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.

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.



64. Youtube playlist full of MOND talks, debates and more

(Guest post by Mark Huisjes, December 8th, 2021)

In the following guest post by Mark Huisjes (GIS Analyst and master student at Utrecht University) we would like to promote a Youtube playlist, which includes talks, debates, Q&A’s, and more videos related to MilgrOmiaN Dynamics (MOND). This playlist is aimed for anyone who is interested in this research field.

Over the past year I’ve built a Youtube playlist of videos related to MOND, which is available online here.

Youtube playlist of talks, debates, interviews, Q&A sessions, and much more hosted by Mark Huisjes.

It contains more than 70 hours of talks, debates, interviews, Q&A sessions, and much more. Most of the listed videos are in English, but videos in French, Spanish, German, and Czech are also available at the end of the playlist. Subjects covered include fundamental MOND phenomenology such as rotation curves, the baryonic Tully-Fisher relation, the central density relation, and the radial acceleration relation, but also more advanced topics such as the external field effect, satellite galaxy planes, wide binaries, TeVeS, superfluid dark matter, and νHDM cosmology, and scientific tests of the hypothesis that dark matter exists.

This way people can easily find a talk if it is available online and delve deeper into the theory of MOND!


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

63. Hybrid models may solve mystery of dark matter

(Guest post by Tobias Mistele, December 1st, 2021)

Tobias Mistele is a PhD student at the Frankfurt Institute for Advanced Studies studying hybrid MOND-dark-matter models. Besides his physics research he also works on Scimeter.

Hybrid models, which combine dark matter and modified gravity, were long neglected. In this post, I explain why such models are now attracting attention as a path out of a stalemate.

There is observational evidence for missing baryonic mass on both cosmological and galactic scales. Most notably, the fluctuations in the cosmological microwave background (CMB) on cosmological scales and rotation curves on galactic scales. Traditionally, this is explained by non-relativistic dark matter particles (cold dark matter, CDM) that do not interact much except gravitationally. These CDM particles form a pressureless fluid on cosmological scales and later accumulate around galaxies, forming a dark matter halo. The pressureless fluid explains the fluctuations in the CMB. The mass of the halo around galaxies explains galactic rotation curves. An alternative paradigm is modified gravity. Instead of postulating particles that produce additional mass, modified gravity postulates a different gravitational force. Modified Newtonian Dynamics (MOND) is a modified gravity model that is quite successful on galactic scales. For example, consider the so-called Radial Acceleration Relation (RAR) shown in Figure 1. This is a relation between the standard Newtonian gravitational acceleration due to the stars and gas in a galaxy, gbar = GMb/r2, and the total acceleration gobs we infer from observed rotation curves. In a world without dark matter and without modified gravity, these two are the same, gbar = gobs. In the real world they are not. This is the missing mass problem in galaxies. More importantly, this relation between gobs and gbar has little scatter. Thus, the total acceleration gobs can be predicted just from the baryonic mass distribution, i.e. from gbar.

Figure 1: The Radial Acceleration Relation (RAR). Credits: One Law to Rule Them All: The Radial Acceleration Relation of Galaxies (Lelli et al. 2017). With kind permission by Federico Lelli.

This is non-trivial in DM models. In principle, two galaxies with the same baryonic mass distribution (the same gbar) can have different dark matter halos and thus a different gobs, but this doesn’t happen. In contrast, MOND naturally explains this. In fact, the RAR shows precisely what MOND postulates. At Newtonian accelerations gbar larger than a0 ≈ 10-10 m/s2 nothing new happens. Newton’s gravitational force law remains. But at accelerations gbar smaller than a0, the total acceleration changes to (a0 gbar)1/2.

Unfortunately, both CDM and MOND remain unsatisfactory when considered individually. MOND, for example, cannot explain all the missing mass on galaxy cluster scales. And, so far, no MOND-based models have been able to explain the fluctuations in the CMB, at least not without introducing some type of dark matter after all. CDM, on the other hand, has its own problems. For example, there is so far no convincing explanation for MOND-like scaling relations like the RAR. There’s just no reason why the dominant dark matter halo should be predictable from the visible baryonic mass in such a simple way. Another problem is that observed galactic bars tend to rotate faster than what CDM predicts. The dynamical friction of a CDM fluid slows down galactic bars. Then there’s the plane-of-satellites problem. Satellites of the Milky Way co-orbit in thin, planar structures. A natural explanation would be that these satellites were created from the tidal tails of interacting galaxies. But then they would not have their own dark matter halo which contradicts their high internal velocity dispersion. Also, CDM seems to be too slow to grow large structures. Massive clusters at high redshift like El Gordo are very unlikely to form so early in CDM.

