Summary:

Background:

As introduced in the previous contribution to The Dark Matter Crisis, Question A: Galaxies do not work in LCDM, sociology and majority views, PK was recently contacted by a few people, and here are excerpts from some of the questions asked and the replies. These help to illustrate some of the issues at hand. The questions are

A) So the LCDM model fails on scales smaller than about 8 Mpc?

B1) What is a galaxy?

B2) What is a galaxy? (Addendum on the relaxation time)

C) What are the three best reasons for the failure of the LCDM model?

I: Incompatibility with observations

II: MOND works far too well ! (this contribution)

III: Fundamental theoretical problems

D) What about the Bullet cluster?  And what about the Train-Wreck cluster Abell 520?

E) Why is the main stream community so reluctant to  go along with accepting the failure of LCDM?

This contribution deals with Question C, which may be taken to be central to The Dark Matter Crisis, while upcoming contributions will concentrate on the remaining questions.

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The three best reasons for the failure of the LCDM model: 

They can be summarised in three categories. Here is category II. Ctegories I and III can be found in seperate contributions as outlined above.

II)MOND works far too well !

In fact, just as planetary systems are Keplerian objects, galaxies are Milgromian objects.

Milgrom’s discoveryof a0 is likely as epochal as Planck’s discovery of h.

Prelude:

How did the central ideas develop?

A) LCDM was developed top-down. This means that LCDM is an attempt to make the real universe and its constituents fit the General Relativity (GR) field equations which Einstein formulated based only on Solra System data via Newton prior to any cosmological or galactic constraints. It is described by many parameters and these have been measured to high precision so that the LCDM model cannot be adjusted or improved further.

B) MOND has been developed bottom-up. This means that MOND was discovered by Prof. Dr. Mordehai Milgrom (1983) as a description of the dynamics of a few bright disk galaxies then known and of the Solar System. That the conservation laws hold in MOND has been shown by Bekenstein & Milgrom (1984). Since then MOND has been found, without adjustment, to work for very different types of galaxies and on vastly different scales (from the smallest dwarf galaxies to elliptical galaxies to the Local Group and galaxy clusters) and formed the basis of the development of a first new covariant theory (TeVeS) by Prof. Dr. Jacob D. Bekenstein (2004) which cointains Einstein’s GR theory.

MOND thus forms the basis or start of a major new development to understand gravitation and thus cosmological physics. Planck’s discovery of the auxilliary number h (“Hilfsgroesse” in German) was just the same basic discovery ultimately leading to the theory of quantum mechanics.

C) And there are other developments as well: e.g. Generalized Einstein-Aether theories (Zlosnik, Ferreira & Starkman 2007), non-minimally coupled scalar-tensor theories (Bruneton & Esposito-Farese 2007), non-uniform dark fluid theories (Halle, Zhao & Li 2008), Bimetric MOND theories (Milgrom 2010), MOG (Moffat 2006), Entropic gravity by Erik Verlinde, a new ReBEL force acting only between dark matter paticles (Keselman, Nusser & Peebles 2010), and also modified inertia theories (Milgrom 1994, Milgrom 1999, see also Section “What is the meaning of the critical parameter a0” below).

It is important to realise that the need for cold dark matter arises only within the framework of Newtonian dynamics. In MOND and other frameworks none is needed.

As we do not yet know what gravitation really is, and given the success of MOND, it emerges that the evidence for the existence of cosmologically relevant cold dark matter is very weak indeed. The interjection that General Relativity (GR) is extremely well tested is not valid here. GR has only been tested in the Solar System and not in the extremely weak field limit. Furthermore, it is rather obvious that the tests which GR has passed must also be passed by any alternative theory of gravitation. MOND does this through the relativistic estension.

Any gravitational theory needs to account for the observed properties of astronomical phenomena, and so astronomical data test our theories of gravitation and mattter. This is what we are doing in the Stellar Populations and Dynamics Research (SPODYR) group (see Question C.I).

But we are also testing MOND. In fact, one of the hardest tests devised for MOND has been developed by SPODYR (Baumgardt, Grebel & Kroupa 2005) “Using distant globular clusters as a test for gravitational theories“. The test is difficul because high-resolution spectroscopic data are needed for many stars in many very distant faint star clusters – it is the stuff for the largest and most-expensive telescopes on Earth.

Here is a listing of some of the tests performed on MOND by a number of research groups. We return to the star-cluster tests at the end :

1) For example: surface density of normal/baryonic matter dictates where the effect attributed to dark matter appears

Stacy McGaugh (2005, PhRvL)  writes in his abstract:

A fine balance between dark and baryonic mass is observed in spiral galaxies. As the contribution of the baryons to the total rotation velocity increases, the contribution of the dark matter decreases by a compensating amount. This poses a fine-tuning problem for ΛCDM galaxy formation models, and may point to new physics for dark matter particles or even a modification of gravity.

