the concordance model. And that’s how the Bullet Cluster became strong evidence in favor of modified gravity. 

However, a few years later some inventive humanoids had optimized the dark-matter based computer simulations and arrived at a more optimistic estimate of a probability of 4.6×10-4 for seeing something like the Bullet-Cluster. Briefly later they revised the probability again to 6.4×10−6. 

Either way, the Bullet Cluster remained a stunningly unlikely event to happen in the theory of particle dark matter. It was, in contrast, easy to accommodate in theories of modified gravity, in which collisions with high relative velocity occur much more frequently. 

It might sound like a story from a parallel universe – but it’s true. The Bullet Cluster isn’t the incontrovertible evidence for particle dark matter that you have been told it is. It’s possible to explain the Bullet Cluster with models of modified gravity. And it’s difficult to explain it with particle dark matter.

How come we so rarely read about the difficulties the Bullet Cluster poses for particle dark matter? It’s because the pop sci media doesn’t like anything better than a simple explanation that comes with an image that has “scientific consensus” written all over it. Isn’t it obvious the visible stuff is separated from the center of the gravitational pull?

But modifying gravity works by introducing additional fields that are coupled to gravity. There’s no reason that, in a dynamical system, these fields have to be focused at the same place where the normal matter is. Indeed, one would expect that modified gravity too should have a path dependence that leads to such a delocalization as is observed in this, and other, cluster collisions. And never mind that when they pointed at the image of the Bullet Cluster nobody told you how rarely such an event occurs in models with particle dark matter. 

No, the real challenge for modified gravity isn’t the Bullet Cluster. The real challenge is to get the early universe right, to explain the particle abundances and the temperature fluctuations in the cosmic microwave background. The Bullet Cluster is merely a red-blue herring that circulates on social media as a shut-up argument. It’s a simple explanation. But simple explanations are almost always wrong.

From Sabine Hossenfelder at Backreaction.

The second reference in the quoted material is to the following paper:

To quantify how rare the bullet-cluster-like high-velocity merging systems are in the standard LCDM cosmology, we use a large-volume 27 (Gpc/h)^3 MICE simulation to calculate the distribution of infall velocities of subclusters around massive main clusters. The infall-velocity distribution is given at (1-3)R_{200} of the main cluster (where R_{200} is similar to the virial radius), and thus it gives the distribution of realistic initial velocities of subclusters just before collision. These velocities can be compared with the initial velocities used by the non-cosmological hydrodynamical simulations of 1E0657-56 in the literature. The latest parameter search carried out recently by Mastropietro and Burkert showed that the initial velocity of 3000 km/s at about 2R_{200} is required to explain the observed shock velocity, X-ray brightness ratio of the main and subcluster, and displacement of the X-ray peaks from the mass peaks. We show that such a high infall velocity at 2R_{200} is incompatible with the prediction of a LCDM model: the probability of finding 3000 km/s in (2-3)R_{200} is between 3.3X10^{-11} and 3.6X10^{-9}. It is concluded that the existence of 1E0657-56 is incompatible with the prediction of a LCDM model, unless a lower infall velocity solution for 1E0657-56 with < 1800 km/s at 2R_{200} is found.

Jounghun Lee, Eiichiro Komatsu, "Bullet Cluster: A Challenge to LCDM Cosmology" (May 22, 2010). Later published in Astrophysical Journal 718 (2010) 60-65.

The next referenced paper is:

The Bullet Cluster has provided some of the best evidence for the Λ cold dark matter (ΛCDM) model via direct empirical proof of the existence of collisionless dark matter, while posing a serious challenge owing to the unusually high inferred pairwise velocities of its progenitor clusters. Here, we investigate the probability of finding such a high-velocity pair in large-volume N-body simulations, particularly focusing on differences between halo-finding algorithms. We find that algorithms that do not account for the kinematics of infalling groups yield vastly different statistics and probabilities. When employing the ROCKSTAR halo finder that considers particle velocities, we find numerous Bullet-like pair candidates that closely match not only the high pairwise velocity, but also the mass, mass ratio, separation distance, and collision angle of the initial conditions that have been shown to produce the Bullet Cluster in non-cosmological hydrodynamic simulations. The probability of finding a high pairwise velocity pair among haloes with M_halo ≥ 10¹⁴ M_⊙ is 4.6 × 10⁻⁴ using ROCKSTAR, while it is ≈34 × lower using a friends-of-friends (FoF)-based approach as in previous studies. This is because the typical spatial extent of Bullet progenitors is such that FoF tends to group them into a single halo despite clearly distinct kinematics. Further requiring an appropriately high average mass among the two progenitors, we find the comoving number density of potential Bullet-like candidates to be of the order of ≈10⁻¹⁰ Mpc⁻³. Our findings suggest that ΛCDM straightforwardly produces massive, high relative velocity halo pairs analogous to Bullet Cluster progenitors, and hence the Bullet Cluster does not present a challenge to the ΛCDM model.

Robert Thompson, et al., "The rise and fall of a challenger: the Bullet Cluster in Λ Cold Dark Matter simulations" (June 29, 2015) and published at MNRAS.

The paper in the final reference is as follows:

We consider the orbit of the bullet cluster 1E 0657-56 in both CDM and MOND using accurate mass models appropriate to each case in order to ascertain the maximum plausible collision velocity. Impact velocities consistent with the shock velocity (~ 4700km/s) occur naturally in MOND. CDM can generate collision velocities of at most ~ 3800km/s, and is only consistent with the data provided that the shock velocity has been substantially enhanced by hydrodynamical effects.

Garry W. Angus and Stacy S. McGaugh, "The collision velocity of the bullet cluster in conventional and modified dynamics" (September 2, 2007) and also published at MNRAS.

In tangentially related new, even Lubos Motl is on record as being at least somewhat agnostic on the question of whether dark matter phenomena are caused by dark matter particles or modifications of gravity (in the context of a debate over who, if anyone should receive a Nobel prize related to dark matter):

[T]hese Zwicky-vs-Rubin disputes aren't too relevant for one reason: We are not terribly certain that dark matter is the right explanation of the anomalies. Given the not quite negligible "risk" that the right explanation is completely different, something like MOND, it could be very strange to give the Nobel prize for "it". What "it" even means? Look at the list of the Nobel prize winners. No one has ever received the Nobel prize for the discovery of "something" that no one knew what it actually was – a new particle? Black holes everywhere? A new term in Newton's gravitational law? The normal contribution rewarded by Nobel prizes is a clearcut theory that was experimentally proven, or the experimental proof of a clear theory. Even though most cosmologists and particle physicists etc. tend to assume dark matter, dark matter-suggesting observations aren't really belonging to this class yet. 

And I think that this is the actual main reason why Vera Rubin hasn't gotten the prize for dark matter – and no one else has received it, either.