So if not MOND or CDM – then what? One answer is both! That’s what hybrid MOND-dark-matter models are about. These are models that have both a pressureless fluid on cosmological scales (to explain the CMB) and a MOND-like force in galaxies (to explain e.g. the RAR).

Let me illustrate the general ideas behind hybrid models with an example – a model called superfluid dark matter (SFDM) proposed by Berezhiani & Khoury. This model has various problems, but it serves as a good illustration of the general features of hybrid models. SFDM postulates a specific new type of particle that behaves like standard CDM on cosmological scales and therefore explains the CMB in the standard way. But around galaxies, these particles condense to form a superfluid. The collective excitations of this superfluid, called phonons, then mediate a MOND-like force in galaxies. This MOND-like force is an emergent property of these particles in the superfluid phase. This is how this model explains MOND-like scaling relations like the RAR.

Of course, the superfluid itself has a mass. This produces a standard gravitational force that affects stars and gas. That is to say the superfluid also acts as dark matter in galaxies. So then we have both a MOND-like force and dark matter around galaxies. But does this not solve the missing mass problem twice? So that rotation velocities end up even larger than what we observe?


Figure 2: The Milky Way rotation curve in superfluid dark matter. The dark matter contribution is small, but becomes more important at larger radii. Credits: Tobias Mistele

The answer to that is that the superfluid DM component is usually subdominant within galaxies because the superfluid halo is very cored. Its mass becomes relevant only at larger radii. This is illustrated in Figure 2 for the Milky Way rotation curve.

One might be tempted to adjust one’s models so that the DM contribution becomes even smaller. Just to reproduce the MOND-like scaling relations even more cleanly. But one must be careful with this. Some amount of dark matter is needed in hybrid models to explain the missing mass on galaxy cluster scales for which MOND cannot fully account and, in some models, also to explain gravitational lensing.

Superfluid dark matter is not the only hybrid model. For example, recently Skordis and Złosnik proposed a model that reproduces MOND in galaxies (SZ model). This is also a hybrid model and has, deservedly, received a lot of attention since it is fully-relativistic and it was demonstrated explicitly that this model fits the CMB. Like in SFDM, the MOND and DM components are related to each other in the SZ model.

Such a common origin for the cosmological and galactic phenomena is theoretically appealing. But not all hybrid models have such a common origin. For example, the so-called νHDM model does not. Moreover, such a common origin often brings about internal tensions that must be carefully avoided.

In SFDM, for example, this common origin means that the phonon field is involved both in providing the DM and the MOND components. One technical consequence is that the usual U(1) symmetry of the superfluid must be explicitly broken which has various non-technical implications. For example, the superfluid equilibrium state might not be valid on timescales longer than galactic timescales.

The common origin for the DM and MOND components complicates things also for the SZ model. In this model, there is a kind of mass term for the static gravitational field in galaxies. Mass terms generally make forces short-range. To keep the gravitational force in galaxies long-range, the mass term must be chosen small. But a smaller mass term in galaxies means a larger pressure of the DM-like fluid in cosmology. Observations indicate a very small pressure of the DM fluid. So the galactic and cosmological phenomena push the model in different directions. This has forced the authors to include certain non-linearities as a counter.

Besides these model-specific constraints, there is also a new type of phenomenon that quite generally constrains models with a common origin for the MOND and DM components. Namely, stars often lose energy just by moving through a galaxy. Let me explain.

Accelerated charges produce electromagnetic waves. Accelerated masses produce gravitational waves. In general, whenever matter is coupled to a force carrier (e.g. the electromagnetic or the gravitational field), matter that accelerates produces waves corresponding to that force carrier. But even non-accelerated matter objects can produce waves. Namely if they move faster than the speed with which these waves propagate. For example, in a medium, electromagnetic waves propagate slower than the vacuum speed of light. Charged particles in such a medium emit electromagnetic waves if they move faster than this reduced speed of light. These waves are then called Cherenkov radiation. Such charged particles lose energy and slow down. A similar phenomenon occurs frequently in modified gravity theories whenever gravitational waves propagate at less than the vacuum speed of light. This is called gravitational Cherenkov radiation. Usually, only highly relativistic matter objects emit Cherenkov radiation, both in modified gravity theories and in electromagnetism. This is because the propagation speed of waves is usually relativistic, so that only relativistic particles are fast enough.

