# I Can dark matter explain Tully-Fisher relation & new paper

1. Oct 13, 2016

### kodama

can dark matter explain Tully-Fisher relation, or is modified MONDlike gravity a better explanation for this?

new paper

The Radial Acceleration Relation in Rotationally Supported Galaxies
Stacy McGaugh, Federico Lelli, Jim Schombert
(Submitted on 19 Sep 2016)
We report a correlation between the radial acceleration traced by rotation curves and that predicted by the observed distribution of baryons. The same relation is followed by 2693 points in 153 galaxies with very different morphologies, masses, sizes, and gas fractions. The correlation persists even when dark matter dominates. Consequently, the dark matter contribution is fully specified by that of the baryons. The observed scatter is small and largely dominated by observational uncertainties. This radial acceleration relation is tantamount to a natural law for rotating galaxies.
Comments: 6 pages, 3 figures. Accepted for publication in Physical Review Letters
Subjects: Astrophysics of Galaxies (astro-ph.GA)
Cite as: arXiv:1609.05917 [astro-ph.GA]

implies dark matter does not explain this as well as modified gravity relations between baryons and galaxy rotations.

can dark matter theorist offer explanation for these mond-like observations and curve fitting?

2. Oct 13, 2016

### Jonathan Scott

This isn't new, just significantly more refined. MOND people have been pointing this out for ages.

As an empirical rule (like Tully-Fisher itself) MOND is astonishingly powerful and predictive for describing how individual galaxies work, far more so than dark matter, needing only one parameter to fit all known galaxies. However, as a physical theory, MOND makes little sense, as in its simplest form it violates basic laws of physics (such as conservation of momentum) and by the time it is dressed up as a relativistic self-consistent modified gravity theory (e.g. STVG/MOG) it has so many arbitrary parameters that I feel its basic appeal is totally undermined. There also seem to be problems with it above and below the scale of galaxies, although dark matter has some of those too.

I'm also not yet convinced by MOND arguments about internal and external field effects, which seem to imply for example that the overall acceleration of a solar system can be governed by MOND even though all internal accelerations within that system are greater than the Newtonian threshold. Milgrom asserts essentially that this is because it's non-linear, which is true, but the nature of the MOND cut-off seems unnatural and incompatible with relativity. There is a relativistic equivalent, but it basically adds the MOND force to the Newtonian force instead of having a cut-off, and this was specifically ruled out by lab experiments a few years ago.

3. Oct 13, 2016

### kodama

is it possible that a modified form of quantum gravity, that deviates from GR in the deep IR range, where the strength of gravity doesn't fall of r^2 but more like r due to quantum gravitational effects can reproduce MOND?

4. Oct 13, 2016

Staff Emeritus
No.

5. Oct 13, 2016

### kodama

why wouldn't it work?

6. Oct 14, 2016

Staff Emeritus
A. Because it doesn't match the data.

B. One reason that we don't allow personal theories here is that it takes much less time to toss one out than to find the evidence against them, and the proponents of such theories are unwilling to do this, and insist that others do it for them. Science doesn't work this way, and neither does PF.

7. Oct 14, 2016

### Jonathan Scott

Lee Smolin has recently written a paper "Four Principles for Quantum Gravity" in which he claims it can reproduce the MOND effect observed in the referenced paper:
https://arxiv.org/abs/1610.01968

8. Oct 14, 2016

### kodama

what is your evaluation of his thesis?

9. Oct 14, 2016

### kodama

i had the smolin paper in mind but this paper also suggests this

Implications of Graviton-Graviton Interaction to Dark Matter
A. Deur
(Submitted on 26 Jan 2009 (v1), last revised 6 May 2009 (this version, v2))
Our present understanding of the universe requires the existence of dark matter and dark energy. We describe here a natural mechanism that could make exotic dark matter and possibly dark energy unnecessary. Graviton-graviton interactions increase the gravitational binding of matter. This increase, for large massive systems such as galaxies, may be large enough to make exotic dark matter superfluous. Within a weak field approximation we compute the effect on the rotation curves of galaxies and find the correct magnitude and distribution without need for arbitrary parameters or additional exotic particles. The Tully-Fisher relation also emerges naturally from this framework. The computations are further applied to galaxy clusters.
Comments: Version published in Phys. Lett. B. Added material: 1) We explicited the steps leading from the Einstein-Hilbert Lagrangian to our simplified Lagrangian. 2) We showed how the Tully-Fisher relation emerges naturally from our framework. 3) We added a discussion on the approximations we used
Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph)
Journal reference: Phys.Lett.B676:21-24,2009
DOI: https://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1016%2Fj%252Ephysletb%252E2009%252E04%252E060&v=e129311f [Broken]
Cite as: arXiv:0901.4005 [astro-ph.CO]
(or arXiv:0901.4005v2 [astro-ph.CO] for this version)
Submission history
From: Alexandre Deur [view email]
[v1] Mon, 26 Jan 2009 13:34:50 GMT (115k

Last edited by a moderator: May 8, 2017
10. Oct 14, 2016

### Jonathan Scott

Sorry, I'm not into quantum gravity and it goes way outside my area of expertise.

