A Dark Matter Real: Studies Confirm, Modifying Gravity Can't Work

[mathman]

Two recent studies have found galaxies with little or no apparent dark matter, indicating modifying gravity can't work.
https://iopscience.iop.org/article/10.3847/2041-8213/ab0e8chttps://iopscience.iop.org/article/10.3847/2041-8213/ab0d92/meta

 

[PeterDonis]

Two recent studies have found galaxies with little or no apparent dark matter, indicating modifying gravity can't work.

Just to be clear, what these galaxies have is a velocity dispersion that is what is expected from the visible matter alone using the standard theory of gravity, correct?

On the dark matter hypothesis, this is possible since it just means these galaxies have negligible amounts of dark matter. In other words, the dark matter model has a free parameter that can be used to predict the velocity dispersion of these galaxies as well as the velocity dispersion of all the other galaxies. Which still leaves an open question of why these galaxies have no dark matter--what makes these galaxies different from all the ones that have large dark matter halos?

But on the modified gravity hypothesis, these galaxies should not exist; every galaxy should have the modified velocity dispersion (the one that, in the dark matter model, is due to the dark matter halo) because in the modified gravity theory this dispersion is a consequence of the visible matter alone, plus the modified gravity equations, so there is no free parameter that can be adjusted. Proponents of modified gravity have given this as an advantage of the theory--fewer free parameters means a simpler theory--but this advantage becomes a fatal liability if new data falls outside the theory's predictions. As Einstein said, every theory should be as simple as possible, but not simpler.

 

[hyksos]

MOND (or "Modified Newtonian Dynamics") is a theory that suggests the canonical equations of gravity do not apply to the dynamics of stars orbiting galaxies , whenever accelerations become vanishingly small. The theory's motivation was to explain anomalous rotational velocities of stars in the outer arms of galaxies. The visible matter in the galaxies' cannot account for the high velocities, and perhaps this is due to the presence of a halo of Dark Matter centered around the galaxies' centers. Or alternatively, if MOND is correct, those velocities simply follow from fundamental physics, and no extraneous Dark Matter is needed.

The danger with modifications to fundamental physical law is that a single counter-example can falsify them. A darkless galaxy was first discovered by the Hubble Telescope and the 10-meter Keck in March of 2018. It was ignored as a statistical fluke. Then another darkless galaxy was found again in March 2019 : Galaxy NGC1052-DF4.

Both DF4 and its precursor are ultra-diffuse, and so contain 1000s of times less stars than the average galaxy. This is worse for MOND, since the accelerations would be even smaller than usual, and the discrepancies predicted by the theory would be relatively larger. This was not observed. Instead both darkless galaxies have rotational velocity curves consistent with canonical gravity. It is as if they simply lack the special Dark Matter that causes the anomalies in most galaxies.

Can MOND survive as a theory given these recent discoveries?

 

[zonde]

Proponents of modified gravity have given this as an advantage of the theory--fewer free parameters means a simpler theory--but this advantage becomes a fatal liability if new data falls outside the theory's predictions.

If observations falsify the theory it means it is indeed a good theory, just not the one that describes reality.

 

[Nik_2213]

Been skimming a conference proceedings on Local Bubble & Co.
One item made the point that supernova bubbles in a low mass galaxy etc can eject stuff faster than the local escape velocity, send it clean out into intergalactic space.
Okay, it may stay in the 'local group', but the shock-driven material and all it sweeps up is traveling too fast to fall back when it cools, as it would in eg Milky Way or Andromeda.

Could such ejecta carry 'Dark Matter' along ??

 

[Vanadium 50]

This is the same galaxy as last time. The degree of DM depends on its distance from us, and there is considerable disagreement on that.

Personally, I am always skeptical of "the single badly measured point that falsifies my opponent's theory thereby proving me right all along".

 

[Bandersnatch]

This is the same galaxy as last time.

There's two now. The second link in the OP is about the new one.

 

[member 656954]

Could such ejecta carry 'Dark Matter' along ??

Possibly. We presume that DM only interacts via gravity (and a further general assumption is "at large scales"), so there would be an interaction with the ejecta, but whether that is sufficient to drag the DM with it - or the counterpoint that the DM inhibits the spread of the ejecta - would have to be an open question given that we still don't understand DM at anything but the "there seems to be something out there" level.

And perhaps the DM's escape velocity is different than the ejecta, so whether it falls back or keeps traveling may be different to baryonic matter.

Honestly, despite the experiments and measurements that suggest a Lambda-CDM model, it's all conjecture at the moment, we really don't know.

 

[Vanadium 50]

There's two now. The second link in the OP is about the new one.

But the new one is in the same association as the old one. I think everyone agrees DF2 and DF4 are at the same distance. I don't think there is agreement on what that distance is.

 

[Ken G]

The question may still be open, but it's not good news for MOND. It is certainly quite ironic-- the systems that end up proving the existence of dark matter may be the ones that don't have it! More importantly, understanding why they don't have it might give us the crucial clues we need as to what it is and how it behaves. I agree with the above point that it is only a win for dark matter if that hypothesis is able to explain the situations where it is not present, since it was invented to explain the situations where it is, and thus the latter cannot be used as a confirmation of the theory, but the former can be if there is some sensible reason for it.

 

[Orodruin]

More importantly, understanding why they don't have it might give us the crucial clues we need as to what it is and how it behaves.

I am not an expert in structure formation, but it seems to me that explaining the existence of ultra-diffuse galaxies without dark matter could be possible in several ways. Since it would be speculation (against forum rules) and I don't want to make a fool of myself (bad karma), I will keep those thoughts to myself.

 

[Vanadium 50]

I'll just say that stripping the dark matter from a galaxy without disrupting it is not a simple thing to do. It's not impossible, but it adds to the list of oddball features to these galaxies. It would be unusual for our first example, and more unusual still for the first two examples.

Many of the odd features go away if the galaxies in question are closer to us. In particular, the unusually bright globulars (which in fact are the mass tracers used in determining M/L) look much more typical if they are closer.

Everyone agrees DF2 and DF4 are associated (but probably not bound to each other). This means that many of the pecuilar features are shared, so it's not a particulalrly clarifying data point. Another example somewhere else in the sky would be very valuable An inability to find a second example would also be clarifying.

