Why does MOND fit rotation curves so exactly?

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wolram said:
so why does Mond fit so well over dark matter models?
Hi wolfram:

I think this is a very interesting question, but the way it is phrased ignores some of the characteristics of MOND.
For larger scales than galaxies, MOND's "fit" is no longer quite so impressive.

One approach that takes the MOND results seriously is Self-Interacting Dark Matter (SIDM). That is, rather than modifying gravity, SIDM explores models with assumed speculative properties of DM that will hopefully approach MOND's good fits for galaxies.
https://arxiv.org/pdf/astro-ph/0605637.pdf (2007)
https://www.cfa.harvard.edu/events/2014/sackler/index/talks/Harvard2014_Bullock.pdf (2014)
http://iopscience.iop.org/article/10.3847/1538-4357/aa9710/meta (2018)​
I confess that I am unable to understand much of the contents of these references. I am hoping that some PF participants might be able to explain these papers at the B or I level.

Regards,
Buzz
 
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Hi Buzz.
Thanks for the references, from one of them.
The accurate measurement of the speed of gravitational waves compared to the speed of light in 2017 ruled out many theories which used modified gravity to explain dark matter.[4] However, both Milgrom’s bi-metric formulation of MOND and nonlocal MOND are not ruled out according to the same study.
What is Migroms bi metric theory?
 
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wolram said:
What is Migroms bi metric theory?
Hi wolram:

Quite a few things showed up when I browsed with: "milgrom's bimetric gravity".

Regards,
Buzz
 
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I can not understand all this but it seems to give credence to MOND
So the question still stands . why does MOND give such good result compared to DM theories?
 
wolram said:
I can not understand all this but it seems to give credence to MOND
So the question still stands . why does MOND give such good result compared to DM theories?
The simplest answer is that MOND was designed specifically to fit galaxy rotation curves, while DM theory predictions of galaxy rotation curves depend upon lots of complicated physics that are not that well-understood. It's really not surprising that MOND would do well for galaxy rotation curves, when fitting those is its entire reason for existence.

MOND isn't a real theory of gravity, however, and it can't explain features of the universe beyond galaxy rotation curves, such as galaxy cluster dynamics or the CMB. Dark matter explains the CMB superbly, explains galaxy cluster dynamics quite well, and has potential difficulties with explaining the details of galaxy structure.

I believe the take-away of most cosmologists is that the discrepancies regarding galaxy rotation curves are telling us one of two things:
1) There's something interesting about how galaxies behave that we're not understanding.
2) There's some interesting property of dark matter (such as the self-interactions mentioned by Buzz Bloom) that these discrepancies are telling us about.
 
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wolram said:
why does MOND give such good result compared to DM theories?

Nobody knows.

I believe it is telling us something about galaxy formation, and results in an empirical "law" that has nothing to do with gravity modifications, but nobody knows for certain.
 
Thanks for the replies

I did not know that MOND was designed to fit galaxy curvatures
It is also interesting that there is still some thing we do not know about galaxy formation or the way they behave
could it be the way Dark matter clumps in galaxies?
 
wolram said:
Thanks for the replies

I did not know that MOND was designed to fit galaxy curvatures
It is also interesting that there is still some thing we do not know about galaxy formation or the way they behave
could it be the way Dark matter clumps in galaxies?
I think this is an active area of research. Unfortunately, I don't have a clear understanding of the status of the field at the moment.
 
wolram said:
I did not know that MOND was designed to fit galaxy curvatures
That might be too simplistic. Here's a reference I found very useful:

Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions ,
Famaey, B. & McGaugh, S.S.
Living Rev. Relativ. (2012) 15: 10.

In particular, in section 5.1, they write:
Famaey & McGaugh said:
It is often wrongly stated that Milgrom’s formula was constructed in an ad hoc way in order to reproduce galaxy rotation curves, while this statement is only true of these two observations: (i) the asymptotic flatness of the rotation curves, and (ii) the slope of the baryonic Tully-Fisher relation (but note that, at the time, it was not clear at all that this slope would hold, nor that the Tully-Fisher relation would correlate with baryonic mass rather than luminosity, and even less clear that it would hold over orders of magnitude in mass). All the other successes of Milgrom’s formula related to the phenomenology of galaxy rotation curves were pure predictions of the formula made before the observational evidence. The predictions that are encapsulated in this simple formula can be thought of as sort of “Kepler-like laws” of galactic dynamics. These various laws only make sense once they are unified within their parent formula, exactly as Kepler’s laws only make sense once they are unified under Newton’s law.
 
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wolram said:
I have been reading this article
https://tritonstation.wordpress.com/2018/10/05/it-must-be-so-but-which-must/

so why does Mond fit so well over dark matter models?

In short, that is what we don't know and want to find out. But MOND is just a heuristic law (kind of like a rule-of-thumb), not a fundamental law, like General Relativity. This is a very active field of research, in combination with the search for Dark Matter in the form of particles. As it turns out, Dark Matter is a better explenation in some cases, MOND is a better explenation in other cases. We do not have a unifying theory yet that can explain all the anomalous cases in a uniform manner, and maybe there is no such uniform solution. And besides the two options (either adding mass in the form of dark matter, or modifying gravity), there might also be third options (maybe magnetic fields can have something to do with flat rotation curves).
 
There have been some attempts to derive MOND rules from a deeper theory. One of the more notable is by Alexandre Deur. Some of his papers on point are:

A. Deur, “A possible explanation for dark matter and dark energy consistent with the Standard Model of particle physics and General Relativity” (August 14, 2018) (Proceeding for a presentation given at Duke University, Apr. 2014. Based on A. D. PLB B676, 21 (2009); A.D, MNRAS, 438, 1535 (2014). The published version is https://link.springer.com/article/10.1140/epjc/s10052-019-7393-0).

and

Alexandre Deur, Corey Sargent and Balša Terzić, "Significance of Gravitational Nonlinearities on the Dynamics of Disk Galaxies" 896(2) The Astrophysical Journal 94 (January 2020) DOI: 10.3847/1538-4357/ab94b6

and

Alexandre Deur, "Relativistic corrections to the rotation curves of disk galaxies" (April 10, 2020) (last updated February 8, 2021 in version accepted for publication in Eur. Phys. Jour. C).

and

Alexandre Deur, "Effect of gravitational field self-interaction on large structure formation" arXiv: 2018.04649 (July 9, 2021) (Accepted for publication in Phys. Lett. B) DOI: 10.1016/j.physletb.2021.136510
 
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The theory of "entropic gravity" by Eric Verlinde, just tries to model gravity in a different way as an entropic force, emergent from quantum physics, which could both explain dark energy and dark matter. See: Entropic Gravity (wikipedia).
 
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elcaro said:
The theory of "entropic gravity" by Eric Verlinde, just tries to model gravity in a different way as an entropic force, emergent from quantum physics, which could both explain dark energy and dark matter. See: Entropic Gravity (wikipedia).
Connecting the dots from the link: "Entropic gravity provides the underlying framework to explain Modified Newtonian Dynamics, or MOND, which holds that at a gravitational acceleration threshold of approximately 1.2×10−10 m/s2, gravitational strength begins to vary inversely linearly with distance from a mass rather than the normal inverse-square law of the distance."

It is a step more ambitious than Deur's work, however, seeking to derive gravity itself from Standard Model physics, and not just seeking to derive dark matter and dark energy phenomena from General Relativity (and elegantly explaining the strength of gravity as an emergent phenomena determinable in principle without any fundamental gravitational constants).

There are, however, serious doubts about whether Verlinde's hypothesis actually works.
 
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