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

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

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

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

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

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

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

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

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

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

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

a) Presentations by Prof. White and Prof. Kroupa

Summary of both presentations:

b) The Debate

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

Part I

Part II


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

60. Recent review talks about MOND, the Hubble tension and MOND cosmology including major problems of the dark matter models to match data

1) To obtain an introduction to MOND and MOND-cosmology, those interested might like to watch the talk below by Dr. Indranil Banik (past AvH Fellow in the SPODYR group at Bonn University, now at St.Andrews University). It was held on Sept. 30th, 2021 at the University of Southampton.

Indranil Banik

https://drive.google.com/file/d/1wJvYvpDWDtDk0xs47H6-Dr0Lr987wf5m/view?usp=sharing

Also, the following two previous talks are relevant:

2) In the recent Newton 1665 physics seminar series on  “MOND, the KBC void and the Hubble tension” by Dr. Indranil Banik and Moritz Haslbauer (SPODYR group):

Moritz Haslbauer

3) And also recently, as a CosmoStat Journal Club seminar on “El Gordo: a massive blow to LCDM cosmology” by Dr. Indranil Banik and Elena Asencio (SPODYR group): 

Elena Asencio


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

59. Are “darker psychological mechanisms” at work ?

(by Pavel Kroupa)

Two related essays have been published by aeon :

1) David Merritt wrote an essay for aeon with the title “A non-Standard model”. It is a very short version of his prize-winning Cambridge Universe Press book “A philosophical approach to MOND” and addresses the problem the cosmological scientist is faced with when needing to reach a conclusion as to the merit of a theory, given the data

Note that “true prediction” is used throughout this text to mean a prediction of some phenomenon before observations have been performed. Today, many numerical cosmologists and an increasing number of astrophysicists appear to be using a redefinition of “prediction” as simply being an adjusted calculation. Thus, the modern scientists observes data, then calculates what the cosmological model would give, adjusts the calculation to agree with the data, and then publishes this as a model prediction.

On the one hand side there is the standard dark matter based model which never made a successful true prediction (in the sense of pre-data) but is believed widely in the community to be true,

while on the other hand side Milgromian dynamics has made many successful true predictions of new phenomena but is deplored by the community.

David concludes this essay with “But I hope that scientists and educators can begin creating an environment in which the next generation of cosmologists will feel comfortable exploring alternative theories of cosmology.”

In addition to the performance of a model in terms of true predictions, a model can also be judged in terms of its capability to be consistent with data. This is a line of approach of model-testing followed by me and collaborators, and essentially applies the straight-forward concept that a model is ruled out if it is significantly falsified by data. Rigor of the falsification can be tested for using very different independent tests (e.g. as already applied in Kroupa et al. 2010). We have been covering this extensively in this blog. For example, the existence of dark matter particles is falsified by applying the Chandrasekhar dynamical friction test (as explained in Kroupa 2012 and Kroupa 2015): Satellite galaxies slow down and sink to the centre of their primary galaxy because of dynamical friction on the dark matter haloes. This test has been applied by Angus et al. (2011) demonstrating lack of evidence for the slow down. The motions of the galaxies in the nearby galaxy group M81 likewise show no evidence of dynamical friction (Oehm et al. 2017). Most recently, the detailed investigation of how rapidly galactic bars rotate again disproves their slow-down by dynamical friction on the dark matter halos of their hosting galaxies, in addition to the dark-matter based models having a completely incompatible fraction of disk galaxies with bars in comparison to the observed galaxies (Roshan et al. 2021a; Roshan et al. 2021b). All these tests show dark matter to not exist. Completely unrelated and different tests based on the larger-scale matter distribution and high-redshift galaxy clusters have been performed in great detail by, respectively, Haslbauer et al. (2020) and Asencio et al. (2021). Again, each of these individually falsify the standard dark-matter based models with more than five sigma confidence.

In summary: (a) By applying the formalisms of the philosophy of science to the problem whether the dark-matter-based models or the Milgromian models are the better theories in terms of their track record in true predictions, David Merritt demonstrates the latter to be far superior. (b) By applying the model-falsification approach by calculating the significance of how the models mismatch the data, we have come to the exact same conclusion.

As alluded to by David Merritt, the frightening aspect of our times is that the vast majority of cosmological scientists seem either not capable or willing to understand this. The lectures given by the leaders of cosmological physics, as can be witnessed in the Golden Webinars in Astrophysics series, collate an excellent documentation of the current disastrous state of affairs in this community. In my Golden Webinar in Astrophysics I describe, on April 9th 2021, this situation as

the greatest scientific crisis in history ever,

because never before have there been so many ivy-league educated researchers who en masse are so completely off the track by being convinced that a wrong theory (in this case dark matter cosmology) is correct while at the same time ignoring the success of another theory (in this case Milgromian dynamics). At next-to-all institutions, students appear to be indoctrinated by the “accepted” approach, with not few students in my lectures being surprised that the data appear to tell a different story. Many students even come to class believing that elliptical galaxies are the dominant type of galaxy, thus having an entirely wrong image of the Universe in their heads than what is truly out there. Once before there was a great clash of ideas, famously epitomised by Galileo Galilei‘s struggle with the Church. But this was very different, because traditional religious beliefs collided with modern scientific notions. Today, the Great Crisis is within the scientific community, whereby scientists ought to be following the evidence rather than belief. Belief should not even be a word used by scientists, as it implies a non-factual, not logical approach. Rather than belief, we as scientists need to objectively test hypotheses which need to be clearly stated and the results of the tests must be documented in terms of significance levels.