The above figure (klick on it to get a larger version) is Fig.4 from McGaugh (2005). Each pair of open and filled circles lying above or below each other is for one and the same galaxy. The blue open circles show the fraction of the peak rotational velocity of a galaxy which is due to the normal matter in the galaxy, while the black filled dots are the contribution by dark matter in the galaxy (assuming Newtonian dynamics holds true). Note how dark matter magically appears when the normal matter (blue circles) becomes unimportant. 

The above Fig. 4 of this research paper is a completely theory-independent demonstration that in real galaxies there is an extremely fine balance where dark matter is allowed to emerge. Fig.4 shows the relation between the baryon surface density (and hence the typical baryon-induced gravitational acceleration in a given galaxy) and the contribution of  “dark matter” to the rotation curve at its peak-radius.

This correlation is completely unexpected and unexplained in LCDM. But, it is a direct consequence of MOND if MOND is the correct description of the dynamics of galaxies. In a MONDian universe, the dark matter in Fig.4 is phantom dark matter (see below), i.e. unphysical dark matter which a Newtonian observer requires to put into the galaxy in order to explain the observed rotation curve.

Related to to the above, Gentile et al. (2009, Nature) make a perplexing discovery. They write in their abstract

Here we report that the luminous matter surface density is also constant within one scale-length of the dark halo. This means that the gravitational acceleration generated by the luminous component in galaxies is always the same at this radius. Although the total luminous-to-dark matter ratio is not constant, within one halo scale-length it is constant. Our finding can be interpreted as a close correlation between the enclosed surface densities of luminous and dark matter in galaxies.

That is, MOND is more to galaxies than merely their rotation curves: Real galaxies have a disribution of normal, i.e. baryonic, matter which can be observed. It then turns out that somehow, magically, the “dark matter” emerges according to this disribution. In LCDM this simply cannot be and is not the case: in LCDM it is the distribution of dark matter which dictates what is happening through the formation process. Different formation histories and different environments will hence lead to different relative distributions of dark and baryonic matter in different galaxies, meaning that knowing the distribution of normal matter should be an insufficient ingredient to predict the distribution of dark matter.

In real galaxies it is the other way round: normal matter dictates what the gravitational field should do. Only the normal matter is relevant in defining a galaxy. This is essentially a disprove of LCDM, and one may stop considering LCDM further given this observational fact.

2) For example: Rotation curves of disk galaxies

Given the observed distribution of matter in a disk galaxy, its rotation curve can be predicted with great success in MOND. In the vast number of all galaxies these predictions are met with beautiful success (de Blok & McGaugh 1998; Sanders 2010).

Examples can be found on Prof. Stacy McGaugh’s pages:

1. rotation curves1 (blue dots are observations, red lines are MOND models)
2. rotation curves2 (blue dots are observations, red lines are MOND models)
3. comparison  LCDM/MOND
4. Virtually all galaxies can be fit by MOND, with a few uncertain cases.

The rotation curve fits are obtained for good matches to real stellar mass to light ratia and distances. de Blok & McGaugh (1998) perform a beautiful experiment by showing that any arbitrary, i.e.  even an unphysical, galaxy rotation curve can be fitted by a tailored dark-matter halo. That is, a solution with some dark matter halo can be found. But, only physical, i.e. true galaxies can be described by MOND. This is similar to planetary systems: One can design any kind of planetary orbits (e.g. using wrong force laws) but only the physically correct ones follow Kepler’s laws, namely those where the force law is Newton’s.

As emphasised by Prof. Mordehai Milgrom (2011)in his recent presentation at the Hector Rubinstein Memorial Symposium:

“… all the salient MOND predictions on galactic scales follow as unavoidable, simple, and immediate corollaries of the theory–independent of any messy formation scenario–just as Kepler’s laws, obeyed by all planetary systems, follow from an underlying theory, not from complex formation scenarios. To think, as dark-matter advocates say they do, that the universal MOND regularities exhibited by galaxies will one day be shown to somehow follow from complex formation processes, is, to my mind, a delusion.”

Not purposefully related to MOND, the fact that the majority of galaxies, namely disk galaxies, are found to be simpler than expected, is the same basic tennet (Disney et al. 2008, Nature).

In LCDM a rotation curves cannot be predicted from the observed matter distribution, because of the large variance of CDM halos. For example, Libeskind et al. (2009) analyse an N-body sample of 30946 MW-mass DM host halos with mass in the range 2 × 10^11 Msun to 2 × 10^12 Msun for the properties of their substructure distribution. They first select from this sample only those halos that host a galaxy of similar luminosity as the Milky Way (specifically, galaxies more luminous in the V-band than MV = −20). From this remaining sample of 3201 (10 per cent) hosts, they select those that contain at least 11 luminous satellites, leaving 436 (1.4 per cent) host halos. In this sample of 436 systems, about 30 per cent have 6 luminous satellites with orbital angular momenta aligned to a degree similar to that of the MW system. Thus, only 0.4 per cent of all existing MilkyWay mass CDM halos host a MilkyWay-type galaxy with the right satellite spatial distribution. And, in the Local Group the other major dark halo is that of Andromeda, and Andromeda is quite similar to the MilkyWay. This is consistent with the above Disney et al. (2008) finding, but not with the variance expected in LCDM as documented by Libeskind et al.

