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.
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.
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.
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.”
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.
(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 M̃ 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.
(Guest post by Dr. Jörg Dabringhausen, Charles University in Prague, Dec. 18th 2020)
The hypothesis of dark matter in galaxies was originally brought up by observations. Zwicky (1933) first found out that galaxies were usually moving too fast to stay in the observed galaxy clusters, if the luminous matter was all there is in galaxies. With “luminous matter”, essentially all stars were meant. Stars are understood well in terms of how much mass in a star leads to a certain light strength, or luminosity. But if the light emitted by the galaxies in a galaxy cluster is translated to a stellar population similar to the stellar population of the Milky Way, the stellar population would not have enough mass by a factor of a couple hundreds to keep the galaxies bound to the cluster. Thus, the galaxy clusters would have dispersed billions of years ago, and today we would be surrounded by a uniform distribution of galaxies. But that is not what we see: galaxies are still in galaxy clusters today.
But the problem was not only with galaxy clusters. Rubin & Ford (1970) found out, that the Andromeda Galaxy rotates so fast, that its stars would disperse if only the standard gravity would keep them together. And the Anromeda galaxy turned out be the rule rather than the exception; all spiral galaxies that were studied later on showed similar trends (for example Rubin et al. 1980). So, not only galaxy clusters would disperse, but also the (spiral) galaxies themselves. It is like the riders (that is the stars) on a merry-go-round (that is the galaxy). Forces keep the riders on circles around the merry-go-round, and if the forces for some reason become weaker or cease to exist (for example because the link between the rider and the merry-go-round breaks), the riders would move away from it. But again, this is against our observations: There are large spiral galaxies everywhere around us (including our Milky Way), and the stars in them move on stable orbits.
In general, the problem of missing mass in galaxies is nowadays omnipresent. It arises because there are different ways to estimate masses in astronomy. One such way is to make educated guesses about the age and the composition of the stellar population of a galaxy, and calculate from there how much units of mass it should have per unit of luminosity. Astronomers call this a stellar mass estimate. Another way is to measure the radius of a galaxy and how fast stars move on average in it, then make some educated guesses about the dynamics of the galaxy, and calculate the ratio of mass to light from there. Astronomers call this a dynamical mass estimate. Ideally, stellar and dynamical mass would agree for the same galaxy, because the galaxy only has one real mass (within uncertainties, of course). In practice however, the dynamical mass is usually larger than the stellar mass, and the factor ranges from slightly above one to 10000 or so. Apparently, the error lies somewhere in the guesswork leading to the two different mass estimates. Astronomers tried to solve the problem of the missing visible matter in two general ways: Either by adding more matter, so that the matter in total would produce the observed gravitational force, or by changing the laws of gravity themselves and saying that the visible matter is all the matter there is in galaxies.
Adding more matter is mathematically the simpler solution, which is also why many people favoured it at first. The gravitational force is then linear in the critical range of values, that is weak to moderate gravity. This means that if there is twice the matter, there is also twice the gravitational force, independent of the total amount of matter there is. Note that from this point of view, the type of matter does not matter, as long as it is invisible, or nearly so. Also the Earth is near invisible next to the Sun, even though they both consist basically of the same kind of matter (that is atoms, not something exotic). It is only a matter of temperature that makes the Sun brighter than the Earth. Indeed, there was a theory that the missing matter are earth-like bodies (that is free-floating planets and brown dwarfs), until the needed quantity of those bodies was observationally excluded. More and more alternatives for the additional matter were excluded as well, so that we are today at the Lambda-Cold-Dark-Matter Model (LCDM-model) for this class of models. However, the LCDM-model requires exotic dark matter beyond the standard model of particles. But this kind of matter has not been discovered yet, including in the largest accelerators like CERN. Nevertheless, this first group of physicists still believes the LCDM-model to be true in general (even though there are some changes to be made) and therefore they continue to search for the so far still hypothetic dark-matter particle.
The second group of physicists rather correct the law of gravity than adding a hypothetic particle beyond the standard model of particle physics. It is like whichever way you go, you have to expand a theory which has been extremely succesful so far: you either have to give up the standard model of particle physics in order to save the LCDM-model, or have to have to give up general relativity, with Newtonian gravity as its limiting case for weak and moderate gravity. This new theory of gravity is, unlike Newtonian gravity, not linear in the critial range. This means that twice the matter does not necessarily mean twice the gravity when the gravitational force is weak enough. This has a funny consequence, which is in contrast to our daily-life experience, namely that the same amount of matter suddently looks like it becomes more gravitating when you spread it out thinly enough. Lüghausen et al. (2015) therefore called it “phantom dark matter”, because this dark matter is a mirage that disappears when the real matter is put close enough together. (Of course, inside the Solar system, the matter must be on average dense enough for the gravitational force to be linear – otherwise we would not be able to send spaceships with high precision to other planets using Newtonian gravity.) This second set of theories leads to Modified Newtonian Dynamics or Milgromian Dynamics (MOND).
Here, I will concentrate on the “missing” matter of elliptical galaxies – “missing” in the sense that there is usually less matter if seen from a stellar perspective than if seen from a dynamical perspective on the same galaxy. Are there alternatives to adding exotic dark matter to the visible matter, and thus supportive to the second group of physicists?
First of all, let’s start with the question of what an elliptical galaxy is. A very short answer would be that they are more or less like the spiral galaxies, but without the disks that contain the spirals. So, only the central bulge is there, and hence, they are called ellipitical because of their elliptical shape. That central bulge can however be very massive, and the most massive elliptical galaxies are even more massive than the most massive spiral galaxies (bulge and disk of the spirals together)!
Going a bit more to the details of elliptical galaxies, they show however some diversity in their mass and radius. I will distingish them into three different kinds of objects, namely ultra-compact dwarf galaxies (UCDs), conventional elliptical galaxies (Es) and dwarf spheroidal galaxies (dSphs), and discuss the invisible matter in each of them. We will see that the invisible matter is just a mirage in some of them, while others contain really some more matter than originally accounted for, but not the exotic dark matter predicted by the LCDM-model.
UCDs (Figures 1 and 2) stand a little apart from the other elliptical galaxies, and some doubt that some of them really are galaxies, and not just very massive star clusters. The reason lies in their compactness, which makes them look much like very massive globular clusters. However, their compactness also places them deeply in the Newtonian regime, so there is literally no room for the phantom dark matter of MOND. Yet, it was claimed that they may contain dark matter (see for example by Drinkwater et al 2004 and Hasegan et al. 2005).
The reason for that is that at the turn of the millenium, it was popular among atronomers that the stellar initial mass function (IMF) is universal (see for example Kroupa 2001). What this means is that all stellar systems formed with a fixed ratio of massive stars to light stars, and only the age of the stars and their chemical composition may change from stellar system to stellar system. This is not to say that people back then were unaware of the influence that, for example, different temperatures and chemical composition had on the process of star formation. Rather, they were looking for different IMFs, but did not find supportable evidence for them in resolved stellar populations. However, when modeling a UCD (or any other kind of stellar system) with the universal IMF, there is maximum ratio between stellar mass and stellar light that can be reached for any reasonable stellar ages and chemical compositions. Nevertheless, there are many UCDs above that limit, and Dabringhausen et al. (2008) showed that this is not just a statistical uncertainty. So, there must be a reason for this unseen mass, and the exotic dark matter that comes with the LCDM-model was a proposition.
However, Murray (2009) voiced serious doubts that the LCDM-model could accomodate enough exotic dark matter inside the tiny radii of UCDs. This is even though the dark-matter halos around the galaxies can be very massive in the LCDM-model. However, the LCDM-model then also predicts that the halos would be very extended, and thus the density (that is mass per volume) of the dark-matter halo would be very thin. So, the total mass of the dark-matter halo may be gigantic, but the fraction of its mass inside a UCD would be tiny because of the small radius of the UCD, and this tiny amount of dark matter inside the UCD would not influence the internal dynamics of the UCD much. Thus, in short, it is not the exotic dark matter of the LCDM-model that increases the mass of the UCDs. It is then likely “conventional” matter, for example from a different IMF. Thus, the word “universal” IMF is then misleading because the IMF is in fact not universal, but “standard” IMF or “canonical” IMF are pretty good replacements. After all, this IMF pretty much seems to be the standard in our immediate surroundings (in an astromical sense); that is regions whose mixture of chemical elements is like that of the Sun and which do not form so many stars at present.
In UCDs, the conditions under which star formation took place were probably far away from those we know to produce the standard IMF. Thus, Dabringhausen et al. (2009) proposed that the UCDs may have formed with an IMF that had a different shape than the standard IMF, namely one that formed more massive stars. (IMFs that have more massive stars than they should have according to the standard IMF are called “top-heavy”.) These massive stars are known to be short-lived, and after they have burned all their nuclear fuel, they leave remnants which produce little or no light compared to their mass. These remnants exist of course in any aged stellar population, but if the IMF had more massive stars once, it has more stellar remnants now. The stellar remnants thus increase the ratio between mass and light, and make a UCD “darker”. Dabringhausen et al. (2012) also tried an alternative way to detect those additional stellar remnants by looking for systems, where a stellar remnant accretes matter from a companion star. Those stellar systems become distinctive X-ray sources, and are thus countable. They compared the numbers they found in UCDs to the numbers they found in globular clusters (that is stellar systems more or less like UCDs, but less massive), and they found more X-ray sources in UCDs than they expected. This as well could indicate that there are more high-mass stars per low-mass stars in UCDs. Based also on their works, Marks et al. (2012) proposed an IMF that changes with the mass of the stellar system (that is from globular clusters to UCDs) and with the chemical composition. Thus, they gave up the notion of the universal IMF, but explained changes in the ratio between mass and light in UCDs with changes in their IMFs.
