71. From galaxy bars to the Hubble tension: a comprehensive review of evidence concerning MOND

This is a guest post by Dr. Indranil Banik (past Alexander von Humboldt Fellow in the SPODYR group at Bonn University and now at Saint Andrews University) on a comprehensive 150 page review of MOND.

The Banik & Zhao (2022) paper is an invited review for the journal Symmetry, in particular for their special issue on modified gravity theories and applications to astrophysics and cosmology. Dr. Banik consulted the community widely and incorporated many comments and suggestions into the review, including several from the referees.

First comes a preamble, followed by the guest post:


Preamble by Pavel Kroupa:

How can a theory be assessed in terms of us (i) trusting it to provide a physical model of a phenomenon we can comprehend rationally (i.e. in terms of mathematical language) and (ii) perhaps even more importantly, trusting it to allow predictions that we need (e.g. to send astronauts into space).

One possibility of how to assess theories in terms of the above two points was approached in two previously published invited reviews, Kroupa 2012 and Kroupa 2015. In these I analysed the dark-matter based theories that rest on Newtonian/Einsteinian gravitation being valid also on the scales of galaxies and beyond. In the 2012 paper, I introduced a visualisation and test of how theories fare by plotting the evolution of confidence in the theory with time. Each time a given theory fails a test, confidence is lost, e.g. by 50 per cent (to be conservative). A total falsification would be achieved if a test or sum of independent tests achieves a threshold where the confidence remains at one in one point seven million. This is the “5sigma” threshold that signifies a discovery, e.g. of a particle (meaning that the hypothesis that the particle does not exist has a remaining confidence of 1 in 1.7 million, the non-existence of the particle therewith being falsified with a confidence of 5sigma). I concluded that the dark-matter-based models are falsified with more 5sigma confidence (i.e. the discovery is made that the dark matter models are not valid). The dark-matter-based cosmological models are thus not viable descriptions of the Universe. Blog Nr. 51 shows this graphically.

Put in other words: if you would send out astronauts to another part of the Milky Way and if you believe in the dark matter theories, then the astronauts have a chance of below 1 in 1.7 million to reach the destination and to live. Obviously we want to raise the chances of hitting the target. That is why we need a different theory. MOND appears to be such a theory. As an astronaut with a desire to live, I would navigate my ship according to Milgrom’s equations of motion, and not Einstein’s ! This is true because application of the “confidence graph” to MOND shows that MOND has not lost confidence (Kroupa 2012).

Since 2012, the dark-matter-based cosmological models are thus ruled out as viable theories for the Universe with more than 5sigma confidence. This is also discussed independently by Bjorn Ekeberg in “The Breakdown of Cosmology” and David Merritt’s “A Philosophical Approach to MOND”.

Nevertheless, the scientific establishment has a great inertia, and the majority of cosmology-related scientists work on the basis of belief (that dark matter exists and these theories remain valid despite the evidence), implying that much effort and taxpayers money needs to be kept being wasted in showing they are ruled out using additional tests. This is very necessary because the scientific establishment can just keep on ignoring results as long as the majority of scientists go along with this (see the previous blogs here on this issue). The weaker majority can be shepherded into a main-stream behaviour of ignoring a falsification through pressure and power exerted by “ΛCDM priests”.

The new very major and highly detailed review by Banik & Zhao, described below, is therefore essentially needed to keep up an opposing pressure such that, hopefully, a few very talented and bright researchers can break away from the dark matter mainstream. The more scientists that show brightness, the better. This review also updates us on the performance of MOND.


Indranil Banik writes:

One of the great mysteries in astrophysics today is why galaxies rotate so fast in their outskirts compared to the circular velocity that we expect from applying Newtonian theory to the distribution of visible stars and gas. This flat rotation curve problem has been around for fifty years, but there is still no consensus on the solution. More generally, astronomical observations on a range of scales imply that there must be more gravity than classical theory predicts based on the directly detectable mass. This missing gravity problem could indicate the presence of large amounts of undetected mass (dark matter), a breakdown of our gravitational laws, or some combination of both. In this review, I considered the standard cosmological paradigm (ΛCDM) and Milgromian dynamics (MOND) as the best-developed alternative that has been around for almost forty years. I focused on all major areas of astronomy where the observations are reasonably accurate and different outcomes are expected depending on which of these models is correct. I also considered some future tests in Section 11. Other alternatives to these two approaches are briefly discussed in Section 3.6 (which covers superfluid dark matter and emergent gravity), but I conclude that it is highly unlikely for any model beyond ΛCDM and MOND to ever explain all the presently available evidence. I therefore focused on these two paradigms.

To assess which works better, I used a 2D scoring system developed with my co-author Dr. Hongsheng Zhao, also at Saint Andrews. One of these dimensions is the usual assessment of how well each theory matches astronomical observations of a particular kind, e.g. data from strong gravitational lenses. I assigned a score between –2 and +2 based on my assessment and that of other researchers. The other dimension used to score each theory against each test is the flexibility of the model when applied to the relevant observations. A strong a priori prediction would lead to a score of –2. At the opposite extreme, a score of +2 represents situations where the theory can explain any plausible data, i.e. observations that are plausible based on prior knowledge but without the benefit of the theory. The use of this second dimension to the scoring system was motivated by A Philosophical Approach to MOND, an award-winning book by David Merritt on why it is important for scientific theories to be predictive. While this was common knowledge in the past, this basic aspect of science has been all but forgotten by astronomers thanks to the lack of predictive power inherent to the prevailing cosmological paradigm. To come up with an assessment of whether a theory matches a particular test, I subtracted the theoretical flexibility score from the level of agreement with observations. The results for different tests were then averaged, giving a score for each theory that could in principle be anywhere between –4 and +4.

The idea behind this scoring system is that in an unphysical theory with many free parameters (e.g., the geocentric model), any agreement with observations should generally involve areas where there is a lot of theoretical flexibility. If any strong predictions are made by such a theory, these should typically fail at high significance. There is always the possibility of agreement by pure luck, but this should be very rare. Consequently, we expect very similar scores for theoretical flexibility and the level of agreement with observations. While results for individual tests can differ, we generally expect an unphysical theory to give an average confidence score close to 0 once the results for many tests are averaged. On the other hand, if the physical content of a theory is partly or largely correct, then we expect it to make clear predictions or have unavoidable consequences which are in agreement with observations. In other words, we expect there to be many situations where the model has little theoretical flexibility but still agrees well with observations. We do not expect a positive confidence score in all cases because there could be problems with the observations or other issues, but even so, the average confidence score across many tests should be significantly above zero. In this way, it is possible to assess a theory on its own merits without considering any other theory.

Another important consideration is that some observations are used in the construction of the ΛCDM theory and to set its free parameters. The same applies for MOND. To account for this, I do not consider the test based on the cosmic microwave background (CMB) anisotropies for ΛCDM as their power spectrum is typically used to set the cosmological parameters. The main free parameter in the MOND framework is a0, a fundamental acceleration scale that is sometimes referred to as Milgrom’s constant. a0 was fixed before I was born based on the rotation curves of high surface brightness (HSB) galaxies (Begeman+ 1991). Fortunately, there are a great many lines of astronomical evidence, so the loss of one test for each theory is not a major setback in my attempt to quantify which paradigm better matches the observations.

Table 1: Summary of how well ΛCDM fares when confronted with the data and how much flexibility it had in the fit. The open dot shows that CMB observations were used in theory construction, so this test is not used when assessing ΛCDM. (Table 3 of Banik & Zhao 2022)

My assessment of the ΛCDM paradigm is summarized in Table 1. The test involving the CMB is shown with a hollow dot to indicate that it should not be used to test the model because nowadays the CMB power spectrum is used to fix the free parameters of ΛCDM cosmology. There were referee comments about this and a few of the other tests, which required various changes to the scores. For example, the lithium problem forced a bleaker assessment of how well ΛCDM agrees with the observed primordial light element abundances. Section 10 of my review provides further discussion of the scores assigned to tests where the score was difficult to assign or runs contrary to what people intuitively expect, including also tests where the referee requested alterations to the scores or the splitting of a test into two or more tests. Very few tests of ΛCDM are located towards the top left. Most tests are located close to or even slightly below the line of equality, implying a zero or slightly negative confidence score. As argued above, this suggests an epicycle-like theory where there is some limited validity, e.g. the geocentric model is wrong but it is right about the Moon, which does after all orbit the Earth. 

