This year, Pavel Kroupa was asked to hold a Golden Webinar in Astrophysics on the dark matter problem. This contribution provides the link to the recording of this presentation which has now become available on YouTube. In this presentation, Pavel Kroupa argues that the dark matter problem has developed to become the greatest crisis in the history of science, ever. This contribution also provides links to recordings available on YouTube of previous related talks by the same speaker from 2010 (the Dark Matter Debate with Simon White in Bonn) and 2013 (in Heidelberg). This might allow some insight into how the debate and the research field have developed over the past dozen or more years.
1) Golden Webinar: “From Belief to Realism and Beauty: Given the Non-Existence of Dark Matter, how do I navigate amongst the Stars and between Galaxies?”
On April 9th, 2021, Prof. Pavel Kroupa presented a talk in the Golden Webinars in Astrophysics series on “From Belief to Realism and Beauty: Given the Non-Existence of Dark Matter, how do I navigate amongst the Stars and between Galaxies?”. The talk is now available on Youtube:
The slides to the talk without the fictitious story can be downloaded here:
If you are interested in other talks presented during The Golden Webinars in Astrophysics series, you can find the record of those already presented on their Youtube Channel, and here is a list of upcoming talks. The Golden Webinars are provided as a free public service and have no registration fees.
2) The vast polar structures around the Milky Way and Andromeda
In November 2013, Prof. Pavel Kroupa presented “The vast polar structures around the Milky Way and Andromeda” in the Heidelberg Joint Astronomical Colloquium. In the talk he discussed the failures of the Standard model of cosmology and the implications for fundamental physics.
A blog entry from 2012 on the vast polar structure (VPOS) of satellite objects around the Milky Way can be found here.
3) Bethe-Kolloquium “Dark Matter: A Debate”
In November 2010, Prof. Simon White (Max Planck Institute of Astrophysics, Garching) and Prof. Pavel Kroupa (University of Bonn) debated on the concept and existence of dark matter during the Bethe Colloquium in Bonn. Their presentations and the subsequent debate are available here:
a) Presentations by Prof. White and Prof. Kroupa
Summary of both presentations:
b) The Debate
The German-language television channel 3sat produced a TV report on the Bethe Colloquium, which can be also found on Youtube (available only in German):
In The Dark Matter Crisis by Moritz Haslbauer, Marcel Pawlowski and Pavel Kroupa. A listing of contents of all contributions is available here.
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.
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 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.
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.
Spiral galaxies rotate too fast. If they would only consist of the visible (baryonic) mass we observe in them and Newton’s Law of gravity is correct, then they would not be stable and should quickly fly apart. That they don’t has been one of the first indications that the galaxies (and the Universe as a whole) either contains large amounts of additional but invisible “dark matter”, or that the laws of gravity don’t hold on the scales of galaxies. One possibility for the latter, Modified Newtonian Dynamics (MOND), proposes that gravity needs to be stronger in the low acceleration regime present in galaxies (for more details see the extensive review by Famaey & McGaugh 2012 and Milgrom’s Scholarpedia article). That the rotation curve (i.e. the function of circular velocity of the galactic disc with radius) of our Milky Way galaxy follows the same trend as the rotation curves of other spiral galaxies has been known for a long time, too. So it appears to be a bit surprising that the Nature Physics study “Evidence for dark matter in the inner Milky Way” by Fabio Iocco, Miguel Pato and Gianfranco Bertone makes such a splash in the international press. That the MW should contain dark matter is not news, but nevertheless the paper got a hugeamount of presscoverage.
Rotation curve of the Milky Way: Observed velocities (squares), baryons + Newtonian Dynamics (black line) and MOND rotation curve (magenta line).
One thing emphasized a lot by the press articles (and press releases) is that the authors claim to have found proof for the presence of dark matter in the ‘core‘, ‘innermost region‘, or even ‘heart of our Galaxy‘1, not just in the intermediate and outer regions. This might be worrisome for modified gravity theories like MOND, which predict that regions very close to the center of the Milky Way should be in the classical Newtonian regime, i.e. the rotation curve should be consistent with that predicted by applying Newton’s law to the observed mass distribution. The underlying reason is that due to the higher density of baryonic matter in the center of the Milky Way the gravitational acceleration of the baryons there already exceeds the low-acceleration limit. But only once the acceleration drops below a certain threshold the non-Newtonian gravity effect kicks in. Interpreted naively (i.e. assuming Newtonian dynamics), this would mimic dark matter appearing only beyond a certain radial distance from the Galactic Center.