This immediately implies that, given an observed disk galaxy’s distribution of normal matter, its rotation velocity cannot be predicted (prior to the actual measurement) in LCDM. With MOND, however, the observed distribution of light in a galaxy allows a precise prediction of the rotation curve, modulo knowledge of the surrounding matter distribution (the “external field effect“).

3) For example: the external field effect

The external field effect plays an important role in MOND. It is related to, but not the same as a tidal field, and is rather complicated. It arises due to the non-linearity of MOND. For example, a galaxy or star cluster which has an internal gravitational field which is very weak and in the MOND limit will appear Newtonian if the external field is sufficiently strong. This means that a star’s motion in such a system will obey Newton’s laws rather than MOND, although MOND is correct.

Famaey et al. (2007) write in their Introduction:

In practice however, no objects are truly isolated in the Universe and this has wider and more subtle implications in MOND than in Newton-Einstein gravity, for the very reason that MOND breaks the Strong Equivalence Principle (SEP).

They show that the local escape speed from the Milky Way is predicted to be 550 km/s with a realistic estimate of the MONDian external field acting on the Milky Way from Large Scale Structure of a0/100… This 550 km/s is precisely what is measured in the solar neighbourhood from a local sample of high velocity stars moving faster than 300 km/s.

Furthermore, isolated warped disk galaxies are difficult to understand in standard gravity, even in the LCDM context, apart from invoking unlikely huge starless CDM halos. But in MOND (Combes & Tiret 2010), the external field, even when it is very weak, induces a differential precession of the galactic disk around its direction, which creates warps even in isolated galaxies.

4) For example: The Milky Way

Of course, not only the local escape speed is compatible with MOND in the Milky Way. As all other disk galaxies, the Miky Way is of course also MONDian.

Famaey & Binney (2005) state in their abstract:

Both microlensing surveys and radio-frequency observations of gas flow imply that the inner Milky Way is completely dominated by baryons, contrary to the predictions of standard cold dark matter (CDM) cosmology. We investigate the predictions of the modified Newtonian dynamics (MOND) formula for the Galaxy given the measured baryon distribution. Satisfactory fits to the observationally determined terminal-velocity curve are obtained for different choices of MOND’s interpolating function.

While McGaugh (2008) writes:

Using the Tuorla-Heidelberg model for the mass distribution of the Milky Way, I determine the rotation curve predicted by MOND (modified Newtonian dynamics). The result is in good agreement with the observed terminal velocities interior to the solar radius and with estimates of the Galaxy’s rotation curve exterior thereto. There are no fit parameters.

Thus, within the closest galaxy we can study, namely our Milky Way, where we have highly resolved observational three-dimensional data, there is absolutely no astronomical evidence for cold dark matter and MOND works.

5) For example: Elliptical galaxies 

That disk galaxies are perfect Milgromian objects is well established by now. This accounts for nearly 80% of all galaxies. But what about the other major class of galaxies, namely elliptical galaxies? These mostly occur in galaxy clusters and are much rarer than disk galaxies. The stars in elliptical galaxies move on chaotic (often boxy) orbits which are all over the place, which is why elliptcal galaxies appear ellitpical, i.e. nearly round (in disk galaxies the stars and gas move on nearly circular orbits about a common center).

So if MOND is the correct dynamical theory for galaxies in general, then it must obviously also hold for elliptical galaxies:

Tiret et al. (2007) studied the predictions for elliptcial galaxies made with Newtonian gravity, either containing pure baryonic matter (i.e. without CDM), or embedded in massive CDM haloes. Tiret et al. also studied the properties of elliptical galaxies in MOND.

The standard CDM model has problems on a small scale (within the central 20kpc), and the Newtonian pure baryonic model has difficulties on a large scale (out to 200 kpc from the galaxies), that is, in LCDM there is no consistently fitting description of elliptical galaxies.

However, with MOND both scales are accounted for naturally.

While MOND thus makes excellent predictions for relatively isolated elliptical galaxies, when these are embedded in a strong external field (see above) the predictions can be slightly different (Wu et al. 2010), but no observations have ruled out these small predicted effects.

In a very recent research paper Richtler et al. (2011) study the apparent dark matter halos of ellitpical galaxies.