Another way to increase the mass of UCDs, but not their emission of light, are central massive black holes. In a black hole so much mass is kept, that nothing that comes too close to it can escape it, not even light. Black holes are a prediction of general relativity and known to exist. For example, very massive stars become black holes when all their nuclear fuel is burned, and the pressure from stellar radiation no longer opposes the pull of gravity. Or, as another example, there is a massive black hole at the center of the Milky Way, and many other galaxies as well, even though it is less clear than for massive stars how those came to be. (This year’s Nobel Prize for physics was about the detection of this central black hole.) But if massive black holes are common at the centers of galaxies, why can’t UCDs have them as well? However, a massive central black hole is easy to overlook at the distance of known UCDs. That is because at the distance of UCDs, the stars look like they are almost located at a single point in space, whereas the mass of the central massive black hole is precisely located a this single point. Thus, if seen from Earth, there is not much difference in the distribution of matter, while the central massive black hole would still add its mass to the mass of the stellar population. Therefore, only by careful observations with the telescopes with the best optical resolution, one has a chance to detect them. Nevertheless, massive central black holes were indeed proposed as a solution for the problem of the missing mass in UCDs; for example by Mieske et al. (2013) and Janz et al. (2015). Seth et al. (2014) then observationally confirmed a massive central black hole in a UCD for the first time. Later, massive black holes were also discovered in other UCDs, see for example Afanasiev et al. (2018).
Naturally, also a mixture of non-standard IMFs and central massive black holes is possible to explain why UCDs are so massive for their light. However, what is important here is that there are less far-fetched alternatives to exotic dark matter in UCDs.
2.) Conventional elliptical galaxies
The conventional elliptical galaxies are not only usually more massive than the UCDs, but also far more extended. What I mean with “conventional” is that they were among the first galaxies to be identified as galaxies – this was in the 1920ies, when people like Hubble first discovered that some “nebulae” are not just gas clouds inside the Milky Way, but distant stellar islands just like the Milky Way. It is unclear what mass exactly is required for an elliptical galaxy in order to be coventional, perhaps 108 Solar masses or so. This unclearity is because there is an extension of elliptical galaxies to even lower masses, which are however not (compact, star-cluster-like) UCDs, but (extended, galaxy-like) dwarf Spheroidal galaxies (dSphs). However, there are some specialities on dSphs about dark matter and its seeming existence, and therefore I will treat them in an own section. What I will not do, though, is to distinguish the elliptical galaxies into dwarf elliptical galaxies and elliptical galaxies proper, because this distinction in merely historical in my eyes (see also Ferguson & Binggeli 1994 about this). The most massive of all galaxies (about 1012 Solar masses) are conventional elliptical galaxies, too.
So, how much exotic dark matter do elliptical galaxies contain, if any? Cappellari et al. (2006), for instance, found out that the conventional elliptical galaxies they observed had on average 30 percent too much mass for the IMF they assumed. They suggested that the missing mass could be the dark matter predicted by the LCDM-model. However, for this finding, they also assumed that the standard IMF is universal for all star-forming regions. Tortora et al. (2014) later tried to fix this without exotic dark matter, but MOND. They also failed with a universal IMF, but not if the IMF was changing with the mass of the galaxy. So, the real question is: Can the IMF change with galaxy mass or is the standard IMF also the universal IMF?
For answering this question, let’s look at star clusters, which are the building blocks of galaxies. Could a star cluster have a star more massive than the cluster itself? Of course not. Actually, Weidner et al. (2010) found out that the mass of the most massive star of a star cluster is much lower still. An impressive example of this was observed by Hsu et al (2012): They compared a large cluster of some mass with several adjacent small star clusters with the same mass in total. All the other parameters like age, chemical composition, and so on are the same, just how the total mass of the stars is bundled is different. However, the massive star cluster has heavier stars than the several small star clusters. This would not be a problem by itself, if the overall star formation was the same in all galaxies; that is when all galaxies form the same number of light star clusters per massive star cluster. But this is not the case. Weidner et al. (2004) found that the mass of the most massive cluster that can form in a galaxy depends on its star formation rate; that is how many stars form in a galaxy per time unit. Low-mass elliptical galaxies have low star formation rates and massive elliptical galaxies have high star formation rates. Thus, low-mass conventional elliptical galaxies have a lack of massive stars. This already is an argument against a universal IMF in all star clusters and in all galaxies.
The galaxies with the highest star formation rates (that is also the most massive galaxies) produce also star clusters in the mass range globular clusters and UCDs. Now, lets assume that these most massive star clusters are in fact UCDs and that these UCDs have IMFs with more massive stars per low-mass stars than “normal” star clusters (see the section about UCDs). Then the real IMF deviates from the once-thought universal IMF not only in low-mass star clusters (by not having any massive stars), but also in high-mass star clusters (by having too many massive stars). Now, remember what we have said about IMFs with more massive stars than the standard IMF: when they grow old, they produce less light per unit mass than the standard IMF. Or when a certain amout of light is observed, a stellar population with more massive stars and a certain age must have more mass to produce it. The stellar populations of elliptical galaxies are usually that old that the massive stars (which are short-lived) have already evolved into dark stellar remnants, and only the light stars continue to shine. So, if the IMF behaves with the star formation rate of the galaxies like it is assumed nowadays (see for example Kroupa & Weidner 2003 or Fontanot et al 2017), then the low-mass elliptical galaxies have a little less mass than assumed with the standard IMF for their light, and the massive elliptical have a little more mass than assumed with the standard IMF. This goes up to about twice the mass for the most massive conventional elliptical galaxies, and the point where the mass estimate is equal to that for the standard IMF is at approximately 109 Solar masses. Thus, for most conventional elliptical galaxies, the mass estimates are above the mass estimates for the standard IMF, and the “missing” mass is about the mass detected by Cappellari based on the standard IMF. (See also Dabringhausen et al. 2016 if you want to follow the brightness of elliptical galaxies with their mass, and Dabringhausen 2019 if you wish to go deeper on elliptical galaxies and non-standard IMFs). Thus, again like with UCDs, there is an alternative, more down-to-earth explanation for the excess mass of those elliptical galaxies.
3.) Dwarf speroidal galaxies (dSphs)
Dwarf spheriodal galaxies (dSphs, Figure 3) are in a way the low mass extension to “conventional” elliptical galaxies, because in a plot of their radius against their mass, they continue the line established by the conventional elliptical galaxies to lower masses. However, the brightest ones are in light and mass like UCDs, but way more extended than UCDs. In other words, there is a gap in radius between dSphs and UCDs (see Gilmore et. al 2007), in contrast to conventional elliptical galaxies and dSphs.
If it is true that dSphs are in fact very low-mass conventional elliptical galaxies, then we would expect them to be about 20 percent or so lighter than expected based on their light with a standard IMF. But in fact, they are way more massive. Just in order get a feeling for the numbers we are dealing with: Let’s say the standard IMF would predict a ratio of mass to light of 2 for a dSph, the ratio for the corrected IMF would then give 1.5, but the measured value is 2000 (all numbers are in Solar units). So, how can we be wrong to a factor up to approximately 1000 (even though in many cases less)?
This is where MOND finally kicks in, because the visible matter in dSphs is actually thin enough, in contrast to UCDs and Es. MOND can rise the ratio of the mass of a dSph over its light from values of a few (that is a stellar population in Newtonian dynamics) to values up to about 100. This fits the dynamical values of many dSphs, which would contain plenty of “dark” matter in Newtonian dynamics. Thus, in MOND, their dark matter is actually phantom dark matter – it would disappear if the matter was denser. Or, in other words, the difference between stellar and dynamical mass estimates disappears for those dSphs, and all is well. The precise value for a given dSph depends on which value the mass-to-light ratio of the stellar population would have according Newtonian dynamics and on how many stars are distributed over which volume, that is the density of visible matter. Estimates for the mass-to-light ratios in Newtonian and MONDian dynamics for a number of dSphs are for example given in Dabringhausen el al. (2016).
But it is also visible in Dabringhausen el al. (2016) that even MONDian dynamics cannot explain the mass-to-light ratios of the few dSphs, which have a mass-to-light ratio far beyond 100. So, have we finally found a failure of MOND? Not necessarily. So far, we have implicitly always assumed that the galaxies are in virial equilibrium. What this means is for instance the absence of tides because of other distracting souces of gravity. The tides on Earth are the best-known example, even though Earth is dense enough to be near tidal equilibrium, given the gravitational forces from the Moon and the Sun. We only see them so well because because in this case, the tides are happening right under our noses. Ultimately, there are tides on Earth because the Earth is an extended body. Thus, the gravitational force from the Moon pull on the near side of the Earth a bit stronger than on the far side, and the Earth is being stretched a bit by the tides. There are ebb and flow of the oceans on Earth, because the Earth also rotates, while the tides are always directed towards the Moon. There of course also other sources of gravity on Earth which cause tides (the Sun for instance), but the Moon is the strongest.
Also UCDs and conventional elliptical galaxies are dense enough to be nearly unaffected by neighboring galaxies, which are the potential reason for tides in them. But the internal gravity is comparatively weak on the thin matter of dSphs, so that they are easy to stretch by outside forces of other galaxies. Thus, the tidal forces form gigantic tidal “waves” consisting of stars. Every encounter with another galaxy pulls on the galaxy, because the gravitational force is stronger on the near side of the encounter than on the far side. This heats the galaxy up, meaning that the galaxy is being pulled out of virial equilibrium by the encounter and that the average velocities of the stars get faster with enconters. Finally, the tidal forces from encounters with other galaxies make the galaxy break apart.
Now, what would an observer from Earth see? The observer could for example see a dSph that has been heated up by a recent encounter with another galaxy, and is thus out of virial equilibrium. Or the dSph has found its virial equilibrium again, but at the cost of stars which have left the dSph, and are now moving faster or slower than the stars which are still bound to the galaxy. But the observer could be ignorant of this fact, and assume that all the stars (s)he sees are bound to the galaxy. Or the dSph has dissolved already completely, but the stars still move all along on similar orbits, even though they are not bound to each other any more. The radius in which the stars are is then just much larger than it would be, if the stars were bound to each other. If the observer then wrongly assumes the dSph to be in virial equilibrium, all these effects increase the dynamical mass estimate (not the real mass!) (s)he makes for the mass of the galaxy. And those effects could indeed raise the dynamical mass estimate by the required factor. For a discussion of tidal heating of dSphs under Newtonian gravity, see for example Kroupa (1997). McGaugh and Wolf (2010) made a similar study with MOND. Notably, they found for observed dSphs surrounding the Milky Way that if a dSph is more susceptible to tidal forces, it is also more likely to be outside virial equilibrium for MOND. For an interesting theoretical discussion of how a dissolving star cluster in a tidal field could be mistaken for a much more massive (but evidently not more luminous) dSph, see Dominguez et al. (2016).