But this is different in hybrid MOND-DM models with a common origin for the MOND and DM components. Such models usually contain a force carrier (for the MOND-like force) whose associated waves propagate with non-relativistic speed (because this force is related to the non-relativistic dark matter fluid). Thus, even non-relativistic objects like stars might move faster than the wave propagation speed associated with the MOND force. Such stars will then lose energy and slow down, because they emit a special type of gravitational Cherenkov radiation. For example, in SFDM stars that move faster than the superfluid’s speed of sound will lose energy by emitting sound waves and slow down until they are slower than the superfluid’s speed of sound. This is illustrated in Figure 3. A star may be on a standard circular orbit when it is sufficiently slow, but will otherwise lose energy and circle towards the center of a galaxy.

Figure 3: The orbit of a star in the plane Z = 0 of a galaxy with (dotted orange line) and without (straight blue line) the Cherenkov radiation typical of hybrid MOND-DM models with a common origin for the MOND and DM components. The two cases are labeled as “With friction” and “Without friction” because in the specific approximation used, the Cherenkov radiation acts like an effective friction force on the star. Credits: Tobias Mistele

This reasoning applies only to models with a common origin for the DM and MOND components. So it does apply to SFDM and the SZ model, but not to the νHDM model. When actually doing the calculation one needs to be careful because of the non-linearities that are inherent in any MOND model. Still, it is possible to rule out part of the parameter space of SFDM using the observed Milky Way rotation curve. Basically, one requires that stars that orbit around the Milky Way with the rotation curve velocity do not lose much of their energy during the Milky Way’s lifetime. The SZ model avoids such constraints due to a special property. The coupling to matter is much larger in the static limit than in dynamical situations, which suppresses the energy emitted by Cherenkov radiation. Though I should say that the calculation for this model was done in a simplified setup so that the result should be taken with a grain of salt.

To sum up, the observational evidence for both MOND-like scaling relations on galactic scales and a DM-like fluid on cosmological scales has only become more convincing in recent years. This motivates hybrid MOND-DM models. We may not yet have a completely satisfactory model and much remains to be explored. Still, this general type of model will likely become ever more relevant in the future.


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

62. Mailing list for the MOND community

(Guest post by Indranil Banik, November 22nd, 2021)

In the following guest post by Dr. Indranil Banik (past AvH Fellow in the SPODYR group at Bonn University and now at the St.Andrews University), we would like to promote a mailing list for the MOND community and anybody who is interested in this research field.

Following a request, I have set up a mailing list for the MOND community and anybody who wants to stay updated about our work. The idea is that if someone wants to advertise an upcoming talk or an article they have recently posted but they are at an early career stage and do not know everyone in the MOND community, they can just send an email to the mailing list. Also if some discussions between more senior researchers take place through this list, then any early career researchers signed up to it will be included in the conversation even if nobody thought explicitly to include them in the conversation. Regardless of whether you are signed up, you can send an email to the mailing list and everyone on it should receive the message.

The email address is: mondworkers@gmail.com

Please contact Elena Asencio if you want to sign up to this mailing list and thus receive the emails sent to it, she will be in charge of sending an invitation link which you need to accept in order to complete the sign up: s6elena@uni-bonn.de

We think it is not appropriate to send such invitation links to people who have not requested it, as such a request would take only a little time and we would not ask for any reasons for why you want to sign up.
At the moment, only a very small number of emails have been sent to the mailing list because I have only recently set it up. I envisage that it would not be used all that often for a while, and slowly catch on as more people know about it. Obviously it is not suitable for a great many emails as the sender might only want specific people to see it rather than the whole mailing list. But there are times when people want their email to gain extra visibility, and that is what this is about.

Please advertise this to especially early career researchers, it is intended for sharing adverts for upcoming talks, notifying others of articles and blogs, and discussing research ideas you want to share. In general, it is for anything you want to share with everyone on the list, including I suppose asking for advice. It is important that the more senior researchers working on MOND are signed up to it so that early career researchers who want to e.g. advertise a talk or get advice about a project manage to contact everyone on the list without knowing all their names and email addresses. In principle, a fair amount of customisation is possible with the filters that are used, and different filters can be used for different people on the list. At the moment, the only filtering in place is to prevent administrative emails being sent to everyone on the list. Requests to modify filters can be considered, and of course you can be removed from the mailing list if you ask. Thank you to those of you who have already signed up.