 

[Ken G]

I don't think it would be too speculative to note that we have observed cases of baryonic gas getting separated from dark matter, as in the Bullet cluster. There, two galaxy clusters are colliding, and the dark matter that controls the galaxy gravitational potential wells just goes right through. But the gas between the galaxies, which is most of the baryonic matter in the universe, collides in the center and gets left behind. Then all you'd need is for that dark-matterless gas to form stars in the distant future, and it could form diffuse galaxies without much dark matter. So that would seem to be one potential mechanism that we can see playing out, though I don't know if there is an expectation for what will ultimately happen to that baryonic gas. (And the Bullet cluster is already a kind of "smoking gun" for dark matter, as no MOND models can explain the gravitational lensing pattern in that cluster, but as with the dark matterless galaxies, MOND proponents can claim the cluster is a kind of fluke that is not being correctly analyzed somehow.)

 

[strangerep]

Many of the odd features go away if the galaxies in question are closer to us. In particular, the unusually bright globulars (which in fact are the mass tracers used in determining M/L) look much more typical if they are closer.

Thanks for mentioning this.

But, (pardon my density),... could you explain this in a bit more detail, pls?

 

[BWV]

Do dark matter-less galaxies imply anything about the nature of dark matter or lend more support to one hypothesis vs another? Seems puzzling that DM would be absent in some tiny percentage of galaxies.

 

[Vanadium 50]

Bullet cluster

Yes, but there's all sorts of disruption in the Bullet Cluster.

The people who model such things tell me that the way you strip dark matter from a galaxy without disrupting it is to have multiple small interactions, not one big one. Not impossible, but unusual.

could you explain this in a bit more detail, pls?

DF2 and DF4 are examples of low-surface-brightness galaxies. LSB galaxies are dim, gas-rich, and tend to be found disproportionately away from other galaxies. They live quiet lives, because without gravitational interactions with nearby galaxies, star formation is not triggered, so they stay gassy. Wikipedia claims they don't have supernovae, and this isn't entirely true: SN 2009z appears to be from an LSB galaxy. But the rate is way, way down.

So this history of DF2 needs to be unusual to have had interactions just so - you need enough perturbation to get the dark matter out, but not enough to trigger star formation. You can make the same argument for DF4, and I would agree that it too has to be unusual, but since it's in the same general area, it probably is not any more unusual.

OK, now what is the actual measurement? The claim of "no dark matter" is actually a claim the M/L is unusually low. It's much lower than the typical M/L for LSB galaxies, which tends to be above M/L for bright galaxies. (That's what LSB means after all). They measure M by looking at redshifts of nearby globular clusters, presumed to be in orbit around DF2. (Converting angle to distance, redshift to velocity, and distance and velocity to mass). They measure L by seeing how bright it is.

Both depend on the distance to the galaxy - the farther away the galaxy is, the farther away the globular is from the central galaxy (we see only the angular displacement) and the heavier the galaxy they orbit must be. However, it is not this simple, since you need to subtract off the Hubble flow, and this means the farther away the galaxy is, the slower the relative motion of the globulars, and therefore the lighter the galaxy they orbit must be. These partially cancel and you end up with a complicated but well-understood relation between the velocity of the globulars, the distance to DF2 and its mass. In the range of distances we are talking about, I believe the closer DF2 is to us, the heavier it is.

As an additional complication, there are only ten tracers - ten globulars thought to be associated with DF2. Everybody would like more, as ten is less constraining than "more than ten". But it is what it is.

Luminosity, of course, depends on the inverse square of distance.

OK, onto specifics. "DF2 has no DM" is, as I said, a statement that M/L is too low, which can be interpreted as either M is too low (no DM), or L is too high - i.e. DF2 is too bright. The associated globulars are also unusually bright. If the distance to DF2 were ~13 Mpc instead of ~19 Mpc away, the globulars would be of normal brightness, and M/L for DF2 would be a value more typical for LSB galaxies.

There is controversy in the literature about whether 19-ish or 13-ish is the right value.

I'll reiterate my position: DF2 has some oddball features that make it less than the smoking gun that some have claimed. DF4 is associated with DF2 so it ends up with the same oddball features. Before accepting any explanation for these features, I'd like to see an example in some other part of the sky.

 

[Ken G]

I don't really see how these observations can be made sense of either with MOND, or with dark matter. If we say MOND is right, and there is not dark matter, then these galaxies have low M/L due to their weird star formation history that somehow increases L efficiency relative to the Milky Way. But then we have the problem that these galaxies are low surface brightness and should have weak star formation, so they should have high M/L not low M/L.

But if we say dark matter exists, and these galaxies have low M/L due to the loss of dark matter, then we might be pleased to see the M/L corresponds to the baryonic Milky Way M/L, without dark matter. But that doesn't make sense either, because you still have an unusual type of galaxy that shouldn't have a normal baryonic M/L ratio, regardless of its dark matter history. Hence the bottom line is, it doesn't matter if you think there's MOND, or if you think there's dark matter, either way you still have a diffuse LSB galaxy that has no business having a normal baryonic-only Milky-Way-like M/L. MOND vs. dark matter is actually irrelevant to the real puzzle here, which is why don't diffuse LSB galaxies always have high M/L?

You could certainly say the ones that aren't high have had their dark matter stripped, but you still can't get them down to baryonic Milky-Way M/L, which is where these apparently are. It would be like claiming that whatever causes these galaxies to be diffuse and LSB has no effect on their baryonic M/L, which seems hard to swallow. That means something is rotten in Denmark.

 

[PeterDonis]

The claim of "no dark matter" is actually a claim the M/L is unusually low.

I'm not sure this is the best way to say it. The claim of dark matter is based on more mass being present, as seen in rotation curves, than the visible matter can account for using standard gravitational theory. The claim of no dark matter in these particular galaxies simply means that is not the case: the rotation curves can be accounted for using just the visible matter with standard gravitational theory. So M/L isn't "unusually low" except in comparison to all the other galaxies that are hypothesized to have dark matter; but that really means that all those other galaxies have M/L unusually high--too high to be accounted for by the visible matter alone. These galaxies, by contrast, have M/L "just right"--just right to be accounted for by the visible matter.

Of course it's true that all of this depends on the estimate of L being right for these galaxies, which, as you note, is still open to question.

 

[PeterDonis]

If we say MOND is right, and there is not dark matter, then these galaxies have low M/L due to their weird star formation history that somehow increases L efficiency relative to the Milky Way.

What does this mean? I don't know of any free parameter in MOND that corresponds to "star formation history that somehow increases L efficiency relative to the Milky Way".

you still have an unusual type of galaxy that shouldn't have a normal baryonic M/L ratio

Why not?

 

[Ken G]

What does this mean? I don't know of any free parameter in MOND that corresponds to "star formation history that somehow increases L efficiency relative to the Milky Way".

