75. No trace of dark matter in the dwarf galaxies of the Fornax Cluster

(by Pavel Kroupa and Elena Asencio) 

In disagreement with dark-matter-theory, dwarf galaxies in the Fornax Galaxy Cluster are void of dark matter. They behave exactly as expected from MOND. The inequality of gravitating mass and inertial mass of galaxies is indepedently confirmed using rotation curves of field disk galaxies.

Dwarf galaxies are supposed to be the most dark-matter dominated galaxies in the Universe. At least according to the standard Einsteinian/Newtonian-gravitation and dark-matter based LCDM model of galaxy formation (Battaglie & Nipoti 2022). In this LCDM model, the dark-matter-dominated dwarf galaxies must, if they are satellite galaxies,  be distributed spheroidally around their host galaxies.  But several studies focussed on the dwarf galaxies in the nearby Universe (the Local Group and its vicinity) have already shown that the LCDM model fails to explain many of their observed properties, in particular, that most of them are in disk-like configurations around their host galaxies (Pawlowski 2018; Pawlowski & Kroupa 2020; Pawlowski 2021; Pawlowski 2021).

Concentrating only on their dark matter content, such dwarf galaxies will be protected, though their large and massive dark matter halos that surround them, from tidal effects if they orbit through a cluster of galaxies. It is well known since at least 2004 that dwarf galaxies cannot be much affected by tides in LCDM theory. Citing from Kroupa et al. (2010, Sec. 2.8): “… the inner region of a satellite is only affected by tides after significant tidal destruction of its outer parts (Kazantzidis et al. 2004).” Therefore, for the visible part of the galaxy, which is the innermost part of any galaxy’s dark-matter halo in the LCDM model, to be affected/perturbed/distorted by tides, the galaxy must first be rid-of most of its dark matter halo. This takes many orbits such that only a very small fraction of observed dwarf galaxies can show tidal deformation if dark matter halos exist. The window of opportunity for catching a dwarf galaxy in this perturbed-by-tides state is brief: When most of the dark matter halo has been removed, it only takes about one more orbit for the dwarf galaxy to be completely destroyed.

By counting the number of observed dwarf galaxies that show signs of tidal deformation, we can thus test for the existence of dark matter: if too many dwarfs are distorted, then dark matter does not exist

In this recently published work (Elena Asencio, Indranil Banik et al. 2022, MNRAS, in press), we present a new line of evidence for the unsuitability of the standard dark-matter-based models to describe these objects. This study, lead by Elena Asencio, is a very extensive analysis of the statistics of the perturbations of dwarf galaxies in the Fornax Cluster of galaxies, and is a result of a multiple-year collaboration between researchers working at the University of Bonn, the University of St. Andrews, the European Southern Observatory in Chile, the University of Oulu in Finland, the University of Groningen in the Netherlands, and Charles University in Prague.

The dwarf galaxies of the Fornax Cluster are subject to the gravitational effects of the cluster environment. In the standard (Newtonian-gravity) dark-matter models, the dwarf galaxies are surrounded by a dark matter halo, so they should be mostly shielded from these gravitational forces. However, many of the Fornax dwarfs are observed to have distorted morphologies, which highly contradicts the LCDM-model expectation – as the results of this study show.

The above image shows the Fornax galaxy cluster. This is fig.9 in Venhola et al. (2018): “Magnification of Field 5 with the detected objects and masks (black circles) overlaid on the image. The yellow points and red symbols correspond to the initial detections of our detection algorithm, and the objects that pass the A_IMAGE > 2 arcsec selection limit, respectively. Aladin (Bonnarel et al. 2000) was used for generating the image. The image is best viewed in color on-screen.

We performed a similar test assuming a MONDian model (i.e. based on Milgromian gravitation without dark matter), which turned out to be very consistent with observations. In MOND, the dwarf galaxy is surrounded by a “phantom dark matter halo” (e.g. Lueghausen et al. 2013; Oria et al. 2021, ApJ) when it is far away from the centre of the galaxy cluster. This phantom dark matter halo is not real, it is merely Newtonian-speak to describe the true Milgromian potential of the galaxy. This potential is deeper and more extended when the dwarf is nearly isolated. When the dwarf plunges into the cluster, this phantom dark matter halo disappears. This is merely the mathematical consequence of the generalised (Bekenstein/Milgromian) Poisson equation and only means that the true Milgromian potential becomes less deep and shrinks. In other words, the galaxy’s gravitating mass is reduced, while its inertial mass remains the same. In this naked state, every dwarf galaxy is susceptible to tides, and so many dwarf galaxies are expected to show signs of distortion. It can happen that the dwarf is completely destroyed, but this would be a rare event and would remove dwarf galaxies quickly that are on orbits that take them very deep into the inner parts of the galaxy cluster. As the dwarf then orbits out from the central region, its phantom dark matter halo grows back (again this is merely a mathematical consequence) and the dwarf galaxy stabilises, having regained its gravitating mass which is much larger than its inertial mass in Milgromian dynamics. This process of loosing the phantom dark matter halo and regaining it as the satellite galaxy orbits within its galaxy cluster or around its host galaxy has been studied in detail in “The dynamical phase transitions of stellar systems and the corresponding kinematics” by Xufen Wu & Pavel Kroupa in 2013.