The authors conclude that the benchmark scaling relations that have been found for dark halos of ellipticals, especially on the central DM phase-space density and volume density as a function of the galaxy’s baryonic mass, are remarkably similar to the scaling relations of the predicted phantom halos of MOND.

What are “phantom dark matter halos”?

Perform the following Gedanken experiment: Assume you live in a MONDian universe, but you think you live in a Newtonian universe.

When you observe an elliptical galaxy (or any kind of galaxy), you will see that the matter in the galaxies moves differently than it ought to. Since you are convinced that you live in a Newtonian world, you have no option but to explain the strange motions through the presence of additional unseen matter, i.e. dark matter. It must be cold dark matter (i.e. massive particles that cannot travel at relativistic speeds), because hot dark matter (made of particles moving near the speed of light) cannot cluster on galaxy scales. You can then calculate the distribution of the cold dark matter from the strange motions.

But in truth the strange motions are only strange to an observer who thinks he/she lives in a Newtonian world. In actuality, he motions are perfectly correct in the real MONDian universe, in which there is no dark matter.

So the Newtonian observer deduces cold dark matter, but it is phantom dark matter because it has no physical reality and is only needed to explain the motions of stars and gas in a MONDian universe for someone who interprets the motions using Newtonian dynamics.

The conclusion of Richtler et al is that

whatever the true physical reason for the strange motions, it is remarkable that a recipe (MOND), which is known to fit rotation curves of spiral galaxies with remarkable accuracy, also apparently predicts the observed distribution of “dark matter” in elliptical galaxies.

6) For example: Tully-Fisher law  and  Faber-Jackson relation

While MOND thus works amazingly well to reproduce the details of the dynamics of individual galaxies, it also sheds light on very general scaling relations that are difficult to understand otherwise.

The Tully-Fisher law (which all known rotationally supported galaxies obey) comes out precisely in MOND (Sanders & McGaugh 2002, ARAA). And, the Faber-Jackson relation (which all known elliptical galaxies obey) also comes out in MOND precisely (Sanders 2010). There is no natural (i.e. plausible) path to any of these observed relationships in LCDM.

But, the Tully-Fisher data depend, for individual normal disk galaxies, largely on the mass of the galaxy which is in stars. For example, our Galaxy’s disk is made up to about 85% of stars, and only about 15% of it is in gas and dust. MOND-critics would claim that the excellent MOND-fit to the observed data depends on this mass which is, however, claimed to be uncertain.

Stacy McGaugh (2011) has just very recently concentrated on testing MOND and LCDM for disk galaxies in which most of the mass is in gas. The gas distribution in the galaxy can be measrued well with radio telescopes, and with the most recent deep surveys excellent data are now available for such low-surface brightness galaxies (they are faint because their  baryonic mass is mostly in gas rahter than stars).

In his abstract:

Here I report a test using gas rich galaxies for which both axes of the BTFR can be measured independently of the theories being tested and without the systematic uncertainty in stellar mass that affects the same test with star dominated spirals. The data fall precisely where predicted a priori by the modified Newtonian dynamics (MOND). The scatter in the BTFR is attributable entirely to observational uncertainty. This is consistent with the action of a single effective force law but poses a serious fine-tuning problem for LCDM.

In the paper he writes

The specific BTFR that the data follow is unique to MOND. Indeed, to the best of my knowledge, MOND is the only theory to make a strong a priori prediction for the BTFR. The dark matter paradigm makes no comparably iron-clad prediction.

and

In order to reconcile LCDM with the data, we must invoke additional parameters.

plus

Reproducing the observed BTFR in LCDM requires a remarkable degree of fine-tuning.

This research paper caused major interest in the press:

Science has written a story about it:  More Evidence Against Dark Matter?

BBC also: Dark matter theory challenged by gassy galaxies result

and Science Daily: Gas Rich Galaxies Confirm Predictions of Modified Gravity Theory  

and Nature: Alternate theory poses dark matter challenge

and The Weizmann Institue of Science also: Dark Matter: A rruling Theory with no Clothes?

The Weizmann Site contains a vigorous and partially very aggressive discussion started by commentators who objected its contents. This discussion gives an insight as to the current scientific atmosphere in which gravitational research needs to be conducted.

7) For example: Tidal Dwarf Galaxies (TDGs) are MONDian

Sensational movie of a galaxy collision calculated using a MONDian integrator by Tiret & Combes (2008), from the TDGBonn 2009 conference website. Klick on the movie and a new page appears. Then download the movie or klick on “tiret-mond1.m4v”. This movie is sensational because it showsfor the first time how galaxies collide in MOND without any dark matter, and how tidal dwarf galaxies form naturally in MOND. 