It's not an element of the MOND theory, it is a logical ramification of applying MOND to the Milky Way galaxy and the low M/L galaxies at the same time. If all is baryon, then the lower M/L for those special galaxies must mean they are efficient (per baryon) at making L relative to the Milky Way. That is precisely the opposite of what we would expect for diffuse LSB galaxies which should have weak star formation, so does not seem a likely explanation of the situation.

Why not?

Same reason-- it's an LSB galaxy, so should not have the same L efficiency per baryon as the Milky Way. The point being, raising the Milky Way M/L with lots of dark matter doesn't explain why an LSB galaxy would have the same M/L as would the Milky Way if you restrict to baryon M. If one holds to the dark matter explanation, then the Milky Way has a deeper gravity well which should create a more rapid star formation rate and lower the M/L compared to a galaxy with no dark matter.

 

[PeterDonis]

If all is baryon, then the lower M/L for those special galaxies must mean they are efficient (per baryon) at making L relative to the Milky Way.

So again, what free parameter would you vary to change the "efficiency" at making L? You can't just wave your hands and say it can change; what free parameter allows it to change?

it's an LSB galaxy, so should not have the same L efficiency per baryon as the Milky Way

Same question as above.

 

[Ken G]

The star formation rate per baryon is the light-creating efficiency per baryon. That's the parameter in question. So the issue is, what is it about a galaxy that affects the star-forming efficiency? There are a lot of things, but one would certainly expect dark matter to deepen the gravity well and increase that efficiency, which can also be thought of as the timescale for baryons in the ISM of the galaxy to get included into stars. Wouldn't that timescale be expected to be longer in a diffuse LSB galaxy with no dark matter, than in a galaxy with dense spiral arms?

 

[PeterDonis]

The star formation rate per baryon is the light-creating efficiency per baryon.

Ok, so the free parameter is basically the fraction of baryonic matter that is in stars (as opposed to gas clouds, dust clouds, etc.). But while that would be expected to affect the overall visible brightness of the galaxy, it would not necessarily affect the rotation curve (since the non-visible baryonic matter would be expected to be distributed similarly to the visible baryonic matter). And it's the rotation curve, not the overall brightness, that is well matched to the visible matter in these new galaxies, whereas it does not match the visible matter well in galaxies which are believed to have large dark matter halos. And dark matter can explain that difference because it does not have the same interactions as baryonic matter, so its distribution can be very different. Whereas MOND says that all galaxies should have rotation curves that do not match the visible matter if you use standard gravity theory, because the whole point is that it's a different gravity theory, that changes the predicted rotation curve from the visible matter.

 

[Ken G]

Yes that's an interesting point, that we also have information from the rotation curve. I'm just saying that if we take dark matter to be the explanation, at first it seems satisfying that the M/L in these galaxies is similar to the baryonic M/L for the Milky Way. But on further thought, that actually sounds like a problem, since I would expect galaxies like this to be less efficient at forming stars (they are more diffuse and we are saying they don't have the deep dark matter well). If that's true, then we'd actually expect a higher M/L than for the baryons in the Milky Way, not the same M/L. It's just curious.

 

[ohwilleke]

Two recent studies have found galaxies with little or no apparent dark matter, indicating modifying gravity can't work.
https://iopscience.iop.org/article/10.3847/2041-8213/ab0e8chttps://iopscience.iop.org/article/10.3847/2041-8213/ab0d92/meta

Actually not.

In fact, systems like DF2 and DF4 are natural and predicted results of MOND as originally formulated in 1983 via its external field effect which essentially means that MOND effects do not arise when the system in buried in an external gravitational field stronger than the MOND cutoff strength when combined with the local gravitational field strength. DM in contrast, needs DM to form galaxies so these systems shouldn't exist in that theory.

This post (by one of the leading MOND researchers) suggests that the correctly calculated MOND prediction is 14+/- 4 and that the measured value is 8.4 with a 90% confidence interval upper limit of 10. So, it does not disprove MOND, the paper's calculation simply failed to consider the external field effect (a part of the original MOND theory since 1983 that is not widely known). A paper by MOND's inventor further spells out this scenario and others where the external field effect is absent or only partial, for example, in this published paper from the year 2000. The limited data points used in the calculation (ten) also suggests that the measured value is likely to be an underestimate as it was in FORNAX. From the comments to the previous link by its author:

On closer reading, I notice in the details of their methods section that the rms velocity dispersion is 14.3 km/s. It is only after the exclusion of one outlier that the velocity dispersion becomes unusually low. As a statistical exercise rejecting outliers is often OK, but with only 10 objects to start it is worrisome to throw any away. And the outlier is then unbound, making one wonder why it is there at all.

Consider: if they had simply reported the rms velocity dispersion, and done the MOND calculation correctly, they would have found excellent agreement. This certainly could be portrayed as a great success for MOND. Instead, tossing out just one globular cluster makes it look like a falsification. Just one datum, and a choice of how to do the statistics. Not a wrong choice necessarily, but a human choice… not some kind of statistical requirement.

One of the authors of the original DF2 papers addresses a variety of concerns (of the kind that quite honestly should have been addressed at a pre-print/peer review stage rather than post-publication) (hat tip Backreaction).

In particular, he justifies at great length his velocity dispersion calculation, although the paper really fails seriously in failing to address just how problematic and assumption prone it really is and the reasoning behind the choices made. The uncertainty due to fundamental assumption issues is greatly understated.

He acknowledges that he screwed up the MOND calculation and shifts attention from that mistake to a different dwarf galaxy (Dragonfly 44) where MOND might be off without conclusively showing that this is the case. The original DF2 article author states:

The whole MOND / alternative gravity discussion in the paper rests on a misunderstanding on my part.

He acknowledges the need for more and better data to get a more accurate measurement, some of which can be done quite easily (and really should have been done prior to publication in Nature).

He unconvincingly argues that "lacking" and "without" have different meanings while backpedaling on the "no" dark matter claim, although this criticism isn't honestly such a big deal since other language in the abstract does clarify the point (and indeed highlights that the dark matter a priori prediction was off by a factor of 100 v. a factor of about 0.4 at most for the correctly done MOND prediction).

These immediate responses to the claims of MOND falsification were elaborated in a more formal format in a 2018 pre-print which has been submitted to MNRAS for publication.

Crater II Compared

The same external field effect had already been predicted and observed in a galaxy known as Crater II.