We thus have a beautiful convergence of LCDM failures – And at the same time, we also have a beautiful convergence of verifications of MOND:

Dwarf satellite galaxies are in planes around their host galaxies, like planetary systems around their stars, and dwarf galaxies have no dark matter.

Both of these properties show dark matter to not exist (and thus the entire LCDM model to be ruled out), and, at the same time, both are well understood if gravitation is Milgromian (see also DMC Blog 49). Both are well understood (i) because dark matter does not exist but the “dark-matter” content of dwarf galaxies is merely due to their orbit-dependent phantom dark matter halos, and (ii) because the planes of satellite galaxies are completely naturally produced when major gas-containing galaxies interact, like what happened between the Milky Way and Andromeda about 10Gyr ago (Bilek et al. 2018; Bilek et al. 2021; Banik et al. 2022).

Is there independent evidence for the waning and waxing phantom dark matter halo around galaxies predicted by MOND?

Haghi et al. (2016, MNRAS) had suggested that this may be nicely tested using rotation curves of galaxies: As stated above, if isolated, the gravitational mass of the galaxy is much larger than its inertial mass. Mathematically this spells out as it having a logarithmic Milgromian potential, which is synonymous to it having a phantom dark matter halo, the mass of which that is within R increases proportionally with distance, R, in Newton-language [Mphantom(<R) propto R]. This is demonstrated in the figure below (Fig.1 in Haghi et al. 2016).

Fig.1 from Haghi et al. (2016): The rotation speed, V, around the centre of a Milky-Way like galaxy as a function of distance, R, from the centre. An isolated galaxy has a flat rotation curve (uppermost solid line), but when other galaxies are placed in its vicinity they exert an external field across the galaxy leading to the external field effect (EFE) which leads the rotation curve to fall. The lowest thin curve is the pure-Newtonian (i.e. Keplerian) rotation curve when all of the phantom dark matter halo of the galaxy has vanished due to a strong EFE – the galaxy being “naked”. The strength of the EFE is described by the external acceleration ae.

The rotation curve is perfectly flat to very large R. Place this same galaxy into a region where there are other galaxies, then Mphantom will be smaller, and the rotation curve will fall. Thus Haghi et al. (2016, MNRAS) wrote the paper “Declining rotation curves of galaxies as a test of gravitational theory” pointing out that a signal is evident. And, using this approach and much improved data, extremely strong independent evidence for the breaking of the equality between inertial mass and gravitating mass described above and as predicted by MOND has thereafter been published by Chae et al. (2020, ApJ) and Chae et al. (2021, ApJ). Clearly, this constitutes a very major progress in fundamental physics.

Press releases about this publication:

in German from Bonn University,

in English: from the University of Bonn and from the University of St. Andrews,

in Czech from Charles University in Prague.

This post is related to the previous DMC Blog 58.

Talks about this project are available (the criticisms raised in the discussion of the ESO talk have been accounted for in our publication Elena Asencio, Indranil Banik et al. 2022, MNRAS, in press).

Elena explains the results in St. Andrews:

And at ESO (critical questions were raised at 34 minutes into the video – see below):

Jumped to 34m:


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

74. Fundamental Ideas in Cosmology: Scientific, philosophical and sociological critical perspectives, by Martin Lopez-Corredoira 

Dr. Martin Lopez-Corredoira from the Instituto Astrofisica de Canarias published the book “Fundemantal Ideas in Cosmology: Scientific, philosophical and sociological critical perspectives“. It constitutes an objective documentation of the various modern ideas that have been generated in order to describe the observed Universe, and stresses how very unclear the picture is.