There are quite a few ways to come up with theories which make the galactic rotation curves match MOND, basically by adding extra gravitational acceleration in some form. The difficult thing is to account for why the additional acceleration isn't detectable in laboratory and solar system experiments.

11. Oct 14, 2016

### kodama

wouldn't dark matter also have the same problem? i.e dark matter in the solarsystem skew results predicted from GR?

12. Oct 14, 2016

### Jonathan Scott

No, because dark matter is extremely thinly spread across the whole galaxy, with negligible effect in any part of it. MOND accelerations are caused by normal matter, so they are stronger close to masses, and although they are far weaker than Newtonian accelerations, the predicted effects should be detectable if they simply added on.

I recently saw a paper from about 2010 where someone had specifically done laboratory tests to constrain possible MOND variants. I can't find it right now, but if I find it later I'll post a link.

13. Oct 14, 2016

### kodama

most dark matter models predict the density of the particles to be in the center of the galaxy, not evenly distributed. not different in principle to the solar system formation from a solar nebular disk and dust and gas.

14. Oct 14, 2016

### Jonathan Scott

I didn't say it was the same everywhere, but it is spread very evenly on the scale of the area around the solar system so its gravitational effect is too small to measure.

15. Oct 14, 2016

### Jonathan Scott

I've found the paper relating to MOND effects in the laboratory:
https://arxiv.org/abs/1112.0434 "Test of the Law of Gravitation at small Accelerations"

They do not find any deviation from Newtonian predictions, which means they can rule out the MOND scheme (numbered 5 in the paper) which assumes that there is no specific cut-off but that the MOND acceleration simply adds to the Newtonian acceleration. Alternative scheme for the MOND cut-off are not ruled out but the whole concept of a cut-off leads to all sorts of theoretical complications.

16. Oct 14, 2016

### kodama

yes paper says mond1 and mond2 still viable.

perhaps classical GR is only valid over certain ranges, distances, masses and accelerations, and that in the galaxy level, quantum corrections become significant causing deviations from GR equivalent to MOND1/2.

17. Oct 14, 2016

Staff Emeritus
Except they can't. MOND does not say that if you add a_0 to g you get g. It says that if you add a_0 to 0 you get 0. MOND and Newtonian gravity make the exact same predictions for this experiment.

Now, one can complain that these means MOND is manifestly non-relativistic, and people have. This is news to nobody, not even Moti Milgrom, and this is the motivation for models like TeVeS (which has its own problems). But one cannot claim this kind of experiment rules out MOND,

18. Oct 14, 2016

### kodama

why not MOND for galaxy rotation + black holes for bullet cluster. so MOND for galaxies + dark matter as black holes for large galactic clusters and lensing

19. Oct 15, 2016

### Jonathan Scott

Did you read the paper? They investigate what five different MOND schemes would predict as the modification to the gravitational field of a nearby mass, taking into account different MOND interpolation functions. The experimental results appear to be purely Newtonian. For schemes 1/2 (from the original MOND theory) the interpolation function suppresses MOND effects to the point that it cannot be distinguished from Newtonian results, so this does not rule them out. For 3/4, the MOND effect might be expected to be detected, so the experiment says that is unlikely but not ruled out. For 5, which is derived from a relativistic variant of MOND, the interpolation function simply adds the local effects, and that is clearly incompatible with the laboratory experiments (and also with solar system results).

It may well be that a more sophisticated variant of MOND may eventually be able to give consistent results by using a detailed non-linear field theory without the problems caused by the arbitrary interpolation function that is needed to hide the effect in the Newtonian realm. A modified gravity theory with enough parameters can probably duplicate any required result, but even then I find it difficult to see how external/internal field effects can be explained in a satisfactory way.

The success of the MOND model strongly suggests that there is some important physics behind it. However, so far I've not seen any convincing physical theory to support it.

20. Oct 15, 2016

Staff Emeritus
I did. Did you?