However, the dSphs which are out of virial equilibrium far enough to increase the dynamically estimated mass-to-light ratio by a few or more compared to the real mass could just be a few dSphs out of a larger sample. For the majority, the effect would simply be too weak now, although their time to dissolve will also come. In other words, this scenario is highly improbable if gravity was Newtonian, because then all dSphs around the Milky Way must be in dissolution. However, if gravity is MONDian, only a few would be near their dissolution, while most would be in or near virial equilibrium – see Dabringhausen el al. (2016).
There is also another argument against dark matter in dSphs. Galaxies are usually not by themselves, but surrounded by other galaxies. Together, these galaxies form gravitationally bound galaxy clusters. But how do these galaxy clusters form? According to the LCDM-model, this happens by the infall of galaxies from all directions. They can come, the dSphs included, with any amount of exotic dark matter into a galaxy cluster. We will call those galaxies “primordial galaxies” from now on, because there is also another way to form galaxies that look like dSphs to an observer. This other way is through close encounters of already existing galaxies. In such encounters, matter is pulled away from the existing galaxies by gravity though tides (Figures 4 and 5), and new small galaxies can form from this matter. We know that this process happens. Otherwise, the elongated streaks of matter of, for instance, the Antennae Galaxies and the Tadpole Galaxy would be difficult to explain. Simulations of interacting galaxies, which are set up to reproduce situations like in the Antennae Galaxies, show also those streaks of matter like the ones observed (see for example Bournaud & Duc 2006 or Wetzstein et al. 2007). They are called tidal tails for obvious reasons. The Tadpole Galaxy even has a new small star-forming regions in its tidal tail, which may become dSphs. If aged enough, these dwarf galaxies may be difficult to distinguish from primordial galaxies of the same mass, though (see Dabringhausen & Kroupa 2013). However, in the following, we call galaxies of tidal origin “tidal dwarf galaxies”, in order to distinguish them from primordial galaxies. The tidal dwarf galaxies cannot contain the exotic dark matter of the LCDM-model, even if their progenitor galaxies did. The reason is that all matter that ends up in a tidal dwarf galaxy, whether visible or not, must have occupied similar regions of space with similar velocities also before the encounter of the existing galaxies. The total amount of the exotic dark matter may be huge, but most dark matter had other velocities and other locations, and therefore does not qualify to be bound to the tidal dwarf galaxy. After all, simulations of galaxy encounters by, for example, Barnes & Hernquist (1992) show that most visible matter that is to become a tidal dwarf galaxy comes from the disks of spiral galaxies. This visible matter does not only form a thin disk, as opposed to the presumed dark matter halo, but it also moves with the same velocity in the same direction, again in contrast to the presumed dark matter halo. Also, the tidal dwarf galaxies that form in an encounter of galaxies can only move in the plane of the encounter (because of the conservation of angular momentum). Thus, there is an easy way to distinguish the dSphs in the LCDM-model: those which move in a plane and those which cannot be assigned to a plane. Those in a plane are very likely tidal dwarf galaxies and cannot have any exotic dark matter. Those, however, which cannot be assigned to a plane might also be primordial and can thus contain dark matter (see for example Kroupa et al 2010). Now, what do observations tell us about the pattern of motion of the dSphs? In the Milky Way, it was shown by Lynden-Bell (1976) and by Kroupa et al. (2005) that the then known dSphs are most likely arranged in a plane. Later, additional objects and also velocities were added, but the long-lasting disk of Satellites was always confirmed (see for example Pawlowski et al. 2012 and Pawlowski & Kroupa 2020). This was according to some proponents of the LCDM-model just an exception, while other, they said more normal galaxies would have dSphs with random motions around them. However, it was shown then that also the Andromeda Galaxy has a disk of dSphs around it (for example Ibata et al 2013), and Centaurus A as well (Mueller et al 2018). In short, disks of satellites around major galaxies are more the rule than the exception, see for example Ibata et al (2014) for an attempt of a census. Thus, galaxies in these planes must manage their high dynamical mass-to-light ratios without exotic dark matter, despite numerous claims to the contrary from the LCDM-community. If MOND is the correct description of gravitation, then the large gravitating (phantom) masses of the satellite galaxies, as opposed to their small masses in stars, is beautifully resolved.
I have discussed the reasons for “dark” matter in elliptical galaxies, which comes ultimately from the comparison of different mass estimates. Also, some assumptions which were used for the lack of better knowledge have been proven wrong by now. This concerns the theory of a universal IMF in all star-forming regions, which was leading to a mismatch between the mass estimates from stellar populations and from the dynamics in UCDs and conventional elliptical galaxies. If the “one-size-fits-all” IMF is replaced by a more elaborate picture of the IMF, those differences disappear easily without using exotic dark matter or MOND. For dSphs, the situation is different. They cannot have exotic dark matter because it could not bind to them, but neither can their extreme mass-to-light ratios be explained with different stellar populations. Here, MOND and tidal fields offer an answer. Thus, adding more exotic dark matter to all galaxies until their dynamics is fitted might appear the simpler solution on first sight, but it is not necessarily the correct one. The seemingly more complicated solution without exotic dark matter stands a better test result here.
In The Dark Matter Crisis by Joerg Dabringhausen. A listing of contents of all contributions is available here.
The Universe evolves through expansion and gravitation of matter, which leads to some regions having more galaxies and others having fewer. These variations directly reflect the way in which gravity has created structures out of initial density fluctuations over the last 14 billion years. Thus, the observed spatial arrangement of galaxies on scales ranging from 100 kpc to a Gpc is a very powerful test of different cosmological models and gravitational theories.
In our paper “The KBC void and Hubble tension contradict ΛCDM on a Gpc scale − Milgromian dynamics as a possible solution” (Moritz Haslbauer, Indranil Banik, Pavel Kroupa 2020), we tested if the observed spatial arrangement of galaxies on a Gpc scale can be explained by the standard model (Lambda-Cold Dark Matter, ΛCDM) of cosmology. We also tested if a Milgromiandynamics (MOND) model works.
Several surveys covering the entire electromagnetic spectrum (ranging from radio to X-rays) made an exciting discovery: we are in a Gpc-sized region of the Universe containing far fewer galaxies than ought to be in this volume if ΛCDM were correct.
For example, Karachentsev 2012 found a significant lack of galaxies within a sphere of radius 50 Mpc centered on the Local Group. He reported that the average mass density is a factor of 3-4 lower than predicted by the standard model of cosmology. In 2013, Keenan, Barger, and Cowie discovered that the local Universe is underdense on a much larger scale by counting galaxies at near-infrared wavelengths. They found evidence for an incredibly huge void (hereafter the KBC void) with a density about two times lower than the cosmic mean density and with a radius of about one billion light years (or 300 Mpc). This is about 2% of the distance to the observable Universe’s horizon (about 14 Gpc). The KBC void is shown in Figure 1 below.
Figure 1. The KBC void: the actual density of normal matter divided by the mean cosmological density is plotted in dependence of the distance from the position of the Sun (which is in the Local Group of galaxies). The grey area indicates the density fluctuations allowed by the ΛCDM model. Taken from fig. 1 in Kroupa (2015).
The results by KBC are striking because the ΛCDM model predicts root-mean-square (rms) density fluctuations of only 0.032, while the observed value is 0.46 with an uncertainty of 0.06. This drew our attention, so we decided to investigate the local matter field further in both the ΛCDM and MOND paradigms.
First, we started to quantify the likelihood of a KBC-like void in the ΛCDM model. Using one of the largest cosmological ΛCDM simulations (called MXXL), we rigorously confirmed our suspicion: Einsteinian/Newtonian gravity is simply too weak to form such deep and extended underdensities like the KBC void. Our calculations showed that the KBC void alone falsifies ΛCDM with a significance much higher than the typical threshold used to claim a discovery, e.g. with the famous Higgs boson. Consequently, the KBC void is totally inconsistent with the current standard model, implying that the observed Universe is much more structured and organized than predicted by ΛCDM. A similar conclusion was reached by Peebles & Nusser 2010 on much smaller scales by studying the galaxy distribution within the Local Volume, a sphere with 8 Mpc radius centred on the Local Group. And the whole Local Group is also “grievously” structured (Pawlowski, Kroupa, Jerjen 2013), showing a “frightening symmetry” as called by Pavel Kroupa.
The observed spatial arrangement of galaxies on scales ranging from 100 kpc (the satellite planes) to 300 Mpc (our work) strongly suggests that structure formation is much more efficient than possible by Newton’s gravitational law, implying a long-range enhancement to gravity over that allowed by Newtonian gravity. This is in fact not surprising, given that Newton and Einstein both only had Solar System data at their disposal to formulate their theories; gravitation is after all, the least understood of the fundamental interactions. Consequently, we next studied the formation of structures in Milgromian dynamics, which was developed by Israeli physicist Mordehai Milgrom in 1983 (Milgrom 1983). MOND is a corrected version of Newtonian gravitation taking into account galaxy data which were non-existing for Newton and for Einstein. MOND successfully predicted many galaxy scaling relations, but has rarely been applied to cosmological scales.
