Is NGC 1277 a problem for MOND?
tritonstation.com
tritonstation.com
Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaining why galaxies do not appear to obey the currently understood laws of physics.
NGC1277: The galaxy is unique in that it is considered a relic of what galaxies were like in the early universe. The galaxy is composed exclusively of aging stars that were born 10 billion years ago. But unlike other galaxies in the local universe, it has not undergone any further star formation. Astronomers nickname such galaxies as "red and dead," because the stars are aging and there aren't any successive generations of younger stars.
Basically normal matter goes both ways, back-and-forth, compresses and expands, but dark matter goes only one-way, only expands. And this can be seen in the microwave background.
It should be considered "a nice feature" that LCDM explains this but when you have a mass distribution that can be arbitrarily assigned in space, it feels like there are a lot of "nice things you could explain".
For example, they tried to explain the precession of mercury with a hunk of dm orbiting the sun called "Vulcan" (we now know you don't need dark matter to explain this). I believe the Vulcan steps in SF are named after this hypothetical dark matter planet. It's in the same neighborhood as mars, Venus, and Saturn and built around the same time
Both DM and MOND have problems explaining various data and do well at others. DM in particular seems to require a lot of parameters and tuning to make it work.
For example, Korean scientists went looking to disprove MOND by showing there isn't something called the External Field Effect, which they found as a result of their studies.
MOND predicted that JWST would see old galaxies, which mainstream astronomers are now flipping out over.
MOND predicts that binary stars that are far apart would enter the MOND regime. Two studies confirm this observation. A third refutes it but there appears to be methodological problems in this third study.
Having been a scientist, I have little faith that the median practicing scientists have any concept of discernment in terns of following the scientific method.
You're supposed to flip your opinion on models when predictive data shows up. As far as I can tell LCDM can explain a lot of stuff but it hasn't predicted much.
Think of it this way. When you train a ML model if you have a ton of parameters you run the risk of over fitting unless you have a regularization scheme. LCDM easily has at least one parameter per galaxy, and the only regularization is "can we come up with some explanation for this?" Over fitting is a huge risk for LCDM.
By contrast, MOND has one (maybe two or three, if you believe in relativistic MOND) parameters for the whole universe.
Which is why it's making a priori predictions versus a posteriori explanations, it's very hard to make a priori predictions when your parameter for any given galaxy could be anything.
It should say something that "why don't we have a picture of it: is the center of the milky way a blob of dark matter and not a black hole" (paraphrased of ciurse) was a real publication in between the time that we "took a picture" of a black hole in one galaxy and before we had done so for Sagittarius X-1
In fact LCDM shouldn't predict the bullet cluster, a collision that fast between galaxies is extremely rare in LCDM models.
Do you know of any studies that try to combine them?
Like an eight-planet star system, or a star system with a hot Jupiter, or a multi-star system with no planets, all arising within the same giant molecular cloud (GMC)? Even though the cloud-elements behave sanely, even small arbitrary changes in initial values can produce dramatically different later arrangements. Replace the galactic GMC with a dark matter filament in the cosmic web, and why be surprised that all sorts of galaxies form within?
I don't think there is reason to fear arbitrary mass distributions so long as they obey constraints (if you're interested in the maths, the Einstein constraint equations are a good starting point you'll find in textbooks -- Robert Wald's chapter 10 is good and mathy, Alcubierre's or Baumgarte and Shapiro's numerical relativity textbooks are good alternatives for people who think computationally -- and lecture materials). We know empirical constraints and lots of solutions at many scales in the known universe already, and that constraint equations can be found for many other classical field theories; Dirac and successors (Regge et al., Rothe & Rothe et al.) are good resources wrt quantum field theories.
