5. “But the Bullet Cluster …” – Proof of Cold or Warm Dark Matter in galaxy clusters is but a myth

Whenever a discussion about the problems of the Cold Dark Matter Hypothesis and possible alternatives like Modified Newtonian Gravity (MOND) emerges, one argument you can be sure to hear soon is “But the Bullet Cluster …”. It is the same whether you discuss with scientists or other people interested in astronomy. But can the Bullet Cluster be considered as a proof of Cold or Warm Dark Matter? No, because that conclusion rests on further assumptions and is in itself not logically valid. Furthermore, the problems of the Dark Matter Hypothesis are independent of the Bullet Cluster, making it a false argument in many discussions. Even worse, the collision velocity of the Bullet Cluster seems to be incompatible with the concordance cosmology. At the same time, alternative gravity theories, while often said to fail in explaining galaxy clusters, can account for them rather naturally.

In this first post in a series of three we will discuss the Bullet Custer as a “smoking gun” for Dark Matter. The other two parts about “The Bullet Cluster and galaxy clusters in modified-gravity theories” and “The Train Wreck Cluster – an ‘anti-Bullet-Cluster’: disproof of Cold or Warm Dark Matter?” will follow in a few days.


What is the “Bullet Cluster”?

It all started in 2006 with a paper titled “A direct empirical proof of the existence of dark matter” and a press release with the no-less lurid headline “NASA Finds Direct Proof of Dark Matter”. Right in the title the authors claimed that their discovery would immediately settle the question whether there is Dark Matter (DM) or not. Naturally, the spectacular announcement was adopted by the majority of the media and could well be one of the most successful press releases in astronomy. Since then, the picture of the Bullet Cluster (BC) has been shown countless times:

Credit: X-ray: NASA/CXC/CfA/M.Markevitch et al.; Optical: NASA/STScI; Magellan/U.Arizona/D.Clowe et al.; Lensing Map: NASA/STScI; ESO WFI; Magellan/U.Arizona/D.Clowe et al.  


What do we see in this picture? There are two clusters of galaxies (left and right). Overlaid are blue and pink colors. The two pink clumps in the middle shows where x-ray observations find the hot gas, the Bullet Cluster got it’s name from the bullet-like shape of the gas on the right. The gas usually sits in the center of a galaxy cluster, but is here shifted to the point between the clusters. Some time ago the two galaxy clusters have passed through each other, making their gas collide. As gas interacts electromagnetically, it is slowed down when it collides, like two streams of air that can not pass through each other unhindered in opposite directions. That is why the gas is a bit behind the galaxies. Those do only interact through gravity and therefore pass each other unhindered without being slowed-down like the gas. This is maybe similar to two swarms of flies that can fly through each other.

The blue blobs were derived in a bit more complicated manner using the gravitational lens effect. To put it simple, since Einstein we know that matter deforms space-time. This leads to a bending of light rays when they come close to a large amount of matter, like a galaxy cluster. Thus, when the light of distant galaxies passes a massive cluster of galaxies before it reaches us, we will see a deformed image of the distant galaxies. The effect can be calculated and astronomers are able to trace it back. From the distorted shapes of distant galaxies behind a galaxy cluster they can infer the distribution of mass in that galaxy cluster. The heavier a galaxy cluster is, the more it bends the light and the more it distorts background galaxies. For the Bullet Cluster, the blue blobs in the picture above show the distribution of mass as inferred from the gravitational lensing effect assuming General Relativity to be valid. One can see that it follows the distribution of galaxies, not the gas.

If the hot gas would be the most massive part of a galaxy cluster, the mass found through gravitational lensing would have to be centered on it. But as this is not the case, it is said that the majority of matter in the galaxy cluster has to be close to the galaxies. Because the visible mass in the galaxies is not enough to account for the velocity dispersion of a galaxy cluster (assuming Newtonian Dynamics, i.e. General Relativity), it is conjectured that there is Dark Matter, which by definition only interacts through gravity, too. Thus distributions of DM can pass through each other just like the galaxies and the majority of mass should be found close to the galaxies in such a cluster collision.

This is why the Bullet cluster is often said to be the “smoking gun” of the Standard Cosmological Model. It behaves just like it is expected. But is it really that simple? Does this proof the existence of Dark Matter? No, it doesn’t.