We extrapolated the MOND model from galactic to a Gpc scale by applying the Angus 2009 cosmological MOND model. This Angus cosmological model has a standard expansion history, primordial abundances of light elements, and fluctuations in the cosmic microwave background (CMB), mainly because both the ΛCDM and MOND cosmology have the same mass-energy budget. However, instead of cold dark matter particles, the MOND model assumes fast-moving collisionless matter, most plausibly in the form of 11eV/c^2 sterile neutrinos. The existence of sterile neutrinos is motivated by particle physics, since they could explain why the ordinary neutrinos have mass. The low mass of hypothetical sterile neutrinos means they would clump on large scales (e.g. galaxy clusters), but not in galaxies, thus leaving their rotation curves unaffected. The following is in fact a most important point to emphasize: The Angus cosmological model needs extra fast moving matter which comes from standard particle physics (but still needs to be verified experimentally). This is very different to the ΛCDM model which needs dark matter particles that account for the observed rotation curves in disk galaxies but which are not motivated to exist by the standard model of particle physics.
The enhanced growth of structure in Milgromian gravitation generates much larger and deeper voids than in Einsteinian/Newtonian gravity. This leads to the formation of KBC-like voids as shown in our paper. Such an extended and deep underdensity causes an interesting effect: parts of the Universe beyond the void with more galaxies pull galaxies in the void outwards. This changes the motions of galaxies, making the local Universe appear to expand faster than it actually is. The situation is illustrated in Figure 2.
Figure 2: Illustration of the Universe’s large scale structure. The darker regions are voids, and the bright dots represent galaxies. The yellow star represents the position of our Sun. Note that the Sun is not at the centre of the KBC void. The arrows show how gravity from surrounding denser regions pulls outwards on galaxies in a void. If we were living in such a void, the Universe would appear to expand faster locally than it does on average. This could explain the Hubble tension. Interestingly, a large local void is evident in the entire electromagnetic spectrum. Credit: Technology Review
Indeed, local observations of how quickly the Universe is expanding exceed the prediction of ΛCDM by about 9%. This so-called Hubble tension is one of the greatest mysteries in contemporary cosmology. In our paper we showed that the unexpectedly high locally measured Hubble constant is just a logical consequence of enhanced structure formation in MOND, and us residing within a particularly deep and large void. This Hubble bubble scenario is however not consistent with ΛCDM because it does not allow for a sufficiently extreme void (Figure 3).
Figure 3: In our paper we showed that that the KBC void cannot form out of the initial conditions of the CMB at redshift z = 1100 if Einsteinian/Newtonian gravity is assumed. Adding the speculative cold dark matter does not help. Therefore, the Hubble tension cannot be explained by the KBC void in the context of the ΛCDM paradigm. Consequently, we aimed to study the formation of structures in Milgromian dynamics. The long-range enhancement to gravity in MOND allows the formation of KBC-like voids, which simultaneously explains the high locally measured Hubble constant.
Thus, the current hot debate among astronomers about the expansion of the Universe being different close to us than far away only exists because astronomers are using the wrong model. A universe which does not have exotic cold dark matter particles but runs on Milgromian gravitation ends up looking just like the real Universe, at least with the tests done thus far.
There is now a real prospect of obtaining a MOND theory of cosmology that explains the data from dwarf galaxies up to the largest structures in the Universe much better than the ΛCDM framework. Consequently, the here described cosmological MOND framework could be a way out of the current crisis in cosmology.
Given my affiliation with Charles University, I have been travelling to Prague and beyond frequently and now the CORONA Pandemic has stopped this flying about the planet — I have already written about the first wave and my getting marooned on a beautiful island next to the Strand. Being this time stranded in Bonn without a Strand during the second wave, I have a little more time on my hands I guess. So here we are, back to the Crisis.
In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.
We have not blogged for some time and an update on some of the developments concerning The Dark Matter Crisis has been posted here. Below are recent scientific developments which strongly suggest that the standard model of cosmology (the SMoC) which relies on the existence of cold or warm dark matter (C/WDM) particles is not a correct description of the observed Universe. Note that the SMoC which is based on the hypothesis that cold dark matter particles exist comprises the currently widely accepted LCDM cosmological model, while the SMoC which assumes warm dark matter particles exist constitutes the currently less popular LWDM cosmological model. The difference of both models in terms of structure formation and the type of galaxies formed is minimal, which is why both are referred to as the SMoC.
Why has the Cosmology Crisis become catastrophic?
First of all, C/WDM particles have still not been found after more than 40 years of searching! The account of the situation published on October 11th, 2020, on the Triton Station by Stacy McGaugh is worth reading. Stacy writes “… the field had already gone through many generations of predictions, with the theorists moving the goal posts every time a prediction was excluded. I have colleagues involved in WIMP searches that have left that field in disgust at having the goal posts moved on them: what good are the experimental searches if, every time they reach the promised land, they’re simply told the promised land is over the next horizon?“. In view of the available evidence challenging the existence of C/WDM particles, it is stunning to read “The existence of Dark (i.e., non-luminous and non-absorbing) Matter (DM) is by now well established” in Sec. 26.1.1 of the 2018 version of the Review of Particle Physics. Some five years ago I had dared to suggest to the editors and section authors to change this very statement to “The existence of Dark (i.e., non-luminous and non-absorbing) Matter (DM) is currently a leading hypothesis” or similar, but the short reply was quite unpleasant. It is unfortunate that only the cosmological argument leads one to the C/WDM particle hypothesis, there being no independent (non-cosmological and non-astronomical) evidence. Such evidence could have come from indications in the Standard Model of Particle Physics, for example, but this is not the case. Put in other words, if we had not known about cosmology or galaxy rotation curves, we would not be contemplating C/WDM particles. Thus, by the astronomical evidence having gone away (follow the Dark Matter Crisis), the physicists are left with nothing apart from belief. I would argue that the words “belief” and “opinion” should be banned from the language of natural sciences. Note that the situation is different for the fast collisionless matter (FCM, or “hot dark matter”) which appears in MOND-cosmological models (Angus 2009). Independetly of the astronomical evidence, the experimental fact that neutrinos have mass and oscillate suggests the existence of an additional sterile neutrino. Candidates for FCM particles thus arise independently of astronomy or cosmology. FCM particles do not affect galaxies as they are too low mass, so even at their maximum allowed phase space density as set by the Tremaine-Gunn limit, they cannot be dynamically relevant to the masses of galaxies. Returning to the SMoC: the lack of experimental verification of C/WDM particles comes in hand with additional failures of the SMoC:
Testing for the presence of the speculative C/WDM particles through the very well understood physical mechanism of Chandrasekhar dynamical friction leads to the conclusion that the dynamical friction through the putative dark matter halos around galaxies which are, in the SMoC, made up of C/WDM particles, is not evident in the data (Angus, Diaferio & Kroupa 2011; Kroupa 2015; Oehm & Kroupa 2017). That is, a galaxy which falls towards another galaxy should be slowed down by its dark matter halo, and this slow-down is not seen. The galaxies pass each other with high velocities, like two stars passing each other on hyperbolic orbits, rather than sinking towards each other to merge. This evidence for the non-existence of C/WDM halos around galaxies is in-line with the above mentioned lack of experimental detections (point 1 above). Customarily, an image of two strongly interacting galaxies is automatically interpreted as being a galaxy merger. But this is an over-interpretation of such images, since the implied mergers are not happening in the frequency expected in the standard dark-matter-based theory. Renaud et al. (2016) calculate ant document the theoretical description of an observed strongly interacting galaxy pair in the C/WDM framework and in MOND. Indeed, that the population of galaxies does not evolve significantly since a redshift of one has been found by Hoffmann et al. (2020) and has already been described by Kroupa (2015). This lack of evolution and the hugely vast preponderance of disk galaxies, of which a large fraction is without bulges, means that galaxies merge rarely as mergers nearly always transform the involved disk galaxies into earlier types of galaxies (disks with massive bulges, or even S0 or elliptical galaxies).
The Hubble tension is now much discussed. The Hubble Tension comes about as follows: the Hubble constant we should be observing today can be calculated assuming the standard dark-matter based SMoC is correct and that the Cosmic Microwave Background (CMB) is the photosphere of the Hot Big Bang (but see also point 6 below). The actually measured present-day value, as obtained from many independent techniques including supernovae 1a standard candles, gravitational lensing time delays, and mega-masers, comes out to be significantly larger though. The evidence is compiled in Haslbauer et al. (2020). The observer today sees a more rapidly expanding Universe than is possible according to the SMoC. More on the Hubble tension below (point 7).
The planes of satellites (or disk of satellites) problem has worsened: Our own Milky Way has been found to have a more-pronounced disk of satellite galaxies around it than thought before (Pawlowski & Kroupa 2020; Santos-Santos, Dominguez-Teneiro & Pawlowski 2020). Andromeda has one (Ibata et al. 2013, Sohn et al. 2020) and the nearby Centaurus A galaxy too (Mueller et al. 2018). The majority of other galaxies also show evidence for such planes or disks of satellites (Ibata et al. 2015). That the three nearby major galaxies simultaneously show such disks of satellite galaxies, and that disks of satellite systems are indicated by the majority of more distant galaxies, where the SMoC expects such satellite planes only in very rare cases (Pawlowski et al. 2015; Pawlowski 2018), eliminates with de facto complete confidence (i.e. much more than 5sigma) the SMoC, given that the satellites are in the great majority of cases ancient and void of gas such that they must have orbited their hosts many times. The Milky Way satellites also seem to be on almost circular orbits, strongly suggestive of a dissipative origin (Cautun & Frenk 2017) similar to the process that forms solar systems.
Astronomical data have uncovered, with extremely high confidence (more than 5sigma), that the strong equivalence principle is violated on the scale of galaxies (Chae et al. 2020 ), exactly in-line with a central expectation by MOND (Milgrom 1986), and in contradiction to the SMoC. While apparently not receiving much attention (e.g. via news coverage), this work by Chae et al. (2020) is a game-changer, a break-through of the greatest importance for theoretical physics. Independent evidence for the violation of the strong equivalence principle is also evident in asymmetrical tidal tails around globular clusters (Thomas et al. 2018). Gravity therefore behaves non-linearly on galaxy scales, preventing a simple addition of the fields contributed by different masses. This is a consequence of the corrected, generalised Poisson equation (Bekenstein & Milgrom 1984) which these authors point out is also found in classical theories of quark confinement.
