Dark Matter, Part 2: Self-Interacting Dark Matter and other Models

Cluster Abell 383, zoomed in on its Brightest Cluster Galaxy, gravitationally lensing background galaxies. Credit: NASA/STScI

Introduction

In my last post, we discussed some of the ways we know dark matter exists. But what is dark matter? This is one of the million dollar questions of cosmology. The answer is that we really don’t know what it is, yet. But we do have some ideas of what it might be. In the following sections, I will give a brief overview of a few dark matter models. However, the model I’ll go into detail about is a type of dark matter I study called Self-Interacting Dark Matter, a model that isn’t particularly well-known, yet. But that’s about to change, starting with this post! Without further ado, let’s talk dark matter models!

WIMPs and Supersymmetry

Because we don’t know what they look like, here’s some cute art of WIMPs. Credit: Sandbox Studio, Chicago

One of the most widely accepted models for dark matter is the Weakly Interacting Massive Particle, or WIMP for short (because, you know, the physicist’s naming game is strong). WIMPs are particles that come from a theory called supersymmetry, which unifies the strong, weak, and electromagnetic forces¹ very early in the Universe’s history, after which they split up into the distinct forces we see today. Supersymmetry postulates that every particle has a supersymmetric partner whose spin differs by 1/2; that is, bosons² and fermions³ reverse their roles in supersymmetry. And again, because our naming game is on fire, particles become sparticles, electrons become selectrons, gluons become gluinos, and so on. A good candidate for WIMP dark matter would be the neutralino, a supersymmetric particle. It would be the Lightest Supersymmetric Particle, because as the LSP, it can’t decay into anything else—it’s already the lightest possible sparticle.

WIMPs are classified as Cold Dark Matter (CDM), where cold means that the particles move at non-relativistic speeds. But CDM also implies that the dark matter particles are collisionless—ie, they do not interact with each other at all. WIMPs also match the relic density, or the amount of dark matter determined by cosmology, extremely well, a coincidence often referred to as the “WIMP Miracle”. Because of this, WIMPs are superb candidates for dark matter. They’d also provide evidence for supersymmetry. However, despite the numerous searches for WIMPs, evidence for these elusive particles has yet to be established.

¹The Grand Unified Theory, or GUT, unifies gravity with these as well.
²Bosons have integer spins, ie 0, 1, 2,… Note: the Standard Model of Particle Physics does not have any bosons with spins 2 or greater. The Higgs has spin 0, while force mediators (the photon which mediates the electromagnetic force, the gluon which mediates the strong force, and the W and Z bosons which mediate the weak force) have spin 1; the graviton, which is physics Beyond the Standard Model, is said to have spin 2.
³Fermions have half-integer spins, i.e. 1/2, 3/2, 5/2,…

Axions: the Strong CP Problem Solvers

More artistic impressions: the axion. Credit: Sandbox Studio, Chicago

Axions, subatomic particles that were theorized to solve something called the “strong CP problem” in particle physics, are another candidate for dark matter. In a nutshell, CP violation, where C stands for charge conjugation¹, and P for parity², is observed in weak interactions. It should also be observed in strong interactions, but it’s not. CP violation in strong interactions would result in the neutron having an electric dipole moment that’s about a trillion times stronger than the value experimentally measured, so we know it doesn’t happen, or happens very little.

Conserving CP symmetry in strong interactions requires lots of fine-tuning: briefly, there’s a parameter theta that can take on a wide range of values, but to conserve CP symmetry (or to ensure CP violation does not occur), the parameter needs to be very nearly zero. The fact that it could take on so many different values, but somehow, sits at almost exactly zero, is troublesome; it means the theory needs a lot of fine-tuning to make it work, and fine-tuning in physics is usually a sign that something is wrong. But it is possible to preserve CP symmetry without fine-tuning by something called the Peccei-Quinn mechanism: introduce a symmetry and break it³, which results in the production of a new subatomic particle—the axion. The axion replaces the parameter theta and relaxes its value to zero, explaining why this value has to be so close to zero.

Axions happen to be a great candidate for dark matter. They’re light particles with no charge and very rarely interact with matter, and are categorized as a type of CDM. And if they exist, they should’ve been produced in copious amounts in the Big Bang, so there should be lots of it lying around in space. Like the WIMP, axions have not yet been detected, but the fact that they’re well-motivated theoretically by particle physics and could potentially solve a longstanding problem in cosmology make these particles really appealing.