Observations and Interpretations

In the most-often given description of the Bullet Cluster, what is observation and what is interpretation get mixed up. The observations tell us that the hot gas component and the lensing mass have an offset. One good conclusion from this is: The visible, hot gas can not make up the majority of mass in the system. But a wrong conclusion is: The Cold Dark Matter Hypothesis is right.

While we can argue that the majority of mass has to be close to the galaxies, we can not immediately conclude that it has to be in the form of Dark Matter as a new type of particles. Actually, we can only say that the majority of gravity, or even more specific, the major bending of space-time, happens close to the galaxies. Whether the reason is missing mass or a different law of gravity is not that easy to distinguish (there is gravitational lensing in modified gravities, too). The whole, most-mentioned conclusion is therefore based on one important, but never mentioned assumption: that gravity is best described by Newtons law. In addition to that, it supposes that other, known forms of dark matter (e.g. neutrinos) can not be the reason. Without those assumptions, the case of the Bullet-Cluster is not decided at all.

We see that the “direct proof for the existence of Dark Matter”, is an indirect hint at best, in that it is based on untested assumptions and does not even look at other possible predictions of alternative gravities. But there are more problems to come.


A Proof of Dark Matter?

Even if the cluster can be explained in the standard or concordance cosmological LCDM framework, this does not proof the theory. Because there can be no proof of a scientific theory. For the BC to be a proof of a scientific theory, it would have to rule out each and every alternative explanation, even those of which we can not even think of today. This, of course, is impossible. This fact is well known in the philosophy of science and I guess most scientists know this. Scientific inference does not function without this elementary fact.

Furthermore, there are different possible explanations for the BC. There even are different possible forms of Dark Matter. Not only the currently favored Cold Dark Matter, on which the Concordance Cosmology Model rests, but a model with Hot Dark Matter (where the DM-particles are fast/relativistic because they would be of low mass, like neutrinos) could explain the BC as well. So, please don’t state that the Bullet Cluster has proven the LCDM-model right. It has not. And it can not.


The Bullet Cluster, a problem for Dark Matter?

In fact, the Bullet Cluster might not only not be a proof of the DM hypothesis but it actually appears to be a major problem for the concordance model. Mastropietro and Burkert (2008) have found that the two colliding clusters need to have a relative velocity of about 3000 km/s to produce the observed X-ray gas properties. This result was compared to a cosmological simulation named MICE. Such cosmological large-volume simulations show the formation of structure in the universe and are often said to be another important success of the Concordance Cosmological Model. In the MICE simulation, Lee and Komatsu (2010) determined the probability that the Bullet Cluster’s velocity could be found in the concordance cosmological model. It is roughly one in ten billion! They …

“… conclude that the existence of [the Bullet Cluster] is incompatible with the prediction of the ΛCDM model …”.

This is a paradoxical situation: While the structure formation simulations are used to argue in favor of Dark Matter because they fit so well, and the Bullet Cluster is used in favor of Dark Matter as a “direct proof” or “smoking gun”, putting them both together leads to an incompatibility.


Does the Bullet Cluster matter at all?

So far we have shown that the Bullet Cluster can not be understood as proof for the Dark Matter Hypothesis. We took the argument seriously. But in doing so, we have repeated the same mistake as many people who bring up the BC when they try to dismiss our work on testing the Dark Matter Hypothesis. Why that? Well, usually the discussion follows these lines:

  • “Testing the predictions of the Cold Dark Matter Hypothesis on galaxy scales, we have found several serious problems.”
  • “But don’t you know about the Bullet Cluster? It is the proof that there is Dark Matter!”

Put that way, it is easy to spot the mistake: Even if the Bullet Cluster could only be explained with Dark Matter, the problems on small scales persist. The BC does not tell us anything about the Local Group of galaxies, the two arguments are completely independent. There is a serious problem with the DM Hypothesis and even a thousand Bullet Clusters would not make it go away. In fact this is similar to the hypothetical scenario that someone, for example at the LHC, would find “The Dark Matter Particle”. Even in that case, the current problems of the model would not go away. Rather, this would point at a much more serious issue with our understanding of physics.

