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A lot of papers say that even the theory of MOND requires the existence of dark matter, particularly in the central regions. However this is a bit counterintuitive to me considering that rotation curves become flat only far from the galactic centre. I would love to have more insight on this.

One example is this paper.

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    $\begingroup$ Could you give examples of papers that say this? $\endgroup$
    – Sten
    Jul 5 at 5:19
  • $\begingroup$ The linked paper is: R. H. Sanders, "Clusters of galaxies with modified Newtonian dynamics" 342(3) Monthly Notices of the Royal Astronomical Society, 901-908 (July 2003) doi.org/10.1046/j.1365-8711.2003.06596.x (emphasis added). $\endgroup$
    – ohwilleke
    Jul 6 at 18:31

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MOND, in generally, does not show a need for dark matter in the central regions of galaxies. The central regions of galaxies outside of galaxy clusters, in contrast, are a problem for cold dark matter theories which is known as the cusp-core problem. See, e.g., James S. Bullock, Michael Boylan-Kolchin, "Small-Scale Challenges to the ΛCDM Paradigm" (September 2, 2019). See also Jorge Sanchez Almeida, Angel R. Plastino, Ignacio Trujillo, "Can cuspy dark matter dominated halos hold cored stellar mass distributions?" arXiv:2307.01256 (July 3, 2023) (Accepted for publication in ApJ).

What MOND does do is underestimate the phenomena attributed to dark matter (e.g. lensing, dynamics) in the central region of galaxy clusters which are groups of multiple galaxies with significant gravitational influences on each other because they are sufficiently close together. In galaxy clusters, MOND reduces the amount of inferred dark matter needed to explain the phenomena observed relative to a plain vanilla conventionally applied general relativity scenario (in practice, Newtonian gravity with GR effects except gravitational lensing ignored), but not completely. As the astrophysicist who invented MOND explains in the Scholarpedia article linked above in this paragraph:

It has been evident from early on (The and White, 1988; Gerbal, et al., 1992; Sanders, 1994; Sanders, 1999; Sanders, 2003; Aguirre, et al., 2001; Pointecouteau and Silk, 2005; Takahashi and Chiba, 2007; Angus, et al., 2008a; Milgrom, 2008; Ettori, et al., 2019) that MOND does not fully explain away the mass discrepancy in galaxy clusters. One then has to attribute the remaining discrepancy to yet undetected standard-model matter. It is likely that this matter is baryonic in some yet unidentified form, such as cold, dense clouds (Milgrom, 2008). Another possibility that has been considered are massive neutrinos (Sanders, 2003; Angus, et al., 2008). Modified versions of MOND were also proposed to account for this remaining discrepancy (Zhao & Famaey, 2012).

The following rough picture emerges regarding the mass discrepancy in clusters, based on observations of galaxy motions, x-ray emitting gas, weak and strong lensing, and Sunyaev-Zeldovich signals: In Newtonian dynamics, the discrepancy decreases with distance from the cluster’s center. In the cluster’s core it is of the order of 10-50 and decreases with radius to a value of ∼5−10, at (1−2)Mpc.12

The measured accelerations at intermediate radii (of about 1 Megaparsec) in the clusters are roughly (0.2−0.5)a0. So, MOND reduces the discrepancy in clusters at these radii to only a factor of ∼2−3 (Sanders, 1999; Ettori, et al., 2019). At larger radii (about 2 Megaparsecs) MOND leaves even smaller disscrepancies, as low as only 15 percent typically (Ettori, et al., 2019). In other words, MOND still requires yet-undetected matter in clusters whose amount is only a fraction of the already-observed baryonic matter, which is largely in the form of hot gas. If this undetected matter is in some form of baryons, it adds only little to the baryonic budget in the Universe: A rough estimate is that less than 5% of the amount of baryons implied by Big-Bang nucleosynthesis would suffice to account for this extra baryons that MOND requires in clusters. Since a large fraction of the baryons in the Universe are still missing, and their whereabouts are anyway unknown (e.g., Bhattacharjee, 2012), a small fraction of them could account for the remaining MOND discrepancy in clusters.

The typical observed accelerations in the cores of clusters are of the order of, or a few times larger than, a0. Thus, MOND implies only a small correction there. So most of the discrepancy observed in the core must be due to the extra, undetected matter. This matter is thus found to be more centrally concentrated than the observed baryons, which are largely in the form of hot gas. In fact, its distribution resembles that of the galaxies in a cluster (which make up only a small fraction –about 20 percent – of the observed baryonic mass).

If the extra matter required in MOND is made of compact macroscopic objects–as is most likely–then like the galaxies, these must have sloshed across the cluster, through the hot gas, many times. So, when two clusters collide, we expect this extra matter to follow the galaxies in going through the collision zone, and not to be greatly affected even in head-on collisions, while the gas components of the two clusters coalesce at the center.

One way to explain this is that dark matter (or simply excess ordinary baryonic matter in clusters which is not easily visible) makes up the difference (as discussed in the quoted material above) and this is only found in galaxy clusters. There is not a well-established mechanism to do this, however.

Another way to explain this is that galaxy clusters are beyond the domain of applicability of MOND and that some other gravity based theory yet to receive wide acceptance or be discovered explains dark matter phenomena in both clusters and galaxies without the need for dark matter.

For example, this 2017 paper sought to address the issue in this manner. So have John Moffat's MOG theory, see, e.g., J. W. Moffat and M. H. Zhoolideh Haghighi, "Modified gravity (MOG) can fit the acceleration data for the cluster Abell 1689" (16 Nov 2016), Gianni Pascoli, "A comparative study of MOND and MOG theories versus the κ-model: An application to galaxy clusters" arXiv:2307.01555 (July 4, 2023), and Alexandre Deur's approach to looking at alleged non-perturbative effects in General Relativity which are generally disregarded, see, e.g., A. Deur, “Implications of Graviton-Graviton Interaction to Dark Matter” (May 6, 2009) (published at 676 Phys. Lett. B 21 (2009). My intent isn't to debate or express any opinion one way or the other on a particular solution along these lines, but merely to illustrate proof of what the concept could look like. The latter three theories also address the "Bullet cluster" issue in MOND, which is part of its general failure to explain cluster phenomena in its simple "toy-model" form.

Yet another complication is that the lensing profiles of inferred dark matter halos in galaxy clusters that are observed does not match what cold dark matter theories would predict. See Massimo Meneghetti, et al., "An excess of small-scale gravitational lenses observed in galaxy clusters" 369 (6509) Science 147-1351 (September 11, 2020). DOI: 10.1126/science.aax5164.

Cold dark matter also predicts the wrong predicted dark matter halo size scaling exponent in clusters. See Yong Tian, Han Cheng, Stacy S. McGaugh, Chung-Ming Ko, Yun-Hsin Hsu "Mass-Velocity Dispersion Relation in MaNGA Brightest Cluster Galaxies" arXiv:2108.08980 (August 20, 2021) (published in 24 The Astrophysical Journal Letters 917).

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