¹Charge conjugation takes a particle and turns it into its antiparticle.
²A parity transformation takes a point x and transforms it to -x.
³Spontaneous symmetry breaking, which occurs when the equations of motion of a system are symmetric, by necessity results in the production of a particle called the Nambu-Goldstone boson, a particle that has no spin and is massless. If the symmetry is not exact, but approximate, then the symmetry breaking is explicit, and the particle that comes out of such symmetry breaking is a pseudo Nambu-Goldstone boson, which also has no spin but is not massless. In the case of the strong CP problem, the pseudo Nambu-Goldstone boson is the axion.

Sterile Neutrinos: a Fourth Neutrino Flavor?

A sterile neutrino just hanging out on its own while the other neutrinos play. Credit: Sandbox Studio, Chicago

Neutrinos have been long considered as candidates for dark matter, but because their mass is really small, they move at relativistic speeds; this means they’d be hot rather than cold, and simulations have shown that hot dark matter cannot produce the structure we see today. But there is a more suitable possibility for dark matter in the form of a fourth neutrino flavor: the sterile neutrino.

Prior to the discovery of neutrino oscillations, physicists kept coming up short on their detections of the number of solar neutrinos coming out of the Sun compared to what was theoretically expected—two-thirds short, to be exact. When it was discovered that neutrinos oscillated between three flavors¹, the discrepancy of detected solar neutrinos was explained exactly. However, the the Liquid Scintillator Neutrino Detector (LSND)² found anomalies in the amount of neutrinos produced in accelerators that cannot be explained by the three flavors alone. But if sterile neutrinos exist, then the weird observations make sense. This motivates the existence of the sterile neutrino.

Another thing that makes things strange about neutrinos is that all fermions are found to have both right- and left-handed chirality, while the neutrino only has left-handed chirality (and the antineutrino, right-handed). Sterile neutrinos are right-handed, which would fill in the right-handedness blank in the neutrino picture, so their existence is well-motivated by theory as well.

Neutrinos are tough to detect as it is. They don’t interact with anything but the weak force and gravity—there are billions of them running through your finger as you read this, like it wasn’t even there. Sterile neutrinos are even tougher, because they interact only with gravity³. The mass of the sterile neutrino is unknown; it can be of order GeV scale, or as light as sub-eV scale. With the right mass, the sterile neutrino could be a fantastic candidate for dark matter.

Bonus: the CDM paradigm works very well on large scales, but on small scales, simulations form galaxy halos that are far too dense in their central regions (they are cuspy) compared to observations, which show that halos tend to have flatter density profiles (are less dense) near the central region (they have cored profiles)—this is known as the core-cusp problem. Sterile neutrinos can resolve this problem, producing cores that match observations better than CDM, which further makes sterile neutrinos good candidates for dark matter. 

¹The three neutrino flavors are the electron neutrino, the muon neutrino, and the tau neutrino, which are associated with the electron, muon, and tau leptons in weak interactions, respectively.
²You can read a bit about the anomalous results from LSND, here.
³It’s because they don’t interact with the weak force that they were named “sterile” neutrinos.

Kaluza-Klein Dark Matter: Stuck in Higher Dimensions

I clearly need to up my art game, these are great. Credit: Sandbox Studio, Chicago

A dark matter model that I find really cool comes from string theory, a theory that replaces point-like particles with strings and requires more dimensions¹ than the three spatial and one time dimensions we’re familiar with, but they cannot be accessed because they require really high energies—Kaluza-Klein dark matter.

Early in the Universe’s history, matter was really hot and had very high energies. If these extra dimensions exist, then matter would’ve had enough energy to access these higher dimensions. Here’s where Kaluza-Klein dark matter comes in: when the Universe cooled, matter that lost lots of energy could no longer access higher dimensions, and became confined to the three spatial and one temporal dimensions we know; however, some got stuck in higher dimensions, and this matter is Kaluza-Klein dark matter. The idea is that, having access to dimensions that are out of reach to us, these particles appear to have more momentum than they actually do, because they have momentum in dimensions that we can’t see; this makes them appear to be more massive. And so these particles, stuck in dimensions we cannot access, reveal themselves through their gravitational interactions, all while being out of reach to us, which explains why we haven’t detected them yet. Sounds a lot like dark matter, doesn’t it?

