Ranku said:
How do we distinguish between the effect of dark matter and MOND with respect to flat rotation curves in galaxies? How would the shape of the rotation curve differ between the two?
Comparing dark matter and MOND is comparing apples and oranges.
One could compare a specific version of dark matter to MOND, or you could compare dark matter to modified gravity theories generally.
We know, and have known for decades, that pure toy-model MOND or a pure relativistic generalization of it is not correct, due mostly to its failures to fully describe galaxy cluster scale phenomena which are outside its range of applicability, but also that it is "close" to a correct theory and is perfect or nearly so in its domain of applicability of galaxy scale and smaller systems.
But there are also multiple proposed gravity based explanations for dark matter phenomena that work in domains of applicability where MOND fails.
One easy way to screen modified gravity theories is to determine if they reproduce MOND where MOND works.
Also, you really need two pieces of a dark matter theory: a theory of what properties the dark matter particles have (spin, mass, cross-sections of interaction with different kinds of particles, mean velocity, number of types), and a theory of how dark matter came to be distributed throughout the universe in the manner that it does.
Astrophysicists who support dark matter particle theories tend to ignore the second half of that problem, which make the theory capable of describing almost any system but also deprive it of most of its predictive value. You can imagine a distribution that explains any particular system, after the fact, but can't predict what systems will form or what properties they will have.
Key Relationships And Facts
In the case of rotation curves, one of the arguments for a modified gravity theory, although not an overwhelmingly decisively one, is that in a modified gravity theory, it is possible to determine the dynamics of a galaxy entirely from the baryonic (i.e. ordinary) matter distributions in the system. Every feature of the ordinary matter distribution should be reflected in the rotation curves. And, every galaxy with an identical ordinary matter distribution should have exactly the same rotation curves.
There are specific dark matter theories that can be basically ruled out by examination of the dark matter distribution that is inferred from galaxy rotation curves/dynamics and gravitational lensing.
Most importantly, you can rule out a dark matter theory in which dark matter is truly collisionless (i.e. interacts only via gravity), with particle masses sufficiently large to make quantum interactions between the particles negligible (pretty much any particle 20 keV or more of mass) in which dark matter would take an NFW distribution (named after the people who first calculated it) with a strong central cusp, modified by baryonic gravitational feedback which is too small to significantly modify this distribution.
This is not what is observed. See, e.g., 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).
So, any viable dark matter particle theory must have: (1) dark matter-dark matter interactions a.k.a. self-interacting dark matter, (2) wave-like quantum effects of very light dark matter particles with an effect similar to dark matter-dark matter interactions, or (3) dark matter-ordinary matter interactions.
In practice, the correlation between distributions of ordinary matter and inferred distributions of dark matter (which is natural and necessary in modified gravity theories) is so tight that some sort of dark matter-ordinary matter interactions beyond mere gravitational interactions is very strongly favored over options (1) and (2) above.
In support of this conclusion,
see, e.g., Paolo Salucci, "
The distribution of dark matter in galaxies" (November 21, 2018) (60 pages, 28 Figures ~220 refs. Invited review for The Astronomy and Astrophysics Review); Antonino Del Popolo et al., "
Correlations between the Dark Matter and Baryonic Properties of CLASH Galaxy Clusters" (August 6, 2018),
https://arxiv.org/abs/2008.04052; Man Ho Chan, "Two mysterious universal dark matter-baryon relations in galaxies and galaxy clusters"
arXiv:2212.01018 (December 2, 2022) (Accepted in Physics of the Dark Universe); Xuejian Shen, Thejs Brinckmann, David Rapetti, Mark Vogelsberger, Adam Mantz, Jesús Zavala, Steven W. Allen, "X-ray morphology of cluster-mass haloes in self-interacting dark matter" arXiv:2202.00038 (January 31, 2022, last revised November 1, 2022) (accepted by MNRAS); Aidan Zentner, Siddharth Dandavate, Oren Slone, Mariangela Lisanti, “A Critical Assessment of Solutions to the Galaxy Diversity Problem” arXiv:2202.00012 (January 31, 2022); Lorenzo Posti, S. Michael Fall “Dynamical evidence for a morphology-dependent relation between the stellar and halo masses of galaxies” arXiv:2102.11282 (February 22, 2021) (Accepted for publication in A&A); Camila A. Correa, Joop Schaye, "The dependence of the galaxy stellar-to-halo mass relation on galaxy morphology" arXiv:2010.01186 (October 2, 2020) (accepted for publication in MNRAS); Paolo Salucci, Nicola Turini, Chiara Di Paolo, "Paradigms and Scenarios for the Dark Matter Phenomenon" arXiv:2008.04052 (August 10, 2020); Paolo Salucci and Nicola Turini, “Evidences for Collisional Dark Matter In Galaxies?” (July 4, 2017); Edo van Uitert, et al., “Halo ellipticity of GAMA galaxy groups from KiDS weak lensing” (October 13, 2016); and Zhixing Li, Hong Guo, Yi Mao, “Theoretical Models of the Atomic Hydrogen Content in Dark Matter Halos” arXiv:2207.10414 (July 21, 2022)(distributions of hydrogen in interstellar space are also inconsistent with a dark matter particle that interacts only via gravity)
On the other hand, dark dark matter searches tightly constrain the cross-section of interaction between dark matter and ordinary matter for dark matter particles with masses on the order of the proton mass or greater, limiting any interaction between dark matter and ordinary matter to an interaction many orders of magnitude weaker than the weak force interactions between neutrinos and ordinary matter. (Direct dark matter searches don't themselves rule out dark matter particle candidates well in excess of 1000 GeV or more, but other considerations disfavor heavy dark matter candidates.)