Roughly the slogan is to lay down some arbitrary but plausibly generic configuration and see how it evolves. Do it often enough and you should get familiar structures, or you're back to the drawing board. Large cosmological dark matter simulations that do exactly this are new hat. Standard cosmology solutions often get compared in the same project with alternative theories, sometimes following the spirit of the Standard Model Extension in parametrizing everything possible and plugging in different coefficient values, sometimes simply trying to trace cosmological implementations of an IV formalism on some published alternative to general relativity. For example, Vogelsberger et al., <https://www.nature.com/articles/s42254-019-0127-2>, <https://arxiv.org/abs/1909.07976v6> in which §5.3 has a brief literature review.
"That sounds normal for this type of galaxy, but I guess if you disliked MOND without understanding it, you might misinterpret that title to mean there was no mass discrepancy at all, hence a problem for MOND. I guess. I’m an expert on the subject; I don’t know where non-experts get their delusions."
Still fun to read though.
For that matter, how is QM considered to be an effective model when we can't even reconcile it with gravity?
And if you say "don't take it seriously until it explains all those things" then why should anyone bother to do the heavy lifting for all that math?
Let me make a different suggestion: As soon as you have one or two very interesting observations that modern GR can't explain that are apparently gravitational, then you should start encouraging people to take it seriously and start working on the hard math.
It's a misconception that MOND involves abandoning GR:
Fluid dynamics is a field of study, not any kind of model. Navier-Stokes is just what you get when you apply F=ma to Newtonian fluids.
Or that doesn't count as MOND because it effectively adds another source of gravity and thus dark matter in disguise?
[1] https://journals.aps.org/prx/pdf/10.1103/PhysRevX.11.041050
A question for me is how dark matter theories can reproduce mondian dynamics naturally without each case requiring special tuning.
Or possibly there is a deeper theory of gravity that explains both mercury's precession and galactic rotation.
General relativity simply equates the local density of the stress-energy tensor with the Einstein tensor (and possible scalar multipliers like the cosmological constant) at every point in the whole spacetime. If we measure curvature with e.g. Einstein lensing, we know what the stress-energy tensor must be. The stress-energy tensor encodes all moving matter, including internal non-gravitational degrees of freedom (DOFs). The ~seventeen fields of the Standard Model of particle physics fill all spacetime too, and contribute to the stress-energy tensor. Notably, invisible (in the sense that they do not couple to electromagnetism) DOFs exist in those fields and how they couple to each other; these standard-model mechanisms happily generate non-negligible stress-energy but nothing that we can see at a fine-grained level in any of our telescopes. Gluons' complicated self-interactions are the paradigmatic example: their whizzing about is most of the proton invariant mass, and so most of the mass of visible matter, and so most of the stress-energy in stars (gluon-gluon interactions is especially important in neutron stars, and neutron stars are an important diagnostic of any theory of gravitation) and molecular gas and dust; but gluons themselves are invisible and massless.
Dark matter, in a nutshell, says that "empty space" (ignoring the thin, cold relic fields of the cosmological microwave background and its neutrino equivalent) has some unknown internal degrees of freedom whose action generates stress-energy. Very broadly we call the generator(s) of that stress-energy dark matter.
The distribution of luminous matter (and different species thereof, and how it interacts (e.g. pressure, like ram pressure, can be important in galactic dynamics)) within a galaxy or cluster varies from galaxy to galaxy. Why shouldn't the distribution of dark matter?
So,
> possibly there is a deeper theory of gravity that explains both mercury's precession and galactic rotation
it's just General Relativity. The difference is that we know the distribution of stress energy within our solar system much better than we know the distribution of stress energy in much more distant, or much more complicated, systems (like galaxies or clusters of thousands of galaxies).