As of now, there is no evidence of dimensions beyond the four spacetime dimensions we live in. If Kaluza-Klein dark matter exists, we’d need to be able to access the extra dimensions in order to detect it. In theory, we could access them if we were able to create conditions with high enough energies. To do that, we’d need the LHC to operate at far higher energies, or perhaps a new particle accelerator altogether. So hold tight and get comfy in our 4D spacetime for now—we’re a long way from proving (or disproving) the existence of higher dimensions, and thus, this type of dark matter.

¹String theory most commonly requires 10 or 11 spacetime dimensions, but one variant has 26 spacetime dimensions.

Self-Interacting Dark Matter: Turning Galaxies in to Cosmic Particle Colliders

Particles colliding and scattering outwards in the most creative attempt I could come up with, atop a galaxy cluster that’s full of dark matter. The scattering particles were done by me in Adobe Photoshop, and the background image of Abell 1689 credit goes to NASA, ESA, E. Julio, P. Natarajan, and J. P. Kreib

Now that we’ve gone over some of the possible dark matter candidates, let’s talk about a dark matter model beyond the CDM paradigm that’s not widely known, but has been gaining attention in recent years: Self-Interacting Dark Matter (SIDM), a type of dark matter that, in contrast to CDM, does experience self-scattering. Because it self-scatters, galaxies become cosmic particle colliders in space! 

SIDM was introduced in large part to solve the core-cusp problem in astrophysics, which mostly plagues small galaxies, like dwarfs: CDM simulations create halos that are way too dense in their cores compared to observations. But if we turn on self-interactions, the over-densities in the cores are alleviated. This is because self-interactions act to thermalize the dark matter halo, warming up the core and easing up the central density. The scale of the self-scattering interaction requires a new force to mediate the interactions, expanding the dark sector further.

Another problem seen in galaxies is known as the diversity problem: spiral galaxies that are expected to have similar rotation curves, don’t, and CDM isn’t able to explain how similar galaxies can have such different rotation curves. SIDM has recently been shown to do a good job at explaining the diversity in rotation curves as well (you can read more about this in an article I wrote for the UCI blog, here).

The core-cusp problem discussed above isn’t seen in elliptical galaxies and galaxy clusters. These halo scales are known to be denser in their cores than dwarfs are, so CDM tends to explain them pretty well. If SIDM is to provide a better representation of galaxy halos than does CDM, then it needs to be able to explain galaxy halos on all scales. If the interaction cross-section¹ has a velocity dependence², such that the cross-section decreases as velocities increase, then SIDM can explain all galactic scales, and it’s looking like it does have a velocity-dependent cross-section. 

It’s important to point out that the SIDM profile combines two profiles for its halo: an isothermal profile (where the halo thermalizes via self-scattering) for the inner part of the halo, matched onto a profile that’s essentially CDM (no scattering) for the outer part of the halo. These two profiles are matched at at a point where the number of scatterings per dark matter particle is equal to one (we call it r₁; not too important, but I’ll refer back to it later); this separates the isothermal part of the halo from the CDM part. Within this radius that we call r₁, the number of self-scatterings per dark matter particle is greater than one, and hence the halo is thermalizing within this region. Outside, the number of scatterings per dark matter particle is less than one, so the region outside r₁ is effectively CDM. The size of r₁ in a halo depends on some of the halo’s properties, one of them being the interaction cross-section.

Just a cute little Feynman diagram I made of two dark matter particles (the m_X‘s) scattering and exchanging a dark force particle (the ϕ).

Okay, now that we’ve discussed how the SIDM profile looks, let’s talk about its interaction cross-section. For every galaxy scale, we have different velocities. So, particles in dwarf galaxies have velocities of order 10s of km/s, while galaxy clusters have velocities greater than 1000 km/s. That is, velocities increase as the mass of the system increases, which intuitively makes sense as more mass means a deeper gravitational potential, or larger gravitational force. This allows us to use various galaxy systems to probe collisions at different speeds. Since SIDM should have a velocity-dependent cross-section, such that the cross-section decreases with increasing velocity, this translates to having a different r₁ for each galaxy, depending on the system; large systems tend to have a small r₁ (relative to the size of the system), while smaller systems will have larger r₁ (relative to the system). That means that galaxy clusters should have really small isothermal regions, while dwarf galaxies will have pretty large ones. This is important, because it tells us that SIDM fixes the small-scale problems of CDM while preserving all the conjectures of CDM cosmology on large scales. So, not only does SIDM not mess with the strong successes of CDM, it fixes its problems on small scales, too! Needless to say, SIDM is an excellent dark matter candidate. 

