II. The Fritz Zwicky Paradox and its solution

What is the Fritz Zwicky Paradox?

In our previous contribution we gave three historical examples of previous failures of Newtonian mechanics or dynamics. These failures implied quantum mechanics, special and general relativity. While not evident at start, each of these break-throughs lead, many decades later, to very major technological advances with industries worth trillions of dollars today. In the present era physics is experiencing the fourth failure. But how does the failure arise?

The Fritz Zwicky Paradox is one aspect of the fourth failure. The fourth failure means that cold or warm dark matter particles, if evidence were to be found which may be interpeted to be due to some particle decay (e.g. by the Alpha Magnetic Spectrometer or AMS), cannotplay a significant role in cosmology: If additional massive particles would be found to exist outside the Standard Model of particle physics, then they must be rare or too short lived to affect the mass budget of a galaxy. That is, concordance cosmology cannot be the correct description of the universe.

This statement goes massively against the widely held “believe” that the dynamics of the universe is driven largely by these particles, because in the presently widely  accepted cosmological model such (heavy) elementary particles are understood to be dominating all forms of matter.

But why do we have this “standard” or “concordance” dark-matter-based cosmological model?

It rests on two fundamental assumptions:

First: The Theory of General Relativity is correct on galactic and cosmological scales.

Second: All matter is created during the Big Bang.

This leads to the concordance cosmological model according to which the cold or warm dark matter particles clump in an expanding universe gathering up the normal matter which we experience. The formation and evolution of galaxies are defined, in this model, by the collisions of myriads of small dark-matter clumps, some of these contain gas leading to the formation of stars. The concordance cosmological model is thus, strictly logically, tied up with very specific predictions concerning how galaxies look like, and also which types of galaxies ought to exist. And this is where the Fritz Zwicky (FZ) Paradox spoils the show:

The FZ Paradox arises due to two observations which famous CALTECH astronomer Fritz Zwicky made:

1) 1937: he notes that galaxies must be about 500 times heavier in the Coma galaxy cluster than judged from their light emission (e.g. Zwicky 1937). This is his famous conjecture that there must be cold or warm dark matter.

2) 1956: he notes that when galaxies interact (e.g. when they collide), the expelled matter can re-condense in regions and form new smaller (dwarf) galaxies. This is his famous conjecture that tidal-dwarf galaxies can form out of the collisional debris of other galaxies (Zwicky 1956, p.369, point 4).

Astronomical observations have traditionally been interpreted as being strongly supportive of  both of these Fritz Zwicky Conjectures:

The first conjecture is supported by stars moving much faster about their galaxy than would be the case if there were no additional (dark) matter to hold them in (see galaxy rotation curves). And, it is also supported by the motions of galaxies in galaxy clusters, as noted by Fritz Zwicky. The overall cosmological evolution also supports this, but only if it is additionally speculated that Dark Energy exists. One needs to postulate the existence of Dark Energy to pull the matter apart again through an accelerating expansion in order to match, roughly, the large-scale structure that is observed. Without the speculative Dark Energy the clumping of Dark Matter would proceed too fast, and the cosmological model, based on the above two fundamental assumptions, would fail. Most cosmologists would also claim that Dark Energy is suggested by supernova Ia (SNIa) distances.

The second conjecture has been observed many times in real galaxies, and also in computer simulations. The formation of tidal dwarf galaxies is an inherent, strictly necessary, process coming from energy and momentum conservation. Young tidal dwarf galaxies are small disk galaxies with star-formation, and there is no viable physical mechanism which destroys them (as shown by Recchi et al.2007 and Kroupa 1997), except if they end up on a plunging orbit through the central region of their host galaxy. But this is very unlikely. The typical tidal dwarf galaxy finds itself on an orbit about the larger post-merger host galaxy, and it may loose its gas because of ram-pressure stripping. A young tidal dwarf galaxy can thus evolve to a dwarf elliptical galaxy if it remains quite close to a larger host galaxy. Tidal dwarf galaxies that are lost to “outer intergalactic space” remain dwarf galaxies with gas and continue forming stars, just like any other small galaxy (Hunter et al. 2000).