Alternatives to General Relativity broadly can take the approach that "empty space" (again ignoring the cosmic microwave background) is just that: there are no hidden non-gravitational degrees of freedom to discover there. Instead, stress-energy of the Standard Model as it is understood today generates the measured curvature seen in lensing by galaxy clusters like "El Gordo" (ACT-CL J0102-4915). Typically this is done by a redefinition of curvature to include auxiliary gravitational fields beyond the Einstein tensor, thus we get families of theories like tensor-scalar gravity, tensor-vector-scalar gravity, and so on. These fields couple with each other, so that the Newton-Einstein-like coupling in the bright parts of galaxies persists but the dynamics of that coupling generates auxiliary curvature in empty space outside the bright parts of the same galaxies. One often hears this described as introducing a new force or a "new fifth-force" produced by matter comparable to Newtonian's force of gravity; the new "force" has a different fall-off at a distance from the source matter than the 1/r^2 of Newtonian gravity or electromagnetism, and that fall-off is designed to produce Milgrom's low-acceleration relation. However (and in the spirit of a thread that started off with the words "generally covariant", MOND-compatible relativistic gravitation is still just gravitational fields being sourced by matter, but with more gravitational fields and interactions and self-interactions among and within those gravitational fields (with the weakness of gravitation proposed as cutting off these extra interactions' inducement of novel behaviours of bound systems like protons). Relativistic MOND approaches tend to be quite complicated in the gravitational sector, and of course must be no less complicated than general relativity (but for "dark matter") in the stress-energy sector.
In short, the GR approach is that the apparently empty space in front of a clearly distorted smaller-angular-diameter/higher-redshift/lower-brightness galaxy (like "La Flaca" <https://webbtelescope.org/contents/media/images/2023/119/01G...>) is not really empty -- there is stress-energy there that does not interact electromagnetically (it also sticks around unlike known standard-model particles that do not interact electromagnetically: photons, relativistic neutrinos -- those fly off to infinity rather than hang around in a halo structure). Studying these systems means understanding how the non-electromagnetic stress-energy is generated, and there are many hypotheses.
Conversely, the MONDian approach is that the apparently empty space around galaxies that flatten their rotation curve (and tbf there are MONDian approaches that capture some aspects of lensed objects) is really empty. Instead, the way that the standard model of particle physics generates curvature is different from General Relativity. Studying how gravity works for a particular (and more restrictive) distribution of matter is what relativistic MOND people set themselves up to do, and again there are also many hypotheses.
In both these broad approaches, the distribution of visible matter varies at different scales and in different systems at the same scale. Local matter distribution drives local gravitational phenomena. MONDian approaches roughly hold that there is no wiggle room -- gravitation must be generated by what we can see, and not by anything else. General Relativity is more lax -- there is no reason to expect that we can see every generator of stress-energy, or that the distribution of the generators must be uniform in space or in spacetime, and gravitational theory should not turn its back on the possibility of discovering new beyond-the-standard-model spacetime-filling matter fields.
One can also go really crazy and say that matter is not the (only or primary) generator of curvature, and that geometric curvature and matter simply coincide mostly by chance. A distribution of curvature that evolved in the early universe -- a cosmic gravitational background -- is taken to be relevant to the dynamics of galaxies and clusters about as old as ours. In these theories there are also auxiliary gravitational fields, and those typically allow for a MOND but are also designed to allow for the acceleration of the expansion of the universe and other features that relativistic MOND essentially imports from general relativity (in the form of a scalar multiplier on one or more of the curvature field(s)).
So, in summary I'll return to your first question:
> how [can] dark matter theories reproduce mondian dynamics naturally without each case requiring special tuning
They can't. There is an initial (or at least early) values surface that the laws of the theory turn into galaxies and clusters of all sorts. The initial values set up some distribution of interacting and self-interacting matter (that is initially, or evolves into, the standard model and dark matter). It also may set up primordial gravitational radiation not produced by the matter, and things like an evolving cosmological (non-)constant.