Table 2: Similar to Table 1, but for MOND. The open dot shows that the rotation curves of a handful of HSB galaxies were used to set a0, so these data cannot be used to test MOND. (Table 4 of Banik & Zhao 2022)

Table 2 provides my assessment of how well MOND fares against the considered observational tests. It is sometimes claimed that MOND was designed to fit galaxies, so its successes here do not provide support for MOND. However, a careful reading of the literature reveals that MOND was formulated many decades before the relevant observations became available, with its free parameter fixed more than thirty years ago based on the rotation curves of a handful of HSB galaxies. The many other successes of MOND on galaxy scales are extremely impressive for such an old and inflexible theory. One particularly noteworthy example is low surface brightness (LSB) galaxies, where MOND correctly predicted a large enhancement to the Newtonian gravity of the baryons. Recent work has revealed several important successes of MOND on scales larger than those of individual galaxies. These successes lead to many tests of MOND appearing towards the top left. Importantly, MOND at least plausibly works in all tests considered for my review. There are no areas in strong disagreement with MOND once we consider both theoretical and observational uncertainties.

Table 3: Comparison of ΛCDM (red dots) and MOND (blue dots) with observations based on the tests listed in Tables 1 and 2, respectively. The 2D scores in those tables have been collapsed into a single score for each test. The open dots show tests used in theory construction or to fix free parameters. (Table 5 of Banik & Zhao 2022)

My main goal in this review was to assign a numerical score for how well each theory performs against each test, but in a better way than past such assessments by considering both the agreement with observations and the level of theoretical flexibility. The confidence scores obtained in this way are shown in Table 3. The scores are higher for MOND in nearly all tests on all astrophysical scales. There are a few exceptions, especially on small scales. For instance, General Relativity predicted the observation that gravitational and electromagnetic waves travel at the same speed despite both going through the deep-MOND regions between galaxies. Relativistic extensions of MOND can be made compatible with this constraint, but do not have to be. However, this is only one test. MOND outperforms ΛCDM in the vast majority of tests, especially on the scales of galaxies and galaxy clusters. The addition of a sterile neutrino component is important to MOND elegantly passing the larger scale tests that have been possible so far given the limited work on this area. I argued that a purely baryonic MOND universe is highly unlikely to match the observed properties of galaxy clusters, a fact which has been known for several decades. A hybrid solution is thus required where the dominant mass component of rich galaxy clusters is an undiscovered particle but a known type of particle. In particular, MOND works best if we postulate a fourth type of neutrino with a rest energy of 11 eV (Angus 2009). The average mass density of such neutrinos as a whole would be the same as that of the cold dark matter in the ΛCDM paradigm. This would also explain the acoustic oscillations in the power spectrum of the cosmic microwave background radiation, where MOND differs little from General Relativity due to the strong gravitational fields prior to recombination and a standard expansion history. In the review, I also discussed some very recent evidence that strongly suggests the presence of a sterile neutrino with rest energy of order 1 eV and how this could be consistent with the reported null detections in some experiments.

Table 4: The total confidence in ΛCDM and MOND based on how well each theory performs against each test, bearing in mind its theoretical flexibility (Table 3). The test used to construct each theory is not counted here. The final column shows the average confidence score for each theory across all the tests considered in my review. It is clear that overall, MOND significantly outperforms ΛCDM. (Table 6 of Banik & Zhao 2022)

The average confidence scores for ΛCDM and MOND are listed in Table 4 along with the number of tests used, which is slightly higher in ΛCDM due to it being better developed. The ΛCDM score of 0 is in line with expectations for an unphysical model which may have some right elements and gets some things right by chance. The MOND score of almost +2 indicates plausible agreement in a test with a clear prior prediction. It also corresponds to excellent agreement in a test where we need to make auxiliary assumptions beyond MOND but these only slightly affect the results. I think the score for MOND is about as much as we can expect given the limited funding causing many aspects to be understood after the relevant observations when they could have been predicted a priori with greater investment, the fact that MOND is obviously not a perfect theory, and observational limitations that cause tests with no tension to receive lower observational agreement scores due to measurement errors and astrophysical systematics, e.g. line of sight contamination of galaxy groups. Thus, MOND is strongly favoured over ΛCDM by the huge range of presently available astronomical observations. While some of the data could change in the future, it is almost inconceivable that the 57 point lead of MOND over ΛCDM will ever drop to a negative value such that ΛCDM is favoured over MOND.

Another aspect of the review is that it rebuts many claims to have falsified MOND. I will not go through all of these here, but suffice to say that all these claims were later shown to be erroneous. A common reason is that subsequent observations paint a different picture, e.g. by reducing the velocity dispersion of a galaxy, changing its distance, etc. I encourage readers to check whether a particular paper they are interested in is in the bibliography, and if so, to read what I have said about it in the review. It should already address most of the common objections to MOND, including some very recent ones.

Based on the many diverse lines of evidence considered in the most comprehensive published review of MOND to date, I conclude that ΛCDM is falsified at overwhelming significance by multiple interlocking lines of evidence from a huge range of astrophysical scales, ranging from the kpc scales of galaxy bars to the Gpc scale of the KBC void and Hubble tension. Most if not all of the evidence can be understood in MOND, which in many cases predicted the observations many years if not decades prior to the relevant data becoming available. Making such predictions often took only a very small amount of time and effort due to the ease with which one can do MOND calculations of important observables, e.g. the rotation curve of a galaxy. This stands in stark contrast to the ΛCDM paradigm, where predictive successes are very rare. To paraphrase Laurence J. Peter, “ΛCDM theorists are people who come up with good excuses for why what they predicted yesterday would happen tomorrow failed to happen today.” This has been the situation for many years, with some of the failures now reaching a high level of statistical significance. Therefore, we are at the beginning of a major paradigm shift in astrophysics. In my opinion, the only reasonably analogous situation in the history of science is the heliocentric revolution, since opposition was not so significant in the relativity or quantum revolutions. These are exciting times for astrophysics!


In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.

70. The List of Flawed Falsification Claims about MOND

Modern theories in physics need to be tested and, if they significantly fail a test, discarded. Significant means a prediction that is different from the measurement many times the uncertainty. For example, a calculation in a theory A predicts the space ship to end up at a point which is five million km away from where the astronauts are meant to be, and if the uncertainty is only 100km, then we need to reconsider if this theory A might not pose a threat to the lives of the astronauts. A calculation in theory B might, on the other hand, place the astronauts on target (say only 50km away) and they live. Clearly, theory B is preferred over theory A.

In this sense, the dark-matter based theories (case A above) have been rigorously and robustly falsified to any high degree of standard in the physical sciences (see previous and next post). What about MOND (theory B above)? It too is a physical theory allowing predictions. It too can be ruled out.

Srikanth Togere Nagesh has put a large effort to track down and document the published falsifications of MOND. It turns out that the claimed falsifications of MOND have all been shown, in the published scientific research literature via rebuttals, to be flawed. In every case either wrong calculations were done or some essential physical process that acts within MOND and normal matter has been wrongly applied or even ignored. This is touched upon in the Addendum to post 69, and here we publish the full list of tests of MOND that claim MOND is out. As found by Srikanth, all are erroneous and have published rebuttals:

Why do so many researchers publish such sub-standard results? This is probably a sociological issue: a researcher benefits in the eyes of the “ΛCDM priests” if the researcher shows MOND to be wrong. The “ΛCDM priests” disfavour MOND, because if MOND is the valid approximation to the physical Universe, then the dark-matter based models are invalid. This would put “ΛCDM priests” out of job. A researcher who hopes (i) to get a prize, (ii) to publish in Nature, (iii) to get a raise in salary, (iv) to rise up in the career ladder, will thus like to publish anti-MOND results, and would often get away with it, if there were not brighter scientists who still upkeep the ideals and standards of research in the natural sciences.

Cases in point are the incorrect claims that MOND is ruled out published in Nature and Nature Astronomy (see items 17 and 18 and in The List of MOND-falsification claims).

Doing the work needed to write a rebuttal is costly, and so the here documented largely sub-standard “MOND-falsification” research is pulling down the entire research effort. The bright researchers cannot spend as much of their valuable time on actually advancing our understanding of nature, because they are constantly paralysed by needing to react to some new MOND-falsification claim. While it is necessary to keep testing MOND, this needs to be done at high quality.


In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.

66. The observed high fraction of thin disk galaxies is incompatible with ΛCDM cosmology: The angular momentum problem in galaxy formation is more severe than ever

(by Moritz Haslbauer & Pavel Kroupa, Friday 25th February 2022)

A directly related press-release by the University of Bonn can be found here: Too many disk galaxies than theory allows & Mehr Scheibengalaxien als die Theorie erlaubt

The observed Universe consists of a mix of various types of galaxies ranging from ellipticals, spirals, lentriculars, and irregulars. Generally speaking, elliptical and lentricular galaxies are roundish, while spiral galaxies are typically very flat rotating disks, looking round face-on but are like knife edges when seen edge-on. A galaxy morphological classification has been originally introduced by J. H. Reynolds and adapted later by Edwin Hubble in 1936 and has been further developed for example by  Gérard de Vaucouleurs and Allan Sandage. Interestingly, most of the observed galaxies are very flat disk galaxies, with ellipticals making up only a small fraction out to a redshift of 0.6 (see e.g. Delgado-Serrano et al. 2010). Our own Milky Way is also a spiral galaxy. If we would be able to move away from our own galaxy sufficiently far to see its full dimension, the Milky Way would look similar to the galaxy NGC 891. This spiral galaxy is seen edged-on from Earth and has a very thin disk consisting of stars and gas as shown in Figure 1.