The authors of the paper - submitted five years ago to EPJ and still not there - say "It has been argued, that such a test is not meaningful in the strong gravitational eld of the earth, but, due to a lack of a deeper understanding of MOND, this view is not shared by everybody [3]." They fail to mention that the view is that of the developers of MOND, and that "not everybody" means one person, and that citation was the proceedings from a conference that had speakers like Eric Lerner (author of "The Big Bang Never Happened", Oliver Manuel ("iron sun"), and Tom van Flandern (crackpotteeries too numerous to mention).

21. Oct 15, 2016

### Jonathan Scott

Yes, but thanks for the clarification of your position. I was aware of the "not shared by everybody" quote. Although I was somewhat sceptical, I was giving the authors the benefit of the doubt relating to their conclusions.

I have yet to find an explanation I can believe of how the MOND internal/external field effects work, rather than just hand-waving combined with "non-linear". Even modified gravity variants which seem to follow other physical laws still seem to have problems with that. Perhaps it's my problem; if anyone knows of a good quantitative explanation of those effects I'd be interested in a reference.

22. Oct 15, 2016

### kodama

would you consider a QG where the quantum gravity regime gives rise to MOND in deep IR, but GR in classical regime be a "modified gravity variant"?

23. Oct 18, 2016

### RUTA

I only started looking into the dark matter phenomena last year, so I'm relatively new, but I did use MOND to fit THINGS data for galactic rotation curves, MSTG to fit ROSAT/ASCA data for X-ray cluster mass profiles, and STVG to fit Planck 2015 data for the CMB angular power spectrum. While all these phenomena involve non-baryonic dark matter (DM) with a mass ~10 times that of baryonic matter, they are all nonetheless small perturbations of a background spacetime structure. For example, in galactic rotation curves $\frac{2GM}{c^2r} \sim 10^{-6}$, so an increase $M \rightarrow 10M$ still results in a very small metric correction to flat spacetime. Another way to see how small the geometric changes are to spacetime is to look at how much the spatial curvature scalar deviates from its Schwarzschild value of zero inside a typical galaxy. We have $^{(3)}R = \frac {16 \pi G\rho}{c^2} = \frac {12 v_{max}^2}{r_b^2c^2}$ for the spatial curvature scalar in the annulus at $r$ rather than its Schwarzschild value of zero. $v_{max} \approx 300 \mbox{km/s}$ and $r_b \approx 2000 \mbox{pc}$ gives $^{(3)}R \sim 10^{-45}/\mbox{m}^2$. So an increase in $\rho$ by a factor of ten is geometrically inconsequential. We already know that matter can simultaneously have different values of mass in general relativity (GR), so what is now viewed as DM might simply be small geometric corrections to spacetime geometry over large astronomical distances resulting in large differences between the local mass of baryonic matter and the global mass of baryonic matter. Cooperstock et al. used GR instead of Newtonian gravity in fitting galactic rotation curves and found that the non-luminous matter in galaxies "is considerably more modest in extent than the DM extent claimed on the basis of Newtonian gravitational dynamics." Moffat and Rahvar used "The weak field approximation of MOG" as a perturbation of "the metric and the fields around Minkowski space–time" in fitting THINGS data and X-ray cluster mass profiles without DM. MOND can be viewed in this fashion, since MOND advocates an extremely small modification to acceleration on astronomical scales in the context of flat spacetime (Newtonian gravity), and acceleration due to gravity in flat spacetime is replaced by curved spacetime in GR. So, MOND could be viewed as saying that a small change in spacetime curvature (equivalent to a small change to acceleration in Newtonian gravity) replaces the need for a greatly increased mass in accounting for galactic dynamics. Since we have highly idealized GR solutions in play, such small corrections don't seem unreasonable.

24. Oct 18, 2016

### Jonathan Scott

We do? Please can you clarify.

Thanks for a very interesting post.

I had forgotten about the Cooperstock paper (I presume you mean https://arxiv.org/abs/astro-ph/0507619 "General Relativity Resolves Galactic Rotation Without Exotic Dark Matter"). However, I thought that by the time the dust settled there was still a significant unexplained effect to be attributed to DM or modified gravity.

25. Oct 18, 2016

### RUTA

If you embed a sphere of FRW dust in a Schwarzschild vacuum, the proper mass of the dust (measured by local observers inside the sphere) can be larger, smaller or equal to its dynamical mass M in the Schwarzschild metric http://users.etown.edu/s/STUCKEYM/AJP1994.pdf [Broken] .

Yes, the Cooperstock work did not entirely replace DM as MOND and MOG do. My point is that they're thinking along the same lines, i.e., dark matter phenomena as a small perturbation to spacetime geometry even though the mass of DM is many times greater than that of its baryonic counterpart.

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