What Would Dark Matter Have To Be Like To Fit Our Observations?

Stacey McGaugh at his Triton Station blog (with some typological errors due to the fact that he's dictating since he recently broke his wrist) engages with the question of what properties dark matter would have to have to fit our astronomy observations.

Cosmology considerations like the observed cosmic background radiation (after astronomy observations ruled out some of the baryonic matter contenders like brown dwarfs and black holes) suggest that dark matter should be nearly collisionless, lack interactions with ordinary matter other than gravity, and should be non-baryonic (i.e. not made up of Standard Model particles or composites of them).

But observations of galaxies show that dark matter with these properties would form halos different than those with the cosmology driven properties described above. Astronomy observations of galaxies show us that inferred dark matter distributions intimately track the distributions of ordinary matter in a galaxy, which Newtonian-like gravitational interactions can explain on their own.

As his post explains after motivating his comments with the historical background of the dark matter theoretical paradigm, the problem is as follows (I have corrected his dictation software related errors without attribution. The bold and underlined emphasis is mine):

If we insist on dark matter, what this means is that we need, for each and every galaxy, to precisely look like MOND. 

I wrote the equation for the required effects of dark matter in all generality in McGaugh (2004). The improvements in the data over the subsequent decade enable this to be abbreviated to:

This is in McGaugh et al. (2016), which is a well known paper (being in the top percentile of citation rates). 

So this should be well known, but the implication seems not to be, so let’s talk it through. g(DM) is the force per unit mass provided by the dark matter halo of a galaxy. This is related to the mass distribution of the dark matter – its radial density profile – through the Poisson equation. The dark matter distribution is entirely stipulated by the mass distribution of the baryons, represented here by g(bar). That’s the only variable on the right hand side, a(0) being Milgrom’s acceleration constant. So the distribution of what you see specifies the distribution of what you can’t.

This is not what we expect for dark matter. It’s not what naturally happens in any reasonable model, which is an NFW halo. That comes from dark matter-only simulations; it has literally nothing to do with g(bar). So there is a big chasm to bridge right from the start: theory and observation are speaking different languages. Many dark matter models don’t specify g(bar), let alone satisfy this constraint. Those that do only do so crudely – the baryons are hard to model. Still, dark matter is flexible; we have the freedom to make it work out to whatever distribution we need. But in the end, the best a dark matter model can hope to do is crudely mimic what MOND predicted in advance. If it doesn’t do that, it can be excluded. Even if it does do that, should we be impressed by the theory that only survives by mimicking its competitor?

The observed MONDian behavior makes no sense whatsoever in terms of the cosmological constraints in which the dark matter has to be non-baryonic and not interact directly with the baryons. The equation above implies that any dark matter must interact very closely with the baryons – a fact that is very much in the spirit of what earlier dynamicist had found, that the baryons and the dynamics are intimately connected. If you know the distribution of the baryons that you can see, you can predict what the distribution of the unseen stuff has to be.

And so that’s the property that galaxies require that is pretty much orthogonal to the cosmic requirements. There needs to be something about the nature of dark matter that always gives you MONDian behavior in galaxies. Being cold and non-interacting doesn’t do that. 

Instead, galaxy phenomenology suggests that there is a direct connection – some sort of direct interaction – between dark matter and baryons. That direct interaction is anathema to most ideas about dark matter, because if there’s a direct interaction between dark matter and baryons, it should be really easy to detect dark matter. They’re out there interacting all the time.

There have been a lot of half solutions. These include things like warm dark matter and self interacting dark matter and fuzzy dark matter. These are ideas that have been motivated by galaxy properties. But to my mind, they are the wrong properties. They are trying to create a central density core in the dark matter halo. That is at best a partial solution that ignores the detailed distribution that is written above. The inference of a core instead of a cusp in the dark matter profile is just a symptom. The underlying disease is that the data look like MOND.

MONDian phenomenology is a much higher standard to try to get a dark matter model to match than is a simple cored halo profile. We should be honest with ourselves that mimicking MOND is what we’re trying to achieve. Most workers do not acknowledge that, or even be aware that this is the underlying issue.

There are some ideas to try to build-in the required MONDian behavior while also satisfying the desires of cosmology. One is Blanchet’s dipolar dark matter. He imagined a polarizable dark medium that does react to the distribution of baryons so as to give the distribution of dark matter that gives MOND-like dynamics. Similarly, Khoury’s idea of superfluid dark matter does something related. It has a superfluid core in which you get MOND-like behavior. At larger scales it transitions to a non-superfluid mode, where it is just particle dark matter that reproduces the required behavior on cosmic scales.

I don’t find any of these models completely satisfactory. It’s clearly a hard thing to do. You’re trying to mash up two very different sets of requirements. With these exceptions, the galaxy-motivated requirement that there is some physical aspect of dark matter that somehow knows about the distribution of baryons and organizes itself appropriately is not being used to inform the construction of dark matter models. The people who do that work seem to be very knowledgeable about cosmological constraints, but their knowledge of galaxy dynamics seems to begin and end with the statement that rotation curves are flat and therefore we need dark matter. That sufficed 40 years ago, but we’ve learned a lot since then. It’s not good enough just to have extra mass. That doesn’t cut it.