Relativistic MOND is not different on this front -- there must be some initial or early values surface that the laws of the theory turn into the standard model and the various gravitational fields around MONDian galaxies, mondian wide binaries, MONDian relativistic stars (like white dwarfs and neutron stars, especially in wide binaries of those), and so forth. These approaches may be even more sensitive to the distribution of things like primordial gravitational radiation because in general gravitational radiation is considerably more complicated by the presence of fields beyond the Einstein tensor: any additional scalar, tensor, or vector field may have their own polarizations, and their polarizations may modify the polarization of the mathematical structure closest to that of the metric tensor or the Weyl tensor parts of the Einstein tensor. Thus the considerable interest in the small variations in the cosmic microwave background by people who spend any time comparing General Relativity and relativistic MONDian theories.
Ultimately the "special tuning" is the "past hypothesis", which is highly similar for both approaches: the distant past of the universe was hotter, denser, and lower entropy than the universe full of galaxies. The lower entropy is the puzzle. What ordered that? Again, there are many and various thoughts, and a handful of plausible hypotheses.
You seem to be saying that there is no way for DM theories to reproduce mondian dynamics naturally, it's all just about the distribution of DM.
It seems obvious that DM theories have to get the distribution (and how it interacts with itself and/or other things) right to account for the motions we observe in all cases. This seems to be difficult with our current theories, at least to my layman's eye. I see things like superfluid DM proposed, etc.
An ELI would be good to confirm my understanding, if you have time.
> ELI ... my understanding
I don't know what level to pitch an ELI at; below is my best guess, and it's probably uneven. I did't want to aim for a reader who is perfectly capable of picking up a textbook and reading the academic literature starting with Famaey & McGaugh 2012. I also don't want to aim so low that it's basically slogans; there are enough of those in forums like this, and they're often inconsistent or outright wrong. I'm also conscious that we are not the only two participants in this particular discussion.
I'm not sure what I can do to improve your understanding and I'm not about to examine you to assess it; as I said there are textbook treatments (any decent galaxy dynamics or galactic astronomy text updated in the last twenty years will touch on the empirical MOND relation, and the standard grad textbook by Binney & Tremaine goes quite deep on MOND) and more cutting-edge literature that has developed since the 1980s. Likewise, I'm not here to help you choose between MOND or dark matter as ways of resolving observed acceleration anomalies, only to try to describe the two approaches and offer some contrasts to the extent that these very different approaches can be contrasted (IIRC McGaugh, of triton station at the top of the discussion here, calls this the theoretical "incommensurateness problem"). There are plenty of blogs by partisans.
I also don't do galactic dynamics; it has little appeal for me. However, MOND vs Newton/Einstein is a debate that arises almost exclusively because of galactic dynamics. I do do weak field General Relativity, which is rarely used in galaxy astrophysics since more tractable approximations are available, and more still are forthcoming. That colours some of what's below, as it is those approximations which are compared with MOND (which one will want to think of as an approximation of some yet unknown alternative to General Relativity).
> naturally
Don't get hung up on that; nature is what selects the distribution. Nature also selects the distribution of stars in our sky, the particles in the standard model zoo, their masses, spins, couplings, dimensionless constants, and so forth. It's not human scientists who decided to make Mizar a double double-star system with their particular orbits. Newtonian gravitation, invented by humans, can describe those orbits well enough, but you must first measure some initial positions and velocities for those four bodies. Heck, only recently (about 1997) did we discover (through such measurement) that Mizar is a four-body system!
(In fact, Mizar is possibly a test of one aspect of MOND as an adaptation of Newtonian gravitation: the External Field Effect ought to produce marginally different orbits compared to Newtonian Kepler orbits because of the system's immersion in the Galaxy's MOND field. General Relativity agrees completely with Newtonian gravitation because of the former's strong equivalence principle and because dark matter, if it exists, is such a small part of the local stress-energy tensor around Mizar that its generation of curvature is negligible. Maybe Mizar ends up as evidence in favour of MOND-like post-Newtonian gravitation because of the external field effect, who knows?)
We don't choose the matter-energy distribution of the moon, but as we've gotten better at measuring it we can now describe very precisely its orbit millions of years in the future, as long as nobody blows it up or feeds Earth to a giant space goat.