In trying to understand the universe, we as good scientists should thus look for alternative explanations that account for all independent observations and discuss these without ideological pre-conceptions.

Solutions to the Bullet cluster in modified Newtonian dynamics (MOND) have indeed been shown to exist (Angus, Famaey & Zhao 2006). The authors conclude

In multicentred models, the convergence map does not always reflect the projected matter in the lens plane in MOND. This cautions simple interpretations of the analysis of weak lensing in the bullet cluster 1E 0657−56 (Clowe et al. 2004; see fig. 7).

Similarly for Modified Gravity (MOG):  Brownstein and Moffat (2007) write

The MOG prediction of the isothermal temperature of the main cluster is T = 15.5 +/- 3.9keV, in good agreement with the experimental value T = 14.8+2.0-1.7keV. Excellent fits to the 2D convergence κ-map data are obtained without non-baryonic dark matter…” and they uncover a significant disagremenet with the dark-matter based analysis (the baryon fraction is to high in a dark-matter model).


Stay tuned, there is more to be said about galaxy cluster and the Bullet Cluster in modified gravity theories in our next post.

by Anton Ippendorf, Pavel Kroupa and Marcel Pawlowski (30.07.2010): “But the Bullet Cluster … – Proof of Cold or Warm Dark Matter in galaxy clusters is but a myth” in “The Dark Matter Crisis – the rise and fall of a cosmological hypothesis” on SciLogs. See the overview of topics in  The Dark Matter Crisis.

4. Is it absurd to throw out the idea of Cold or Warm Dark Matter?

In an interesting comment Daniel Fischer (22.07.2010, 17:00) points out the contribution by Ethan Siegel. In essence Ethan Siegel writes “saying that, ‘since the naive predictions we can make are inadequate, the entire idea of dark matter needs to be thrown out’ is absurd.”

 What is absurd is to presume that a theory that is adequate on one scale will inevitably succeed on another scale.  That LCDM is consistent with large scale measurements is no guarantee that it will work on smaller scales.  The widespread presumption among cosmologists seems to be that it must surely work out, though this is hardly a scientific attitude.

The failure of dark matter to explain galaxy scale phenomena is not just a failure of detail.  A single effective force (modified gravity) suffices to explain (and indeed,
predicted a priori) many aspects of galaxy dynamics.  To explain this with dark matter is like asserting that really the solar system operates on an inverse cube law; there just happens to be dark matter arranged just so as to always make it look like an inverse square law.

It is hard to imagine a more bizarre requirement for the distribution of dark matter.”Prof. Dr. Stacy McGaugh (his MOND papges).

It is noteworthy that the community seems to stress aparent successes of dark matter but when failures occur these are often put down as occuring in a regime not testable.  A good example is the current statement by Daniel Fisher in contrast to the statements found at the beginning of Section 2.4.


We see that Ethan Siegel’s argument is wrong logics. The dark matter hypothesis was introduced to specifically solve the “small-scale” problem of flat rotation curves of disk galaxies. To later argue that the dark matter hypothesis cannot be tested on these scales is throwing out logics and the very basics of how scientific inference works. Actually, in our research paper the problems found are not only on small scales but extend to scales of a million pc.

A Gedanken experiment helps to clarify the problem: Take one observed normal disk galaxy which you know to be in equilibrium (i.e. is not disturbed by another galaxy). Call this galaxy 1. It has a flat rotation curve. Put in the correct distribution of dark matter to explain the rotation curve. Now observe another disk galaxy which you know to be in equilibrium (galaxy 2). Measure the distribution of normal matter. Ask the astronomer to predict the shape of the rotation curve of galaxy 2 based on the observation of galaxy 1. Then measure the rotation curve of galaxy 2. The predicted and observed rotation curve will almost certainly be different.

Now, repeat the exercise in MOND (no dark matter, but a gravitational theory modified according to Milgrom). The astronomer will be able to exactly predict the rotation curve of galaxy 2 based purely on the observed distribution of normal matter in galaxy 2 and one universally valid number (a universal acceleration scale, a_0) obtained from the fit to galaxy 1. In fact, the astronomer can predict the shapes of all rotation curves using this one number a_0.