Crater II is an unusual object among the dwarf satellite galaxies of the Local Group in that it has a very large size for its small luminosity. This provides a strong test of MOND, as Crater II should be in the deep MOND regime (gin≈34km2s−2kpc−1≪a0=3700km2s−2kpc−1). Despite its great distance (≈120 kpc) from the Milky Way, the external field of the host (gex≈282km2s−2kpc−1) comfortably exceeds the internal field. Consequently, Crater II should be subject to the external field effect, a feature unique to MOND. This leads to the prediction of a very low velocity dispersion: σefe=2.1+0.9−0.6kms−1.

Stacy S. McGaugh, "MOND Prediction for the Velocity Dispersion of the `Feeble Giant' Crater II" (November 3, 2016).

This is a big deal because under a wide range of dark matter hypotheses, the velocity dispersion could have been no lower than 5 km/s and was expected to be more like 11 km/s to 24 km/s.

The actual velocity dispersion of Crater II was measured with the latest and greatest telescopes in a result first announced six and a half weeks after this prediction was made on December 19, 2016. What did they find?

A velocity dispersion of 2.4 km/s to 3.0 km/s.

 

[ohwilleke]

(And the Bullet cluster is already a kind of "smoking gun" for dark matter, as no MOND models can explain the gravitational lensing pattern in that cluster, but as with the dark matterless galaxies, MOND proponents can claim the cluster is a kind of fluke that is not being correctly analyzed somehow.)

Actually, not so much.

MOND has never explained all dark matter in clusters at all, but it does address the fact that CDM is even more inconsistent with the bullet cluster in terms of collisional velocity expectation and at least five of its close cousins can explain the Bullet cluster. Three of those theories, conformal gravity, Deur's Quantum Gravity, and f(R) gravity, each make only very conservative deviations from general relativity on very subtle points that don't arise in most conventional tests of general relativity in strong gravitational fields in simple physical systems.

At a minimum, the success of four different modified gravity theories in explaining the Bullet cluster disproves by example the claim that the Bullet cluster negates the possibility that some form of modified gravity theory, rather than a dark matter particle theory, is correct.

We consider the orbit of the bullet cluster 1E 0657-56 in both CDM and MOND using accurate mass models appropriate to each case in order to ascertain the maximum plausible collision velocity. Impact velocities consistent with the shock velocity (~ 4700km/s) occur naturally in MOND. CDM can generate collision velocities of at most ~ 3800km/s, and is only consistent with the data provided that the shock velocity has been substantially enhanced by hydrodynamical effects.

Garry W. Angus and Stacy S. McGaugh, "The collision velocity of the bullet cluster in conventional and modified dynamics" (September 2, 2007) and also published at MNRAS.

Extended MOND

MOND itself underestimates dark matter phenomena in clusters, in general (it is merely a toy model). But, a 2017 paper accepted for publication discusses two generalizations the phenomenological toy model modified gravity theory that is MOND to explain dark matter in clusters, one called EMOND from 2012 that is less accurate and a second of their own devising that is more accurate but has some theoretical issues. This solution is admittedly less than perfect, however:

EMOND has some success in fitting some clusters, but overall has issues when trying to explain the mass deficit fully. We also investigate an empirical relation to solve the cluster problem, which is found by analysing the cluster data and is based on the MOND paradigm. We discuss the limitations in the text.

Conformal gravity

A published 2017 paper demonstrates that clusters can be correctly modified in a modified gravity theory known as conformal gravity: James G. O’Brien et al., "Recent advancements in conformal gravity" J. Phys.: Conf. Ser. 845 012004 (2017).

At its simplest level, conformal gravity is a theory based on fourth derivatives of the relevant function, while general relativity is based upon the second derivatives of that function. See Philip D. Mannheim, "Is dark matter fact or fantasy? -- clues from the data" (March 27, 2019).

Why use the higher order derivatives that general relativity manages without?

Among other things, this makes the theory renormalizable, unitary and ghost free at the quantum gravity level, and in addition to explaining dark matter, its equations also have emergent properties that have effects very similar to the cosmological constant without fine tuning.

Deur's Quantum Gravity

Another paper shows that this can be achieved by considering graviton-graviton interactions in a scalar graviton static case approximation of a quantum gravity theory. A. Deur, “Implications of Graviton-Graviton Interaction to Dark Matter” (May 6, 2009) (published at 676 Phys. Lett. B 21 (2009).

The quantum gravity expansion in this theory is done via an infinite series expansion that, in principal, can be carried out to arbitrarily many terms, but in practice, is only worked out to a couple of additional terms beyond the ones that explain gravity at a Newtonian level, with the remaining terms (involving higher powers of Newton's constant which is very small relative to one, making higher powers of it very small) neglected on the grounds that they are negligible in magnitude by comparison. The additional terms that are included quantify the effects of graviton-graviton interactions in a quantum gravity theory.

As this paper explains:

Estimating the non-Abelian effects in galaxy clusters with our technique is difficult: 1) the force outside the galaxy is suppressed since the binding of the galaxy components increases (this will be discuss further at the end of the Letter), but 2) the non-Abelian effects on the remaining outside field could balance this if the remaining outside field is strong enough.

Since clusters are made mostly of elliptical galaxies for which the approximate sphericity suppresses the non-Abelian effects inside them, we ignore the first effect. We assume furthermore that the intergalactic gas is distributed homogeneously enough so that non-Abelian effects cancel (i.e. the gas does not influence our computation). Finally, we restrict the calculation to the interaction of two galaxies, assuming that others do not affect them.

With these three assumptions, we can apply our calculations. Taking 1 Mpc as the distance between the two galaxies and M=40×109 M⊙ as the luminous mass of the two galaxies, we obtain b = −0.012 in lattice units. We express this from the dark matter standpoint by forcing gravity to obey a Newtonian form: V (r) = −G M 2 ( 1 r − b a r) ≡ −G M′ 2 1 r (4) with M′/M = 1−r 2 b/a = 251. Gaseous mass in a cluster is typically 7 times larger than the total galaxy mass. Assuming that half of the cluster galaxies are spirals or flat ellipticals for which the non-Abelian effects on the remaining field are neglected, we obtain for the cluster 7 a ratio (M′/M)cluster = 18.0, that is our model of cluster is composed of 94% dark mass, to be compared with the observed 80-95%.

Non-Abelian effects emerge in asymmetric mass distributions. This makes our mechanism naturally compatible with the Bullet cluster observation [15] (presented as a direct proof of dark matter existence since it is difficult to interpret in terms of modified gravity): Large non-Abelian effects should not be present in the center of the cluster collision where the intergalactic gas of the two clusters resides if the gas is homogeneous and does not show large asymmetric distributions. However, the large non-Abelian effects discussed in the preceding paragraph still accompany the galaxy systems.