> it's all about the distribution of DM
It's all about the initial position and velocity of every teensy mote of matter however you want to think about matter (e.g. as excitations in a dozen or more quantum matter fields, or as individual interacting particles or whatever). That's the case in every one of these classical field theories be it Newton (in the Newton-Poisson sense), modified Newton (ditto, e.g. Bekenstein & Milgrom 1984), or Einstein. We have no hope of specifying all that data much less evolving every mote of it at every tiny step, so we must coarse-grain the initial data. A dark matter halo is a coarse graining of some very fine properties of matter that we do not understand yet and haven't been directly detected much less produced in a laboratory. MOND is a coarse graining of some very low-energy dynamics that somehow arises from matter as we know it today; no laboratory in our solar system is able even in principle to produce orbital accelerations low enough or decoupled enough from the Milky Way's external field to demonstrate those dynamics -- we would need a laboratory at the edge of our galaxy.
We haven't found any hypothesized candidate for quantum-field dark matter ("particle dark matter") yet. But we also haven't found the generator of the dynamics in any candidate relativistic MOND theory either. The failure for one is in no way a success for the other.
We need a relativistic version of MOND because relativistic gravitational effects are readily apparent in gravitational lensing (they are feasible to just see with off-the-shelf telescopes, although professional telescopes and Hubble and Webb can see more of them and in better detail), gravitational radiation (which for now requires a LIGO/Virgo/KAGRA type laboratory or arrays of radiotelescopes and long observation times), the decays of inspiralling orbits, the formation of stellar remnants (or some alternative explanation for pulsars), the spectrum of quasars and blazars, the expansion history of the universe (the Lyman-alpha forest and the cosmic microwave background) and so forth.
> DM theories have to get the distribution ([and dynamics]) right
yes.
But equivalently
> Modified gravity theories need to get the (distribution) and dynamics right
The distribution in the latter case is that of the luminous matter and its self-interactions and couplings with the extra gravitational fields.
In General Relativity there is only one field to which all matter couples identically. That leads to things like the universality of free-fall (cannon balls, feathers, and entire moons free-fall the same way in empty space), the equivalence between uniform acceleration and a uniform gravitational field, the equality between passive and active gravitational masses and the inertial mass, and the Einstein equivalence principle which holds (simplifying somewhat) that you can repeat the same non-gravitational experiment at different times, at different locations, and with different orientations and get the same results. There are good mathematical proofs that afaik nobody has seriously challenged which demonstrate that General Relativity is the unique theory that produces these equivalences. Any other theory will deviate in one or more of them. Relativistic MOND, quite generally, breaks the strong equivalence principle: the gravitational motion of a star within a galaxy depends on how deep in the galaxy it is, rather than on its initial position and velocity. We have excellent evidence of the strong equivalence principle from pulsars in multi-star systems in our galaxy, so this is a puzzle for MOND.
> my understanding
The field equations of Newtonian gravitation has a relativization in the form of the Einstein Field Equations of General Relativity.
The Modified Newtonian field equations of MOND et al do not have such a relativization.
Relativistic effects are mostly negligible in galaxy dynamics, so because of insufficient evidence one has for now a free choice of describing galaxy dynamics with Newton where one modifies the dynamics ("MOND") or with Newton where one modifies the distribution (initial positions, velocities) of matter ("Dark matter").
If relativistic effects are non-negligible -- for instance, if one is interested in how merging galaxies' central black holes evolve -- then neither adaptation of Newton is suitable, you need a relativistic theory. Newton + DM -> GR + DM is the only generally useful theory today.
Moreover, because we know more about mathematics than Einstein did in the early 20th century, we can justify approximations of General Relativity such as linearized gravity. These are one-way justifications: you can pick out a simplification of General Relativity and prove it has compatible dynamics in some limit, but you can't start with some approximation and derive General Relativity. You likewise can't derive a relativistic MOND theory from the non-relativistic MOND -- the latter maps to a vast number of possible relativistic theories, all with practical differences. And there is no relativistic theory from which you can extract MOND as a weak field approximation.