Possibly a “nuclear bomb” nuked standard cosmology: Although the SMoC is only valid if the Universe is transparent, observations show there to be dust between galaxies. This intergalactic dust is ancient, and it radiates as it is heated by photons from the surrounding galaxies. Vaclav Vavrycuk (2018) has added all photons from this dust in an expanding Universe (i.e., in the past the intergalactic dust density was higher in a warmer Universe) and found the photon emission received by us to be very (nearly exactly) comparable to the measured CMB with the correct temperature of about 2.77K. For an explanation of his research paper see this YouTube video by MSc student Rachel Parziale at Bonn University. Note that the measured weak but large-scale magnetic fields around galaxy clusters and voids produce a correlated polarisation signal. The total number of infrared photons received at Earth is an integral over the time evolving density distribution along the line of sight such that the observed mass distribution within a small redshift around us should not correlate with the overall fluctuation of photon intensity seen in projection on the sky. The calculations by Vavrycuk thus suggest that CMB=cosmological dust emission, rather than being the photosphere of the Hot Big Bang. CMB research comprises an incredibly precise science, but the role of intergalactic dust needs to be considered very carefully and by avoiding pre-conceptions. Note that even if only a few per cent of the CMB were to be due to ancient intergalactic dust, then this would already bring down the SMoC.
The Universe around us contains far too few galaxies out to a distance of about 0.3 Gpc. This Keenan-Barger-Cowie (KBC) void falsifies the SMoC at more than 6sigma confidence. The KBC void kills the SMoC because the SMoC relies on the Universe starting off isotropically and homogeneously with the observed CMB fluctuations at the redshift z=1100 boundary condition about 14Gyr ago and cannot evolve density differences to the observed KBC under-density at z=0 which is the present time. Combined with the Hubble tension, the SMoC is falsified with more than 7sigma confidence. Newtonian gravitation plus the hypothetical C/WDM particles are together nowhere near strong enough to generate the observed density contrasts and the observed velocity differences between neighbouring Gpc-scale volumes. The next blog by Moritz Haslbauer will explain this situation. Note that here we still treat the CMB as the photosphere of a Hot Big Bang, but this may need to be reconsidered (see point 6 above).
The SMoC relies on the Universe having no curvature, but Di Valentino, Melchiorri & Silk (2020) find the enhanced lensing amplitude in CMB power spectra to imply a closed and thus curved Universe. However, this could be related to structure formation being more efficient than is possible in the SMoC (see point 7 above).
Cosmic isotropy is challenged at the 5sigma confidence level by X-ray selected galaxy clusters (Migkas et al. 2020), with the implication that the Universe appears to expand faster in a certain direction. A discussion of this evidence is provided by Scientific American. Cosmic isotropy is also challenged by the significant evidence for a dipole in the number counts of quasars beyond redshift one (Secrest et al. 2020). Independently of this, Javanmardi et al. (2011) also found evidence for a directionally dependent expansion rate.
Last for now but not least, the observation of massively interacting galaxy clusters such as the El Gordo cluster at high redshift (z=0.87) independently falsifies the SMoC with more than 6sigma confidence. In the SMoC, galaxy clusters cannot grow to such masses by this redshift – there is not enough time, or alternatively, Newtonian gravitation is too weak even with the help of the hypothetical C/WDM particles. This is shown by Asencio, Banik & Kroupa (2020). Elena Asencio is researching for her MSc thesis in the SPODYR group in Bonn.
Combining the above KBC void/Hubble Tension/El Gordo falsifications with the previously published tests (Kroupa et al. 2010, Kroupa 2015; see the figure below taken from Kroupa 2012) means that it has become, by now, wrong to still consider the standard dark-matter based cosmological model, the SMoC, as being relevant for describing the Universe. The falsification of the SMoC has reached well above the 7 sigma confidence — Remember: the Higgs Boson was accepted as having been discovered once the experimental confidence rose to 5sigma. It is important to emphasise that independent tests on very different scales lead to the same result, the SMoC being ruled out by many tests with more than 5sigma confidence.
The loss of confidence until 2012 in the Standard Model of Cosmology (SMoC) with each documented failure (numbered here from 1 to 22 and explained in Kroupa 2012) which has never, to date, been resolved. Thus, if each such failure (meaning the SMoC prediction is falsified by observational data) is assumed very conservatively to lead to a loss in confidence of only 30% that the SMoC is valid, then, by today (including the catastrophic >6sigma falsifications described in this blog) the statement that the SMoC describes the real Universe can be defended with a confidence=epsilon, with epsilon being arbitrarily close to zero (taken from figure 14 in Kroupa 2012).
The above list, but more importantly, the very high significance of the results, seem to indicate that a paradigm change may be under way in the sense that our current understanding of the Universe may be entirely rewritten at a very fundamental level. This is already indicated by gravitation being Milgromian. The paradigm shift would be epochal (see also this previous blog on the historical context) if the suggestion by Vavrycuk concerning the physical nature of the CMB were correct (point 6 above) because in this case our very concept of a Hot Big Bang and the origin of matter would be up in the air. There is independent evidence that a once-in-a-century paradigm shift may be under way:the Universe is much more structured than allowed by the SMoC. Thus, the Local Group of Galaxies (on a scale of 3Mpc across, Pawlowski, Kroupa & Jerjen 2013 ) shows a frightening symmetry in its matter arrangement (I call this frightening because there is currently no known theory to explain this distribution of matter). The arrangement of galaxies (Peebles & Nusser 2010) in the nearby cosmological volume (20Mpc across) does not correspond to the SMoC model and these very galaxies show a history of star-formation which appears to be far too tuned and non-varying (Kroupa et al. 2020). This begs the question how they manage to do so? The entire local Universe appears to be engaged in a significant bulk flow generated by major voids and over-densities (Haslbauer et al. 2020; Hoffmann et al. 2020).
Galaxies provide formal and precise observational data that allow us to correct the work of Newton and Einstein on gravitation, who did not have these data at their disposal. Rather, they formulated the currently assumed theories of gravitation subject to Solar System constraints only, which are now many decades if not centuries old. In his book “A Philosophical Approach to MOND“, David Merritt (2020)addresses the formal philosophical measures concerning how the Newtonian/Einsteinian formulation of gravitation needs to be assessed in terms of its success in describing the observed Universe in comparison with the correction to the law of gravitation through incorporation of galaxy data as formulated by MilgrOmiaN Dynamics (MOND). (Next sentence added Jan 3rd, 2021:) In Merritt (2017) we read his conclusion “The use of conventionalist stratagems in response to unexpected observations implies that the field of cosmology is in a state of ‘degenerating problemshift’ in the language of Imre Lakatos.” This would tend to close a circle: if Newtonian/Einsteinian gravitation needs to be revised, then we cannot use Einsteinian gravitation to formulate the evolution of the Universe, which opens the whole issue of how it started, what are the boundary conditions and how does it evolve? The Catastrophic Crisis in Cosmology (i.e. the fact that the observational data do not fit to the SMoC) is thus merely exactly the statement that we may well be in the process of a very major paradigm shift.
The big challenge for the future will be to find out how the Universe truly does work. The next blog by Moritz Haslbauer will indicate how a step towards this goal might have been achieved by Haslbauer, Banik & Kroupa (2020).
In The Dark Matter Crisis by Pavel Kroupa. A listing of contents of all contributions is available here.
…and are we at the beginning of a major historical paradigm shift?
(by Pavel Kroupa and Moritz Haslbauer, 07th Nov. 2020; 15:00)
There have not been posts on this blog for some time. The reason is certainly not that the dark matter crisis has gone away. Quite the contrary — the dark matter crisis, or more generally the cosmological crisis, has worsened and is now quite catastrophic. More on this in the next blog “The Crisis in Cosmology is now catastrophic”. With this contribution we provide an update on recent developments and some philosophical contemplation concerning paradigm shifts.
As a reminder: this blog on the Dark Matter Crisis was started in 2010 through the pressure (which I first resisted) by staff of the journal Spektrum der Wissenschaft in Germany (equivalent to Scientific American) who wanted Marcel Pawlowski (then a PhD student in the SPODYR group in Bonn) and me to blog about the developing crisis. This was related to the research I was involved with at that time leading me to the conclusion that the astronomical data rule out the standard dark-matter-based cosmological model as being relevant for a description of the Universe. This was in tension with my peers.
In January 2013 the blog was moved, along with all English blogs on Spectrum, to Scilogs.com. Later this same year there was a temporarily successful attempt by an amateur-science blogger (a sworn MOND enemy) to have the Dark Matter Crisis close down. This failed and the Dark Matter Crisis continued, simply because it’s content is scientifically solid. In 2016 SciLogs.com decided not to host the English Spektrum blogs any longer, and they were transferred to WordPress.com, where they are now. We have not blogged since this last move which had not gone perfectly well technically, with quite a few images having been lost. Just now we repaired most of the losses after some historical digging and with the help of Srikanth Togere Nagesh, MSc student at the University of Bonn. The corrections are continuing, and we are finding that some old links out of the Dark Matter Crisis blogs do not work any longer – we are trying to update them as far as possible and given the limited time available. This has taught me that documentation developed for the internet is fleeting. But we hope the WordPress platform will remain stable.