Jacket Image

This book is particularly useful in view of how the first deep observations of the James Webb Space Telescope are already now impacting non-trivially on cosmological theory. The observations are indicating that the observed Universe has formed massive galaxies, weighing some 1000 million solar masses within merely a few hundred million years from the nominal Big Bang. The standard, dark-matter based cosmological models cannot form such galaxies so rapidly.

These observations also have some exciting implications for cosmological models based on MOND. We are working on these. More on that in future posts.


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

73. A composition for iai: Dark matter doesn’t exist! Yearly, a three quarter billion USDollars are wasted on an illusion.

After attending the “HowTheLightGetsIn” Festival in Hay on Wye in Wales, June 2nd-5th, 2022, I was asked by the Institute for Art and Ideas (iai) to draft a text capturing the current state of the dark matter science. It was published on July 12th, 2022. Here it is:

Dark matter doesnt exist

A straight pdf version for download is available here:

For a version in Spanish see “Einstein estaba equivocado: necesitamos una nueva teoría del cosmos“. A critique appeared as “Kroupa on Dark Matter vs MOND“.

Related to the above iai publication is the piece that appeared on Nov.25th, 2016, in aeon: “Has dogma derailed the scientific search for dark matter?“. Presentations are available on YouTube: Heidelberg Colloquium (November 2013), “The Vast Polar Structures around the Milky Way and Andromeda“, Golden Webinar (April 2021), “On the Non-Existence of Dark Matter“, and Astronomy on Tap Koeln (March 2022), “Dark Matter Kindergarten Stuff“. In May, 2021, Sabine Hossenfelder explained “Dark Matter, The Situation has Changed“.

While composing the iai text the question returned about how much money is being spent each year on a) salaries of all dark matter people, b) dark matter searches. The draft I had sent to iai (the above text) was immediately accepted and I did not have the opportunity to include the following updated estimate into it. But here it is:

My estimate: There are 12131 IAU members.

If half work on dark matter and if the average salary is 40000 USDollars per year, we have 242 million dollar per year being spent on dark matter research.

If there are currently ten dark matter searches, each costing on average 50 million per year, we have 500 million dollars per year (much of it on salaries for engineers, equipment, astronauts).

That is, the tax-payer is expending something like three-quarter of a billion dollars each year on largely useless “research”. A large fraction of scientific funding thus meanwhile goes into an activity which is based on pure belief contrary to evidence. One might interject that some of the experiments lead to the development of new technology. This would be equivalent to the situation where a state organises, using tax-payer money, a job-programme which employs people to dig many holes. The useful aspect of this would be that the unemployment rate would decrease, but the measure would leave no lasting benefit. In terms of the dark matter problem, it would be advisable to support research projects on non-falsified theories which lead to innovative technologies. Another way to express the above is to say that our modern, 21st century technological civilisation is essentially actively funding religion camouflaged as science with the above amount.

The dark-matter based models were clearly ruled out already in 2010 (read “Local-Group tests of dark-matter concordance cosmology . Towards a new paradigm for structure formation“) and definitely falsified in 2012 (read “The Dark Matter Crisis: Falsification of the Current Standard Model of Cosmology“). Today, ten years later, ample time has passed even for the dimmest scientist to be able to catch up. Given that the arguments against dark matter have not been shown to be invalid, and have in fact multiplied manyfold (see the iai piece above), it is simply not to be understood from a rational point of view why we keep expending so many valuable resources into a falsified theory while, at the same time, suppressing a highly interesting and successful alternative. The scientists who continue pushing for this falsified dark-matter theory are hurting the sciences and are, by ignoring the falsifications, being unscientific. They appear to behave more like ancient Egyptian priests who fervently guard their particular god(s) to thrive on the citizens by faking the ability for communicating with these imaginary deities.

What keeps this system going? The LCDM model is a gold of mine for those, the “LCDM priests”, who are able to sell the dark matter and dark energy stories to the funding agencies. An impression of how this works can be gleaned by watching the Golden Webinars in Astrophysics (see e.g. Post 65). An excellent example of the process is evident the time following 1:13:18 in the Golden Webinars in Astrophysics by Martin Rees as a consequence of Martin Rees suggesting that the non-detection of dark matter is trouble.