Figure 1: The image shows the edge-on spiral galaxy NGC 891, which has a very thin stellar disk. This galaxy has an appearance similar to our Milky Way galaxy and the faint disk extends to much larger distances than shown on this photograph. Most of the galaxies in the local Universe are such spirals and only a few are roundish ellipticals (Delgado-Serrano et al. 2010). Credits: https://en.wikipedia.org/wiki/NGC_891.

The observed thinness can be used as a test of cosmological models and of gravitational theories as follows: In a cosmological theory, in which galaxies collide and merge, the final galaxies would be crash-damaged and would appear thicker and roundish. In a cosmological theory in which galaxies form from contracting rotating gas clouds (Wittenburg, Kroupa & Famaey 2020) without later crashing into each other or merging, the vast majority of galaxies would remain thin rotating disks. This happens because, as a gas cloud collapses, it flattens under it own gravitation and spin-up due to conservation of rotational momentum thereby automatically becoming a thin disk. On the vastly smaller scale of planetary systems, the Solar system formed in just this way.

In our recent publication titled “The High Fraction of Thin Disk Galaxies Continues to Challenge ΛCDM Cosmology” (Moritz Haslbauer, Indranil Banik, Pavel Kroupa, Nils Wittenburg, Behnam Javanmardi 2022) we applied such a test to the current standard model of cosmology (ΛCDM, or SMoC).

In this SMoC, galaxies begin to form in the early Universe first as very small dark matter haloes into which gas falls and where stars begin to form. As the Universe expands the small dark matter haloes merge and the galaxies become larger and more massive. The dark matter haloes are always much larger in extend than the gas and stellar parts of the galaxies, and this has important implications for the evolution of galaxies: If a galaxy with its own dark matter halo moves through a dark matter halo of another galaxy, it experiences a drag and decelerates. This effect is called “Chandrasekhar dynamical friction” (see the discussion on dynamical friction to our Blog Post 51). As a consequence, interacting galaxies merge within a short time scale of about 1-3 Gyr. Because of the huge dark matter haloes, we expect a higher merger rate of galaxies in the SMoC compared to models without cold or warm dark matter. Galaxy mergers typically decrease the angular momentum of galaxies causing a thickening of the galactic disk. This dramatic loss of angular momentum of galaxies in ΛCDM simulations has been widely discussed over the past decades. That is, it has been known for a long time that the dark-matter based models lead to galaxies that are too thick compared to their diameter. Interestingly, it has been shown that simulated galaxies with a very quiescent merger history do not suffer from an excessive loss of angular momentum and are able to form and retain fairly flat disks. This suggests that mergers need to be less frequent in the observed Universe than predicted by the ΛCDM framework – and this questions at the same time the existence of the hypothetical cold or warm dark matter particles because dynamical friction is much less efficient in nature than expected to be the case in the SMoC. However, the situation appeared to have changed in 2014: Vogelsberger et al. 2014 claimed, in their Nature paper, that the angular momentum problem has been solved in the self-consistent hydyrodynamical cosmological ΛCDM Illustris simulation:

Simulating the formation of realistic disk galaxies, like our own Milky Way, has remained an unsolved problem for more than two decades. The culprit was an angular momentum deficit leading to too high central concentrations, overly massive bulges and unrealistic rotation curves. The fact that our calculation naturally produces a morphological mix of realistic disk galaxies coexisting with a population of ellipticals resolves this long-standing issue. It also shows that previous futile attempts to achieve this were not due to an inherent flaw of the ΛCDM paradigm, but rather due to limitations of numerical algorithms and physical modelling.

Although these simulations form a variety of galaxy types, any viable cosmological model also has to reproduce the observed fraction of late and early type galaxies. Using the latest state-of-the-art hydrodynamical cosmological ΛCDM cosmology, we showed that the produced galaxy morphology distribution significantly (at more than the five sigma confidence level) disagrees with local observations. Galaxies formed in the ΛCDM simulations are systematically thicker than in reality as shown in Figure 2. Thus, contrary to the claim by Vogelsberger et al. 2014, the angular momentum problem has not been resolved: The high fraction of thin disk galaxies falsifies ΛCDM cosmology!

Figure 2: Sky-projected aspect ratio distribution of observed and simulated ΛCDM galaxies. A typical disk galaxy has a thickness of about 0.7kpc and a diameter of about 30kpc such that the true aspect ratio is q=0.023. But galaxies on the sky are tilted at various angles and the observer only sees the projected ellipse, such that the on-sky distribution of this ratio, qsky, shows larger values. The observed thicknesses of galaxies in the GAMA and SDSS surveys are plotted above as the solid black and dashed grey lines. Galaxies formed in the cosmological ΛCDM simulations (Illustris, IllustrisTNG, and EAGLE) are systematically far too thick compared to the observed galaxies in the SDSS and GAMA Galaxy Survey. Credits: The High Fraction of Thin Disk Galaxies Continues to Challenge ΛCDM Cosmology (Haslbauer et al. 2022)

It is often argued that the thickening of galaxies in the ΛCDM simulations is related to the implemented “baryonic feedback description”, i.e, the algorithm that defines how the gas is turned into stellar particles and how these stellar particles heat the surrounding gas through their radiation, winds and supernova explosions. The Illustris(TNG) and EAGLE simulations rely on two completely different feedback models as well as using very different computer programmes and calculation methods but both fail to reproduce the vast number of observed thin galaxies. Moreover, the same baryonic feedback description must also explain other various small-scale problems faced by the ΛCDM model: the formation of early type galaxies (the downsizing problem, e.g. Yan, Jerabkova & Kroupa 2021), bar pattern speeds of galaxies, the missing satellite problem, the core-cusp problem, the disk of satellites problem, the local Gpc-scale void, etc. It is highly implausible that all the problems can be solved by just changing the feedback description.

It is quite possible that the angular momentum problem (or the too-thick-galaxy problem) is the consequence of a failure of the hierarchical structure formation of the ΛCDM framework – this framework not being the correct one to model the real Universe. We tested this: We pulled those galaxies out of the simulation that have a quiescent merger history, and yes, these are indeed slightly thinner than galaxies which had at least one major merger in the past. However, this still cannot explain the discrepancy between the observed and simulated galaxies. In addition to the major mergers, the ΛCDM model predicts a high frequency of minor mergers, meaning that many small galaxies merge with a massive galaxy. These mergers are unavoidable in a cold- or warm-dark-matter-based model, i.e., in the SMoC, leading to a thickening of the galactic disks. In fact, in the dark matter based models, galaxies grow largely through mergers and every galaxy has its own rich history of mergers, a so-called “merger tree”.

Consequently, the fraction of thin disk galaxies is expected to be higher in a model which does not rely on cold or warm dark matter, in which galaxies form mostly through the above mentioned collapsing rotating gas clouds (Wittenburg, Kroupa & Famaey 2020) and in which mergers are rare. But this would imply that we also need a different law of gravity, for example MilgrOMiaN Dynamics (MOND). In these models dynamical friction is less efficient, resulting in a much smaller number of merger events. Simulations of interacting galaxies indeed demonstrate that the galaxies merge much less efficiently: even very strong encounters lead to mergers only after a few orbits, in contrast to the very rapid (within one to two orbits) mergers of the galaxies in the dark matter based models (Renaud, Famaey & Kroupa 2016). Self-consistent cosmological MOND simulations are underway in the Bonn-Prague research group to test if a MOND cosmology can indeed account for the observed vast number of thin disk galaxies.

Almost 50 years after the postulation that galaxies are surrounded by dark matter haloes (Ostriker & Peebles 1973), the ΛCDM simulations still cannot explain the structural properties of observed galaxies.

How does the Milky Way galaxy fit into the above conclusions?:

The usually-encountered thinking amongst the vast majority of astronomers is that the Milky formed, according to the SMoC, i.e. through mergers, and the stellar and gas streams such as the Gaia-Sausage-Enceladus structure are taken to be, essentially, the proof of this (e.g. Naidu et al. 2021). But, as discussed above, this very rich merger history (after all, the Galaxy is a major galaxy) would not allow the Milky Way to remain a thin disk galaxy, and the SMoC is falsified as a relevant model for the Universe in any case. So, can the Milky Way be understood in MOND?