To paraphrase, because it has a gaseous component that is more or less spherically symmetric, that component has little apparent dark matter, while the galaxy components, which come close to the two point mass flux tube paradigm displays great inferred dark matter. So, the gaseous portion and the core galaxy components are offset from each other. The apparent dark matter tracks the galaxy cores and not the interstellar gas medium between them.

f(R) gravity

f(R) gravity is a scalar-tensor gravity theory that adds a term that is a function is the Ricci scalar, doing in the world of classical gravitational theories something quite similar to Deur's consideration of graviton self-interaction terms in a quantum gravity theory.

A pre-print last modified on December 29, 2018, illustrates that this theory can (or at least may) address the Bullet cluster concerns with modified gravity theories.

MOG

A fifth gravity based solution with a phenomenological and classically formulates scalar-vector-tensor gravitation modification (i.e. a formula that is not a quantum gravity approach) can also do the trick:

The galaxy cluster system Abell 1689 has been well studied and yields good lensing and X-ray gas data. Modified gravity (MOG) is applied to the cluster Abell 1689 and the acceleration data is well fitted without assuming dark matter. Newtonian dynamics and Modified Newtonian dynamics (MOND) are shown not to fit the acceleration data, while a dark matter model based on the Navarro-Frenk-White (NFW) mass profile is shown not to fit the acceleration data below ~ 200 kpc.

J. W. Moffat and M. H. Zhoolideh Haghighi, "Modified gravity (MOG) can fit the acceleration data for the cluster Abell 1689" European Physical Journal Plus (2017) 132, 417 (preprint posted 16 Nov 2016).

The introduction observes that:

MOG has passed successful tests in explaining rotation velocity data of spiral and dwarf galaxies (Moffat & Rahvar (2013)), (Zhoolideh Haghighi & Rahvar (2016)), globular clusters (Moffat & Toth (2008b)) and clusters of galaxies (Moffat & Rahvar (2014)). Recently, it was claimed (Nieuwenhuizen (2016)) that no modified gravity theory can fit the Abell 1689 acceleration data without including dark matter or heavy (sterile) neutrinos. The cluster A1689 is important, for good lensing and gas data are available and we have data from 3kpc to 3Mpc. We will show that MOND (Milgrom (1983)) does not fit the A1689 acceleration data, nor does the dark matter model based on an NFW mass profile. However, MOG does fit the A1689 acceleration data without dark matter.

The conclusion of the paper notes:

The fully covariant and Lorentz invariant MOG theory fits galaxy dynamics data and cluster data. It also fits the merging clusters Bullet Cluster and the Train Wreck Cluster (Abell 520) without dark matter (Brownstein & Moffat (2007); Israel & Moffat (2016)). A MOG application to cosmology without dark matter can explain structure growth and the CMB data (Moffat & Toth (2013)). The fitting of the cluster A1689 data adds an important success for MOG as an alternative gravity theory without dark matter.

 

[Ken G]

Those are all excellent points, and you clearly know a lot more about alternative gravity theories than I do. But in your post I do detect a clear signal of the main problem of MOND approaches: it is like juggling balls. You say one MOND theory has an external field effect, and that explains DF2 and Crater II. But then you don't invoke that MOND to explain other observations, instead you refer to different MOND theories. Then you even say these are all currently toy models in that they tend to undertreat the discrepancies that dark matter addresses. So which is the MOND theory you are talking about? It really doesn't work to say there's a different MOND theory that can explain any individual observation, you need just one.

Now, that said, I don't mean to suggest this means MOND approaches should be dropped. I think everyone is glad there are MOND proponents looking in all the dark corners, and no doubt this will take a long time and lots of data to resolve. You are saying MOND isn't dead, but it isn't exactly alive either-- until there is just one MOND theory that works for everything (like Lambda-CDM claims to do, though I am no kind of judge on how well that claim can be supported).

 

[Vanadium 50]

At the risk of derailing the last half dozen or so posts, I maintain that whatever one's personal position is on alternative gravity theories is, it tells us nothing about whether this particular galaxy has dark matter or not.

 

[Ken G]

There are six posts that have something to do with people's personal positions on alternative gravity?

 

[Jimster41]

The Mannhiem discussion of Conformal Gravity is wild.

Dumb question - has the presence of super-massive rotating black holes at galactic centers (the variance in scale and properties of same, or overall lack of one at all) been ruled out as a possibly relevant effect on the shape of a Galaxy's gravitational well? I mean is the amount of mass expected from the even the most super-massive black hole nowhere near the ballpark?

And I guess going the other way, is the presence of super-massive black holes at galactic centers a puzzle that Dark Matter is invoked to explain - i.e. they are a possible effect of whatever it is that is odd that is going on, and otherwise hard to explain?

In my cartoon I have always sort of included them in the mass halo, rotation and luminosity puzzle - wondering if that's just way off order of magnitude-wise.

 

[Jimster41]

In the Mannheim paper don't the extra r dependent terms (the increasing distance driven effects) just sort of proxy the inclusion of more and more non-local sources. IOW, isn't it possibly an effect of "unusual" connection to regular mass correlated to distance ? In this sense does CG Sort of suggest a Bell compatible quantum G?

 

[PeterDonis]

it tells us nothing about whether this particular galaxy has dark matter or not.

But if there isn't agreement on which theory of gravity to use, there is no way to get a unique answer to this question. So disagreements about which theory of gravity is right do end up being disagreements about whether particular galaxies contain dark matter or not.

 

[PeterDonis]

has the presence of super-massive rotating black holes at galactic centers (the variance in scale and properties of same, or overall lack of one at all) been ruled out as a possibly relevant effect on the shape of a Galaxy's gravitational well?

A black hole's gravity well, unless you are pretty close to the hole, looks just like the gravity well of any other conglomeration of matter with the same total mass. So a black hole at the center of a galaxy won't make its gravity well, except close to the center (which is not where the issue is), look any different than a central core of stars of the same total mass would.

is the presence of super-massive black holes at galactic centers a puzzle that Dark Matter is invoked to explain

Not to my knowledge.