Given that and the non-relativstic-limit free choice of theory (DM has neither been proven nor disproven), if one wants to solve for anomalous accelerations (which are pretty obvious) in galaxy dynamics, one can choose MOND or Newton + DM.
Meanwhile, people wonder about the nature of the anomalous acceleration. Neither MOND nor approximations of General Relativity get it right in all respects, and there isn't a complete solution in the full-theory-of-General-Relativity-in-microscopic-detail available because it's too hard to compute in 2023, and there are aesthetic choices in how one coarse-grains for tractability.
[superfluid in sibling reply]
> I don't know what level to pitch an ELI at
I think you nailed it mostly. I can handle concepts, but my math isn't really up to it. I might have a look at the textbooks you cite.
> Likewise, I'm not here to help you choose between MOND or dark matter as ways of resolving observed acceleration anomalies, only to try to describe the two approaches
That is all I want; I am not qualified to make that choice anyway.
> DM theories have to get the distribution ([and dynamics]) right >> yes But equivalently >> Modified gravity theories need to get the (distribution) and dynamics right
True.
The main differences as I see it is that MOND only requires standard model matter that we can already observe, and it makes some predictions. DM requires additional matter and doesn't seem to predict anything, as we can always find a particular distribution that explains each case. But MOND is not compatible with relativity (so far) whereas DM is.
Fascinating stuff, and the truth to the extent we can determine it, will no doubt be surprising and different to what we currently think.
Thanks for taking the time to explain our current state of knowledge to an interested layman.
> we can always find a particular distribution that explains each case.
This is hardly a weakness, nor is it unique to one theory or the other. In order to explain the MOND rotation curve, one needs a specific distribution of luminous matter. The luminous matter is not always straightforward to measure; weighing galaxies is hard (there is lots of obscuring dust and gas and so no hope of counting, much less tracking the orbits of, a trillion or so stars in a galaxy). Nobody's confident of even Andromeda's mass. See for example the excellent <https://aasnova.org/2020/06/09/how-do-you-weigh-a-galaxy/>. So when you read, hey, MOND gets the rotation curve right, remember that both MOND and non-MOND galaxy astronomers can only estimate galaxy masses, and there are big error bars. Rotation is easier to estimate, because astronomers can use interferometry at different wavelengths (e.g. to track particular types of molecular gas cland that ouds, or particular types of stars, by looking at spectral doppler shifts e.g. between the leading edge and the trailling edge of an edge-on disc galaxy).
> ... doesn't seem to predict anything ...
On the contrary, it predicts that free bodies in galaxies, which includes stars and gas clouds, follow free-falling trajectories that are entirely predictable given the free bodies' position and momentum at any moment. It also makes predictions about the aggregation of free bodies (e.g. into Bok globules) due to gravitational collapse, and that the centre of momentum of the aggregate body itself moves as a free body. The predictability is not affected by cold dark matter, which is too sparse and collisionless. MOND-mimicking DM theories, like the superfluid DM model you mentioned, preserve all of these features of Newton-Einstein gravitation except that they tend to add actual collisions involving dark matter and so strictly speaking the collided-with stars are not free bodies. More on pseudo-MOND below.
MOND as a MOdified-Newton gravity theory predicts that given two identical free bodies (two isolated stars each with the same mass, for example) follow trajectories which depend on their position, momentum, and distance from the centre of mass of the host galaxy at any given moment. So such orbits are not entirely predictable unless you know exactly the distribution of mass in the host galaxy. More generally MOND predicts that all sufficiently wide orbits at all mass scales and mass ratios are deformed compared to Kepler's laws, so e.g. wide orbits of black holes would work differently. As a non-relativistic theory MOND says nothing about gravitational waves but it is hard to imagine a relativistic completion of modified-gravity MOND that would produce the waveforms detected at LIGO/Virgo/KAGRA and in pulsar timing arrays: gravitational radiation is determined by the orbital properties, so if the orbital properties differ (widely-orbiting black holes should complete orbits more quickly in MOND, just a star at the edge of a spiral galaxy will orbit more quickly in MOND than in Newton-without-dark-matter) then gravitational waves should too (the frequency should be higher; gravitational wave frequency is directly proportional to the orbital period of the source binary).