The observed rotation curve is well accounted for by MOND (McGaugh 2008). The Milky Way has a thick disk component which consists of stars that are older than about 10 Gyr with a thickness of about 2 kpc, and a still forming thin disk making about 90 per cent of the mass of the whole Galactic disk which is composed of stars up to ages of 10 Gyr and a thickness of about 0.7 kpc. The diameter is about 30 kpc, and this whole disk has a warp. One could argue that the thick disk is a result of a merger and that the SMoC is therefore valid. But this is incorrect, because this line of thinking would imply that the majority of the disk, namely the thin disk, would have to grow without mergers, which is not possible in the SMoC.

But these components (the thick and thin disks and the warp and its orientation) are well explainable in MOND if the Milky Way had an encounter with the Andromeda galaxy about 10Gyr ago, i.e. near a redshift of z=2 (Bilek et al. 2018). This model starts with a young Milky Way having a thin disk, and the encounter with the young Andromeda galaxy thickened this disk and produced a warp. A new thin disk grew within the thickened ageing disk as the Milky Way accreted further gas after receding from Andromeda, fuelling its on-going star formation. While there exists no SMoC calculation which can explain these features of the Milky Way and at the same time the disk of satellites around the Milky Way and around Andromeda, the encounter calculations in MOND between the Milky Way and Andromeda nicely produces all of this for free, therewith also solving the planes-of-satellites problem completely naturally (Bilek et al. 2018; Banik, O’Ryan & Zhao 2018; Bilek et al. 2021; Banik et al., 2022, submitted).

In conclusion, it is therefore apparent that in the modern non-relativistic theory of gravitation, which MOND is, the vast majority of galaxies being thin disks as well as major properties of the Local Group of galaxies become understandable naturally, while the SMoC fails to do so entirely.


In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.

61. The crisis in the dark matter problem becomes a historically unparalleled failure in the scientific method

This year, Pavel Kroupa was asked to hold a Golden Webinar in Astrophysics on the dark matter problem. This contribution provides the link to the recording of this presentation which has now become available on YouTube. In this presentation, Pavel Kroupa argues that the dark matter problem has developed to become the greatest crisis in the history of science, ever. This contribution also provides links to recordings available on YouTube of previous related talks by the same speaker from 2010 (the Dark Matter Debate with Simon White in Bonn) and 2013 (in Heidelberg). This might allow some insight into how the debate and the research field have developed over the past dozen or more years.

1) Golden Webinar: “From Belief to Realism and Beauty: Given the Non-Existence of Dark Matter, how do I navigate amongst the Stars and between Galaxies?”

On April 9th, 2021, Prof. Pavel Kroupa presented a talk in the Golden Webinars in Astrophysics series on “From Belief to Realism and Beauty: Given the Non-Existence of Dark Matter, how do I navigate amongst the Stars and between Galaxies?”. The talk is now available on Youtube:

The slides to the talk without the fictitious story can be downloaded here:

If you are interested in other talks presented during The Golden Webinars in Astrophysics series, you can find the record of those already presented on their Youtube Channel, and here is a list of upcoming talks. The Golden Webinars are provided as a free public service and have no registration fees.

2) The vast polar structures around the Milky Way and Andromeda

In November 2013, Prof. Pavel Kroupa presented “The vast polar structures around the Milky Way and Andromeda” in the Heidelberg Joint Astronomical Colloquium. In the talk he discussed the failures of the Standard model of cosmology and the implications for fundamental physics.

A blog entry from 2012 on the vast polar structure (VPOS) of satellite objects around the Milky Way can be found here.

3) Bethe-Kolloquium “Dark Matter: A Debate”

In November 2010, Prof. Simon White (Max Planck Institute of Astrophysics, Garching) and Prof. Pavel Kroupa (University of Bonn) debated on the concept and existence of dark matter during the Bethe Colloquium in Bonn. Their presentations and the subsequent debate are available here:

a) Presentations by Prof. White and Prof. Kroupa

Summary of both presentations:

b) The Debate

The German-language television channel 3sat produced a TV report on the Bethe Colloquium, which can be also found on Youtube (available only in German):

Part I

Part II


In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.

54. The interacting galaxy cluster “El Gordo”: a massive blow to ΛCDM cosmology

(Guest post by Elena Asencio, University of Bonn, January 16th, 2021)
 
It is currently accepted that structure in the Universe formed in a hierarchical way. In other words, smaller structures formed first and then merged into larger structures. The largest gravitationally bound structures in the Universe are the galaxy clusters. Since the predicted timescale in which these structures formed depends on the cosmological model adopted and, subsequently, on the gravity theory assumed, galaxy clusters can be used to test both gravity theories and cosmological models models on large scales.
 
In the last decades, the improvements in telescope detection capabilities have made possible to observe objects which are deeper in space. The further an astronomical object is from us, the longer it takes for its light to reach us. Therefore, deeper surveys allow us to observe how the Universe looked like in the fairly distant past. Some of the galaxy clusters that were detected in these deep surveys surpass the standard model (ΛCDM) predictions in terms of mass, size and/or galaxy-infall velocities, and could potentially pose a serious problem to the model.
 
El Gordo (ACT-CL J0102-4915) is a galaxy cluster with particularly extreme properties. It is located more than 7 billion light years from Earth and is composed of two sub-clusters weighing together approximately 3e15 Solar masses with a mass ratio of 3.6 and a high collision velocity of approximately 2500 km/s. Due to the highly energetic interaction of its two sub-clusters, it is also the hottest and most X-ray luminous galaxy cluster observed at this distance according to Menanteau et al. (2012).
 

Figure 1: A composite image showing El Gordo in X-ray light from NASA’s Chandra X-ray Observatory in blue, along with optical data from the European Southern Observatory’s Very Large Telescope (VLT) in red, green, and blue, and infrared emission from the NASA’s Spitzer Space Telescope in red and orange. Notice the twin tails towards the upper right.Image from this source. Credits: X-ray: NASA/CXC/Rutgers/J. Hughes et al; Optical: ESO/VLT & SOAR/Rutgers/F. Menanteau; IR: NASA/JPL/Rutgers/F. Menanteau.

 
In our paper “A massive blow for ΛCDM – the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology” (Elena Asencio, Indranil Banik & Pavel Kroupa 2021), we conducted a rigorous analysis on how likely it is that this object exists according to ΛCDM cosmology.
 
In order to do this, we searched for cluster pairs that could potentially be progenitors of the El Gordo cluster in the ΛCDM cosmological simulation developed by the Juropa Hubble Volume Simulation Project  – also known as the Jubilee simulation. The reason why we searched for the El Gordo progenitors instead of directly looking for an El Gordo-like object is because extremely large objects like El Gordo require very large simulation boxes to have their number of analogues estimated in a reliable way. Larger simulation boxes have lower resolution. Therefore, when searching for El Gordo analogues in the simulation, we can not aim to match its morphological properties (e.g. the observed X-ray morphology) — as these would need a high resolution simulation with gas dynamics to be reproduced. Such simulations covering a sufficiently large volume cannot be achieved today even on the most powerful supercomputers (and are in actuality also not necessary for the present aim) — but we can try to find cluster pairs whose configuration matches the initial configuration of El Gordo in terms of total mass, mass ratio and infall velocity. To determine the values of the parameters describing this initial configuration, we need to rely on the results of detailed hydrodynamical simulations. Zhang et al. (2015) performed a series of hydrodynamical simulations of two colliding galaxy clusters trying to find which set of initial conditions would result in a merger with similar properties to El Gordo. Among the 123 simulations that they ran for different parameters, they found that the model that gave the best fit to the observed properties of El Gordo had a total mass of 3.2e15 Solar masses, a mass ratio of 3.6, an infall velocity of 2500 km/s, and an impact parameter of 800 kpc. Models with lower mass or lower infall velocity were not able to reproduce the twin-tailed morphology of El Gordo (see Figure 1) and its high X-ray luminosity.
 
Using the Jubilee simulation, we found no analogues to El Gordo. We therefore relaxed the requirement of a sufficiently high mass, and found out how the number of El Gordo analogues (in terms of mass ratio and infall velocity) decreased with increasing mass. Since the Jubilee simulation was run for different cosmological epochs or redshifts, we were also able to determine how the number of El Gordo analogues (in terms of total mass, mass ratio, and infall velocity) decreased for earlier epochs or larger redshift. From these results and accounting for the fact that the total volume of the Jubilee simulation is significantly larger than the space volume in which El Gordo was found, we obtained the probability of finding a cluster pair with a similar configuration to the expected pre-merger configuration of El Gordo, at a slightly earlier epoch to that at which we observe El Gordo (see Figure 2).
 