Much has happened since the move to WordPress: Indranil Banik, who had contributed the last piece obtained his PhD and is now an Alexander von Humboldt Fellow in the SPODYR group in Bonn. Marcel Pawlowski obtained a Hubble Fellowship and is now a Schwarzschild Fellow at the Leibniz-Institute for Astrophysics in Potsdam, Germany. Moritz Haslbauer, who is now researching towards his PhD in the SPODYR group at Bonn University, joined our editorial team just now and will publish his first post in the next contribution based on his own research on the Keenan-Barger-Cowie void and the Hubble tension. He already published two other research papers, one on galaxies lacking dark matter in cosmological simulations (Haslbauer et al. 2019a), and one on ultra-faint dwarf galaxies in cosmological simulations (Haslbauer et al. 2019b), both finding that the observed galaxies are in conflict with the standard model of cosmology (the SMoC). Concerning myself (PK), I have taken up a joint affiliation with Charles University in golden Prague and have been spending much time travelling there and beyond. I guess the beer, the knedliky and the scientific and cultural importance as well as the open atmosphere at the institutes and the multi-cultural nature and safety of historically extraordinarily beautiful Prague resonate with me. In Bonn, we hosted the large international conference BonnGravity2019: The functioning of galaxies in 2019 and I disjoined myself from the astronomers and have administratively joined a pure-baryonic-physics institute, namely the theory group at the Helmholtz-Institut für Strahlen- und Kernphysik at the University of Bonn. In this context:
Scientists have explorative minds and we know science evolves into new and often unforeseen directions and we should keep our minds open to these in order to allow science to progress rather than stopping scientific advance. It is also important to continue discussions between people working on different ideas without being dismissive. History shows that changes of paradigm can last decades and for those involved it may be impossible at the time to know if they are on the right track.
from Tereza Jerabkova
But are we in a paradigm shift and are we on the right track? The indications for being on the right track come, of course, from constant comparison of the theory one is developing with the observational data, and this blog will be covering this in the future. But are there perhaps some apparently unassociated hints or indications for an ongoing true major paradigm shift?
From the historical record: Very major paradigm changes in world view (religious, scientific) seem to be associated with significant relatively rapid transformations in the arts and with dramatic historical upheavals. Examples of this are (1) the fall of the Roman Empire went along with large-scale change to benign [thou shalt neither lie to nor kill anyone, but love and forgive everyone and all are equal in front of God] monotheism in Europe which improved local social cohesion, removed slavery from Europe and constituted an essentially critical mental step in abstracting the workings of the Universe. This abstraction is critically important because, simply put, until the abstraction there was a deity for every phenomenon (e.g. god of war). (2) The [first] 30 year war in the 17th century which was associated with the Keplerian revolution. In music, the first opera “L’Orfeo” by Monteverdi appeared in 1607. (3) In the early 19th century, the social transformations and associated Napoleonic wars with their large orchestrated battles outside of cities and the “Revolutions of 1848” appear to go in-hand with the development of thermodynamics and electricity as well as the emergence of romantic music and the symphonies by large orchestras (Schumann, Verdi, Wagner, Bruckner, Brahms, Tschaikowsky, and others). (4) The [second] 30 year war in the 20th century (i.e. the first and second world wars combined) happening in-parallel to the Einsteinian/Planckian revolution and being accompanied by the appearance of the twelve-tone technique by Schönberg and the music by the Russian composers Shostakovich, Prokofjew, Stravinsky, and Rachmaninow. (5?) The current world-wide geopolitical developments which appear with rising tensions and increasing dissociation of the power-blocks from each other, the accelerating demographic and potentially negative cultural-religious shifts in Western Europe, the societal changes concerning personal individualism, cancel culture and political correctness, and all of this in combination with the accelerating over-population, climate, micro-plastic-pollution crisis and on-going mass extinction, do seem to be suggestive of a major upheaval which is in the process of unfolding.
The next blog explains why cosmology is in a catastrophic crisis.
Given my affiliation with Charles University, I have been travelling to Prague and beyond frequently and now the CORONA Pandemic has stopped this flying about the planet — I have already written about the first wave and my getting marooned on a beautiful island next to the Strand. Being this time stranded in Bonn without a Strand during the second wave, I have a little more time on my hands I guess. So here we are, back to the Crisis.
In The Dark Matter Crisis by Moritz Haslbauer and Pavel Kroupa. A listing of contents of all contributions is available here.
The following is a guest post by Indranil Banik. Indranil is a PHD student at the University of Saint Andrews, part of the Scottish Universities’ Physics Alliance. He was born in Kolkata, India and moved to the UK with his parents a few years later. Indranil works on conducting tests to try and distinguish between standard and modified gravity, especially by considering the Local Group. Before starting his PhD in autumn 2014, he obtained an undergraduate and a Masters degree from the University of Cambridge with top grades. There, he worked on understanding the dynamics of ice shelves, and on a Masters project on the thick disk of the Milky Way, as well as on a few other problems.
I recently won the Duncombe Prize from the American Astronomical Society’s Division on Dynamical Astronomy for a detailed investigation into the Local Group timing argument. This was to present a recently accepted scientific publication of mine (link at bottom of article) at their annual conference in Nashville, Tennessee.
The timing argument takes advantage of the fact that the Universe has a finite age of just under 14 billion years. Thus, everything we see must have started at a single point at that time, which we call the Big Bang. Due to the finite speed of light, by looking very far away, we are able to look back in time. In this way, we observe that, shortly after the Big Bang, the Universe was uniform to about one part in 100,000. Thus, we know that the expansion of the Universe was very nearly homogeneous at early times. This means that any two objects were moving away from each other with a speed almost proportional to the distance between them. This is called the Hubble law.
The Hubble law also works today, but only on large scales. On small scales, the expansion of the Universe is no longer homogeneous because gravity has had a long time to change the velocities of objects. As a result, our galaxy (the Milky Way, MW for short) and its nearest major galaxy, Andromeda (or M31) are currently approaching each other. This implies that there must have been a certain amount of gravitational pull between the MW and M31.
Although this has been quantified carefully for nearly 60 years, my contribution involves analysing the effects of the MW and M31 on the rest of the Local Group (LG), the region of the Universe where gravity from these objects dominates (out to about 10 million light years from Earth). Recently, a large number of LG dwarf galaxies have been discovered or had their velocity measured for the first time (McConnachie, 2012). We took advantage of this using a careful analysis.
We treated the MW and M31 as two separate masses and found a trajectory for them consistent with their presently observed separation. We treated the other LG dwarf galaxies as massless, which should be valid as they are much fainter than the MW or M31. For each LG dwarf, we obtained a test particle trajectory whose final position (i.e. at the present time) matches the observed position of the dwarf. The velocity of this test particle is the model prediction for the velocity of that galaxy.
The basic feature of the model is that the expansion of the Universe has been slowed down locally by gravity from the MW and M31. At long range (beyond 3 Mpc or about 10 million light years), this effect is very small and so objects at those distances should essentially just be following the Hubble law. But closer to home, the results of this model are clear: the MW and M31 are holding back the expansion of the Universe, and objects within about 1.5 Mpc should be approaching us rather than moving away (see figure above). By comparing the detailed predictions of our model with observations, we were able to show that, for all plausible MW and M31 masses, a significant discrepancy remains. This is because a number of LG galaxies are flying away from us much faster than expected in the model.
An important aspect of these models is that the MW and M31 have never approached each other closely. Although one can in principle get them to have a past close flyby in Newtonian gravity if they are assigned very high masses, there are several problems with this. Such high masses are unreasonable given other evidence. More importantly, if there had been such a flyby, the dark matter halos of the MW and M31 would have overlapped, leading to a substantial amount of friction (of a type called dynamical friction, which is reliant only on gravity). This would have caused the galaxies to merge, contradicting the fact that they are now 2.5 million light years apart.
I was aware of an alternative model for galaxies called Modified Newtonian Dynamics (MOND – Milgrom, 1983). This is designed to address the fact that galaxies rotate much faster than one would expect if applying Newtonian dynamics to their distributions of visible mass. The conventional explanation is that galaxies are held together by the extra gravitational force provided by a vast amount of invisible dark matter. Many galaxies need much more dark matter than the amount of actually observed matter. But, so far, this dark matter has not been detected directly. What MOND does is to increase the gravitational effect of the visible matter so that it is enough to explain the observed fast rates of rotation. In this model, there is no longer any need for dark matter, at least in halos around individual galaxies. You can find out more about MOND here on McGaugh’s MOND pages and here on Scholarpedia.
In MOND, the MW and M31 must have undergone a past close flyby (Zhao et al, 2013). In this model, the absence of dark matter halos around galaxies means that there need not have been any dynamical friction during the flyby (remember that the disks of the MW and M31 are much smaller than their hypothetical dark matter halos, which are only needed if we apply Newton’s law of gravity).
The high relative speed of the MW and M31 at this time (about 9 billion years ago) would probably go a long way towards explaining these puzzling observations. This is because of a mechanism called gravitational slingshots, similar to how NASA was able to get the Voyager probes to gain a substantial amount of energy each time they visited one of the giant planets in our Solar System. The idea in this case would be for the MW/M31 to play the role of the planet and of a passing LG dwarf galaxy to play the role of the spacecraft.
This mechanism is illustrated in the figure above. In the left panel, there is a small galaxy moving at 1 km/s while a much heavier galaxy moving at 5 km/s catches up with it. The massive galaxy sees the dwarf approaching at 4 km/s (right panel). The trajectory of the dwarf is then deviated strongly, so it ends up receding at 4 km/s back in the direction it approached from. Combined with the velocity of the massive galaxy (which is almost unchanged), we see that the velocity of the dwarf has been increased to 5 + 4 = 9 km/s.
We do in fact observe many LG dwarf galaxies moving away from us much faster than in the best-fitting dark matter-based model (see figure below, observed radial velocities are on the y-axis while model-predicted ones are on the x-axis). Moreover, based on the distances and velocities of these objects, we can estimate roughly when they would have been flung out by the MW/M31. This suggests a time approximately 9 billion years ago, which is also when one expects the MW and M31 to have been moving very fast relative to each other in MOND as they were close together.
These high-velocity LG dwarfs would have been flung out most efficiently in a direction parallel to the velocity of whichever heavy galaxy they interacted with. Naturally, the MW and M31 have not always been moving in the same direction. But it is very likely that they were always moving within much the same plane. Thus, one test of this scenario (suggested by Marcel Pawlowski) is that these high-velocity dwarfs should preferentially lie within the same plane.
There is some evidence that this is indeed the case. Moreover, the particular plane preferred by these objects is almost the same as what would be required to explain the distribution of satellite galaxies around the MW and M31. This is described in more detail towards the end of this lecture I gave recently about my work.