Similarly, dark matter made up of "hadrons" of ordinary quarks and gluons bound by the strong force, is pretty much completely ruled out. So, are "sterile neutrino" dark matter candidates that are more massive the the heaviest ordinary neutrinos but no heavier than "warm dark matter" (up to about 20 keV).
Another key fact, is that there is a strict relationship between amount of ordinary matter and inferred dark matter halo size that holds for all isolated galaxies. It does not hold for galaxy clusters, but there is a parallel scaling relationship that does hold for galaxy clusters that is equally tight. Dark matter particle theories, generically, predict a different mass scaling relationship in galaxy clusters than the one that is observed.
See, e.g., 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)
On balance, dark matter phenomena are more wave-like than particle-like which favors low mass dark matter particles or gravitational effects as an explanation.
See, e.g., Alfred Amruth, "
Einstein rings modulated by wavelike dark matter from anomalies in gravitationally lensed images"
Nature Astronomy (April 20, 2023)
https://doi.org/10.1038/s41550-023-01943-9 (Open access copy available at
arxiv).
Hot v. Warm v. Cold Dark Matter And Its Implications
The estimated mean velocity of dark matter particles, which is "cold" to "warm", is something we can infer from the magnitude of large scale structure (galaxies, satellite galaxies, etc.).
Mean velocity of dark matter particles is correlated tightly with dark matter particle mass in "thermal freeze out" theories of dark matter creation in the early universe, and "thermal freeze out" dark matter candidates are all but ruled out.
This consideration, for example, strongly disfavors very heavy thermal freeze out dark matter candidates that can't be ruled out with direct dark matter detection experiments.
If you don't have a thermal freeze out dark matter candidate, however, you need a process to create and destroy dark matter particles in near perfect equilibrium that imparts the right mean velocity to these particles. No process that would do that is known. And, while we could miss a process like that with our current experiments to date for very low mass dark matter candidates, it would be much harder to miss a process like that for heavy dark matter candidates in excess of 1000 GeV.
Dark Matter Decay And Annihilation Signals
The observational constraints on theories with dark matter particles that decay to ordinary matter or photons are also exceedingly strict, so dark matter particle annihilation or decay has to be extremely rare. Mean dark matter particle lifetimes have to be on the order of magnitude of the age of the universe or longer.
Key Discriminants
One key way to distinguish between different dark matter and modified gravity theories is from observations of wide binary stars, i.e. pairs of stars that are very distant from each other but are still a gravitationally bound system, that are not unduly influenced by external gravitational fields (e.g. at the far fringes of galaxies or isolated in open space between galaxies).
In pure toy-model MOND, which generally works at these scale, wide binary stars should be more tightly gravitationally bound than Newtonian gravity would predict. In dark matter particle theories and some other modified gravity theories, this effect shouldn't exist. The data is inconclusive with different groups reaching opposite conclusions.
Another important discriminant between theories (dark matter and gravity-based alike) involves observations of the dynamics of stars well above or below the main disk of spiral galaxies. These observations are also inconclusive so far, and are hard to make, but preliminary results tend to show that MOND effects are predominantly in the radial direction of rotationally supported galaxies - a result that doesn't necessarily support all dark matter particle theories either. A discussion of those observations can be found
here.