Therefore, Milgrom’s theory is far more superior in describing galactic dynamics than the dark matter plus Newtonian hypothesis. What is more, the dark-matter hypothesis does not allow us to understand rotation curves. And this does not depend on unknown small-scale effects, as we are talking about scales of 10,000 to 50,000 pc.

Some explicit references:

In McGaugh & de Blok (1998a) the authors state: “Interpreting the data in terms of dark matter leads to troublesome fine-tuning problems. Different observations require contradictory amounts of dark matter. Structure formation theories are as yet far from able to explain the observations.”

The companion paper, McGaugh &  de Blok (1998b) finds: “One hypothesis, Modified Newtonian Dynamics (MOND), is consistent with the data. Indeed, it accurately predicts the observed behavior. We find no evidence on any scale that clearly contradicts MOND and much that supports it.

Within the dark-matter theory galaxies would be embedded in dark-matter halos with well-known properties. That they do not match observed roation curves is documented convincingly by Kuzio de Naray et al. (2009): “The shape of the modeled NFW rotation curves does not reproduce the data”.

The observed similarity of galaxies being in  contradiction to the expected large variation of galaxies if dark-matter theory were correct is documented by Disney et al. (2008).

In fact, galaxies tell us that the dark matter (if it were to exist) arranges itself according to the distribution of the normal matter, although the normal matter makes only a small fraction of the mass of a galaxy. To explain this insurmountable fine-tuning problem one would need to invoke a dark force coupling dark matter to baryons in a hitherto not understood way (Kroupa et al. 2010), or simply accept that galaxies are made up only of normal matter without dark matter and that gravity is non-Newtonian.

A lesson from history:

In this vain we might remember history: Once upon a time, not too long ago in fact, very clever people knew that heavenly bodies were either at rest or moving about other bodies on perfect circles (the planets and Sun moving around the Earth). So important and widely accepted was this idea that when the observations (of planetary motions) failed to fit the predicted motions, a circle on a circle was introduced to describe the motion of the planets. And if this was still not good enough, then yet another circular motion about a centre which moved on a circle about a centre which moved on a large circle about the Earth was added. But, in this theory of epicyclic motion an astronomer was not able to predict the motions of a new planet.

And here too, one could have argued that “just because there are minor deviations from the calculated motion of the planet and just because a Kepler and a Copernicus thought that the actual motion was on an ellipse about the Sun (!) it is surely absurd to throw out the whole large and divine picture of perfect motions of heavenly bodies, which was so successful overall.”

Note also that two major mental changes had to be accepted: The centre of motion is not the Earth but the Sun and the motions are elliptical. 

In our case (Kroupa et al. 2010) two mental changes are also required: the satellite galaxies of the Milky Way are not dark-matter sub-structures but tidal-dwarf galaxies, and dynamics is non-Newtonian (e.g. Milgrom’s MOND or Moffat’s MOG).

And, although the Kepler laws and Copernican idea proved endlessly more successful in describing planetary motions, they were quite useless in describing the dynamics of star clusters because the deeper (Newtonian) gravitational theory had not been discovered yet. But it was absolutely evident that the epicyclic ansatz was out.

Today we would be saying that modified gravity is endlessly more successful in describing rotation curves of galaxies and galactic dynamics in general, and that cold or warm dark matter is out. But we do not yet have the full underlying gravitational theory which is likely to unite matter and space time as a single entity. 

Epicyclic additions

The concordance cosmological model arose by adding dark matter to the Theory of General Relativity, then adding inflation and then dark energy to get a model which has not been able to account correctly for the way galaxies work nor how they evolve and arrange themselves in space time. Furthermore,  an extra dark force is required as a further addition.

by Anton Ippendorf, Pavel Kroupa and Marcel Pawlowski (28.07.2010): “Is it absurd to throw out the idea of Cold or Warm Dark Matter?” in “The Dark Matter Crisis – the rise and fall of a cosmological hypothesis” on SciLogs. See the overview of topics in  The Dark Matter Crisis.

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3. August-Issue of “Spektrum der Wissenschaft”

The new issue of Spektrum der Wissenschaft (SdW) is in the shops today. Our (Pavel Kroupa and Marcel Pawlowski) article on dwarf galaxies and dark matter is even mentioned on the cover and in the editorial. In Germany and Austria, you can buy the magazine for 7.40 Euros. Alternatively, you can download the free PDF of our article “Das kosmologische Standardmodell auf dem Prüfstand” from the SdW website and read it right away.