 

[ohwilleke]

Those are all excellent points, and you clearly know a lot more about alternative gravity theories than I do. But in your post I do detect a clear signal of the main problem of MOND approaches: it is like juggling balls. You say one MOND theory has an external field effect, and that explains DF2 and Crater II. But then you don't invoke that MOND to explain other observations, instead you refer to different MOND theories. Then you even say these are all currently toy models in that they tend to undertreat the discrepancies that dark matter addresses. So which is the MOND theory you are talking about? It really doesn't work to say there's a different MOND theory that can explain any individual observation, you need just one.

Now, that said, I don't mean to suggest this means MOND approaches should be dropped. I think everyone is glad there are MOND proponents looking in all the dark corners, and no doubt this will take a long time and lots of data to resolve. You are saying MOND isn't dead, but it isn't exactly alive either-- until there is just one MOND theory that works for everything (like Lambda-CDM claims to do, though I am no kind of judge on how well that claim can be supported).

There are a few issues to sort through.

One issue is whether X or Y piece of evidence (e.g. DF2 or the Bullet cluster) proves that dark matter phenomena is the only possible reality and that a modified gravity explanation isn't possible, attacking the entire modified gravity paradigm. Assertions like that can be disproven by a single example of a modified gravity explanation of the same evidence.

Thus, if MOND can explain DF2, then it is not true that it can't be explained by a modified gravity theory. And, if there are one or more modified gravity theories that can explain the Bullet cluster without dark matter, then the Bullet cluster is not proof, by itself, that dark matter exists.

Usually, claims that X or Y piece of evidence proves that dark matter phenomena is the only possible reality flow from a lack of familiarity with the various possible modified gravity theories.

Now, obviously, the ideal situation would be to have a theory that has been rigorously compared to all available evidence and found to fit the data in all circumstances, perhaps barring a few isolated tensions where observational error is present (we see this even in experiments testing the most definitively established parts of the Standard Model and it is excepted by random chance), or an assumption that holds in almost every case and is central to the solution working does not hold (e.g., many DM and modified gravity predictions assume a system that is in or reasonably close to equilibrium).

If there were a theory like that somebody would have walked away with the Nobel prizes long ago and the answer would be in every college textbook. But, there is no fully worked out explanation (let's call them "specific models") of dark matter phenomena consistent with all of the evidence and carefully tested of that kind, in the dark matter particle paradigm, in the modified gravity paradigm, or in any hybrid paradigm.

MOND is notable because (1) it is old, (2) it is a very simple theory with only a single universal physical constant as a parameter, (3) it works in all weak gravitational fields from Earth/solar system scale to the scale of every kind of galaxy, (4) while it doesn't perfectly fit the cluster data, it explains a portion of the dark matter phenomena seen there (so it could be part of a hybrid theory with cluster specific dark matter), (5) it have made numerous genuine predictions that have proven to be correct, (6) its effects are easily described verbally and understood at an intuitive level, and (7) it has received wide scholarly attention and comparisons to the evidence.

MOND is important because even if it is not an accurate description of reality, any other specific dark matter model or specific modified gravity model must reproduce its predictions of this simple formula with a single universal parameter within MOND's domain of applicability which still spans scales from the solar system to basically all kinds of galaxies (including intermediate scale systems like wide binary stars), which is many, many orders of magnitude in scale, and also spans situations where there is or is not an external field effect.

This is a huge stumbling point for the vast majority of specific dark matter models. A large share of specific dark matter models that come close are really hybrid theories rather than pure dark matter particle theories, that also have a self-interaction term or an interaction with ordinary matter of some kind.

But, MOND is not formulated relativistically, so it is only applicable in circumstances where Newtonian gravity is a reasonable approximation of General Relativity (e.g. light bending, black holes and other strong gravitational fields, precession of Mars, cosmology). The need to reproduce the empirically features greatly constrains the form of any modification of gravity. MOND has known weak points such as a failure to explain all of the dark mater phenomena in cluster scale systems and a lack of a cosmology.

There are more than half a dozen well articulated relativistic modifications of gravity that meet the threshold test of explaining spiral galaxy dynamics without dark matter, but few of these have been very comprehensively vetted and only some of them have a good theoretical motivation. Some have been studied in one area, but not another.

I've listed almost all of the relativistic modified gravity theories yet published that work at the cluster scale. None of them have really thoroughly been developed at the cosmology scale although some initial first stabs at cosmology predictions have been made for a few. The answer might not be any specific one of these, but it is likely to have a close similarities to these theories.

 

[Vanadium 50]

So disagreements about which theory of gravity is right do end up being disagreements about whether particular galaxies contain dark matter or not.

I think it's pefectly reasonable to use the determination of whether this galaxy has dark matter or not to inform one's opinion on what the correct theory of gravity is. However, I don't think the reverse works - using one's preferred theory of gravity to inform whether this galaxy contains dark matter or not.

 

[PeterDonis]

I think it's pefectly reasonable to use the determination of whether this galaxy has dark matter or not to inform one's opinion on what the correct theory of gravity is.

But how can you make that determination without assuming some theory of gravity? You have to measure things like the velocity dispersion, brightness, rotation curve, etc. and compare them with a theoretical prediction in order to determine whether the matter you can see can account for the observed properties, which is what you need to do to determine if there is dark matter present.

 

[Ken G]

One issue is whether X or Y piece of evidence (e.g. DF2 or the Bullet cluster) proves that dark matter phenomena is the only possible reality and that a modified gravity explanation isn't possible, attacking the entire modified gravity paradigm. Assertions like that can be disproven by a single example of a modified gravity explanation of the same evidence.

What I can agree with is that no single observation should ever be used to say "this proves theory X is the only possibility." Indeed, no single astronomical observation (as opposed to, say, a single well-controlled and reproducible experiment) should ever be taken without considering the larger context of the full body of astronomical data, because no astronomy observations are well controlled experiments. So I agree we should not say "DF2 proves dark matter is real." Indeed, I find it odd that DF2 does not have a high M/L due to low star-formation efficiency, even if it has a low M due to a lack of dark matter.

So when we look at DF2, we should only say "how does this observation inform what we have already seen everywhere else", never "what does this observation all by itself tell us." But as we look at the body of observations, we should never juggle different versions of our theories as we attempt to explain one or another, we should always select one single theory, and see how well it does for all the observations. We may not require perfect agreement in all cases, but we must also never tolerate a complete failure in any. If we get a complete failure of a single theory in regard to some observation, we must either be able to doubt the observation was interpreted correctly, or we must look at modifying the theory. We don't have to abandon the theory, but it is of no value to swap in other theories at that point. Calling these things "MOND" seems to suggest they are all the same theory, but of course that is not true at all, they are different theories that postulate new force effects instead of new particles. Similarly, different dark matter particles are also different dark matter theories.

