# What Could Dark Matter Be?

So dark matter exists, or at least, the motion of stars in galaxies and galaxies in galaxy clusters requires the presence of something that we can't see that provides enough gravitational binding energy to keep the galaxies or clusters from evaporating.

But that's a mouthfull, so let's just say "dark matter is something that exists."

But what is it? Unfortunately, I don't know. No one knows. But let's go through some of the possibilities anyway.

Normal matter that's just hard to see.

Maybe dark matter is just regular stuff that's hard to see. The dark matter physicist term for "regular stuff" is "baryons" in this context (baryon is a class of particles that includes protons and neutrons, which is what normal stuff is mostly made of). It turns out this idea is completely ruled out, but let's go through why.

First, if you want baryons to be invisible, you can't have them in stars. Stars glow, after all. So, you might just say "spread that baryonic dark matter out as gas or dust." The problem is that gas and dust in a galaxy or galaxy cluster will interact with the background light from the stars and become visible. Dust will reradiate energy in the infrared wavelengths, and we can look for hydrogen gas in the 21 cm radio wavelength.

Milky Way Galaxy 21 CM wavelength  (J. Dickey (UMn), F. Lockman (NRAO))

So you can't put your dark baryons in stars, and you can't leave them as gas molecules or grains of sand (dust). You could put them as a bunch of planet-sized objects drifting in interstellar, or even brown dwarfs - stars that didn't get enough mass to become stars. You'd need a lot of them, but hey, we're trying to solve a problem here.

This solution is called MAssive Compact Halo Object dark matter, or MACHO. Massive because it's a bunch of large objects, compact because they're gravitationally bound planet(oids), halo because they'd have to live in the halo of the spiral galaxies (that is, not in the disk) to explain the observed rotation curves, and objects because you know, they'd be objects.

To find out if MACHOs are dark matter, what you do is look at a large number of stars. If you're lucky, a MACHO will wander between us and the star while we're looking. When that happens, the gravitational pull of the MACHO will act as a gravitational lens, pulling the light from the star in a little bit. The star will appear to get brighter. (This technique, called gravitational microlensing, today can be used to look for planets in orbit around other stars.) Look at enough stars, and if you don't see microlensing events, you can place a limit on the number of MACHOs out there. Doing this, in the late 90's the EROS collaboration proved that MACHOs cannot be dark matter if the MACHOs have masses in the range

$10^{-7} M_{\rm Sun} < M < 15 M_{\rm Sun},$ (Earth is about $10^{-6}M_{\rm Sun}$ ).

Later work has extended this range from $3 \times 10^{-8}M_{\rm Sun}$ to $30 M_{\rm Sun}$ (see Griest, Cieplak and Lehner and references therein).

In addition, using the measurements of the Cosmic Microwave Background, the afterglow from the moment that the Universe cooled enough for electrons to finally become bound to protons, we know that the amount of matter that interacts with light was about a fifth of the amount of dark matter we know exists today.

Since CMB decoupling occurred only 370,000 years after the Big Bang, this measurement is a measurement of the amount of matter and dark matter from well before any objects build of baryons the size of stars or planets could condense out of the primordial plasma. So making dark matter just normal baryons hidden in MACHOs isn't possible: they would have counted as regular baryons for the purposes of the CMB measurement.

As a last kicker, we also have an idea of how the first elements heavier than hydrogen were formed. Helium and small amounts of lithium and beryllium originated in the first 20 minutes or so after the Big Bang, and the ratio of each element created depends delicately on the number of baryons that were around at the time. Again, you guessed it, we find that the observed number of heavy elements is obtained only when the dark matter is not made of regular baryons.

So farewell MACHOs.

Black Holes

So dark matter can't be non-glowing baryons. But lets go back to the MACHO search: dark matter could be small compact objects with mass less than about a tenth of the Earth, if you had a way to avoid the constraints from the CMB and the formation of the elements telling you dark matter can't be baryons.

Suppose though that you could just magically poof into existence a bunch of compact objects that weren't made up of baryons, and so didn't participate in the shenanigans around the CMB or element formation. Then you'd have a fine candidate for dark matter.

The leading candidate for such non-baryonic compact dark matter objects are black holes, in particular primordial black holes formed through some postulated new physics in the very early moments of the Universe (enough we have no measurements, yet). This is basically magic at this point, or at least a huge shrug of the shoulders: I don't know if early Universe physics would create some population of black holes, but I don't know that it wouldn't. And if we found them, that would be a hugely important piece of evidence that would push us in some new directions for figuring out the physics of the Big Bang.