When SdW asked us to start this blog, we agreed. The main reason was to make a direct discussion about the issues we raise in the text possible. We will post additional texts (in English) on this blog, which might lead to interesting debates. In case you would like to comment on the article in SdW, feel free to give your statements or ask questions here.

2. Article available online

from Marcel S. Pawlowski, 24. July 2010, 10:57

The German article on dwarf galaxies and the test of the cosmological standard model is available online. You can download it for free from the website of “Spektrum der Wissenschaft”. On Tuesday, the printed magazin with our text will be in the stores. Subscribers of the popular science magazin already got their copies.

Feel free to discuss the article with us on this blog.

1. A challenge for Dark Matter

There was a time I (Pavel Kroupa) was quite happy with the dark-matter cosmological model. Dark-matter cosmology made a lot of sense, since we were allowed to keep our simple Newtonian “equations of motions” which meant that modelling star clusters, galaxies and the whole universe was simple (but still challenging) computationally. The only price we had to pay was to accept the existence of exotic new “dark” particles which were not part of the otherwise overwhelmingly successful Standard Modell of Particle Physics. Since the neutrino had been predicted in 1933 to exist based on a missing mass problem in beta decay and was then discovered in the laboratory in 1956, the mental pathway had already been laid out towards accepting the existence of dark particles. The dark-matter cosmological model was enhanced over the past decade by the addition of dark energy, that is, the “Lambda Cold Dark Matter Concordance Cosmological Model” (the LCDM CCM) was born. It came to be celebrated as an exquisite physical model of the universe, and many of us astrophysicists knew we live in the era of precision cosmology, given that the CMB, SNIa and large-scale structure observations seemed to provide an excellent fit.

The issue was now merely to work out the details of galaxy formation and evolution, and to confirm the exitence of the dark matter particle through direct experimental detection, and to develop a theory for particle physics which would supercede the Standard Model of Particle Physics and naturally contain the dark matter particles.

Thus the LCDM CCM is currently a widely accepted or should I say “believed” description of the birth and evolution of the universe and of its contents. This comes as no surprise: The many parameters that define this model (see e.g.  Lambda-CDM model) have been measured extremely precisely and at the same time the model excellently accounts for the large-scale structure of the universe, as is evident for example in the distribution of galaxies and galaxy-clusters and the microwave background temperature variations. So people were very impressed and started talking about the advent of precision cosmology.

At the beginning I too did not bother with the fundamental issues raised by some (see e.g. Prof. Dr. Tom Shank’s paper). My own research was very much confined to the early version of the CCM (mid-1990’s) when I began performing numerical experiments on the satellite galaxies of the Milky Way applying, as everyone else, Newtonian dynamics with dark matter. My computational work on the evolution of satellite galaxies as they orbit about the Milky Way within its large massive dark matter halo quite quickly demonstrated that there are very natural mathematical solutions for the observed satellites but without dark matter. I was stunned, because my results were based on observed young satellite galaxies that have no dark matter (tidal dwarf galaxies – TDGBonn) and they evolved into objects that resembled the observed ancient satellite galaxies of the Milky Way and appeared to be full of dark matter. My calculations showed, however, that this was fake dark matter – the stars that make up the satellites move around within the satellite and about the Milky Way, and the observer from Earth interprets these complex motions to be due to an unseen dark matter component in the satellite.

Thus, with time it became increasingly apparent that the CCM accounts poorly for the properties of the satellite galaxies and their distribution around the Milky Way, that is for our cosmological neighbourship. One major problem turned out to be the distribution of satellite galaxies about the Milky Way, in a disk-like structure, which was not in good agreement with the expected distribution within the CCM (Kroupa et al. 2005). The idea that the satellites are a group of dwarf galaxies that fell into the Milky Way dark matter halo (The “Custer’s Last Stand” of the CCM) was ruled out as a viable solution to this Disk-of-Satellites problem because dwarf galaxy groups do not have the required properties (Metz et al. 2009).