Figure 2: Plot showing the frequency of analogues to the El Gordo progenitors for each position in the grid. The grid is constructed for a series of mass values in log10 scale (y-axis) and cosmic scale factor a (x-axis). The a values determine the cosmological epoch (for reference, a = 1 today, a = 0.535 at the epoch at which we observe El Gordo and a = 0.5 at the epoch at which we look for El Gordo progenitors, and generally the expansion factor a and redshift z are related by a=1/(1+z) ). The probability of lying outside a contour (region of fixed colour) can be expressed in terms of the number of standard deviations (σ). The higher the number of standard deviations at a certain point in the grid, the further away will this point be from the expected value of the distribution. It is generally considered that if a model surpasses the 5σ threshold, then this model is falsified. In this plot, the point in the grid corresponding to the and a values of the El Gordo progenitors is marked with a red X and it corresponds to 6.16σ. In terms of probability, this is equivalent to saying that there is a 7.51e-10 chance of finding an interacting pair of El Gordo progenitors or an even more extreme pair in the ΛCDM model.

 
 
The chance of observing an El Gordo-like object in the ΛCDM cosmology is 7.51e-10, which corresponds to 6.16σ (as a reminder: physicists accepted the existence of the Higgs boson once the experimental data reached a 5σ significance level — in general, when a phenomenon reaches a confidence of 5σ or more, then it is formally taken to be certain corresponding to a chance of one in 1.7 million that the phenomenon is untrue). This means that, assuming the ΛCDM model, we should not be observing El Gordo in the sky (but we do observe it). In fact, the tension between the ΛCDM model and the observations is even higher if one takes into account that El Gordo is not the only problematic object found in the sky.
 
Another well-known galaxy cluster that poses a potential problem to ΛCDM is the Bullet Cluster. It is also an interacting cluster composed of two subclusters colliding at high velocity (3000 km/s) which, according to the ΛCDM model, is unexpected at the distance at which it is observed (3.72 billion light-years).
Kraljic & Sarkar (2015) obtained a 10% probability of finding a Bullet Cluster analogue in the ΛCDM cosmology over the whole sky. In order to get a more helpful estimate of the Bullet Cluster probability, the sky area in which the Bullet Cluster was observed should be taken into account – it would not be realistic to use the probability for the whole sky as this would imply that the Bullet Cluster was found in a fully sky survey, which is not the case. Taking into consideration that the survey in which the Bullet Cluster was found only covered 5.4% of the sky, the actual probability of observing a Bullet Cluster-like object is 0.54%, which makes it a 2.78σ outlier. Combining the probability of observing both the Bullet Cluster and El Gordo in the sky raises the tension to 6.43σ.
 
We also considered the possibility that the problem is not in the ΛCDM model but in the Jubilee cosmological simulation, in the Zhang et al. (2015) hydrodynamical simulations, or in our statistical analysis. According to Watson et al. (2014), up to now, the Jubilee simulation has been shown to work correctly in accordance with the ΛCDM cosmological model for which it was designed. So we have no reasons to believe that there might be any problems with the Jubilee simulation in that regard. We also found many lower mass analogues to El Gordo, so numerically our results should be quite sound and allow an accurate extrapolation up to the El Gordo mass. The results of Zhang et al. (2015) for the initial configuration of El Gordo are backed up by previous independent studies of El Gordo. The weak lensing analysis of El Gordo by Jee et al. (2014) confirms the mass estimate of 3e15 Solar masses. The simulations by Donnert (2014) and Molnar & Broadhurst (2015) agree on an infall velocity of 2250 – 2600 km/s. Besides this, Zhang et al. (2015) had already checked that lower values for the mass and infall velocity – which would be easier to explain in ΛCDM – were unable to reproduce the morphology of El Gordo. Regarding our own analysis, in the paper we also performed the statistical analysis with a different method to check the consistency of our results. The results were indeed consistent, so we consider our methods to be reliable. The more conservative and detailed method is shown in Figure 2.
 
Since the ΛCDM model cannot account for the existence of extreme objects like El Gordo or the Bullet Cluster, some authors tested other cosmological models to check how well they work in this respect. Katz et al. (2013) searched for El Gordo analogues in a simulation that adopted a νHDM cosmological model. The νHDM model has the standard hot Big Bang, primordial nucleosynthesis, CMB and expansion history as the ΛCDM model, but assumes the extended gravity law devised by Milgrom (MOND) and the presence of an undetected mass in galaxy clusters composed of particles like sterile neutrinos that only interact with gravity (see the post “Solving both crises in cosmology: the KBC-void and the Hubble-Tension” by Moritz Haslbauer for a more detailed explanation of the νHDM model). Using this model, Katz et al. found that about one El Gordo analogue was expected to be encountered in their simulation box, while they could not find any analogues when they performed a simulation of similar characteristics with the ΛCDM model. Accounting for the fact that the volume of the survey in which El Gordo was found is slightly different from the volume of the simulation used by Katz et al. (2013), we determined that the number of El Gordo analogues that we expect to observe in a νHDM model is 1.16. Therefore, the vHDM model gets the right order of magnitude for the frequency of El Gordo-like objects. The reason for this is that the growth of structure is enhanced in MONDian gravity, so it is more natural to find very massive objects like El Gordo at high redshift in models that assume this type of gravity.
 
But then, if smaller structures formed first and larger structures formed afterwards, how is it possible that we do not observe more super-massive objects like El Gordo at closer distances? The fact that structures form more efficiently in MONDian gravity also implies that larger and deeper voids will be generated with this gravity law. This prediction is in agreement with the results of Keenan, Barger & Cowie (2013), who observationally found that the local Universe is immersed in an underdensity bubble (the KBC void) with a radius of about one billion light years. For this reason, it is not expected that very massive objects will be able to form in the nearby regions of our Universe, as these regions will have a low density with respect to the mean density of the global Universe (see the post “Solving both crises in cosmology: the KBC-void and the Hubble-Tension” by Moritz Haslbauer for a more detailed explanation of the KBC void). Therefore, the νHDM model is capable of explaining the presence of super-massive objects like El Gordo at distant epochs and is also able to explain the absence of objects like this in the local Universe.
 
We conclude that El Gordo falsifies ΛCDM at 6.16σ (6.43σ if we take into account the Bullet Cluster too). We propose the νHDM cosmological model as a possible explanation to the formation of extreme objects like El Gordo or the Bullet Cluster at very early cosmological epochs. Moreover, the νHDM model also explains other observations that cannot be justified with the ΛCDM model, such as the existence of the KBC void, therewith automatically resolving the Hubble tension and accounting for the lack of super-massive galaxy clusters like El Gordo in the local Universe. Since the νHDM cosmological model automatically accounts for  the observed stellar dynamics in the smallest dwarf and most massive galaxies, the rotating-planar distributions of satellite galaxies, and many other observed properties of galaxies and large scale structure, it is clear that it poses a far superior framework than the (in any case falsified) ΛCDM model for understanding the Universe.
 

In The Dark Matter Crisis by Elena Asencio. A listing of contents of all contributions is available here.

53. Dark Matter in elliptical galaxies?

(Guest post by Dr. Jörg Dabringhausen, Charles University in Prague, Dec. 18th 2020)

The hypothesis of dark matter in galaxies was originally brought up by observations. Zwicky (1933) first found out that galaxies were usually moving too fast to stay in the observed galaxy clusters, if the luminous matter was all there is in galaxies. With “luminous matter”, essentially all stars were meant. Stars are understood well in terms of how much mass in a star leads to a certain light strength, or luminosity. But if the light emitted by the galaxies in a galaxy cluster is translated to a stellar population similar to the stellar population of the Milky Way, the stellar population would not have enough mass by a factor of a couple hundreds to keep the galaxies bound to the cluster. Thus, the galaxy clusters would have dispersed billions of years ago, and today we would be surrounded by a uniform distribution of galaxies. But that is not what we see: galaxies are still in galaxy clusters today.

But the problem was not only with galaxy clusters. Rubin & Ford (1970) found out, that the Andromeda Galaxy rotates so fast, that its stars would disperse if only the standard gravity would keep them together. And the Anromeda galaxy turned out be the rule rather than the exception; all spiral galaxies that were studied later on showed similar trends (for example Rubin et al. 1980). So, not only galaxy clusters would disperse, but also the (spiral) galaxies themselves. It is like the riders (that is the stars) on a merry-go-round (that is the galaxy). Forces keep the riders on circles around the merry-go-round, and if the forces for some reason become weaker or cease to exist (for example because the link between the rider and the merry-go-round breaks), the riders would move away from it. But again, this is against our observations: There are large spiral galaxies everywhere around us (including our Milky Way), and the stars in them move on stable orbits.