Even without this evidence, there is a strong case for MOND. One of the astronomers heavily involved in making this case is Professor Stacy McGaugh. I was very pleased to meet him at this conference. We discussed a little about his current work, which focuses on using rotation curves of galaxies to estimate forces within them. For a modified gravity theory which does away with the need for dark matter, it is important that these forces can be produced by the visible matter alone. Stacy was doing a more careful investigation into estimating the masses of galaxies from their observed luminosities and colours (which give an idea of the mix of different types of star in each galaxy, each of which has its own ratio between mass and luminosity, old stars being red and young ones blue). The success enjoyed by MOND in explaining dozens of rotation curves is one of the major reasons the theory enjoys as much support as it does.
This brought us on to discussing how we came to favour the theory over the conventional cosmological model (ΛCDM) involving Newtonian gravity and its consequent dark matter. Stacy explained how it was particularly his work on low surface brightness galaxies which convinced him. This is because such galaxies were not known about when the equations governing MOND were written down (in the early 1980s). Despite this, they seemed able to predict future observations very well. This was somewhat surprising given that the theory predicted very large deviations from Newtonian gravity. In the ΛCDM context, the presence of large amounts of invisible mass makes it difficult to know what to expect. As a result, it is difficult for the theory to explain observations indicating a very tight coupling between forces in galaxies and the distribution of their visible mass – even when most of the mass is supposedly invisible (a feature called Renzo’s Rule). A broader overview of what the observations seem to be telling us is available here (Famaey & McGaugh 2012) and here (Kroupa 2015).
I then explained my own thinking on the issue. I was aware of some of the observations which persuaded Stacy to favour MOND and I was aware of the theory, but I did not favour it over ΛCDM. Personally, what got me interested in seriously considering alternatives to ΛCDM was its missing satellites problem. The theory predicts a large number of satellite galaxies around the MW, much larger than the observed number. Although it is unclear if MOND would help with this problem, that does seem likely because structure formation should proceed more efficiently under the modified gravity law. This should lead to more concentration of matter into objects like the MW with less being left over for its satellites.
Although this suggested MOND might be better than ΛCDM, my initial reaction was to consider warm dark matter models. Essentially, if the dark matter particles were much less massive than previously thought (but the total mass in the particles was the same), then they would behave slightly differently. These differences would lead to less efficient structure formation at low masses, reducing the frequency of low-mass halos and thus making for less satellite galaxies. I hoped this would explain a related problem, the cusp-core challenge which pertains to the inner structure of satellite galaxies.
What finally convinced me against such minor alterations to ΛCDM and in favour of MOND was the spatial arrangement and internal properties of the MW and M31 satellite galaxies. Much has been written in previous posts to this blog about this issue (for example, here), with this 2005 paper by Kroupa, Theis & Boily pointing out the discrepancy between observations and models for the first time.
I have summarised the results in a flowchart (left). Essentially, the hypothetical dark matter halos around the MW and M31 need to be distributed in a roughly spherical way. This is unlike the disks of normal (baryonic) matter in these galaxies. The reason is that baryons can radiate and cool, allowing them to settle into disks. As a result, in an interaction between two galaxies, the baryons with their ordered circular motions in a disk can get drawn out into a long dense tidal tail that then collapses into small tidal dwarf galaxies. But these would be free of dark matter, and they would also be mostly located close to a plane: the common orbital plane of the interacting galaxies. You can see more about this scenario here.
The argument goes that it is difficult to form such planes of satellites in any other way (for example, see Pawlowski et al, 2014). Just such satellite planes are in fact observed around both the MW and M31. Supposedly free of dark matter, they should have quite weak self-gravity and thus low internal velocity dispersions/rotate very slowly. Yet, their observed velocity dispersions are quite high, signalling the need for some extra force to stop them flying apart.
Because the spatial arrangement of these satellites suggests a violent origin, it is unlikely that they have much dark matter. Thus, I became convinced of the need to modify our understanding of gravity. It turns out that exactly the same modification that can help explain galaxy rotation curves without dark matter could also help address this problem (McGaugh & Milgrom, 2013). Although the dark matter plus Newtonian gravity worldview might just about be able to explain galaxy rotation curves (although detailed tests are showing this not to have succeeded: Wu & Kroupa 2015), I do not think it can explain the satellite plane problem. This eventually convinced me to investigate this issue further. I explain some of the more compelling reasons for favouring MOND over ΛCDM in this lecture I gave recently.
Together with Francoise Combes, who was recently appointed as a professor in the most prestigeous institution in France, Le College de France, and Benoit Famaey, who is an expert on Milgromian dynamics and its deeper foundations (e.g. Famaey & McGaugh 2012), we were invited by Mordehai (Moti) Milgrom to spend a whole week at the Department of Particle Physics and Astrophysics in the Weizmann Institute in Rehovot, Israel. A link to the video (dubbed in English) of the inaugural lecture given by Francoise Combes for her new chair and the introduction by Serge Haroche (Nobel Prize 2012 in physics) is available here (alternatives to the dark matter approach are explicitly mentioned by both).
I met Benoit at Frankfurt airport in the very early morning (he was heading in some random direction) since we had booked the same Lufthansa flight to Tel Aviv. We arrived on Sunday, March 6th, and met Moti at his office in the late afternoon.
In the entrance hall of the Department. From left to right: Einstein’s field equation without Lambda, Francoise Combes, Mordehai Milgrom, Pavel Kroupa and Benoit Famaey.
Coming to know the place and first discussions
I am very impressed by the size and beautiful campus of the whole Weizmann Institut, and how pleasant the entire ambiente is.
Chairs and a pond in front of the Department.
The people are very friendly and helpful. And interested. I was staying at the spacious and luxurious San Martin Faculty Clubhouse. At night the various buildings and park areas in the Weizmann Institute are illuminated beautifully, with warm lights setting accents and emphasizing a welcoming atmosphere.
The highly-ranked Weizmann Institute consists of many departments of various natural sciences and seems to be perfectly created for academic pursuit, including leisure areas. Its success in the pursuit of basic research in the natural and exact sciences and in acquiring funding is evident through the architecture, spaciousness, and general design.
There was no planned agenda for us, apart that Benoit was to give a talk on Wednesday, 9th of March, at 11:15, and for Francoise Combes to give a departmental colloquium on Thursday, 10th of March at 11:15. In between these talks we could do either nothing and hang about enjoying the sunshine and exquisite weather and pool, or engage in intense discussions. Perhaps due to the ambiente and of course our comparable research interests, we largely chose the latter.
On Monday, 7th of March, we had a very relaxed day, meeting with Moti at the Department in the late morning and spending our time debating. Typical discussion points (largely between Francoise, Benoit and myself) throughout the visit were the local major underdensity and its possible implications on the value of the cosmological Lambda, the underlying theory of MOND and whether it is due to a “dark” fluid which behaves like dark matter on large scales (e.g. Luc Blanchet’s dipoles and Justin Khoury’s condensate)
Given that Lambda was missing in the equation displayed in the entrance hall of the Department (see first photo above), we began to discuss it. And this is where the “local” underdensity now plays a possibly important role, see this figure from Kroupa (2015),
The underdensity is significant, according to the shown data, and may challenge any cosmological model. From Kroupa (2015).
and in contrast the very recent work by Whitbourn & Shanks where the authors explicitly state agreement with the previous survey by Kennen et al. (2014). The independent finding by Karachentsev (2012) on the local 50 Mpc scale appears to naturally continue the trend evident from the Kennan et al. data (see the figure on the left), IF one assumes the same baryonic to dark-matter ratio as at larger distances. The actually measured stellar density remains similar to the Keenan et al. value at small distance. So the baryonic density (assuming the gas to star ratio and the contribution by dwarf galaxies to remain unchanged out to distances of 800 Mpc [redshift of 0.2]) then within 300 Mpc there is at least a decrease in the baryonic density by factor of two. Conversely, taking Karachentsev’s measurement, we would see a disappearance of dark matter nearby to us since the stellar density remains similar to the Kennen measurement within 150 Mpc while the dark matter density decreases further. So the measurements appear to imply the following picture: within 400 Mpc the luminous (and thus baryonic) matter density decreases significantly by a factor of two. At the same time, the ratio of dark matter to baryonic matter decreases even more. Both findings violate the cosmological principle.
The work by David Wiltshire (his lecture notes) and Thomas Buchert already indicates that inhomogeneities could possibly make the Universe appear to an observer situated within such an underdensity as if it’s expansion is accelerating, although in truth it is not. That is, the inhomogeneities appear to be of the correct magnitude to eliminate the need for Lambda, Lambda (dark energy) merely being an apparent effect mis-interpreted by the supernova type 1a data. The reason lies in that a distant object’s observed redshift depends in reality on the exact paths the photons travel in a universe which consists of time-changing voids and over-densities, and this is a different redshift computed assuming a homogeneous and isotropic expanding Universe.
But we need more detailed calculations taking into account the constraints from the observed under-density shown in the figure to be assured that Lamba=0. It is certainly true that Lambda=0 may be more in line with theoretical ideas than the very small value deduced to explain an apparently accelerating Universe, because it is actually predicted, from quantum field theoretical calculations of the vacuum (for details see e.g. Padilla 2015), to have a value some 60 to 120 orders of magnitude larger. It should be emphasized, though, that “MOND likes Lambda“, in the words of Moti. The reason is that the Lambda derived from astronomical observations (e.g. from supernovae of type 1a observations) and Milgrom’s constant a_0 appear to be naturally related, and MOND may be derivable from vacuum processes (Milgrom 1999).
Within about 300 Mpc, where we can say that we have the best measurements, the Universe is nicely consistent with MOND. The mass-to-light ratios of galaxy groups are less than 10 (Milgrom 1998 and Milgrom 2002), i.e. there is only baryonic matter. The observationally inferred increased density of baryonic matter at distances larger than 300 Mpc would then perhaps be due to cosmological models being inappropriate, i.e. that the currently used red-shift–distance relation may be wrong.