2) And the reader of this blog would probably also be interested in the very related earlier aeon essay by myself on Has dogma derailed the scientific search for dark matter?.


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

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.

57. A splash too far: “On the absence of backsplash analogues to NGC 3109 in the ΛCDM framework”

The isolated but nearby galaxy NGC 3109 has a very high radial velocity compared to ΛCDM expectations, that is, it is moving away from the Local Group rapidly, as shown by Peebles (2017) and Banik & Zhao (2018). One of the few possible explanations within this framework is that NGC 3109 was once located within the virial radius of the Milky Way or Andromeda, before being flung out at high velocity in a three-body interaction with e.g. a massive satellite. In the new research paper “On the absence of backsplash analogues to NGC 3109 in the ΛCDM framework”, which was led by Dr. Indranil Banik, it is shown that such a backsplash galaxy is extremely unlikely within the ΛCDM framework. Basically, such galaxies cannot occur in ΛCDM because they ought to be slowed-down due to Chandrasekhar dynamical friction exerted on NGC 3109 and its own dark matter halo by the massive and extended dark matter halo of the Milky way. Making it worse, NGC 3109 is in a thin plane of five associated galaxies (the “NGC 3109 association”, rms height 53 kpc; diameter 1.2 Mpc), all of which are moving away from the Local Group (Pawlowski & McGaugh 2014), whereby the dynamical friction ought to slow down the galaxies in dependence of their dark matter halo masses. This makes its thin planar structure today unexplainable in ΛCDM.

Interestingly, the backsplash scenario is favoured by the authors (Banik et al. 2021), but in the context of MOND. In this theory, much more powerful backsplash events are possible for dwarf galaxies near the spacetime location of the past Milky Way-Andromeda flyby because in MOND galaxies do not have dark matter halos made of particles. A galaxy thus orbits through the potential of another galaxy unhindered and ballistically. The envisioned flyby could also explain the otherwise mysterious satellite galaxy planes which are found around the Milky Way and Andromeda. It now seems that the flyby may well be the only way to explain the properties of NGC 3109, since a less powerful three-body interaction is just not strong enough to affect its velocity as much as would be required. But a Milky Way-Andromeda flyby is not possible in ΛCDM as their overlapping dark matter halos would merge.

In a series of Tweets, the co-author Dr. Marcel Pawlowski briefly explains on his Twitter account @8minutesold the main results of this recent publication:

Source: https://twitter.com/8minutesold/status/1392430171240677376

Source: https://twitter.com/8minutesold/status/1392430171240677376


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

56. From Belief to Realism and Beauty: Given the Non-Existence of Dark Matter, how do I navigate amongst the Stars and between Galaxies?

(by Pavel Kroupa, 4th of April, 2021, 11:11)

Update (April 15th): After receiving some queries, the slides to the talk w/o the fictitious story can be downloaded here

On April 9th, 2021, I will give this public talk:

If interested, you can join the public lecture by registering here.

The talk, held via zoom, is on April 9that 11:00 Chilean Time (CLT = UTC-4),  8am Pacific Daylight Time (PDT = UTC-7),11am Eastern Daylight Time (EDT = UTC-4), 17:00 Central European Summer Time (CEST = UTC+2)

The Golden Webinars are provided as a free public service and have no registration fees. They are recorded and made available for later viewing via youtube.


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

55. “A Philosophical Approach to MOND” wins prestigious award

It is with delight we learned today that David Merritt’s book on “A Philosophical Approach to MOND” published by Cambridge University Press won the Prose Award for Excellence in Physical Sciences and Mathematics. Other authors also competing for this price were Peebles and Weinberg. 

I had written a review of this book which can be read here.

Note also that in 2013 David published a noteworthy text book on “Dynamics and Evolution of Galactic Nuclei” (with Princeton Series in Astrophysics).


This is an opportunity to recall how I personally stumbled into this whole problem concerning dark matter (see also this article on Aeon): My research up until the mid1990s was based on stellar populations, although in Heidelberg we had also measured, for the first time, the actual space velocity of the Magellanic Clouds (in 1994 and 1997). These were my first endeavours into the extragalactic arena. I had heard a fabulous lecture by Simon White who was visiting Heidelberg, showing movies of structure formation in the LCDM model they had just computed in Garching. I personally congratulated Simon for this most impressive achievement.  One could see how major galaxies were orbited by many dwarf satellite galaxies and how all of that formed as the Universe evolved. I had also noted from photographs that when two gas-rich galaxies interact, they expel tidal arms in which new dwarf galaxies form. These new dwarf galaxies are referred to as tidal dwarf galaxies.