In general, the problem of missing mass in galaxies is nowadays omnipresent. It arises because there are different ways to estimate masses in astronomy. One such way is to make educated guesses about the age and the composition of the stellar population of a galaxy, and calculate from there how much units of mass it should have per unit of luminosity. Astronomers call this a stellar mass estimate. Another way is to measure the radius of a galaxy and how fast stars move on average in it, then make some educated guesses about the dynamics of the galaxy, and calculate the ratio of mass to light from there. Astronomers call this a dynamical mass estimate. Ideally, stellar and dynamical mass would agree for the same galaxy, because the galaxy only has one real mass (within uncertainties, of course). In practice however, the dynamical mass is usually larger than the stellar mass, and the factor ranges from slightly above one to 10000 or so. Apparently, the error lies somewhere in the guesswork leading to the two different mass estimates. Astronomers tried to solve the problem of the missing visible matter in two general ways: Either by adding more matter, so that the matter in total would produce the observed gravitational force, or by changing the laws of gravity themselves and saying that the visible matter is all the matter there is in galaxies.

Adding more matter is mathematically the simpler solution, which is also why many people favoured it at first. The gravitational force is then linear in the critical range of values, that is weak to moderate gravity. This means that if there is twice the matter, there is also twice the gravitational force, independent of the total amount of matter there is. Note that from this point of view, the type of matter does not matter, as long as it is invisible, or nearly so. Also the Earth is near invisible next to the Sun, even though they both consist basically of the same kind of matter (that is atoms, not something exotic). It is only a matter of temperature that makes the Sun brighter than the Earth. Indeed, there was a theory that the missing matter are earth-like bodies (that is free-floating planets and brown dwarfs), until the needed quantity of those bodies was observationally excluded. More and more alternatives for the additional matter were excluded as well, so that we are today at the Lambda-Cold-Dark-Matter Model (LCDM-model) for this class of models. However, the LCDM-model requires exotic dark matter beyond the standard model of particles. But this kind of matter has not been discovered yet, including in the largest accelerators like CERN. Nevertheless, this first group of physicists still believes the LCDM-model to be true in general (even though there are some changes to be made) and therefore they continue to search for the so far still hypothetic dark-matter particle.

The second group of physicists rather correct the law of gravity than adding a hypothetic particle beyond the standard model of particle physics. It is like whichever way you go, you have to expand a theory which has been extremely succesful so far: you either have to give up the standard model of particle physics in order to save the LCDM-model, or have to have to give up general relativity, with Newtonian gravity as its limiting case for weak and moderate gravity. This new theory of gravity is, unlike Newtonian gravity, not linear in the critial range. This means that twice the matter does not necessarily mean twice the gravity when the gravitational force is weak enough. This has a funny consequence, which is in contrast to our daily-life experience, namely that the same amount of matter suddently looks like it becomes more gravitating when you spread it out thinly enough. Lüghausen et al. (2015) therefore called it “phantom dark matter”, because this dark matter is a mirage that disappears when the real matter is put close enough together. (Of course, inside the Solar system, the matter must be on average dense enough for the gravitational force to be linear – otherwise we would not be able to send spaceships with high precision to other planets using Newtonian gravity.) This second set of theories leads to Modified Newtonian Dynamics or Milgromian Dynamics (MOND).

Here, I will concentrate on the “missing” matter of elliptical galaxies – “missing” in the sense that there is usually less matter if seen from a stellar perspective than if seen from a dynamical perspective on the same galaxy. Are there alternatives to adding exotic dark matter to the visible matter, and thus supportive to the second group of physicists?

First of all, let’s start with the question of what an elliptical galaxy is. A very short answer would be that they are more or less like the spiral galaxies, but without the disks that contain the spirals. So, only the central bulge is there, and hence, they are called ellipitical because of their elliptical shape. That central bulge can however be very massive, and the most massive elliptical galaxies are even more massive than the most massive spiral galaxies (bulge and disk of the spirals together)!

Going a bit more to the details of elliptical galaxies, they show however some diversity in their mass and radius. I will distingish them into three different kinds of objects, namely ultra-compact dwarf galaxies (UCDs), conventional elliptical galaxies (Es) and dwarf spheroidal galaxies (dSphs), and discuss the invisible matter in each of them. We will see that the invisible matter is just a mirage in some of them, while others contain really some more matter than originally accounted for, but not the exotic dark matter predicted by the LCDM-model.

1) UCDs

UCDs (Figures 1 and 2) stand a little apart from the other elliptical galaxies, and some doubt that some of them really are galaxies, and not just very massive star clusters. The reason lies in their compactness, which makes them look much like very massive globular clusters. However, their compactness also places them deeply in the Newtonian regime, so there is literally no room for the phantom dark matter of MOND. Yet, it was claimed that they may contain dark matter (see for example by Drinkwater et al 2004 and Hasegan et al. 2005).

Figure 1: A “family picture” of elliptical galaxies. The two bright objects near the center and at the upper right corner, respectively, are the bright “conventional” elliptical galaxies NGC 1404 and NGC 1399. Slightly above NGC 1404 is a UCD, and near the lower border of the image is a small conventional elliptical galaxy. Not all the spots on the image are galaxies. There are stars too, and even bright ones. They can be recocnized by the spikes around them. However, the described galaxies are all members of the Fornax Galaxy Cluster. They are thus at approximately at the same distance, and are consequently to scale to each other. Image credit: Michael Hilker.
Figure 2: This is probably what a UCD would look like if it was a member of the Milky Way. Shown here is actually Omega Centauri, the brigtest globular cluster of the Milky Way. However, it has sometimes been doubted that Omega Centauri really is a globular cluster, and not a UCD, because of some peculiarities of Omega Centauri. For instance, Omega Centauri shows clear evidence for stellar populations of different ages, as opposed to other, less massive globular clusters. Image credit: ESO.

The reason for that is that at the turn of the millenium, it was popular among atronomers that the stellar initial mass function (IMF) is universal (see for example Kroupa 2001). What this means is that all stellar systems formed with a fixed ratio of massive stars to light stars, and only the age of the stars and their chemical composition may change from stellar system to stellar system. This is not to say that people back then were unaware of the influence that, for example, different temperatures and chemical composition had on the process of star formation. Rather, they were looking for different IMFs, but did not find supportable evidence for them in resolved stellar populations. However, when modeling a UCD (or any other kind of stellar system) with the universal IMF, there is maximum ratio between stellar mass and stellar light that can be reached for any reasonable stellar ages and chemical compositions. Nevertheless, there are many UCDs above that limit, and Dabringhausen et al. (2008) showed that this is not just a statistical uncertainty. So, there must be a reason for this unseen mass, and the exotic dark matter that comes with the LCDM-model was a proposition.

However, Murray (2009) voiced serious doubts that the LCDM-model could accomodate enough exotic dark matter inside the tiny radii of UCDs. This is even though the dark-matter halos around the galaxies can be very massive in the LCDM-model. However, the LCDM-model then also predicts that the halos would be very extended, and thus the density (that is mass per volume) of the dark-matter halo would be very thin. So, the total mass of the dark-matter halo may be gigantic, but the fraction of its mass inside a UCD would be tiny because of the small radius of the UCD, and this tiny amount of dark matter inside the UCD would not influence the internal dynamics of the UCD much. Thus, in short, it is not the exotic dark matter of the LCDM-model that increases the mass of the UCDs. It is then likely “conventional” matter, for example from a different IMF. Thus, the word “universal” IMF is then misleading because the IMF is in fact not universal, but “standard” IMF or “canonical” IMF are pretty good replacements. After all, this IMF pretty much seems to be the standard in our immediate surroundings (in an astromical sense); that is regions whose mixture of chemical elements is like that of the Sun and which do not form so many stars at present.

In UCDs, the conditions under which star formation took place were probably far away from those we know to produce the standard IMF. Thus, Dabringhausen et al. (2009) proposed that the UCDs may have formed with an IMF that had a different shape than the standard IMF, namely one that formed more massive stars. (IMFs that have more massive stars than they should have according to the standard IMF are called “top-heavy”.) These massive stars are known to be short-lived, and after they have burned all their nuclear fuel, they leave remnants which produce little or no light compared to their mass. These remnants exist of course in any aged stellar population, but if the IMF had more massive stars once, it has more stellar remnants now. The stellar remnants thus increase the ratio between mass and light, and make a UCD “darker”. Dabringhausen et al. (2012) also tried an alternative way to detect those additional stellar remnants by looking for systems, where a stellar remnant accretes matter from a companion star. Those stellar systems become distinctive X-ray sources, and are thus countable. They compared the numbers they found in UCDs to the numbers they found in globular clusters (that is stellar systems more or less like UCDs, but less massive), and they found more X-ray sources in UCDs than they expected. This as well could indicate that there are more high-mass stars per low-mass stars in UCDs. Based also on their works, Marks et al. (2012) proposed an IMF that changes with the mass of the stellar system (that is from globular clusters to UCDs) and with the chemical composition. Thus, they gave up the notion of the universal IMF, but explained changes in the ratio between mass and light in UCDs with changes in their IMFs.