Furthermore, the LCDM model is guarded by suppressing fundamental empirical evidence: David Merritt eloquently documents how virtually all important modern textbooks fail to report essential information on galaxies (see Table 1 in Merritt 2017). From my own personal experience I know of significant mobbing within universities and general massive discouragement of young researchers against touching MOND. More than one student working with me have told me that it was recommended by other very senior researcher that they not work with me. When I was younger, I was too told that one may publish on MOND, but only to show it is wrong. It appears that this “guiding” by senior researchers of younger ones may have contributed to the long list of flawed such claims (“The List of Messups” or “The List of Shame”, Post 70). A classical example of continued mis-representation of MOND is the repeated claim that the Bullet Cluster falsifies MOND (this was shown to be wrong already by Angus, Famaey & Zhao 2006, MNRAS ), and a present-day example can be found in the Introduction of a MNRAS publication which dismisses MOND altogether but ends up discovering a trivial MOND result.

It has thus become a perpetually repeating cycle: young scientists are, in nearly all research institutions, not confronted with the essential information, and at best learn about it in the context of fringe science, something better not to touch if a career is desired. They need a post-doctoral or better position, or the one or other prize. To ensure success they do what is needed. In this way the scientific system appears to have become corrupt: despite being ruled out by the evidence (see the iai composition above), dark matter has come to be seen as a non-exotic and established part of physics. For the benefit of ones own career one sticks with dark matter rather than following the “fringe evidence”.

This text is my (Pavel Kroupa’s) responsibility only.


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

72. The first MSc-level lecture course on MilgrOmiaN Dynamics (MOND)

News:

Jan Pflamm-Altenburg (SPODYR group, Bonn) successfully applied for a lecture on MOND to be introduced in the winter semester 2022/2023 (WS22/23) and to be held each WS as part of the MSc-in-Astronomy syllabus in Bonn. The process of having the lecture accepted involved appreciable behind the curtain activity. This is a historic moment because we now have the first-ever lecture course at the MSc level in which the theory of Milgromian dynamics will be taught:


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

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.

69. The ultradiffuse Galaxy AGC 114905 works in MOND

“One can publish one paper on MOND

as long as it shows MOND to be wrong.”

Many “ΛCDM priests”

The above I heard many times before I was branded a “MOND person” by those in authority. Students working with me also reported that they were told the very same thing. I suppose the “LCDM priests” call me a “MOND person” because I published more than one paper on MOND and each of my MOND-related publications showed MOND to work very well. Below is an account on our just-published paper by Banik et al. who rebuts a recent prominent claim that argues (wrongly again) that MOND is falsified. The account is by co-author Srikanth Togere Nagesh who just finished his MSc thesis at the University of Bonn in the SPODYR group with two first-author research publications. After the guest post I add a brief account of two other claims of falsifying MOND that underline the validity of the above quote.

Pavel Kroupa

(The guest post by Srikanth Togere Nagesh follows below. A press release on our publication was published by St. Andrews University.)

Newton formulated a law of gravitation in 1687 that explained the motion of objects with speeds much smaller than the speed of light c. In fact, this was a first unification theory of physics, since he explained two phenomena that people did not think belonged together: the falling apple and the motion of the moon. Einstein developed a theory of gravitation that explains gravitation at speeds comparable to the speed of light c, and becomes Newtonian at speeds much less than c (Einstein 1916). Both the theories were developed using Solar System observations available at the corresponding times. Many decades later, when observations of galaxy rotation curves (RCs) became available in the late 1970s, Newtonian gravitation was applied to understand the behavior of the RCs. But the observed RCs were flat even at the outskirts of the galaxies (see Figure 1 below), which contradicted the conventional expectation of a Keplerian decline beyond the luminous matter, where the Newtonian inverse square law implies that the circular velocity, Vc, should scale with the distance, R, from the center as Vc proportional to R-1/2. The predicted rotation curve using Newtonian gravity and the observed rotation curve had strong discrepancies, and in order to solve this, it was postulated that galaxies reside in haloes of invisible mass, called cold dark matter (CDM), which boosts the gravity and was thought to reconcile the models with the observations. But the addition of dark matter to fix the RC has many extremely serious problems, addressed in a number of research publications (e.g. Kroupa et al. 2010; Peebles & Nusser 2010; Kroupa 2012; Kroupa 2015; Haslbauer et al. 2020; Asencio et al. 2021, Di Valentino et al. 2021; Haslbauer et al. 2022). The models based on the dark matter paradigm combined with dark energy, called ΛCDM models, constitute the standard model of cosmology (SMoC). Warm dark matter variants are essentially the same, as are fuzzy dark matter models (e.g. Dalal & Kravtsov 2022). The “Λ” stands for dark energy, another addition needed in order to make the Newtonian/Einsteinian cosmological models behave more like the observations.