Assuming both Fritz Zwicky conjectures to be true, Okazaki & Taniguchi (2000) calculated the number of tidal dwarf galaxies that should exist in a standard cosmological universe. This can be done because the frequency with which galaxies of different types (e.g. spiral galaxies, elliptical galaxies) interact can be computed from the standard-cosmological merger tree. This merger tree is a logical outcome of the dark-matter standard cosmological model, and tells us how the small dark matter clumps coalesce to form the larger dark matter halos within which galaxies such as the Milky Way reside. Modelling of star-formation processes then tells the astronomer which dark halos host what type of galaxy.Okazaki & Taniguchi set up rate equations, for example  S + S  ->  S0 + ndE, where S is a spiral galaxy (containing gas), S0 is a lenticular galaxy and ndE are n dwarf elliptical galaxies of tidal origin.

The merger tree also tells us how many dark-matter dominated satellite galaxies each larger galaxy must have, and how they are distributed.

The result, obtained by Okazaki & Taniguchi, is that the standard cosmological model makes so many tidal dwarf galaxies that all dwarf elliptical galaxies in galaxy groups and galaxy clusters are easily accounted for. There is therefore no room for the expected dark-matter dominated dwarf galaxies.

This can be stated differently: Assuming there are two types of dwarf galaxy:

Type A is the traditional dark-matter dominated galaxy, which the standard model expects to be there in huge numbers as a result of the merger tree. For example, the Milky Way galaxy ought to have thousands of dark-matter satellites swirling about it.

Then there is the type B dwarf galaxy, which is the tidal dwarf galaxy.

We can go to a telescope and observe the dwarf galaxies in galaxy clusters and around our own Galaxy and in our Local Group. It then turns out that Okazaki & Taniguchi calculate that the number of type B galaxies is enough to account for all observed dwarf galaxies in these environments.

One could now argue that type A and type B co-exist. That is, that there are two types of dwarf galaxy. But this argument is difficult to uphold by the simple fact that all observed, that is real, dwarf galaxies in galaxy clusters and in the Local Group of galaxies, look virtually identical in the sense that one cannot identify two distinct populations of dwarf galaxies. That some dwarf galaxies appear as gas-rich (i.e. dwarf irregular galaxies), and others as gas-poor, elliptical dwarf galaxies, is easily understood through the former getting rid of their gas when closer to a larger galaxy (the gas is essentially blown away through the large galaxy).

Therefore, there seems to be only one kind of dwarf elliptical galaxy. Since it is not possible to destroy the tidal dwarf galaxies, and their formation is an established fact of standard physics, one comes to the Fritz Zwicky Paradox:

By assuming that dark matter drives structure formation we end up knowing that all dE galaxies ought to be of tidal origin. But, astronomers have identified all known dE galaxies as dark-matter dominated sub-structures, which are predicted by the dark-matter based concordance cosmological model to be present in very large numbers. Thus a contradiction emerges, because a given dE galaxy cannot be both types at the same time, and the observed satellite galaxies are way too few to account for both satellite galaxy populations predicted by the concordance cosmological model.

The dark-matter universe thus leads to two types of dwarf galaxy populations, each supposedly being abundant, but only one type is observed. In fact, the number of observed dwarf galaxies is nicely consistent with the number expected if they are all tidal dwarf (type B) galaxies. On the other hand, the existence of dark-matter dominated galaxies (of type A) strictly depends on the postulated existence of cold or warm dark matter and the number of such dwarf galaxies is vastly larger than the number of observed dwarf galaxies. This is the “missing satellite problem“, whereby the community has agreed to have solved this problem by stating that there are partially unkown physical processes which keep most small dark matter halos dark. According to Fritz Zwicky’s second conjecture, this agreement is falsified because tidal dwarf galaxies must also exist, thereby leaving essentially no room for the type A dwarf galaxy, making the missing satellite problem catastrophic.


Additional independent arguments:

There are in fact other arguments that, independently, suggest that dwarf galaxies in galaxy groups or galaxy clusters are much more naturally interpreted to be tidal dwarf galaxies. These are put together in this poster: Dabringhausen et al., 2010 (presented at the Annual Meeting of the German Astronomical Society, September 2010 at Bonn University). The poster is based on the more extensive research paper by Kroupa et al. (2010).