Another way to increase the mass of UCDs, but not their emission of light, are central massive black holes. In a black hole so much mass is kept, that nothing that comes too close to it can escape it, not even light. Black holes are a prediction of general relativity and known to exist. For example, very massive stars become black holes when all their nuclear fuel is burned, and the pressure from stellar radiation no longer opposes the pull of gravity. Or, as another example, there is a massive black hole at the center of the Milky Way, and many other galaxies as well, even though it is less clear than for massive stars how those came to be. (This year’s Nobel Prize for physics was about the detection of this central black hole.) But if massive black holes are common at the centers of galaxies, why can’t UCDs have them as well? However, a massive central black hole is easy to overlook at the distance of known UCDs. That is because at the distance of UCDs, the stars look like they are almost located at a single point in space, whereas the mass of the central massive black hole is precisely located a this single point. Thus, if seen from Earth, there is not much difference in the distribution of matter, while the central massive black hole would still add its mass to the mass of the stellar population. Therefore, only by careful observations with the telescopes with the best optical resolution, one has a chance to detect them. Nevertheless, massive central black holes were indeed proposed as a solution for the problem of the missing mass in UCDs; for example by Mieske et al. (2013) and Janz et al. (2015). Seth et al. (2014) then observationally confirmed a massive central black hole in a UCD for the first time. Later, massive black holes were also discovered in other UCDs, see for example Afanasiev et al. (2018).

Naturally, also a mixture of non-standard IMFs and central massive black holes is possible to explain why UCDs are so massive for their light. However, what is important here is that there are less far-fetched alternatives to exotic dark matter in UCDs.

2.) Conventional elliptical galaxies

The conventional elliptical galaxies are not only usually more massive than the UCDs, but also far more extended. What I mean with “conventional” is that they were among the first galaxies to be identified as galaxies – this was in the 1920ies, when people like Hubble first discovered that some “nebulae” are not just gas clouds inside the Milky Way, but distant stellar islands just like the Milky Way. It is unclear what mass exactly is required for an elliptical galaxy in order to be coventional, perhaps 108 Solar masses or so. This unclearity is because there is an extension of elliptical galaxies to even lower masses, which are however not (compact, star-cluster-like) UCDs, but (extended, galaxy-like) dwarf Spheroidal galaxies (dSphs). However, there are some specialities on dSphs about dark matter and its seeming existence, and therefore I will treat them in an own section. What I will not do, though, is to distinguish the elliptical galaxies into dwarf elliptical galaxies and elliptical galaxies proper, because this distinction in merely historical in my eyes (see also Ferguson & Binggeli 1994 about this). The most massive of all galaxies (about 1012 Solar masses) are conventional elliptical galaxies, too.

So, how much exotic dark matter do elliptical galaxies contain, if any? Cappellari et al. (2006), for instance, found out that the conventional elliptical galaxies they observed had on average 30 percent too much mass for the IMF they assumed. They suggested that the missing mass could be the dark matter predicted by the LCDM-model. However, for this finding, they also assumed that the standard IMF is universal for all star-forming regions. Tortora et al. (2014) later tried to fix this without exotic dark matter, but MOND. They also failed with a universal IMF, but not if the IMF was changing with the mass of the galaxy. So, the real question is: Can the IMF change with galaxy mass or is the standard IMF also the universal IMF?

For answering this question, let’s look at star clusters, which are the building blocks of galaxies. Could a star cluster have a star more massive than the cluster itself? Of course not. Actually, Weidner et al. (2010) found out that the mass of the most massive star of a star cluster is much lower still. An impressive example of this was observed by Hsu et al (2012): They compared a large cluster of some mass with several adjacent small star clusters with the same mass in total. All the other parameters like age, chemical composition, and so on are the same, just how the total mass of the stars is bundled is different. However, the massive star cluster has heavier stars than the several small star clusters. This would not be a problem by itself, if the overall star formation was the same in all galaxies; that is when all galaxies form the same number of light star clusters per massive star cluster. But this is not the case. Weidner et al. (2004) found that the mass of the most massive cluster that can form in a galaxy depends on its star formation rate; that is how many stars form in a galaxy per time unit. Low-mass elliptical galaxies have low star formation rates and massive elliptical galaxies have high star formation rates. Thus, low-mass conventional elliptical galaxies have a lack of massive stars. This already is an argument against a universal IMF in all star clusters and in all galaxies.

The galaxies with the highest star formation rates (that is also the most massive galaxies) produce also star clusters in the mass range globular clusters and UCDs. Now, lets assume that these most massive star clusters are in fact UCDs and that these UCDs have IMFs with more massive stars per low-mass stars than “normal” star clusters (see the section about UCDs). Then the real IMF deviates from the once-thought universal IMF not only in low-mass star clusters (by not having any massive stars), but also in high-mass star clusters (by having too many massive stars). Now, remember what we have said about IMFs with more massive stars than the standard IMF: when they grow old, they produce less light per unit mass than the standard IMF. Or when a certain amout of light is observed, a stellar population with more massive stars and a certain age must have more mass to produce it. The stellar populations of elliptical galaxies are usually that old that the massive stars (which are short-lived) have already evolved into dark stellar remnants, and only the light stars continue to shine. So, if the IMF behaves with the star formation rate of the galaxies like it is assumed nowadays (see for example Kroupa & Weidner 2003 or Fontanot et al 2017), then the low-mass elliptical galaxies have a little less mass than assumed with the standard IMF for their light, and the massive elliptical have a little more mass than assumed with the standard IMF. This goes up to about twice the mass for the most massive conventional elliptical galaxies, and the point where the mass estimate is equal to that for the standard IMF is at approximately 109 Solar masses. Thus, for most conventional elliptical galaxies, the mass estimates are above the mass estimates for the standard IMF, and the “missing” mass is about the mass detected by Cappellari based on the standard IMF. (See also Dabringhausen et al. 2016 if you want to follow the brightness of elliptical galaxies with their mass, and Dabringhausen 2019 if you wish to go deeper on elliptical galaxies and non-standard IMFs). Thus, again like with UCDs, there is an alternative, more down-to-earth explanation for the excess mass of those elliptical galaxies.

3.) Dwarf speroidal galaxies (dSphs)

Dwarf spheriodal galaxies (dSphs, Figure 3) are in a way the low mass extension to “conventional” elliptical galaxies, because in a plot of their radius against their mass, they continue the line established by the conventional elliptical galaxies to lower masses. However, the brightest ones are in light and mass like UCDs, but way more extended than UCDs. In other words, there is a gap in radius between dSphs and UCDs (see Gilmore et. al 2007), in contrast to conventional elliptical galaxies and dSphs.

Figure 3: The Fornax Dwarf Galaxy. This is arguably the largest dwarf speroidal galaxy around the Milky Way. Image credit: ESO / Digitized Sky Survey 2.

If it is true that dSphs are in fact very low-mass conventional elliptical galaxies, then we would expect them to be about 20 percent or so lighter than expected based on their light with a standard IMF. But in fact, they are way more massive. Just in order get a feeling for the numbers we are dealing with: Let’s say the standard IMF would predict a ratio of mass to light of 2 for a dSph, the ratio for the corrected IMF would then give 1.5, but the measured value is 2000 (all numbers are in Solar units). So, how can we be wrong to a factor up to approximately 1000 (even though in many cases less)?

This is where MOND finally kicks in, because the visible matter in dSphs is actually thin enough, in contrast to UCDs and Es. MOND can rise the ratio of the mass of a dSph over its light from values of a few (that is a stellar population in Newtonian dynamics) to values up to about 100. This fits the dynamical values of many dSphs, which would contain plenty of “dark” matter in Newtonian dynamics. Thus, in MOND, their dark matter is actually phantom dark matter – it would disappear if the matter was denser. Or, in other words, the difference between stellar and dynamical mass estimates disappears for those dSphs, and all is well. The precise value for a given dSph depends on which value the mass-to-light ratio of the stellar population would have according Newtonian dynamics and on how many stars are distributed over which volume, that is the density of visible matter. Estimates for the mass-to-light ratios in Newtonian and MONDian dynamics for a number of dSphs are for example given in Dabringhausen el al. (2016).