We also debated galaxy evolution, the fraction of elliptical galaxies and the redshift dependence of this fraction. Notably, fig.7 in Conselice (2012) shows that the observed fraction of massive galaxies does not evolve although the LCDM model predicts a strong evolution due to merging. This is consistent with the independent finding by Sachdeva & Saha (2016) that mergers are not a driving mechanism for galaxy evolution, and this is in turn consistent with the independent findings reached by Lena et al. (2014) on the same issue.
We further talked about how LCDM is faring on large, intermediate and small scales, how stellar populations change with physical conditions, the variation of the IMF, as well as political topics. The discussions were far from reaching consensus, we had different views and data sets we could quote on various problems, and time flew by such that we barely noticed.
However, Moti managed to drag us away from his Department, and showed us around the Weizmann institute. An particular station was the famous landmark tower which once housed the Koffler Accelerator and which now houses, in its “bubble”,
The tower which housed the Koffler Accelerator and which now houses a conference room (in its “bubble”) and the Martin S. Kraar Observatory.
a conference room and also the Martin S. Kraar observatory which is also used in international top-level research projects. The director of the observatory, Ilan Manulis, kindly explained to us in much detail its functionality and design for full remote-observations without human interference.
Viewing the lands from the top of the Koffler Accelerator Building. From left to right: Benoit Famaey, Francoise Combes and Mordehai Milgrom.
Part of the Weizmann Institute as viewed from the top of the Koffler Accelerator Building.
The Group at the Koffler Accelerator. From right to left: Benoit Famaey, Francoise Combes, Mordehai Milgrom and Pavel Kroupa
On this Monday Moti took us to lunch at the Lebanese restaurant Petra located in Nes-Ziona, a town 5 minutes drive from the Weizmann Institute. The Lebanese cuisine was fabulous, and I ate far too much.
A diversion to history
And, on Tuesday, 8th of March, Moti and his wife Ivon took us on a drive-around nearby Israel. This trip, involved about 4 hours of driving by Moti, and while driving we discussed, amongst other topics, the new study by Papastergis et al. (2016) in which they use 97 gas-dominated galaxies from the ALFALFA 21cm survey to construct their estimate of the baryonic Tully-Fisher relation showing excellent agreement with the expectations from Milgromian dynamics.
The drive was incredible, as we saw places with many thousands of years of history dating back to the Caananite peoples. It is this land which took the central role in the evolution of the Mediteranean-Sea-engulfing Roman Empire to a Christian empire. It contains the scars of the episodes of the invasion by a newer religion of christian lands, christian reconquest, and reconquest by the newer religion, till the foundation of Israel, issues which remain current to this day.
The author amongst the ruins of Caesarea. “What was the fate of Caesarea’s inhabitants when it fell to the Mamluks?”
Caesarea, once a thriving port for many centuries, from where Paulus was imprissioned and sent to Rome for his hearing at the emperor’s court, was wiped out in the 13th century.
The Group in front of the Roman ampitheater in windy Caesarea, nearly but not quite ready. From right to left: Mordehai Milgrom, Francoise Combes, Benoit Famaey, Pavel Kroupa.
The thriving thousand-year old medieval city of Caesarea, named by King Herod after Octavian (i.e. Augustus Caesar) and which was once the main port in his kingdom, was finally obliterated from existence after a siege by a Mamluk army in the thirteenth century.
Acre: the chief port in Palestine during the crusader epoch still boasting major remains of the huge crusader’s fortress:
Acre: the remains of the Crusader port.
Acre, once a blossoming port and a gate-way to the holy lands for christian pilgrims.
After a wonderful dinner at the seashore between Tel Aviv and old Jaffa at the restaurant Manta Ray, where some action happened just before we arrived judging from the large number of police and other forces around, we visited very beautiful Old Jaffa:
Old Jaffa, which dates back to a history of 4000 years and where alrady the Egyptian empire stationed a garrison.
The restoration of the archeological sites of Caesarea, Acre and of Old Jaffa brings to mind how incredibly rich and beautiful the thousand year old places are along the Mediterranean coast throughout the middle East and northern Africa, if upheld with the corresponding desire to show this history.
Back to science
On Wednesday, 9th of March, we spend the whole day in discussions with staff of the Institute. It began with Benoit Famaey’s presentation on the latest numerical results of modelling the Sagittarius satellite galaxy and its stream in Milgromian dynamics by Strasbourg-PhD student Guillaume Thomas. Natural solutions appear to emerge and this will, once published, clearly add spice to the discussions, given that the only solutions available in LCDM by Law & Majewski (2010) are unnatural in that the dark matter halo of the Milky Way needs to be oblate at right angle to the Milky Way, a solution which poses severe dynamical instabilities for the Milky Way disk. Notably, this polar oblate dark matter halo of the Milky Way alignes with the vast-polar structure (the VPOS) of all satellite galaxies, young halo globular clusters and stellar and gas streams.
In these discussions with the staff members during the aftenoon, we dealt with supernova rates and explosions and types in different galaxies, the relevance to the variation of the IMF in various environments (e.g. metal-poor dwarf galaxies vs metal-rich massive galaxies and the dependency of the IMF on density and metallicity), and cosmological problems such as the local massive under-density mentioned above.
An important point I tried to emphasize repeatedly is that if Milgromian dynamics is the correct description of galactic dynamics, then we must keep an open mind concerning the possibility that all of cosmological theory may have to be rewritten and the large-redshift data may need to be reinterpreted in terms of different redshift–distance and redshift–age relations.
In the evening of Wednesday I tried out the swimming pool on campus, and their sauna as well. I had access to this swimming pool by staying in The San Martin Faculty Clubhouse and the Hermann Mayer Campus Guesthouse – Maison de France. I must admit, that the day was near to being perfect with the sunshine and a closing dinner with Francoise and Benoit again in our meanwhile standard kosher restaurant (Cafe Mada) nearby the San Martin guest house.
On Thursday, 10th of March, Francoise Combes gave her interdepartmental presentation on “The Molecular Universe” which was well visited, and afterwards we went together with some staff of the Weizmann Institute for lunch at Cafe Mada, where a lively and very entertaining discussion ensued on religeos questions. In the late afternoon we joined the Whisky lounge, in which anyone traveling back to Rehovot from abroad can bring a duty-free bottle of Whisky to and donate it to this lounge.
The Local Group of galaxies is highly symmetrical, with all non-satellite dwarf galaxies lying in two planes symmetrically and equidistantly situated around the axis joining the Milky Way and Andromeda. From Pawlowski et al. (2013).
Young researchers meet every Thursday (remember, this is in Israel the end of the week) to sip Whisky and thereby to elaborate on various problems, such as in our case on the local underdensity, or how the two critical constraints we have from the highly organized structure of the Local Group of galaxies and the CMB together constrain the cosmological model.
An interesting statement made was that while one needs about ten LCDM Universes to get one Bullet cluster (Kraljic & Sarkar 2015), an infinite number of LCDM Universes will not give a single Local Group with its symmetries.
At least these are some of the questions we discussed while there on this Thursday. We were also impressed by all the connections of this Department with Princeton, Caltech and Harvard.
Friday and Saturday
Shops begin to close down and it becomes a challenge to find food and Francoise left for France. In the morning I went for a swim and sauna, and for luch Benoit and myself had to go out of the Weizmann Institute (exit Main Gate and turn left) to find a sandwich place.
The Basha Bar in Tel Aviv.
After some work and then in the evening and at about 18:00 we decided to take a taxi to Tel Aviv. We arrived at the Basha Bar by about 18:30 and stayed for three hours (see photo).
The Basha Bar, enjoying a three-hour shisha smoke and many Tuborg beers.
On Saturday, the kosher breakfast in the guest house was as excellent as ever, but it was interesting for me to note that neither the toaster nor the coffee machine were to be used, while the water boiler was on so we could still have hot Turkish coffee (which we also drink in Bohemia, by the way, so not much new for me here). Nearly everything is closed. Benoit and myself met for lunch and walked outside the Main Gate turning right, over the bridge to reach the Science Park finding bistro Cezar for lunch.
In the evening Moti picked us up for a dinner at his home with Ivon, where we had a long discussion also on the dynamic situation in Germany, Europe and the future.
At the home of Moti in Rehovot. From right to left: Moti, Benoit and the author.
Benoit and myself stayed on until Monday, joining the astrophysics journal club which serves lunch at the Department on Sunday. I spent most of the afternoon discussing with Boaz Katz how star clusters may be relevant for type 1a supernovae. In the evening of Monday Benoit and I went again to Cafe Mada for a final dinner and drinks. On Monday, 14.03., we flew out around 16:00, taking a taxi to the Tel Aviv airport at 13:00 from the Department. We shared the same flight back. Again the 4+ hour long Lufthansa stretch without personal-screen-based entertainment system! But, this gave Benoit and myself a chance to further discuss at length the above mentioned Khoury condensate and the Blanchet dipoles as models for galaxy-scale MOND and cosmology-scale dark-matter-like behaviour. But I note that these are not dark matter models. During pauses my thinking was that as the coastal line of Tel Aviv receded in the setting Sun we left a small fraction of the Levant and northernmost Africa, all once pat of the Roman Empire, at a level of civilisation mirrored by the clear, brllliantly lit vast and dynamic power- and resource-hungry central-European night with full autobahns, radiant towns and illuminated football fields in nearly every village. In Frankfurt our ways parted after a last small dinner in the train station, Benoit taking a bus to Strasbourg at about 21:30, and me starting my odessey to Bonn at the same time using the available train connections (German trains all too often run late, these days).
The visit was most memorable for all of us, and Benoit and myself agree that we would like to return. We did not reach any conclusions but we came to know many new people and perhaps helped to underscore the very seriousness of alternative concepts to dark matter and the many failures of the LCDM model.
In closing it is probably fair to say that Milgrom contributed the greatest advance on gravitational physics since Newton and Einstein.
In The Dark Matter Crisis by Pavel Kroupa and Marcel Pawlowski. A listing of contents of all contributions is available here.