When galaxies interact they expell matter in the form of tidal tails. In the tidal tails the gas and perhaps some stars may collapse locally to make star clusters or dwarf galaxies. The above movie is a major break through achieved by Oliver Tiret and Francoise Combes as it is one of the very first ever computations, in a MONDian universe, of two colliding galaxies. This calculation is done without cold dark matter! One can nicely see how the tidal tails develop, and how later-on small regions of them collapse to make bound objects of dwarf galaxy mass. In this simulation about 4 or more tidal-dwarf galaxies (TDGs) form, but probably many more would form if a computation with higher-resolution could be done. Thus, the formation of TDGs is natural in MOND, and they would arrange themselves around their host galaxy naturally in a Disk of Satellites, as is in fact seen for the Milky Way (see point 4 in Question CI).

The TDGs cannot have cold dark mater, because the CDM particles cannot be captured in significant quantities by these small objects. But, TDGs which cannot have dark matter in the LCDM model, are observed to have CDM! This is a massive failure of the LCDM model.

TDGs however show a behaviour just as expected in MOND – they are excellently described by MOND. Infact, the prediction of MOND is verified, since the rotation curves of TDGs have been observed only recently decades after MOND was invented:

The TDGs follow the Tully-Fisher law (Gentile et al. 2007, A&A). How is this possible? If LCDM were right, then disk galaxies (which would be in a dark-matter halo which defines the rotation curve) would form a sequence in the rotation speed vs luminosity diagramme. But, TDGs would not be in dark matter halos (Barnes & Hernquist 1992, Nature) and so would not be able to lie on the same sequence. But they do!!

Thus TDGs and normal disk galaxies must be defined by an underlying theory which has nothing to do with dark matter. MOND is precisely such a theory. And indeed, assuming MOND is right, then TDGs as well as normal disk galaxies must lie on the same sequence, as is observed.

This latter point is extremely important, and we need more cases (three TDGs have been observed so far, but telescope time has not been granted to observe more despite quite a few proposals being handed in).

8) For example: Milky Way satellite galaxies are MONDian

The Milky Way has about two dozen dwarf-spheroidal (dSph) satellite galaxies. These are similar but fainter than dE galaxies that are found mostly in galaxy clusters. While the spatial arrangement of the dSph satellites about the Milky Way is not reconciable with the LCDM model (see above), they do appear, to a standard-cosmological (i.e. Newtonian) observer, to be heavily dominated by dark matter.  The normal matter (the stars – these little satellites contain virtually no gas) makes only 1/10th to 1/1000th of the total (CDM+stars) mass of the objects. This comes about if the motions of the stars are interpreted by assuming Newtonian dynamics to be valid.

If MOND were the correct dynamical framework, would a consistent description of the dSh satellites be possible? Consistent means here that their internal properties (see above) and their spatial arrangement would need to make sense.

In the LCDM framework a consistent description fails because their spatial arrangement and their internal properties are not explainable consistently (see Question CI). In LCDM, their spatial arrangement and motion about the Milky Way imply them to be ancient TDGs, but then they cannot have dark matter. If they are taken to be the dark-matter dominated sub-structures expected to be present in the standard model, then their spatial arrangement about the Milky Way cannot be explained, and their internal properties also not.

A number of researchers have studied the Milky Way satellite galaxies in MOND and MOG:

Angus (2008, MNRAS) (“Dwarf spheroidals in MOND“) demonstrates that most of the dSph satellites he studied have normal stellar populations without needing any dark matter, if the satellite masses are computed using MOND.

Hernandez et al (2010, A&A) (“Understanding local Dwarf Spheroidals and their scaling relations under MOdified Newtonian Dynamics“) noticed an interesting correlation between the mass-to-light (M/L) ratios of local dSphs (under MOND or DM), and the ages of their younger stellar populations, in the sense that M/L ratios are clearly smaller for the dwarfs with the younger stars. This is of course naturall in any non-DM scenario, but a contrived coincidence under DM. 

Mendoza et al. (2010, MNRAS) (“A natural approach to extended Newtonian gravity: tests and predictions across astrophysical scales“) investigate mass-velocity scalings of all self-gravitating systems in non-Newtonian frameworks, finding a generally excellent and natural (without needing ad-hoc assumptions) understanding of the observed scaling relations.

McGaugh & Wolf (2010, ApJ) (“Local Group Dwarf Spheroidals: Correlated Deviations from the Baryonic Tully-Fisher Relation“) perform an impressive and comprehensive study of the dSph satellites. They discover remarkable regularities in the data, but only within the MOND famework. LCDM leads to no understanding of these systems: one sees noise and no physics. In MOND however, beautiful correlations emerge which nicely show what intuition would expect in any case, namely the susceptibility of the purely stellar satellite dwarf galaxies to tidal disruption in dependence of their (purely stellar) mass and orbital properties.