A gravitational law was formulated by Milgrom in 1983, 1983b, 1983c after taking galaxy observations into account. It has a fundamental acceleration constant, a0 approximately 1.2 x 10-10 m/s2 (Gentile 2011), that we can refer to as Milgrom’s constant. This new theory of dynamics (strictly speaking, this can be a new theory of gravitation or of dynamics, the latter leaving the possibility open that inertial mass depends on acceleration, Milgrom 2011, see an interesting implication of this for space travel by Avi Loeb 2022) accounts for the observation that all systems with accelerations below a0 follow space-time scale-invariance (Milgrom 2009), and systems with acceleration greater than a0 follow the usual Newtonian dynamics. MilgrOmiaN Dynamics (MOND) has been successful in predicting the rotation curves of all galaxies (Sanders & McGaugh 2002; Famaey & McGaugh 2012) using Vf = (GMa0)1/4, where Vf is the asymptotic flat velocity that a galaxy’s RC reaches. MOND has also been successful in explaining other phenomena spanning from parsec to giga parsec scales (Banik & Zhao 2022).

Figure 1: The rotation curves for two very different galaxies. The left and right galaxies are, respectively, a massive and a dwarf disk galaxy. The measurements are shown by the open circles with uncertainties as vertical bars. The stellar plus gas components are given by the blue dashed (stars), the red dot-dashed (bulge) and green dotted (gas) contributions in the top panels. The black line shows the rotation curve the astronomer obtained in Newtonian gravitation without dark matter by adding these three colored contributions. The vertical red arrow shows how wrong this so-calculated rotation curve is. But taking the stars, bulge and gas and applying Milgrom’s gravitational law shows how the so-calculated rotation curve (the blue line in the two bottom panels) is an excellent match to the data, without any free parameters having been adjusted. Note especially how the wiggles of the rotation curve are automatically accounted for, this being impossible in the standard (Newton+dark matter) theory (Credits: Famaey & McGaugh 2012).

A new paper claiming MOND does not work: Now what’s the problem?

MOND thus accounts for all well-constrained observed rotation curves of normal, Milky-Way-like, and even rotating dwarf galaxies as well as elliptical and dwarf elliptical galaxies (e.g. Lelli et al. 2017). But not long, ago ultra-diffuse galaxies have been discovered as a new class. Will they fit this same Milgromian law? In 2021, neutral hydrogen (HI) observations of the ultra diffuse gas-rich galaxy AGC 114905 were used by Mancera Pena et al. (2021). The authors claimed that MOND fails to match the galaxy’s rotation curve. They also claim that ΛCDM fails to fit the RC of AGC 114905, which seems to render the galaxy unexplainable by both the theories. They inferred an asymptotic rotational velocity value, Vf, of 23 km/s using the MOND equation for this galaxy, which is surprisingly low for a galaxy with a mass of 1.42 x 10^9 M. The validity of this claim relies on the correctness of the measured apparent angle of inclination, i, between the disc and the sky plane. For example, a face-on galaxy has an inclination of i=0°, and an edge-on galaxy has an inclination i=90°.

Measuring the angle of inclination is done as follows. Contours of constant surface brightness are drawn on the images on the galaxies, then the contours are fit with ellipses of a given ellipticity. The ratio of minor axis to the major axis, q, is calculated for the best fitting ellipse. Taking the arc cosine of this q gives the apparent inclination, iapp, while the true inclination, i, might be different than the apparent one. The authors measured iapp,1 = 32° between the disc and the sky plane using the method above. They also measured iapp,2 = 11° by fitting another ellipse to the contour of AGC 114905, and adapted the former as the correct value.

Figure 2: The rotation curve obtained assuming MOND to be correct and iapp,2=11° is shown by the green curve assuming the observed distribution of stars and gas in the galaxy. Newtonian gravitation without dark matter gives the dashed magenta line. (Figure 6 in Mancera Pena et al. 2021)

(Figure 7 in Mancera Pena et. al. 2021)

The angle of inclination is important because the a rotation curve requires a correction factor of 1/sin(i). In this case, the ratio of sin(32°)/sin(11°) is 2.8, which is quite significant because the MOND prediction of Vf for AGC 114905 is 69 km/s, and the measured Vf is 23 km/s at iapp,1 = 32, which is a factor 3 less than MOND prediction. If one considers the inclination of 11° instead of 32°, then 23 x 2.8 = 64 km/s is quite close to the MOND predicted value. Hence, the galaxy can be reconciled with MOND if the inclination is much larger than the adopted 11°.