The Tadpole Galaxy recorded with the Hubble Space Telescope’s Advanced Camera for Surveys. Evident are the new dwarf galaxies in the 100 kpc long tidal tail.

In the 1990’s the community had largely discarded satellite dwarf galaxies being tidal dwarfs because it was known that they cannot have dark matter (this goes back to Barnes & Hernquist,1992,  later confirmed by Wetzstein, Naab & Burkert 2007).  So it was thought that tidal dwarfs just dissolve and play no important role.  The observed satellite galaxies of the Milky Way have large dynamical M/L ratios, going up to 1000 or more. This proved they can contain a 1000 times more mass in dark matter than in stars and gas. So obviously they cannot be tidal dwarfs. I very clearly remember Donald Lynden-Bell exclaiming in Cambridge, when I was still visiting regularly, that his suggestion that the satellites came from a broken-up galaxy cannot thus be correct, since they contain dark matter. Then I made my discovery (truly by pure chance) published in Kroupa (1997), which made me think that what the celebrated experts are telling me seemed not to be quite right. After this publication I was told more than once this work made me un-hireable.
 
I had then noted (Kroupa et al. 2005), that the disk of satellites (DoS, including the newer once which Donald had not known) is in conflict with them being dark-matter substructures, as these ought to be spheroidally distributed around the Milky Way galaxy. 
 
We  argued (to my knowledge for the first time in print, in Kroupa et al. 2010 and in Kroupa 2012 ) that the disk of satellites can only be understood if they are tidal dwarfs. I had also come to the conclusion that my chance discovery above is unlikely to be able to explain the high M/L values of all the satellite galaxies as they would all need to be quite strongly affected by tidal forces which poses a problem for those further than 100 kpc from the Milky Way because their orbital periods begin to approach a Hubble time. And if they are tidal dwarfs (which they must be given they make a disk of satellites),  then this implies we need non-dark-matter models, i.e. , we need to change the law of gravitation to account for the high M/L values these little galaxies display.  Subsequently I was quite fevering (with PhD student Manuel Metz and later Marcel Pawlowski) each time a new satellite was discovered to see where it lay (I used to run to their offices whenever some survey reported a new satellite), and ultimately what the proper motions are doing: if the satellite galaxies form a pronounced disk of satellites then they must be orbiting only within this disk (Pawlowski & Kroupa 2013). I was (this was already in the 2000s) also interested if  John Moffat’s “modified gravity” (MOG) might explain the large M/L ratios, and John Moffat visited me in Bonn. But it turns out that MOG is falsified while Milgromian gravitation (MOND) is, as far as one can tell, the at the moment only possible gravitational theory we can use which accounts for all data and tests so far performed.  Oliver Mueller, Marcel Pawlowski  et al. (2021) affirm that the Milky Way is not unique in having a disk of satellites system. Observing disks of satellites around larger galaxies is not a “look elsewhere effect” since the very-nearest large galaxies are looked at, rather than finding such DoSs around some host galaxy in a very large ensemble of observed galaxies. I think the disk-of-satellites or satellite-plane problem is the clearest-cut evidence why we do not have dark matter. 
 
The (negative) test for the existence of dark matter particles (warm, cold, fuzzy) via Chandrasekhar dynamical friction is the other (Kroupa 2015).
 
Plus, with all the other tests performed in strong collaboration with Indranil Banik (notably Haslbauer et al.  2019a, Haslbauer et al. 2019b,  Haslbauer et al. 2020 and Asencio et al. 2021) it materialises that the tests all lead to mutually highly consistent results – we do not have the situation that one test is positive (for dark matter), the other not. They all turn out to be consistently negative. Indranil Banik concludes correctly (Feb.5th, 2021): “There are so many lines of evidence that no single one is critical any more.”
 
I am personally deeply impressed how everything seems to fall into place (quite nearly everything) once one uses MOND (which is based on a Lagrangian etc.).  Apart from completely naturally resolving the Hubble Tension and easily accounting for massive high-redshift galaxy clusters like El Gordo (see also this account on Triton Station), the DoSs or satellite planes form naturally (as shown independently by Banik et al. 2018 and by Bilek et al. 2018) and these tidal tail dwarf galaxies have large M/L values due to the correct law of gravitation (e.g. this amazing prediction by McGaugh 2016 of the velocities of stars in one of the satellite galaxies and verification thereof by Caldwell et al. 2017).
 
But, just like with the standard model of particle physics, there definitely is a deeper layer to MOND which we have not yet discovered; a more fundamental theory, which may well be the quantum vacuum which also explains particle masses. Milgrom had already published seminally on this issue.
 
The huge success of MOND comes not only in it naturally account for the data on scales of a few 100 pc to a Gpc, but also that it is a “progressive research programme“, with the standard dark-matter based models being “degenerative“.  For details, see David Merritt’s book above. 
 

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

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

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

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

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

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

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

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