This analysis is the main reason that I'm much more inclined to favor gravity based explanations for dark matter phenomena than particle based explanations.

Direct dark matter detection experiments pretty much rule out dark matter particles that interact with ordinary matter with sufficient strength with masses in the 1 GeV to 1000 GeV ranges (one GeV is 1,000,000,000 eV). 

Collider experiments pretty much rule out dark matter particles that interact in any way with ordinary matter at sufficient strength with masses in the low single digit thousands GeVs or less. These experiments are certainly valid down to something less than the mass scale of the electron (which as a mass of about 511,000 eV). 

Astronomy observations used to rule out MACHOs such as brown dwarfs, and large primordial black holes (PBHs), pretty much rule out dark matter lumps of asteroid size or greater (from micro-lensing for larger lumps, and from solar system dynamics for asteroid sized lumps), whether or not it interacts non-gravitationally with ordinary matter. 

This leaves a gap between about 1000 GeV and asteroid masses, but the wave-like nature of dark matter phenomena inferred from astronomy observations pretty much rules out dark matter particles of more than 10,000 eV.

Direct dark matter detection experiments can't directly rule out these low mass dark matter candidates because their not sensitive enough. 

Colliders could conceivably miss particles that interact only feebly with ordinary matter and have very low mass themselves, although nuclear physics was able to detect the feebly interacting and very low mass neutrinos way back in the 1930s with far more primitive equipment than we have now. 

Even light dark matter candidates like axions, warm dark matter, and fuzzy dark matter still can't reproduce the observed tight fit between ordinary matter distributions and dark matter distributions within dark matter halos, however, if they have no non-gravitational interactions with ordinary matter.

All efforts to directly detect axions (which would have some interactions with ordinary matter that can be theoretically modeled) have had null results.

Furthermore, because the MOND equations that dark matter phenomena follow in galaxies are tied in particular to the amount of Newtonian-like acceleration due to gravity that objects in the galaxy experience from the galaxy, envisioning this phenomena as arising from a modification to gravity makes more sense than envisioning it as an entirely novel and unrelated to gravity fifth force between dark matter particles and ordinary matter.

If you take the dark matter particle candidates to explain dark matter phenomena off the field for these reasons, you can narrow down the plausible possible explanations for dark matter phenomena dramatically.

We also know that toy model MOND itself isn't quite the right solution. 

The right solution needs to be embedded in a relativistic framework that addresses strong field gravitational phenomena and solar system scale gravitational phenomena more or less exactly identically to Einstein's General Relativity up to the limitations of current observational precision and accuracy which is great.

The right solution also needs to have a greater domain of applicability than toy-model MOND, by correctly dealing with galaxy cluster level phenomena (which displays a different by similar scaling law to the Tully-Fischer relation which can be derived directly from MOND), the behavior of particles near spiral galaxies that are outside the main galactic disk, the behavior of wide binary stars (which is still currently unknown), and must be generalized to address cosmology phenomena like the cosmic background radiation and the timing of galaxy formation.

Fortunately, several attempts using MOND-variants, Moffat's MOG theory, and Deur's gravitational field self-interaction model, have shown that this is possible in principle to achieve. All three approaches have reproduced the cosmic microwave background to high precision and modified gravity theories generically produce more rapid galaxy formation than the LambdaCDM dark matter particle paradigm.

I wouldn't put money on Deur's approach being fully consistent with General Relativity, which a recent paper claimed to disprove, albeit without engaging in the key insight of Deur's that non-perturbative modeling of the non-Abelian aspects of gravity is necessary. 

But Deur's approach, even if it is actually a modification of GR, remains the only one that secures a complete range of applicability in a gravitational explanation of both dark matter and dark energy, from a set of theoretical assumptions very similar to those of general relativity and generically assumed in quantum gravity theories, in an extremely parsimonious and elegant manner. 

MOND doesn't have the same theoretical foundation or level of generality, and some of its relativistic generalizations like TeVeS don't meet certain observational tests. 

MOG requires a scalar-vector-tensor theory, while Deur manages to get the same results with a single tensor field.

Deur claims that he is introducing no new physically measured fundamental constants beyond Newton's constant G, but doesn't do this derivation for the constant he determines empirically for spiral galaxies from a(0), so that conclusion, if true, is an additional remarkable accomplishment, but I take it with a grain of salt.

Deur's explanation for dark energy phenomena also sets it apart. It dispenses with the need for the cosmological constant (thus preserving global conservation of mass-energy), in a way that is clever, motivated by conservation of energy principles at the galaxy scale related to the dark matter phenomena explanation of the theory, and is not used by any other modified gravity theories of which I am aware. It also provides an explanation for the apparent observation that  the Hubble constant hasn't remained constant over the life of the universe, which flows naturally from Deur's theory and is deeply problematic in a theory with a simple cosmological constant.

So, I think that it is highly likely the Deur's resolution of dark matter and dark energy phenomena, or a theory that looks very similar, is the right solution to these unsolved problems in astrophysics and fundamental physics.