Why would anyone choose 11° when the best-fit shows 32°?

This is exactly what is addressed in our recent publication by Banik et. al. (2022) titled, “Overestimated inclinations of Milgromian disc galaxies: the case of galaxy AGC 114905“. In this article, we perform hydrodynamical simulations of a galaxy, computed by myself, with parameters similar to the properties of AGC 114905, in Milgromian gravity using the Phantom of Ramses (PoR) computer code, developed in Bonn in collaboration with Strasbourg by Lueghausen et. al. (2015). We use the observed parameters of AGC 114905 (Mancera-Pena et. al. 2021 above) as initial conditions and evolve the models for 5 billion years with PoR. The simulations include star formation as well. Simulations of such dwarf galaxies have never been done before. Dwarf galaxy simulations are particularly challenging, especially with stellar feedback, as it has never been tested before in MOND. The Bonn-Strasbourg research group did have experience with Milky-Way mass models (Wittenburg et al. 2020). These models of fairly massive galaxies already suggested, as remembered by co-author Pavel Kroupa in our group meeting, that MOND galaxies are much more alive and can appear elongated as they evolve without the help of a mass-dominating dark matter halo. But we did not know if the ultra-diffuse galaxy model would be disrupted due to violent supernova feedback for example, but it seems that stellar feedback does not disrupt the galaxy. In fact, it has the opposite effect of stabilising the galaxy and it evolves to be consistent with the observed one in terms of its present-day constitution.

We ran two models of the same galaxy. An isolated model without an external field, and another model with an external field (wich would come from some distant matter overdensity, e.g. another galaxy). In both cases, the models reproduce the observations and show that AGC 114905 works in MOND. We performed similar analyses on both the models.

What is the external field? It is the overall gravitational field across the galaxy which is generated by the large-scale matter inhomogeneity around the galaxy. A zero external field means the galaxy is completely isolated. A realistic external field, as used in our model, is as expected from the observationally estimate matter distribution. The external field changes the internal dynamics because Milgromian dynamics is a non-linear theory. The external field effect is a prediction of MOND and does not occur in Newtonian dynamics. It has been observationally evident in rotation curves (Haghi et al. 2016) with an observational verification with more than 5 sigma confidence by Chae et al. (2020). Thus, if two completely isolated stars attract each other with a force F, then the force changes to F’ < F if a third star is placed somewhere in the Universe. In Newtonian gravitation, on the other hand, F’ = F.

Initially, the models we simulated using PoR take about 1.5 – 2 billion years to reach dynamical equilibrium, and only the outputs after 2 billion years are used. Movies (see below) show a very active galaxy which changes it’s shape with time and it’s appearance with supernova explosions blowing bubbles into its interstellar medium. We plotted the gas distribution of the model between 2 and 5 billion years and drew a contour of constant surface brightness over each output image. Then we fitted ellipses to these contours and found the best fitting ellipse. We chose only those images where the fitted ellipse had a q value less than 0.86. We found multiple images (outputs) that had non-circular contours, and q << 0.86.

Why is this so important?

If you remember, the angle of inclination, i, is calculated using q, and a lower value of q, gives a higher apparent inclination iapp.

What is so special about it?

Our models have a true inclination of 0°, i.e. they are perfectly face-on throughout the evolution. In MOND, the galaxies are self-gravitating and can easily become non-circular over a period of time, similarly our models become non-circular and when we try to fit an ellipse and calculate iapp, we arrive at a value iapp >> 32°, even though the true inclination is 0°.

We argue that in MOND the same effect is plausible in the case of AGC 114905, where the authors might have arrived at an apparent inclination iapp,1 = 32°, but the true inclination is 11°. The problem was a clear overestimation by Mancera-Pena et. al. (2021) of the inclination based on ellipse fitting, which in turn is due to the non-circular nature of the galaxy, which is possible in MOND. Therefore, if one considers the inclination iapp,2 = 11°, the galaxy is reconciled with MOND. Therefore, the galaxy does not pose any problem to MOND at all, in fact, it backs-up that observed low surface brightness galaxies are known to have such features in MOND (McGaugh, Schombert & Bothun 1995).

In conclusion, it is generally advisable to exclude nearly face-on galaxies for such tests.