Distinguishing the two is presently awfully difficult because precisely tracking the orbits of stars is hard, although there is ongoing progress thanks to the ESA Gaia surveys among others. What makes it hard? Obscured (dust, gas, other stars, ...) views, difficulties in determining the angle the orbital plane makes to our line of sight, tiny tiny tiny angular sizes, and on and on. Also, the relevant orbital periods are many years long, so it also requires patience and some care as newer instruments replace ones that become obsolete over the course of a tracked orbit.
Finally, non-relativistic MOND says nothing about tight orbits of black holes, and it is the detection of final inspirals that give us the best signals. Worse, the MOND modification to Newton falls off with greater mutual acceleration, so it will fall off as inspiralling black holes move closer together (in MOND stars near the core of a spiral galaxy move on essentially Newton-Kepler orbits).
To summarize part of the above:
> MOND is not compatible with relativity (so far)
MOND as a modified gravity theory cannot be compatible with general relativity, and that's quite deliberate.
Pseudo-MOND (e.g. a MOND-mimicking dark matter theory comparable to the superfluid DM you brought up, in which orbits are still Newtonian but there are additional tiny "m"s in the F = GMm/r^2, or some small fifth force F = Gmm/r^2 + f) can be built and even made fully general-relativistic, but it would be really weird (and really really disingenuous) to call that MOND given what the initials stand for and given MOND's origins with Milgrom. At the risk of "no true scotsman" catcalls, real MOND requires V^4 = GMa_0 so F = m (v^2/r)^2/a_0 in the "deep-MOND regime". It just doesn't in a pseudo-MOND, at best you can come pretty close (think along the lines of a long Taylor expansion of 1 + (x^2 + x'^n + ...) where the non-leading terms are corrections from shells of (interacting so not strictly dark "super-dim") matter concentric upon the host galaxy's core and with a long enough "..." you get a decent approximation of 1 + (a_0/a) like how one might try to get a good approximation of π; deep-MOND regime's "standard interpolating function" is strictly sqrt(1/(1+(a_0/a)^2)). Pseudo-MOND DM mimicry will always introduce additional small accelerations in random directions along with a biased acceleration that's the heart of the mimicry.
More succinctly, in pseudo-MOND, Newton is more fundamental than the mimicked MOND, such that everything including the stuff doing the mimicry orbits according to Newton.
> DM requires additional matter
Yes. The matter can be a mix of things already known in the Standard Model (of Particle Physics) and things which aren't. Since the Standard Model is a concordance model that dates from the 1970s (to concord with experimental data confirming the existence of quarks) and has been updated within the past ten years (notably to concord with the experimental data confirming the existence of a Higgs boson), the Standard Model is hardly frozen in time.
There are a number of open issues in the Standard Model that drive the hunt for new particles (you can start at wikipedia, <https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Mo...>) for wholly non-gravitational reasons. Whatever these new particles are, they will be Lorentz-invariant by the nature of the Standard Model as a relativistic quantum field theory. It is straightforward to couple a non-gravitational Lorentz-invariant field theory to General Relativity up to some limits, but the dynamics of galactic spin are very much well within those limits. So if Beyond-the-Standard-Model physics searches discovers one or more new particles, those particles will both feel and source gravitation. If those particles can congregate in galaxy clusters without clumping into molecules and collapsing gravitationally in timescales that are short compared to the age of the universe, those particles would be good candidates to be part of the cold dark matter in the standard model of cosmology (which is also a concordance theory which gets updated when evidence requires that).