Without even going into the details of checking their assumed Milky Way models, the way the observational data is combined and whether there are systematic effects, a simple look at figure 2 in Iocco et al. already reveals that their strong claim unfortunately is not as well substantiated as I would wish.
The plot’s upper panel is what is of interest here. It shows the angular circular velocity in the Milky Way disk versus the Galactocentric radius. The red points with error bars are observed data for different tracers. The grey band is the range of velocities allowed for the range of baryonic mass distributions in the Milky Way considered by Iocco et al. (that are all consistent with observations). If there would be only baryonic matter and Newtonian Dynamics, the rotation curve of the Milky Way should lie somewhere in this area.
First of all, the figure shows that they did not consider any data in the region within 2.5 kpc. That makes sense because that region will be dominated by the bar and bulge of the Milky Way. Stars in the bulge don’t follow circular orbits, so one can’t measure circular velocities there.
So, what is the core, heart or ‘innermost region’ of the Milky Way? Lets try to come up with something motivated by the structure of our Galaxy. The Galactic disk is often modeled by an exponential profile, with a scale length of about 2.2 kpc. What if we say the core of the MW is everything within one scale length? Immediately there’s a problem with the claim by Iocco: They are not even testing data on this scale.
Lets ignore the phrase ‘core’ or ‘heart’ of the Milky Way and focus on the more general formulation they also use in their paper’s title: “Evidence for dark matter in the inner Milky Way”. Looking at their Figure again, we can see that the data start to leave the grey band at a distance of about 6 kpc from the MW center. Thus, within 6 kpc (almost three scale radii of the Milky Way disk!) the purely baryonic models encompass the data. Consequently, here is no need to postulate that dark matter contributes significantly to the dynamics. The figure clearly shows that there is no need, and therefore no evidence for dark matter within 6 kpc of the Galactic Center, which is as generous a definition of ‘inner Milky Way’ as it gets in my opinion. The authors themselves even write that ‘The discrepancy between observations and the expected contribution from baryons is evident above Galactocentric radii of 6-7 kpc’. In this regard it doesn’t matter whether the majority of the possible baryonic models predict a lower rotation curve: as long as the data agree with at least one baryonic model that is consistent with the observed distribution of mass in the Milky Way, there can not be evidence for dark matter.
I really don’t understand why they then claim to have found proof of dark matter in the innermost regions of the Milky Way. My suspicion is that the authors and their press releases seem to have a (literally) quite broad interpretation of the term ‘innermost region’. Judging from the context, they seem to subsume everything within the solar circle of ~ 8 kpc (the distance of the Sun from the Galactic Center) as ‘innermost’. I don’t think it is an appropriate definition, after all it makes the vast majority of the baryonic mass of the Milky Way part of the innermost region. Half the light of an exponential disk is already contained within less than 1.7 scale length (1.7 x 2.2 kpc = 3.7 kpc for the Milky Way), and all of the bulge/bar is in there, too. But if we nevertheless roll with it for the moment we can see that yes, between 7 and 8 kpc there seems to be need for dark matter … or for a MOND-like effect.
Rotation curve of the Milky Way: Observed velocities (squares), baryons + Newtonian Dynamics (black line) and MOND rotation curve (magenta line).
So, lets have a look at one MOND rotation curve constructed for the Milky Way (from McGaugh 2008) to see where we expect to find a difference in Newtonian and MONDian circular velocities. The expected Newtonian rotation curve is shown as a black line in the plot, equivalent to the purely baryonic rotation curves making up the grey band in the figure of Iocco et al.. The rotation curve predicted by MOND is shown as a magenta line and the observed circular velocities are the small squares.
The plot immediately reveals that a discrepancy between the Newtonian and the MONDian rotation curves is expected already at small radii, well within 6 kpc. The findings of Iocco et al. that there appears to be some mass missing within the solar circle therefore do not disagree with the MONDian expectation, in contrast to what one of the authors is quoted saying in a Spektrum article. Furthermore, the plot demonstrates that the need for dark matter (or MOND) in the region inside the solar circle was already well known before this new study.
So, in summary, the study doesn’t show all that much new or surprising, the claimed ‘evidence’ for dark matter in the innermost Milky Way is not present in their data (unless you define ‘innermost’ very generously) and some apparent dark matter contribution within the solar circle is not even unexpected based on MOND predictions.
1: The press releases of the TU Munich and Stockholm University even call it a ‘direct observational proof of the presence of dark matter in the innermost part our Galaxy’ (which is clearly wrong, there is obviously nothing direct about it and the innermost part would imply the very center of the Milky Way).