If the Milky Way satellites can be derived from dark-matter free objects that we definitely know to exist through direct observation (tidal dwarf galaxies), then how can they at the same time be the dark matter sub-structures predicted by the CCM? My work proved that the there were more than one solutions to the satelite galaxies, and that the CCM predictions were therefore not unique. Warm dark matter (WDM) models fared no better. (Warm Dark Matter particles like gravitinos and sterile neutrinos are, to keep it simple for the moment, moving quicker than Cold Dark Matter particles like Axions and WIMPs.

Considering other major galaxies I began to realise that actually I do not know any single galaxy whatsoever which looks like an object that may be described successfully within the framework of the dark-matter CCM (for example in terms of a galaxy’s distribution of dark matter within it, or in terms of the thinness and extent of the visible matter in galaxies, or even in terms of the star-formation behaviour of galaxies).

Perhaps the tide began turning significantly in 1999. Then I heard an excellent talk at Harvard University by Stacy McGaugh on his research on rotationally supported galaxies (see Prof. Dr. Stacy McGaugh for much information on this issue). Stacy explained in a most convincing manner that an alternative description via modified gravity (or “extended gravitational theory”) actually leads to a far superior understanding of galactic properties than the CCM. See McGaugh’s MOND pages  and frequently asked questions for an introduction to Modified Newtonian Dynamics or Prof. Dr. Mordehai Milgroms popular article in Scientific American (2002) article or its version for german readers in Spektrum der Wissenschaft (only html, http://www.spektrum.de/artikel/829190).

Basically “Modified Newtonian Dynamics” or MOND means that Newtonian gravity has to be modified at very small accelerations. If accelerations are small, the gravitational force is a bit stronger than would otherwise be supposed. This may either be due to a change in gravity, or due to a change of inertial mass of the particle (in which case the equivalence between gravitating mass and inertial mass would be broken). Both possibilities offer extremely exciting avenues of research within mathematical physics.

So why should this idea replace the concept of dark matter? Both can possibly account for the same fundamental problem: Apparently many stars rotate too quickly around their galaxies. They rotate so quickly that they would fly away if their galaxies had only the mass we can observe. This observation is quite universal and also holds for galaxies orbiting in clusters of galaxies. The most obvious solution to the problem: There must be more mass than we can observe. Having ruled out other candidates for the missing mass, in the 1980s the notion of “dark matter” became generally recognized: There must be a new kind of matter which should be unobservable via direct measurements (that is: “dark”), but interacting via gravity force.

But until today dark matter has not been observed. Worldwide there are several experiments underway to measure its signals but results have been negative all along. Favoured dark matter particle parameters have by now been excluded. And the consistent failure to find any trace of the dark matter particle is increasingly suggesting that dark matter may not exist at all.

Indeed, in the last few years it has become rather clear, based purely on astronomical evidence,  that the CCM (with cold or warm dark matter with at most very weak coupling to baryonic, i.e. “normal” matter) is ruled out as a viable description of the universe. Our research paper published in 2010, Local Group tests of dark-matter concordance cosmology: Towards a new paradigm for structure formation, leads to this conclusion (the Local Group is a typical environment of galaxies and must therefore be contained in the CCM).

While this is a very strong conclusion,  it rests upon a two-decade-long study towards understanding the dynamical behaviour of the hypothetical dark matter particles and the physical processes at work in normal matter. This study involved working on how stars form and how their birth structures (star clusters) dissolve, and how purely gravitating matter (dark matter) collects in self-gravitating structures with stars and gas. This study compiles the most recent high-resolution models calculated on supercomputers worldwide by various teams with the specific aim to solve the small-scale problems and to explain the properties of satellite galaxies within the logical framework of the CCM. Basically it can now be stated with much confidence that the properties of galaxies and the arangement of their satellite galaxies about them cannot be understood in a universe with cold or warm dark matter and Newtonian dynamics plus the physics of normal matter.

In this research paper five problems for the CCM are found, in addition to the well-documented previously known problems that had mostly not been resolved. Each of the five problems poses a challenge for CCM, and together they exclude it with very high confidence indeed. The Disk-of-Satellite issue is but one of the problems.

To be continued.

by Pavel Kroupa (22.07.2010): “A challenge for Dark Matter” in “The Dark Matter Crisis – the rise and fall of a cosmological hypothesis” on SciLog. See the overview of topics in  The Dark Matter Crisis.

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