It wouldn't surprise many people if suitable new particles were demonstrated. However, it is certainly possible that the there won't be any found, perhaps because there aren't any to be found.
Because of the highly-tested equivalences between acceleration and gravitation and covariant physics in freely-falling and inertial coordinate systems, it would be surprising to find some feature of Standard Model of Particle Physics matter that generates gravitational fields that break these equivalences. Nobody serious would ignore that if it were demonstrated.
> it will no doubt be surprising and different to what we currently think
I would love that, but I am not that optimistic. I expect to be un-surprised (cf. the Higgs boson confirmation, and many tests of the equivalence principles and Lorentz invariance) by yet another confirmation of General Relativity rather than something which might provide usefully different yet correct descriptions of high-energy gravitational physics.
> superfluid DM proposed
Justin Khoury's version is a Bose-Einstein condensate (BEC) of axion-like particles. The BEC forms a halo and is fluid, like a gas, in most of the halo. In the halo's central regions the BEC undergoes a phase change and becomes superfluid, and in that region interactions with baryons are produced which bubble up to the thin nonsuperfluid phase, where they interact with baryons again as a "fifth force" where one would want to understand that as viscosity. Viscosity vanishes in a superfluid. Here the idea is that the superfluid phase does not interact much with baryons except to generate vortex-like ring-perturbations which rise (and I think magnify) from the core, where the sticky-viscosity of the non-superfluid phase deposits energy into baryons, with a bias driven by galaxy's bulk angular momentum (the kicks being more in the direction of rotation and radially outward, generating the flat velocity curve). It's very much a particle dark matter theory, and a somewhat complicated one. It shows that a more than one particle dark matter theory can reproduce empirical results from MOND. And yes, as with any field theory, one would want to take a Hamiltonian approach and consider the dynamic canonical variables (x, p) [position, momentum], so you will need to specify all (x, p) at some time t, and because that's intractable, one coarse-grains.
Axions have yet to be directly detected in astronomical or laboratory settings, and nobody knows how they behave at ultracold temperatures and ultrasparse densities. Do they even BEC?
However, if they did exist and have the properties to form a Bose gas etc etc, and their cosmological participation isn't forbidden by higher-energy completions of the standard model, then there is a nice property here: it's just relativistic quantum fields on curved spacetime. Relativity (specifically in the sense that we can relate physical coincidences in arbitrary systems of coordinates) is baked in from the start. And you would get the empirical MOND relation in galaxy dynamics. But it's certianly not a MONDian theory in spirit. There is no modified gravity to be seen here.
There is no such thing as "purity" in physics. The whole reason most people work on MOND is because it provides a simple effective theory for not only describing observations with fewer parameters than cold dark matter, but predicting them more effectively. Every MONDian paper I've read has effectively been saying, "stop ignoring this obvious relation in preference to unnecessarily complicated and ad-hoc DM that provides no predictive power". If a superfluid or other dark matter theory derived MONDian dynamics, then pretty much everyone would be happy with that.
Over the last 20 years it appears to have moved slightly from "complete tinfoil hat" to "likely wrong longshot, but hard to trivially dismiss". I'm not an astrophysicist, I formed the above observation by asking astrophysicist friends what they think. :)
FTA: Eyeballing/back of the envelope the NGC 1277 data suggests it falls into that category (me: probably a more careful calculation is warranted). Usually galaxies that fit this are dense elliptical; 1277 is ultramassive lenticular, though to be fair lenticular ~elliptical.
It says that because of the acceleration, MOND predicts Newtonian motion.
It does not say that you expect not to see dark matter, just that dark matter is not needed to explain that motion.
However, this is a problem for dark matter theories precisely because we expect galaxies to form in concentrations of dark matter:
"The infall of baryons acts to further concentrate the central dark matter. So the nominal expectation is that there should be plenty of dark matter near the centers of galaxies rather than none at all. That’s not what we see here, so nominally NGC 1277 presents more of a challenge for the dark matter paradigm than it does for MOND"