In brief: the additional arguments pointing at the dE-type galaxies as being tidal dwarf galaxies are as follows:

The satellite galaxies of the Milky Way are arranged in a huge disk like structure which is grossly incompatible with the more spherical distribution expected if the satellite galaxies were to be dark matter dominated dwarfs (of type A). And, the major galaxies in the Local Group show a very well defined bulge-mass versus number of satellites correlation. This correlation is not expected to exist in standard dark matter cosmology, because the infall of low-mass dark-matter dwarf galaxies (of type A) is a stochastic (random) process and is not related to the star-formation at the very centre of the huge hosting dark matter halo. In fact, we know that the same type of dark matter halo, if it were to exist, hosts large galaxies with and without bulges, while the number of dark matter satellite galaxies depends on the mass of the dark matter host halo only. And, last not least, all attempts to understand the brightness of the observed satellite galaxies in terms of how they form stars in a dark-matter satellite-halo fail rather massively: if the dark-matter satellite halos were there, then a more massive halo ought to, on average, contain a brighter satellite simply because it can hold more of the gas before it disperses due to internal and external physical processes. But, the real satelltie galaxies, when interpeted to be in dark matter sub-halos, fail to comply with this very basic and robust prediction. The masses of the satellite dark-matter halos are therefore unphysical.


How can one solve the Fritz Zwicky Paradox?

All three observed results (disk-like arrangement, the correlation and no dark-matter satellite halos) are instead naturally explained if the satellites are tidal dwarf galaxies (type B). And this is trivial to understand: in a galaxy–galaxy interaction matter is expelled along special directions, and the tidal dwarf galaxies that form in these tidal tails then retain a common sense of orbit forming a disk-like structure. And, bulges form in galaxy interactions, leading to a natural correlation between the bulge mass and the number of satellites. This correlation is a measure of the strength or gas-richness of the galaxy–galaxy encounter (more gas => more star formation and more satellites). That the real satellite galaxies appear to be dark matter dominated then naturally emerges if an observer sees the satellites through Newtonian eyes, but if the satellites in truth obey non-Newtonian dynamics and if they are affected by the Galactic tidal field. This is nicely discussed by McGaugh & Wolf (2010).


The history of the early Milky Way

For the Milky Way galaxy this means that about 10-12 Gyr ago it had a major encounter with some other young galaxy. This encounter happened nearly perpendicularly to the present-day disk of the Milky Way, because the other galaxy came from a minor filamentary structure which has been identified by Metz et al. (2009). This encounter, being very gas rich as both the Milky Way and the other galaxy were very young, lead to gas-rich tidal tails within which star formation must have happened. Also, this encounter lead to gas falling towards the center of the young Milky Way, triggering a major episode of star formation there. Today we see the ancient remnants of this early violent event, in the form of the central bulge of the Milky Way and the ancient satellite galaxies that still orbit the Milky Way at large distances and which are arranged in a disk-like structure.


What does the Fritz Zwicky Paradox imply for fundamental physics?

Given that the observed dwarf galaxies are best identified as tidal dwarf galaxies, the internal motions of stars are not compatible with Newtonian/Einsteinian dynamics. Actual observational evidence for this has been found: three tidal dwarf galaxies for which observations have been obtained, show the same rotation curve behaviour as normal galaxies. That is, at larger radii, the stars and gas are orbiting about the galaxies too fast (Gentile et al. 2007). Because tidal dwarf galaxies cannot have much dark matter (they are too small to capture it, even if it were to exist), then these motions of the stars can only be explained by violating the first fundamental assumption above. That is, General Relativity needs to be either discarded, or modified, in order to explain the motions of bodies on the scales of galaxies and beyond.

This is the “fourth failure of Newton“. Indeed, degrading cold or warm dark matter as being insignificant for cosmology, or even as not existing at all, leads to rich new gravitational (non-Newtonian/Einsteinian) dynamics (e.g. MOND or MOG), and to a new and vastly superior understanding of galaxies. This is the subject of our research paper (Kroupa et al. 2010). For those interested, Prof. Milgrom provides a Pedagogical Review of MOND and Prof. McGaugh has prepared the MOND Pages. A gateway to Prof. Moffat’s MOGis found here. Other non-dark-matter approaches via higher-order curvature theories have been discussed, among others, by Capozziello et al. (2004) and Martins & Salucci (2007).