9) For example: Galaxy clusters, the CMB and hot dark matter

As argued by Prof. Robert Sanders (2007, MNRAS), for galaxy clusters there is a mild missing mass problem in MOND, but only at the level of a factor of 2-3. This may easily be accounted for by additional baryons (as suggested by Milgrom 2011;  see also Section “Does MOND still need dark matter?” below). Hot dark matter in the form of 11eV sterile neutrinos would also be a viable and a consistent solution, as computed by Angus, Famaey & Diaferio (2010, MNRAS). The WMAP power spectrum is then also explained very accurately with the same 11eV hot dark matter with a similar cosmological expansion history as LCDM but outperforms LCDM on galaxy scales (Angus 2009, MNRAS)!

Sterile neutrinos are a plausible extension of the standard model of particle physics which could help solving many observed anomalies (see e.g. p. 187 of Strumia & Vissani), and which, as stated in Giunti & Li (2009), “may be heralds of alternative cosmological models”… However, they suffer from one of the important problems of CDM: there is no experimental evidence for them.

Fig. 1 from Angus (2009): “This shows the data of the CMB as measured by the WMAP satellite year five data release (filled circles, Dunkley et al. 2008) and the ACBAR 2008 (Reichardt et al. 2008) data release (triangles). The lines are the LCDM max likelihood (dashed) and the solid line is the fit with an 11eV sterile neutrino” (hot dark matter). Here you can find and share the MOND WORKS poster.

10) For example: distant star clusters

As stated above, one of the hardest tests devised for MOND has been developed by SPODYR (Baumgardt, Grebel & Kroupa 2005) “Using distant globular clustersasa test for gravitational theories“. The test is difficult because high-resolution spectroscopic data are needed for many stars in many very distant (further from the Milky Way than 20kpc) faint star clusters – it is the stuff for the largest telescope on Earth.

MOND is the dynamical model for galaxies. Star clusters probe a different mass and length scale, and because MOND only has an acceleration scale it must be valid on star-cluster scales as well.

The idea here is to seek and observe such star clusters that have an internal (i.e. given by its own stars) and an external (given by the MilkyWay) gravitational acceleration which is below the MOND limit. By observing the motions of stars in such star clusters one can find out if they follow Newton’s laws or MOND.  The motions of the stars need to be analysed statistically from spectroscopic (blue- or red-shift) observations because we can only get current snap-shots, given that the star orbits through a cluster in about Myr.

A list of star clusters suitable for this test has been identified in the above Baumgardt et al. research paper. Subsequently, expensive telescope time has been won and star cluster Pal 14 (distance from Milky Way: 69kpc) was observed (Jordi et al. 2009). The observations suggest MOND may be excluded on star-cluster scales.

But, this exclusion would only be the case if the cluster is on a circular orbit about the Milky Way. And, subsequent work has shown that the exclusion is not statistically significant (Gentile et al. 2010). This is verified with numerical MOND simulations by Haghi, Baumgardt & Kroupa (2011). The line-of-sight velocities of many more stars are required to allow a statistically significant test of MOND.

Similarly, Baumgardt et al. (2009) measure and Sollima & Nipoti (2010) compute the motions of stars in distant star clusters in MOND and find “A comparison with recent spectroscopic data obtained for NGC2419 suggests that the kinematics of this cluster might be hard to explain in MOND.”

Therefore, currently the evidence is against MOND on the scales of star clusters. However, this evidence is not yet conclusive because MOND is non-linear leading to effects which are not intuitive. As PK suggested some years ago (see Haghi et al. 2011) a cluster on a radial orbit about the Milky Way may transcend from the Newtonian regime to the MONDian regime faster than the stellar motions within the cluster can adap. The cluster may look Newtonian even though it is in the MOND acceleration regime. Whether this is a viable scenario for the Milky Way star clusters observed to date needs to be shown through explicit dynamical modelling.

As another test of gravitation, Scarpa & Falomo (2010, and references therein) analyse the motions of cluster stars near the massive globular cluster omega Centauri:

We conclude that there are strong similarities between globular clusters and elliptical galaxies, for in both classes of objects the velocity dispersion tends to remain constant at large radii. In the case of galaxies, this is ascribed to the existence of a massive halo of dark matter, which is physically unlikely in the case of globular clusters. This similarity, if confirmed, is best explained by a breakdown of Newtonian dynamics below a critical acceleration.

Another alternative: Modified Gravity (MOG)

Of the various other developments mentioned near the top, MOG has been most widely applied to galactic problems. Prof. Dr. John W. Moffat at the Perimeter Insitute for Theoretical Physics, Waterloo, Canada, began thinking about an alternative gravity model (MOG) because he was curious about how robust the standard CDM paradigm was regarding the fitting of data (Moffat 2011, private communication). He modifed GR by incorporating additional fields which effectively lead to a scale-dependend strength of gravity which assumes a Yukawa-type behaviour in the week-field limit.  With the current version of MOG, galaxy rotation curves and galaxy clusters as well as a cosmological model can be explained without the need for any dark matter, although the three running parameters need to be fixed through observational data at each relevant scale (globular clusters, disk galaxies, galaxy clusters, cosmology).