Figure 4: The fully self-consistent simulations of AGC 114905 in MOND. (Figure 1 in Banik et al. 2022)

Links to publication and videos

Videos showing the evolution of the models is available here,

Without the external field effect

With the external field effect


Addendum by Pavel Kroupa:

It is noteworthy that the recent peer-reviewed research literature contains claims that MOND does not agree with data that are wrong. That they are wrong could have been readily assessed by consulting with the appropriate experts, which neither the authors nor the editors deemed to be necessary. It appears there is a general feeling that publishing incorrect scientific results is acceptable, as long as these fake MOND to be wrong. Cases in point:

  • van Dokkum et al. 2018: Here the authors claim MOND is wrong by wrongly calculating the velocity dispersion of a dwarf galaxy. Two rebuttals were published: Kroupa et al. (2018) and Famaey et al. (2018). Two other related papers further clarified these types of galaxies (Haghi et al. 2019a; Haghi et al. 2019b). Note that this Nature paper has 12 authors some from ivy-league institutions, three referees and at least one editor. None of these astrophysicists thought it was necessary to ask an expert on Milgromian dynamics whether their calculation was correct. It seems that this whole group of people were all too enthusiastic of showing MOND to be wrong, something that is apparently accepted in the astronomical society. I take this as clear evidence that journals such as Nature distort scientific progress. The damage was great, since such Nature publications draw the attention of reporters, and the ivy-league status of some of the authors enhance the statements made in the publication.
  • Ogle et al. (2019): Analyse very massive disk galaxies and find them to deviate from the baryonic Tully Fisher relation (BTFR) writing in their abstract “The observed high-mass break in the BTFR is inconsistent with the Modified Newtonian Dynamics theory.” In a subsequent study, the same team (Di Teodoro et al. 2021) find this Ogle et al. (2019) work to have been faulty and show (without explaining the flaws of the previous one) that the same galaxies do lie close to the BTFR. They verify the prediction of MOND that all galaxies, also the massive ones, must be on the BTFR for the theory to hold. But these authors do not mention MOND when MOND fails to fail.
  • Mancera-Pena et. al. 2021 – see post by Srikanth above.

This is empirical evidence supporting the quote at the beginning of this post. This evidence also demonstrates how imbalanced and biased the extragalactic research community is against MOND. This community does not uphold the high standards of the scientific method but is corrupt (=statement by Pavel Kroupa) as the research papers written are apparently designed for career advancement rather than scientific advancement. We would falsify MOND with the same vigour as LCDM has been falsified, which is why we, in Bonn, Prague, Strasbourg and St. Andrews, are performing ever more computations using Milgromian dynamics to test and, if necessary, falsify also this rich theory of dynamics.


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

68. A critical essay by Subir Sarkar on the standard model of cosmology

(Guest post by Nick Samaras, April 12th, 2022)

Nick Samaras is a Ph.D. student at the Astronomical Institute of Charles University, in the Faculty of Mathematics and Physics, in Prague, Czech Republic. He works on cosmological simulations with Milgromian Dynamics (MOND). He has obtained his M.Sc. degree in Theoretical Physics at Cergy University, in France after having completed his B.Sc. in Mathematics at the Aristotle University of Thessaloniki, in Greece. In his following guest post he writes about the cosmological principle and a recent essay titled “Heart of Darkness” by Prof. Subir Sarkar.

The Standard Model of Cosmology (SMoC) has been considered as the correct description of the Universe and its evolution for decades now. General Relativity along with the mysterious Dark Energy, embedded on the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, provide the outset for the ΛCDM (Λ Cold Dark Matter cosmological) model. The FLRW metric is a formula derived from the General Relativity and corresponds to a homogeneous, isotropic and expanding universe. It is the mathematical tool with which one calculates distances on a 4-dimensional (time and the 3 dimensions of space) model. Nonetheless, according to more sophisticated investigations and the increase of observational data, the current theory faces a great number of challenges.

The Homogeneity and Isotropy hypothesis holds a convenient ground to do Cosmology. The so-called Cosmological Principle states that the Universe is very much alike anywhere over a typical scale of about 250/h Megaparsec (Mpc) (1 parsec = 1 pc is approximately equal to 3.26 light-years, unit of length). Remember that the Milky Way has a diameter of approximately 40 kpc, the Local Group of Galaxies is about 3 Mpc across, and the Virgo supercluster spans over about 30 Mpc). However, do the observations agree with this? Is there enough evidence to install the Cosmological Principle on a solid paradigm? How concrete are the cornerstones of the SMoC?