Currently very exciting research is being done in this “non-dark-matter” field, albeit with the very serious difficulty of small funding because virtually all public funding for cosmology is allocated to support research in the standard dark-matter-based or concordance cosmological model. But galaxies are, as far as the data allow us to tell, only composed of normal matter. Given the failure of the dark-matter ansatz, it becomes apparent that Dark Energy is most likely unrealistic too (see “Is LambdaCDM or standard cosmology a 4th order speculation, and ought it be further researched ?“). Research on alternative cosmological models will certainly lead to new physics, but a deep understanding may only emerge once the physics of the vacuum is understood.

by Anton Ippendorf, Pavel Kroupa and Marcel Pawlowski (08.09.2010, “The Fritz Zwicky Paradox and its solutionin “The Dark Matter Crisis – the rise and fall of a cosmological hypothesis” on SciLogs. See the overview of topics in  The Dark Matter Crisis.


Author: Prof. Dr. Pavel Kroupa

I am a Czech-Australian teaching and researching at the University of Bonn on dynamics and stellar populations. After studying physics at The University of Western Australia, Perth, I obtained my PhD from Cambridge University, UK, as an Isaac Newton Scholar at Trinity College. After spending eight years in Heidelberg I habilitated at the University of Kiel, Germany. I then took up a Heisenberg Fellowship and later accepted the position as a professor at Bonn University in 2004. I was awarded a Leverhulme Trust Visiting Professorship (2007, Sheffield, UK) and a Swinburne Visiting Professorship (2007, Melbourne, Australia). In 2013 I received the Silver Commemorative Medal of the Senate of the Czech Republic, and I took-up an affiliation with the Charles University in Prague in 2016. Pure innovative science can only truly thrive in non-hierarchical societies in which competition for resources is not extreme. Therefore I see the need for the German academic system to modernise (away from its hierarchies) and warn of academic systems that are based on an extreme competition for resources (USA), as these stifle the experimentation with new ideas.

2 thoughts on “II. The Fritz Zwicky Paradox and its solution”

  1. What is the mathematics describing?I’m a layman in the field of physics and mathematics, but have been wondering what the divergent theories and their mathematical formulations have been describing. This started with my fascination with string theory and led me to the basic question why is the observed influence of gravity so weak in comparison to the strong and weak nuclear forces.
    Is it fair to postulate that gravity is not weak in comparison, but warped in the same fashion that space is purported to be. Assuming that Einstein was not entirely correct about matter warping space. That matter is (as is conventionally understood) not the only perturbation in space or time.
    I realize such thoughts may see me burned as a witch, but our theories of gravity appear flawed. Could it be that conventional matter is only one aspect of the warping of space. If you look at time dilation it appears to be warped by relative motion with respect to matter (point to point subjective). Speed limit.
    What if there was no matter? Does time and space continue to exist? I would argue that time must preexists our known universe for any relevant discussion to be of value. And for time to be relevant space must exist also.
    Mathematics imposes abstract concepts upon our known universe. We can say that 1 + 1 = 2, but we know full well that 1 is not simply 1, but a perceptual representation of what we choose to see as a single element of calculation.
    Let’s go further down the rabbit hole. We have created such a beautiful symphony of mathematics that no one individual can truly grasp the significance of the language. There’s no one person who is completely fluent in the language. Some are very close (Witten, Penrose), but ask either if they understand the language completely.
    As a person of no consequence in this field of study I can afford to be a hieratic. Why are there no others questioning the basis of our mathematical constructs?
    Is it so difficult to experimentally reassign some of our basic concepts of geometry? A point of no distance (measurable) is a single dimension. Why is a point leading to the left or right seen as two dimensional? Why not point of existence, direction 1 2nd, and direction 2 3rd? Because that view does not appear rational in our understanding of mathematics or the universe.
    Empiricism was born of philosophy. A rational development, but philosophy is flawed, so too must be the case for Empiricism (lest we believe ourselves beyond advancement). But, what does that mean?
    Rational perceptions are limited by our ability to interpret what we perceive to be substantial. Mathematics only represent our assumptions, but mathematical experiments reveal things that we have no description for.
    I’m willing to lead you through another rabbit hole, assuming you haven’t decided I should be put to the stake.
    Mathematics should not be restrained by what appears to be ambiguous. Redefining geometry would be tame if only described as ambiguous.
    Food for thought, Time = 3D
    Matter = 3D
    Space = 6D
    Relying upon old assumptions is what empiricism has tried to avoid. Try the equivalent of progressive spacial maps. (time point, forward, backward), (matter weak, strong, gravity), and space as the expression of both 6D.

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