But it is also visible in Dabringhausen el al. (2016) that even MONDian dynamics cannot explain the mass-to-light ratios of the few dSphs, which have a mass-to-light ratio far beyond 100. So, have we finally found a failure of MOND? Not necessarily. So far, we have implicitly always assumed that the galaxies are in virial equilibrium. What this means is for instance the absence of tides because of other distracting souces of gravity. The tides on Earth are the best-known example, even though Earth is dense enough to be near tidal equilibrium, given the gravitational forces from the Moon and the Sun. We only see them so well because because in this case, the tides are happening right under our noses. Ultimately, there are tides on Earth because the Earth is an extended body. Thus, the gravitational force from the Moon pull on the near side of the Earth a bit stronger than on the far side, and the Earth is being stretched a bit by the tides. There are ebb and flow of the oceans on Earth, because the Earth also rotates, while the tides are always directed towards the Moon. There of course also other sources of gravity on Earth which cause tides (the Sun for instance), but the Moon is the strongest.

Also UCDs and conventional elliptical galaxies are dense enough to be nearly unaffected by neighboring galaxies, which are the potential reason for tides in them. But the internal gravity is comparatively weak on the thin matter of dSphs, so that they are easy to stretch by outside forces of other galaxies. Thus, the tidal forces form gigantic tidal “waves” consisting of stars. Every encounter with another galaxy pulls on the galaxy, because the gravitational force is stronger on the near side of the encounter than on the far side. This heats the galaxy up, meaning that the galaxy is being pulled out of virial equilibrium by the encounter and that the average velocities of the stars get faster with enconters. Finally, the tidal forces from encounters with other galaxies make the galaxy break apart.

Now, what would an observer from Earth see? The observer could for example see a dSph that has been heated up by a recent encounter with another galaxy, and is thus out of virial equilibrium. Or the dSph has found its virial equilibrium again, but at the cost of stars which have left the dSph, and are now moving faster or slower than the stars which are still bound to the galaxy. But the observer could be ignorant of this fact, and assume that all the stars (s)he sees are bound to the galaxy. Or the dSph has dissolved already completely, but the stars still move all along on similar orbits, even though they are not bound to each other any more. The radius in which the stars are is then just much larger than it would be, if the stars were bound to each other. If the observer then wrongly assumes the dSph to be in virial equilibrium, all these effects increase the dynamical mass estimate (not the real mass!) (s)he makes for the mass of the galaxy. And those effects could indeed raise the dynamical mass estimate by the required factor. For a discussion of tidal heating of dSphs under Newtonian gravity, see for example Kroupa (1997). McGaugh and Wolf (2010) made a similar study with MOND. Notably, they found for observed dSphs surrounding the Milky Way that if a dSph is more susceptible to tidal forces, it is also more likely to be outside virial equilibrium for MOND. For an interesting theoretical discussion of how a dissolving star cluster in a tidal field could be mistaken for a much more massive (but evidently not more luminous) dSph, see Dominguez et al. (2016).

However, the dSphs which are out of virial equilibrium far enough to increase the dynamically estimated mass-to-light ratio by a few or more compared to the real mass could just be a few dSphs out of a larger sample. For the majority, the effect would simply be too weak now, although their time to dissolve will also come. In other words, this scenario is highly improbable if gravity was Newtonian, because then all dSphs around the Milky Way must be in dissolution. However, if gravity is MONDian, only a few would be near their dissolution, while most would be in or near virial equilibrium – see Dabringhausen el al. (2016).

Figure 4: The Antennae Galaxies (NGC 4038 and NGC 4039), the “poster child” for interacting galaxies with matter trown out as tidal tails. Image credit: Daniel Verschatse.
Figure 5: Another example for interacting galaxies and tidal tails, the Tadpole Galaxy. Despite its name being singular, there is actually two galaxies instead of one at the distance of the Tadpole Galaxy. The smaller galaxy is however currently projected on to the disk of the larger galaxy. It can be seen as blueish blob to the upper right of the larger galaxy. There are also star-forming regions in the tidal tail, which may become tidal dwarf galaxies, if they do not fall back on the primordial galaxies. Image credit: Hubble Space Telescope.

There is also another argument against dark matter in dSphs. Galaxies are usually not by themselves, but surrounded by other galaxies. Together, these galaxies form gravitationally bound galaxy clusters. But how do these galaxy clusters form? According to the LCDM-model, this happens by the infall of galaxies from all directions. They can come, the dSphs included, with any amount of exotic dark matter into a galaxy cluster. We will call those galaxies “primordial galaxies” from now on, because there is also another way to form galaxies that look like dSphs to an observer. This other way is through close encounters of already existing galaxies. In such encounters, matter is pulled away from the existing galaxies by gravity though tides (Figures 4 and 5), and new small galaxies can form from this matter. We know that this process happens. Otherwise, the elongated streaks of matter of, for instance, the Antennae Galaxies and the Tadpole Galaxy would be difficult to explain. Simulations of interacting galaxies, which are set up to reproduce situations like in the Antennae Galaxies, show also those streaks of matter like the ones observed (see for example Bournaud & Duc 2006 or Wetzstein et al. 2007). They are called tidal tails for obvious reasons. The Tadpole Galaxy even has a new small star-forming regions in its tidal tail, which may become dSphs. If aged enough, these dwarf galaxies may be difficult to distinguish from primordial galaxies of the same mass, though (see Dabringhausen & Kroupa 2013). However, in the following, we call galaxies of tidal origin “tidal dwarf galaxies”, in order to distinguish them from primordial galaxies. The tidal dwarf galaxies cannot contain the exotic dark matter of the LCDM-model, even if their progenitor galaxies did. The reason is that all matter that ends up in a tidal dwarf galaxy, whether visible or not, must have occupied similar regions of space with similar velocities also before the encounter of the existing galaxies. The total amount of the exotic dark matter may be huge, but most dark matter had other velocities and other locations, and therefore does not qualify to be bound to the tidal dwarf galaxy. After all, simulations of galaxy encounters by, for example, Barnes & Hernquist (1992) show that most visible matter that is to become a tidal dwarf galaxy comes from the disks of spiral galaxies. This visible matter does not only form a thin disk, as opposed to the presumed dark matter halo, but it also moves with the same velocity in the same direction, again in contrast to the presumed dark matter halo. Also, the tidal dwarf galaxies that form in an encounter of galaxies can only move in the plane of the encounter (because of the conservation of angular momentum). Thus, there is an easy way to distinguish the dSphs in the LCDM-model: those which move in a plane and those which cannot be assigned to a plane. Those in a plane are very likely tidal dwarf galaxies and cannot have any exotic dark matter. Those, however, which cannot be assigned to a plane might also be primordial and can thus contain dark matter (see for example Kroupa et al 2010). Now, what do observations tell us about the pattern of motion of the dSphs? In the Milky Way, it was shown by Lynden-Bell (1976) and by Kroupa et al. (2005) that the then known dSphs are most likely arranged in a plane. Later, additional objects and also velocities were added, but the long-lasting disk of Satellites was always confirmed (see for example Pawlowski et al. 2012 and Pawlowski & Kroupa 2020). This was according to some proponents of the LCDM-model just an exception, while other, they said more normal galaxies would have dSphs with random motions around them. However, it was shown then that also the Andromeda Galaxy has a disk of dSphs around it (for example Ibata et al 2013), and Centaurus A as well (Mueller et al 2018). In short, disks of satellites around major galaxies are more the rule than the exception, see for example Ibata et al (2014) for an attempt of a census. Thus, galaxies in these planes must manage their high dynamical mass-to-light ratios without exotic dark matter, despite numerous claims to the contrary from the LCDM-community. If MOND is the correct description of gravitation, then the large gravitating (phantom) masses of the satellite galaxies, as opposed to their small masses in stars, is beautifully resolved.

Conclusion

I have discussed the reasons for “dark” matter in elliptical galaxies, which comes ultimately from the comparison of different mass estimates. Also, some assumptions which were used for the lack of better knowledge have been proven wrong by now. This concerns the theory of a universal IMF in all star-forming regions, which was leading to a mismatch between the mass estimates from stellar populations and from the dynamics in UCDs and conventional elliptical galaxies. If the “one-size-fits-all” IMF is replaced by a more elaborate picture of the IMF, those differences disappear easily without using exotic dark matter or MOND. For dSphs, the situation is different. They cannot have exotic dark matter because it could not bind to them, but neither can their extreme mass-to-light ratios be explained with different stellar populations. Here, MOND and tidal fields offer an answer. Thus, adding more exotic dark matter to all galaxies until their dynamics is fitted might appear the simpler solution on first sight, but it is not necessarily the correct one. The seemingly more complicated solution without exotic dark matter stands a better test result here.


In The Dark Matter Crisis by Joerg Dabringhausen. A listing of contents of all contributions is available here.