Some of the recent research papers on MOG:

Moffat (2011): “Modified Gravity or Dark Matter?”

Toth (2010): “Cosmological consequences of Modified Gravity (MOG)”

Moffat & Toth (2009): “Fundamental parameter-free solutions in modified gravity”. Quoting their abstract:

Modified gravity (MOG) has been used successfully to explain the rotation curves of galaxies, the motion of galaxy clusters, the bullet cluster and cosmological observations without the use of dark matter or Einstein’s cosmological constant. We now have the ability to demonstrate how these solutions can be obtained directly from the action principle, without resorting to the use of fitted parameters or empirical formulae. We obtain numerical solutions to the theory’s field equations that are exact in the sense that no terms are omitted, in two important cases: the spherically symmetric, static vacuum solution and the cosmological case of a homogeneous, isotropic universe. We compare these results to selected astrophysical and cosmological observations.

Moffat & Toth (2008) point out that distant star clusters are predicted to be Newtonian if MOG were correct. If it turns out that the star-cluster test of MOND described above fails (i.e. if we discover that the star clusters are systematically Newtonian having a small velocity dispersion), then we would have the situation that MOG, which captures MOND behaviour on galaxy scales, would have been verified over MOND or that MOND woud need a length-or mass-scale-dependent acceleration scale (returning to LCDM is out of the question – see Question C.I). The abstract of Moffat & Toth (2008):

Globular clusters (GCs) in the Milky Way have characteristic velocity dispersions that are consistent with the predictions of Newtonian gravity, and may be at odds with Modified Newtonian Dynamics (MOND). We discuss a modified gravity (MOG) theory that successfully predicts galaxy rotation curves, galaxy cluster masses and velocity dispersions, lensing, and cosmological observations, yet produces predictions consistent with Newtonian theory for smaller systems, such as GCs. MOG produces velocity dispersion predictions for GCs that are independent of the distance from the Galactic center, which may not be the case for MOND. New observations of distant GCs may produce strong criteria that can be used to distinguish between competing gravitational theories.

What is the meaning of Milgrom’s a0?

Before proceeding we need to note from observations that in all stellar systems, whenever the force from gravity falls below a critical acceleration a0, we see that the stars or gas move differently than they should. This is very nicely demonstrated by Prof. Stacy McGaugh’s recent research paper, as well as by many other research papers already published.

It is as if a resistance to the motion disappears. And this behaviour is perfectly calculated by the MOND formula which Milgrom discovered in about 1983. This change in motion happens at such a weak gravity that we cannot reach it in our Solar System, not even in the vicinity of the Sun, where our Galaxy is exerting too strong a pull.

The usuall interpretation of this deviation from Newtonian motions is through the appearance of cold dark matter (CDM). This CDM would have to behave differently in different galaxies to account for the observations, which the theory of CDM does not allow though. Unless of course additional “dark forces” are introduced.

In this sense CDM is similar to phlogiston, which had been postulated  to be a substance related to burning phenomena. But in order to account for different phenoma phlogiston had to have incompatible properties and it was discarded as a viable physical entity even before the advent of modern chemistry and quantum mechanics.

Returning to MOND, what does this critical very weak force (or technically critical acceleration, a0) mean? It is quite clear that this new constant a0 (call it Milgrom’s constant) is truly new physics at a fundamental level which is not understood yeat but which is at the very heart of the issue of the origin of mass (Higgs boson), space and time. Theoretical physicists have, so far, not arrived at a good description or theory of these problems.

Here is a citation from Wikipedia’s MOND entry: where we read:

To explain the meaning of this constant, Milgrom said : “… It is roughly the acceleration that will take an object from rest to the speed of light in the lifetime of the universe. It is also of the order of the recently discovered acceleration of the universe.”

Milgrom’s constant thus appears to be related to thel arge-scale propeties of the universe.

Another way of looking at a possible deeper physical meaning of MOND is at the very centre of modern physics:

What is inertial mass? What is gravitational mass? And, why should they be equal?

Inertial mass: If you push any object in free space you will feel a resistance. The heavier the object is, the more resistance you will feel. Thus, there is inertia to a change of motion.

Gravitating mass: The same object also curves space-time around it, i.e. it exerts a gravitational pull on other objects.

One of the major postulates of modern physics is to insist that inertial and graviating mass are equal, that they are equivalent:

inertial mass = gravitating mas

(this is known as the Equivalence Principle and is at the heart of General Relativity).

One way of looking at MOND is as follows:

When the gravitational field becomes extremely weak, inertial mass and gravitational mass may not be equal any longer and the above equivalence may be broken. If this were to be the case, then this would revolutionise physics at a most fundamental level.