So when we ask what DF2 tells us about dark matter vs. MOND, we must ask what it tells us along with everything else we know, and we must look at particular dark matter theories vs. particular MOND theories. If you need one MOND in one context and a different one in a different context, then what is missing is the demonstration that the combination of both would fit both contexts. Until that argument can be made, the theory is simply not working. Similarly, if dark matter theorists are using combinations of warm and dark matter, they are producing a single theory that includes both, not one theory for one set of situations and another for another. IF warm dark matter succeeds in one context, it is of no value if it messes up the success of cold dark matter in some other context.

So keeping the focus on DF2 in the context with all else we know about M/L in galaxies, we find that DF2 has the M/L we associate with Milky Way baryons in any situation where Newtonian gravity is used to characterize M. We could try to explain that by saying that DF2 has only baryons, and those baryons have the same star-formation efficiency as the Milky Way. That doesn't seem entirely satisfactory to me, as I'd expect reduced star-formation efficiency, but I could be wrong. Or, we could adopt a MOND that has an external field effect, and say the external field effect lowers the Newtonian-equivalent M (i.e., not the actual M, the M inferred from Newtonian gravity). But for that to be satisfactory to me, that external field effect must not mess up other things, in particular cosmology (as there the external fields pervasive over the history of the universe have spanned a very wide scale of strengths and should give a clear signal of any such MOND effect).

So yes, taken in a vacuum, DF2 might actually challenge dark matter theories more than it challenges some particular MOND theories that include an external field effect. But the real issue is, what happens when we take everything else we've seen, including cosmology, and then add DF2 into the mix, and ask, what theories still survive with only small modifications? If we think it's dark matter, our challenge is to answer, why is the baryonic M/L the same in DF2 as in the Milky Way? If we think it's MOND, our challenge is to answer, what would the external field effect that we need for DF2 do to the history of the expansion of the universe?

 

[sysprog]

If observations falsify the theory it means it is indeed a good theory, just not the one that describes reality.

Hmm -- maybe I should take a whiff of dephlogisticated air, and ponder that.

 

[RobertArvanitis]

Two recent studies have found galaxies with little or no apparent dark matter, indicating modifying gravity can't work.
https://iopscience.iop.org/article/10.3847/2041-8213/ab0e8chttps://iopscience.iop.org/article/10.3847/2041-8213/ab0d92/meta

Your topic line is appropriate but the phrase "dark matter is real" seems like click-bait.
Humans operate at the meter level. We can hypothesize from 10^-30 to 10^+30 scales, but it is only by inference.
All our models, from Aristotle to the Standard, don't really fix things, but simple make new and more subtle errors.

 

[RUTA]

These new results are perfectly compatible with my idea which argues we don't need dark matter (DM):

The Missing Mass Problem as a Manifestation of GR Contextuality

Abstract: In Newtonian gravity, mass is an intrinsic property of matter while in general relativity (GR), mass is a contextual property of matter, i.e., matter can simultaneously possesses two different values of mass when it is responsible for two different spatiotemporal geometries. Herein, we explore the possibility that the astrophysical missing mass attributed to non-baryonic dark matter (DM) actually obtains because we have been assuming the Newtonian view of mass rather than the GR view. Since an exact GR solution for realistic astrophysical situations is not feasible, we explore GR-motivated ansatzes relating proper mass and dynamic mass for one and the same baryonic matter, as justified by GR contextuality. We consider four GR alternatives and find that the GR ansatz motivated by metric perturbation theory works well in fitting galactic rotation curves (THINGS data), the mass profiles of X-ray clusters (ROSAT and ASCA data) and the angular power spectrum of the cosmic microwave background (CMB, Planck 2015 data) without DM. We compare our galactic rotation curve fits to modified Newtonian dynamics (MOND), Burkett halo DM and Navarro-Frenk-White (NFW) halo DM. We compare our X-ray cluster mass profile fits to metric skew-tensor gravity (MSTG) and core-modified NFW DM. We compare our CMB angular power spectrum fit to scalar-tensor-vector gravity (STVG) and ΛCDM. Overall, we find our fits to be comparable to those of MOND, MSTG, STVG, ΛCDM, Burkett, and NFW. We present and discuss correlations and trends for the best fit values of our fitting parameters. For the most part, the correlations are consistent with well-established results at all scales, which is perhaps surprising given the simple functional form of the GR ansatz.

This is a longer version of the Gravity Research Foundation essay that won Honorable Mention and was published in IJMPD last year. The bottom line is that we can fit DM phenomena without DM and without modifying GR. There is another option, i.e., composite/adjoined GR solutions, consistent with the complex (real world) matter distributions we are dealing with. Essentially, the extrinsic curvature at the interface between the two solutions allows the matter to have different values of mass in the two different geometries. In GR, mass is a geometric consequence of matter, so when you have two different geometries associated with the same matter, you can have two values of mass for the same matter.

 

[PeterDonis]

matter can simultaneously possesses two different values of mass when it is responsible for two different spatiotemporal geometries

How is this possible in GR? I'm not aware of any solution of the Einstein Field Equation that has this property.

 

[RUTA]

How is this possible in GR? I'm not aware of any solution of the Einstein Field Equation that has this property.

Here is an Am. J. Phys. article I published explaining the computational details: http://users.etown.edu/s/STUCKEYM/AJP1994.pdf

There is a graph in the arXiv paper in post #40 showing the possible disparity.

If you've derived the Schwarzschild solution, for example, you know just what I'm talking about when I say mass is a geometric property in GR.

 

[PeterDonis]

If you've derived the Schwarzschild solution, for example, you know just what I'm talking about when I say mass is a geometric property in GR.

Yes, I know what that means. I'm just very confused by the phrase "two different spatiotemporal geometries". At any given event in a spacetime, the geometry is one thing; it can't be two different things.

Skimming through the papers, it appears that what you actually mean is that you have a spacetime with two different regions, one containing matter and a vacuum region surrounding it, and those regions have two different geometries. Of course this is common in GR solutions that are used for real-world problems. But that just pushes the confusion back to the phrase "two different values of mass".

In the vacuum region, there is only one mass, and it's a constant. And since we, observing a distant object, are in the vacuum region with respect to that object, we observe one mass. It is true that if we were somewhere inside the object, i.e., in the matter region, we could observe a different mass, because mass is not a constant there: it depends on position. But I don't see what relevance that has to the mass we, far distant in the vacuum region, observe.