58. The tidal stability of Fornax cluster dwarf galaxies in Newtonian and Milgromian dynamics

(Guest post by Indranil Banik and Elena Asencio, August 2nd, 2021)

A directly-related presentation by Elena Asencio is available here:

The tidal stability of Fornax cluster dwarf galaxies in Newtonian and Milgromian gravity

The slides of the presentation can be downloaded here:

A large number of dwarf galaxies in the Fornax cluster (Figure 1) appear to be disturbed, most likely due to tides from the cluster gravity. In the standard cosmological model (ΛCDM) , the observable structure of the dwarfs is barely susceptible to gravitational effects of the cluster environment, as the dwarfs are surrounded by a dark matter halo. Because of this, it is very hard to explain the observations of the perturbed Fornax dwarfs in this theory. However, these observations can be easily explained in MOND, where dwarfs are much more susceptible to tides due to their lack of protective dark matter halos and the fact that they become quasi-Newtonian as they approach the cluster center due to the external field effect.

Figure 1: Fornax galaxy cluster. The yellow crosses mark all the objects identified in the Fornax deep survey (FDS) for this region of the sky, the black circles are masks for the spikes and reflection haloes, and the red crosses mark the objects that pass the selection criteria to be included in the FDS catalog. Image taken from Venhola et al. 2018.

The impact of tides on what the dwarfs look like is illustrated in Figure 2, which shows the fraction of disturbed galaxies as a function of tidal susceptibility η in ΛCDM and MOND, with η = 1 being the theoretical limit above which the dwarf would be unstable to cluster tides. Moreover, there is a lack of diffuse galaxies (large size and low mass) towards the cluster center. This is illustrated in Figure 3, which shows how at low projected separation from the cluster center, dwarfs of any given mass cannot be too large, but larger sizes are allowed further away. Figure 3 thus shows a clear tidal edge that cannot be explained by selection effects, since the survey detection limit would be a horizontal line at 1 on this plot such that dwarfs above it cannot be detected. Diffuse dwarf galaxies are clearly detectable, but are missing close to the cluster center. Another crucial detail in Figure 3 is that dwarfs close to the tidal edge are much more likely to appear disturbed, which is better quantified in Figure 2 in the rising fraction of disturbed galaxies with tidal stability η. The tidal edge is also evident in Figure 2 in that the dwarfs only go up to some maximum value of η, which should be close to the theoretical stability limit of 1. This is roughly correct in MOND, but not in ΛCDM.

Figure 2: Fraction of disturbed galaxies for each tidal susceptibility bin in MOND (red) and ΛCDM (blue). Larger error bars in a bin indicate that it has fewer dwarfs. The bin width of the tidal susceptibility η is 0.5 in MOND and 0.1 in ΛCDM (each data point is plotted at the center of the bin). Notice the rising trend and the maximum η that arises in each theory.

Figure 3: Projected distances of Fornax dwarfs to the cluster center against the ratio Re/rmax, where Re is the dwarf radius containing half of its total stellar mass, and rmax is the maximum Re at fixed stellar mass above which the dwarf would not be detectable given the survey sensitivity. The dwarfs are classified as “disturbed” (red) “undisturbed” (blue). The black dashed line shows a clear tidal edge – at any given mass, large (diffuse) dwarfs are present only far from the cluster center. This is not a selection effect, as the survey limit is a horizontal line at 1 (though e.g. some nights could be particularly clear and allow us to discover a dwarf slightly above this).

We therefore conclude that MOND and its corresponding cosmological model νHDM (see blog post “Solving both crises in cosmology: the KBC-void and the Hubble-Tension” by Moritz Haslbauer) is capable of explaining not only the appearance of dwarf galaxies in the Fornax cluster, but also other ΛCDM problems related to clusters such as the early formation of El Gordo, a massive pair of interacting galaxy clusters. νHDM also better addresses larger scale problems such as the Hubble tension and the large local supervoid (KBC void) that probably causes it by means of enhanced structure formation in the non-local universe. These larger scale successes build on the long-standing success of MOND with galaxy rotation curves (“Hypothesis testing with gas rich galaxies”). MOND also offers a natural explanation for the Local Group satellite planes as tidal dwarf galaxies (“Modified gravity in plane sight”), and has achieved many other successes too numerous to list here (see other posts). Given all these results, the MOND framework appears better suited than the current cosmological model (ΛCDM) to solve the new astrophysical challenges that keep arising with the increase and improvement of the available astronomical data, which far surpass what was known in 1983 when MOND was first proposed.


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