How can this come about and how does MOND enter? Again, Milgrom has a suggestion which is summarized in the appendix of this paper by Kroupa et al.:

Take an apple in completely empty flat space and push it. As it it accelerates it begins to “see” the vacuum in front of it getting hotter (the energy fluctuations in front of it get blue shifted). The resulting radiation pressure exerts a force against the ball (Unruh radiation) and may be related to what we feel as the inertial mass.

The same apple, if it is in curved space time and pushed it will additionally “see” a radiation field which comes from the cosmological horizon (the Gibbons & Hawking radiation). This radiation is essentially the same radiation you would observe coming from a black hole as the energy vacuum fluctuations at its event horizon get split into a part that ends up in the hole and a part that is left in our universe. That is, we can think of our universe as being the inside of a black hole.

When the push on the ball is extremely weak the Unruh and the Gibbons & Hawking radiation may cancel, such that pushing the apple gets easier. The resitance weakens.  The apple can then move faster more rapidly, and this is exactly what we see in those regions of all stellar systems where the gravitational pull is very weak.

That is, MOND emerges from the quantum mechanics of the vacuum plus the whole universe. Milgrom was able to derive the MOND transition function from this concept. This is why MOND is so amasingly exciting. But, the above is merely a proposition, and it is not clear at this stage whether Unruh radiation exists.

Milgrom’s discovery of a0 is likely as epochal as Planck’s discovery of h.  When Planck introduced h as a “Hilfsgroesse” (German for auxilliary number) he had no idea what it meant. It’s relation to energy quantisation was discovered much later. Likewise, the meaning of a0 is not completely clear yet.

It is evident though that by following the path indicated by MOND we are likely to come closer to a quantum formulation of gravity thereby quite certainly completely revolutionizing our understanding of gravity because the equivalence between inertial and gravitating mass is at the very heart of the whole formulation of General Relativity:

It is not at all certain that the formulation of gravity as being the consequence of the curvature of space-time would even hold anymore if this interpretation of MOND is the right one, even though this description of gravity by Einstein would have proven to be an amazingly powerful approximation in the regime of strong gravity, on Earth, in the Solar System (otherwise GPS wouldn’t work), for binary pulsars, etc.

Does MOND still need dark matter?

. . . and does that mean that dark matter exists whatever happens?

Well, yes, “dark matter” certainly exists!  But it depends on what you call dark matter:

It is well known that there are missing baryons. In fact, after the Big Bang about 60% of all normal matter “disappeared”.  Astronomers do not know where this matter is. It might be hiding as dark clumps of cold gas (Pfenniger, Combes & Martinet 1994), and it would then have the dynamical properties of cold dark matter. Also, there are burned-out stars, neutron stars and black holes, which can, for example, dominate the dynamics of the central region of old star clusters.

So we know that we do not see all of the normal matter (yet),  and one may call it dark matter if one likes to do so.

It is very possible that MOND only needs this kind of  “dark matter”! (but see point 9 above: “For example: Galaxy clusters  and  hot dark matter”).

While it is true that some relativistic extensions of MOND need other forms of it (e.g. hot dark matter or dipolar dark matter), none needs CDM! 

That is, searching for cosmologically-relevant WIMPS would be a waste of time if the real universe is MONDian. 

Axions or axion-like particles, on the other hand, would be relevant only if their mass is varying and as such they break the weak and strong equivalence principles. They thus induce modified gravity effects, thereby perhaps opening a path to explain MOND (Fuzfa & Alimi 2010). But plain CDM axions would be as useless as WIMPS.

Concluding Remarks:

The many attempts to bring LCDM into agreement with reality on scales of about 10Mpc and less have failed (see Question CI). MOND, as discovered by Milgrom in 1983, is the currently best theory for classical, i.e. non-relativistic, dynamics. Without fine-tuning it describes what we observe to a most excellent degree of accuracy.  It accounts for observed astronomical data ranging from dwarf galaxies to massive galaxy clusters and is in excellent agreement with the Cosmic Microwave Background. It reduces significantly the need for dark matter on large scales, and needs no introduction of cold dark matter on small scales. The tremendous success of MOND to account for observed reality compared to the failures of LCDM is nicely summarised by Stacy McGaugh in this table.

The hard reality which many researchers and politicians will have to face is that the success of MOND implies that the expensive searches for cosmologically relevant cold dark matter particles (WIMPS, axions) are futile. There is no reasonable astronomical evidence for cosmologically relevant cold dark matter particles.

The possible addition of some hot dark matter to account for lensing and the CMB makes a fully consistent picture, also with the standard model of particle physics, and is not a problem for MOND. But, since about 60% of all baryons has gone missing since the Big Bang, it is natural that some dark baryonic matter must play a role in galaxy clusters.

Finally, the work on these and other alternatives has demonstrated above all else that the LCDM model is not unique.