 

[Buckethead]

I cringe a little when it is assumed that MOND and DM are the only hypotheses out there to explain the phenomenon which give rise to such hypotheses. This leads to comments such as "This shows that MOND can't work so DM must be the correct hypothesis" But there are other hypotheses. For example this one by Kohkichi Konno et .al:

https://arxiv.org/pdf/0807.0679.pdf
There is also the hypotheses of Emergent Gravity written by Erik Verlinde:

https://arxiv.org/abs/1611.02269
The paper by Kohkichi Konno is particularly interesting as it refers to a frame dragging effect. The part of this paper that grabed my attention was in the introduction:

"The long range feature of frame-dragging effect under the Chern-Simon gravity well explains the flat rotation curves of galaxies which is a central evidence of dark matter. "

The reason this is so fascinating to me is that it seems to imply that if there is no frame dragging, then there should be no appearance of excessive mass in a galaxy. So perhaps the absence of DM in DF4/DF2 may be related to this.

 

[RUTA]

Yes, I know what that means. I'm just very confused by the phrase "two different spatiotemporal geometries". At any given event in a spacetime, the geometry is one thing; it can't be two different things.

Skimming through the papers, it appears that what you actually mean is that you have a spacetime with two different regions, one containing matter and a vacuum region surrounding it, and those regions have two different geometries. Of course this is common in GR solutions that are used for real-world problems. But that just pushes the confusion back to the phrase "two different values of mass".

In the vacuum region, there is only one mass, and it's a constant. And since we, observing a distant object, are in the vacuum region with respect to that object, we observe one mass. It is true that if we were somewhere inside the object, i.e., in the matter region, we could observe a different mass, because mass is not a constant there: it depends on position. But I don't see what relevance that has to the mass we, far distant in the vacuum region, observe.

The mass of the matter in the FLRW ball surrounded by the Schwarzschild vacuum region is an integrated and conserved total. Are you familiar with the FLRW solution? It does not equal the mass in the Schwarzschild metric unless the FLRW spatial geometry is flat. Therefore, the two different techniques for measuring the mass of one and the same matter can yield two different, correct results in GR (contextuality). That is precisely what is going on with DM phenomena -- we obtain two different values of mass for the same matter using two different measurement techniques -- one a local technique for obtaining M/L and the other a global technique, e.g., rotation curves.

 

[PeterDonis]

The mass of the matter in the FLRW ball surrounded by the Schwarzschild vacuum region is an integrated and conserved total.

What is the integral? (I know it's in the papers you cited, but if we're going to discuss it here we should make sure we're looking at the same one and can quote it here.)

Are you familiar with the FLRW solution?

Of course.

It does not equal the mass in the Schwarzschild metric unless the FLRW spatial geometry is flat.

I have no doubt you can exhibit an integral taken over an FLRW region surrounded by Schwarzschild vacuum that gives this result. I'm not so sure what that would mean physically.

we obtain two different values of mass for the same matter using two different measurement techniques -- one a local technique for obtaining M/L and the other a global technique, e.g., rotation curves.

What "local technique" can we possibly use? We aren't in the distant galaxy. We're here. Our observations of M/L are just as "global" as our observations of rotation curves.

 

[RUTA]

What is the integral? (I know it's in the papers you cited, but if we're going to discuss it here we should make sure we're looking at the same one and can quote it here.)

Look at Eq. (12) in the AJP paper and keep in mind ρa³ is a constant.

I have no doubt you can exhibit an integral taken over an FLRW region surrounded by Schwarzschild vacuum that gives this result. I'm not so sure what that would mean physically.

It means mass is not an intrinsic property of matter as we generally suppose.

What "local technique" can we possibly use? We aren't in the distant galaxy. We're here. Our observations of M/L are just as "global" as our observations of rotation curves.

We might determine M in M/L for the Sun using the rotational parameters of the planets. That is a "local" determination of M. [Local versus global determinations for each of the three types of data fits -- galactic, cluster, cosmological -- are explained in the paper.] If you suppose that the local value of M is an intrinsic property of the matter, then of course this value of M should simply contribute with all other locally determined M values to determine the galactic rotation curve. That's what doesn't work. So, we infer the existence of unseen matter when we should simply acknowledge that what is missing is mass, not necessarily matter.

 

[PeterDonis]

Look at Eq. (12) in the AJP paper and keep in mind ρa3 is a constant.

This is just integrating the density over the volume. So the lack of "equality" in the closed and open models is simply because space in those models is not Euclidean, so the amount of volume over a given range of $\chi$ is not the same as it would be in Euclidean space. (In the flat model, it is, so naturally you get equality in the flat model.)

However, the real question is what "mass" corresponds to the "dynamic mass" $M$ measured in the vacuum Schwarzschild region outside the FLRW matter region. As far as I can tell, the answer to that is that the integrals given in Eq. (12) in the paper do. But you labeled those integrals as $M_p$, "proper mass". So it seems to me that either $M_p = M$ for all these models (proper mass = dynamic mass) or you have mislabeled the integrals.

Further, stars and galaxies are not modeled by FLRW spacetimes, since they aren't expanding or contracting, they're stationary (to a good approximation). So I don't see the relevance of any of these integrals to the question of whether there is "missing mass" in galaxies that is not visible.

We might determine M in M/L for the Sun using the rotational parameters of the planets. That is a "local" determination of M.

But we can't do this for stars in other galaxies since we can't even see planets orbiting them, much less get accurate measurements of their orbital parameters, so the fact that if we could do it, we would have to then apply a correction when we summed up all these local M values to get a total for the galaxy is irrelevant.

 

[PeterDonis]

we infer the existence of unseen matter when we should simply acknowledge that what is missing is mass, not necessarily matter.

Apart from the other questions I've been asking, it seems to me that the correction you are saying should be applied is in the wrong direction.

Basically, what I understand you to be saying is that we are totaling up "local" measurements of mass for all the visible matter in a galaxy, and then using the total to infer what the rotation curve should be. But the actual rotation curve is not the one that is inferred; it is the one we would expect if there were more mass present besides what we can see.

In your terminology, we are totaling up the proper mass of the stars, and finding that the total is smaller than the dynamic mass required to account for the rotation curve. So if there is some correction that should be applied to how we total the proper mass, its effect would need to be to make the total of proper mass larger. But it seems like the correction you are talking about would make the total of proper mass smaller, which would make the problem worse, not better.

 

[RUTA]

Apart from the other questions I've been asking, it seems to me that the correction you are saying should be applied is in the wrong direction.

If that were true, how would you explain the data fits? Read the IJMPD paper carefully.