The next step for SIDM is to nail down its particle physics properties. To do that, we need to confirm the dependence of its interaction cross-section on velocity. Both my undergraduate research (which is working on intermediate scales, ie large elliptical galaxies and galaxy groups) as well as my PhD research (reanalyzing the cross-section constraints for large scales, ie clusters of galaxies, with relaxed constraints) is dedicated to doing this. The interaction cross-section is really important because from it, we can learn about particle properties such as the dark matter particle mass, the mass of the new force mediator, and its coupling constant³. Knowing this information is essential, so that experimental searches know what to look for. If you’re interested in a more comprehensive and advanced look at SIDM, here’s a beautiful paper that goes into the problems it solves, the problems it faces, its formalisms, particle physics models, even possible direct detection experiments.  

¹Although it’s a bit more complicated than this, you can think of the cross-section as the area of, say, two balls going in each other’s direction: the larger the area, the more likely the balls are to actually hit each other, or interact. In reality, using the physical area of two scattering particles works for macroscopic objects, like the two balls I mentioned above. For particles, other forces acting on the particles need to be considered, like for example, the effects from the electromagnetic force such as the Coulomb potential. But this will suffice to get a conceptual idea of what a cross-section is.
²This is similar to Rutherford scattering, which also has a cross-section that depends on the velocity and is proportional to 1/v⁴.
³A coupling constant is a dimensionless parameter that tells us how strong interactions are. Each force has a different coupling constant: the strong force has a coupling constant of 1, the electromagnetic force has a coupling constant of 1/137, and the weak force has a coupling constant of about 10^-6.

Other possibilities for Dark Matter

There is another explanation for dark matter: if gravity acts differently on scales larger than those we’ve been able to directly study (like the solar system), then dark matter may not even exist, and may be an artifact of our understanding of gravity being fundamentally wrong. One such attempt at doing away with dark matter is called MOdified Newtonian Dynamics (MOND), which literally attempts to modify gravity so that galaxies and galaxy clusters that should be flying apart without dark matter, don’t. A problem I have with MOND is that dark matter is a cosmological problem, so Newtonian physics doesn’t apply—to solve a problem, you need to be able to speak its language, and for cosmology, that language is General Relativity (GR). Now, there have been attempts at modifying gravity using GR, but again, many of these theories still require additional amounts of matter to explain observations. This brings us right back to square one (needing dark matter), while turning already difficult physics (GR) into something even more beastly. So modifying gravity to take dark matter out of the equation is still a work in progress. And although I don’t think that’s the way to solve this problem, it’s really important that all viable possibilities are looked at so that we can finally solve this longstanding question in physics.

Conclusion

So, why does dark matter, matter, anyway? Well, this stuff makes up a huge chunk of the Universe, and we want to know what the Universe is made of. If it turns out to be an elementary particle that isn’t part of the Standard Model of particle physics, then that means the Standard Model is wrong, and we’ve got some cool new physics! If, on the other hand, it somehow turns out to be that our understanding of gravity is fundamentally flawed, we still get new physics. And new physics is always exciting! Either way, it’s about learning about our Universe. Think about it: right now, the stuff we know and are familiar with accounts for just 5% of the Universe’s contents. Imagine what ticking off another 25% of the Universe would mean. Don’t know? Neither do I, but that’s what’s so exciting about it! My bet is that it’s a new particle, and the Standard Model is wrong. Maybe it’ll be SIDM, maybe WIMPs, or Kaluza-Klein dark matter. Maybe it’ll be several types of dark matter, with new forces in the dark sector; I mean, why shouldn’t it be, when the visible sector is a particle zoo? Whatever it turns out to be, unraveling this mystery will be a ground-smashing achievement in the world of physics.