Subir Sarkar, an Emeritus Professor at the Rudolf Peierls Centre for Theoretical Physics, University of Oxford, argues that the real universe to be very different to the ΛCDM model and in particular the Cosmological Principle to be violated. Unraveling the record, the cosmological constant Λ (often being referred to as Einstein’s biggest blunder, the cosmological parameter causing the accelerating expansion) differs by many orders of magnitude when estimated from Quantum Field Theory (QFT), compared to what is inferred from Cosmology. He also emphasises an inconsistency when attempting to calculate the vacuum energy in QFT. The fact that the zero-point (vacuum) energy does not gravitate (otherwise it would have already dominated the Universe letting it evolve in a completely different way) have been kept aside even by the great Wolfgang Pauli, Prof. Sarkar points out.

Besides “the worst theoretical prediction in the history of physics” (Michael Hobson, George Efstathiou, and Anthony Lasenby), looking at the Cosmic Microwave Background (CMB – the primordial relic radiation released approximately 300,000 years after the Big Bang), its anisotropy dipole is larger than expected at high redshift (a cosmological way to calculate distances from us, based on the redshift of spectral lines). He notes that all matter in our nearby Universe has a coherent bulk flow approximately aligned with the direction of the CMB dipole. Several experiments, spanning from the 70s until these days, show that the bulk flow continues out to approximately 300 Mpc, remarkably not converging to homogeneity. The Indian theoretical astrophysicist wonders about Milne’s quote “the Universe must appear the same to all observers”, advocating historical changes in the field.

Sakar and his collaborators identified that the large dipole is not from the local universe. They have discovered that the cosmic rest frame of matter traced by quasars and the CMB don’t coincide. Thus, it is determined that the apparent acceleration is not happening because of the cosmological constant. It’s only a result of our non-Copernican position in the bulk flow. Consequently, the cosmic acceleration is not isotropic. ΛCDM begins to disintegrate …

Dark Energy, which drives the cosmos to accelerated expansion, in the form of an until-now-completely-not-understood repulsive force increasing with time, is therefore an occurrence generated by an over-interpreted conventionalised model which needs to be seriously revised. Leaving out the inflationary era a few moments after the Big Bang and the ambiguous premise of Dark Matter, the SMoC has been tested sufficiently to be replaced by a more detailed developed theory. Last, Prof. Sarkar, supporting that the Universe has different matter contents in different regions, encourages younger researchers to work out in greater depth an improved model of the real Universe .

Find here the essay “Heart of Darkness” by Prof. Subir Sarkar.


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

67. MOND for Dummies

(Guest post by David Levitt, April 4th, 2022)

David Levitt is a retired biophysicist from the Department of Integrative Biology and Physiology at the University of Minnesota. In the following guest blog he explains his attempt of approaching astrophysics and cosmology and why he decided to write an introduction to Milgromian Dynamics (MOND). Interested readers can download his review “MOND for Dummies” at the end of the guest blog.

I am a retired biophysicist, teaching myself astrophysics and cosmology. Approaching this subject with this fresh perspective, one is immediately struck by the remarkable drama presented by the conflict between the standard Lambda Cold Dark Matter (ΛCDM) and Modified Newtonian Dynamics (MOND) paradigms. In addition to MOND being ignored by most of the astrophysics community, there is also a nearly complete neglect of MOND in current science teaching and popular science presentations. Although there are many detailed technical reviews of MOND along with the wonderful book by David Merritt (see also blog contribution 55) for a general audience, there is a surprising lack of a simple short review of the MOND/ΛCDM issues accessible to someone with, say, a knowledge of college physics but no background in astrophysics. This lack became frustratingly clear when my attempt to convey my excitement about this subject to my scientific colleagues and grandson taking university physics failed because I could not find an appropriate reference to refer them to.

I have, presumptuously, taken it upon myself to write such a review, “MOND for Dummies”, which is linked below. Although there are obvious disadvantages of taking on this project as an amateur in this field, there are also advantages. Firstly, I know the issues that resonate with someone approaching this subject without an astrophysics background. And, secondly, I am aware of the importance of keeping the math and physics simple. I have focused this review primarily on spiral galaxy dynamics because it provides, I believe, the most dramatic confirmation of MOND predictions along with being understandable at the level of college physics. I hope that it conveys my enthusiasm for what, I believe, is the most important and exciting problem in physics today and that it provides a convincing case that MOND is a stunning theory that makes some remarkable predictions that are nearly perfectly confirmed experimentally. For many readers of this blog, the issues discussed in my review are well known and redundant. However, I am sure you also have colleagues and students that are not aware of the drama playing out in this field and to whom you might refer it.

Please find here the link to “MOND for Dummies” (updated April 27) written by David Levitt.


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.