Using improved versions of the microlensing techniques designed for MACHOs, we can now rule out black hole dark matter if the black holes have masses above $10^{-9}M_{\rm Sun}$. In addition, a different observational technique, called femtolensing can rule out all black hole dark matter with masses between $10^{-16}$ and $10^{-13} M_{\rm Sun}$. Mt Everest is about $10^{-15}M_{\rm Sun}$, for comparison.

An additional problem with black hole dark matter is that black holes evaporate. Working out the theory that proves this happens is what made Stephen Hawking famous, and gave us the idea of Hawking Radiation. Bigger black holes radiate less, and so take longer to evaporate away. Black holes of mass approximately $10^{-20}M_{\rm Sun}$ or less should have evaporated by now, and the word evaporation makes it sound slightly calmer of a death throe than our expectation. A black hole as it evaporates in its final moments should explode in a final burst of high energy photons and other particles, which would be visible to our gamma-ray telescopes. We don't see such signals, at least not in the numbers needed for dark matter.

So while dark matter as black holes isn't quite dead, you can see there are only a few corners left. Such black holes would have to be in the mass range $$10^{-20}M_{\rm Sun} < M_{\rm BH} < 10^{-16}M_{\rm Sun},~\mbox{ or }~10^{-13}M_{\rm Sun} < M_{\rm BH} < 10^{-9}M_{\rm Sun}.$$

Neutrinos

So let's move away from dark matter as made up of a macroscopic-sized object, something whose mass I need to measure in units of the mass of the Sun. Let's imagine that dark matter is a particle. As I've discussed, dark matter can't be charged (because of the CMB) or interact with nuclei (from the formation of elements after the Big Bang). So let's look at our options.

Standard Model Particles, via Fermilab

Well, the quarks are out (interact with nuclei), as is the gluon (same reason). The electron and its heavy cousins the muon and tau are out (charged). The W and Z bosons are unstable (as is the Higgs boson, which isn't shown here), and dark matter has stuck around for 13.7 billion years, so it can't be that. Photons move at the speed of light, so they can't be stuck in the galaxy halos like dark matter is.

What about the neutrinos? They're stable (or, at least one of them is stable), they're electrically neutral, and they don't interact with nuclei via the strong nuclear force. Sounds exactly right. So, dark matter is neutrinos then?

No.

The reason why is pretty cool. See, neutrinos are fermions, particles with 1/2 a unit of fundamental "spin." One of the deep facts about the Universe is that fermions obey "Fermi-Dirac statistics." One of the results of this is that you can't cram two fermions into the same state of existence (this is the Pauli Exclusion Principle). This is a very good thing for us, since this prevents all the electrons in your body from collapsing into their lowest atomic orbital and making chemistry, and thus life, impossible. I have no good layperson explaination for Fermi-Dirac statistics right now, so take it as a given.

A galaxy is a big place. But there are still only a finite number of ways you can fit a neutrino into a galaxy, if you're limited to 1 neutrino per quantum state. It turns out that, if you wanted to make all the dark matter out of neutrinos, you'd need each neutrino to weigh at least 92 eV (about 100 billionth of a proton's mass). We don't know the neutrino masses for sure yet, but we do know that they are no heavier than about 1 eV.

So dark matter can't be neutrinos because you physically can't cram enough neutrinos into a galaxy. Which should give you a sense of either a) how much dark matter is in a galaxy or b) how incredibly tiny neutrinos are.

For the pedants, this is one version of the Tremaine-Gunn bound, using Fermi-Dirac statistics. There is an alternative version using phase mixing of the neutrino distribution which doesn't require the Pauli Exclusion principle. I mention it only for completeness. Everyone else can ignore this paragraph.

A Thermal Relic of the Early Universe

So, no known particle can be dark matter. Let's start inventing new particles. We're theorists, that's what we do (TM).

We'd like to have a reasonable story for dark matter, so let's ask "how can we create enough of some new particle to be all the invisible mass in the Universe?" Looking at the Early Universe might give us a clue. We know the Universe was really hot to start off with, because it was very small and very dense. We see the evidence of this early heat in the CMB: the relic photons as the Universe cooled, and from the formation of the first elements, which indicate that the Universe was once hot enough to melt protons and neutrons into their consituent quarks and gluons.

Let's keep running the clock backwards, and imagine the Universe just kept being hotter and hotter. As the temperature increased, you can imagine heavier and heavier particles being present in the thermal bath. Two photons could smash together and create a top quark and a top antiquark, or fuse to create a Higgs boson, or create new particles we haven't found yet. Indeed, you can think of particle colliders like the Large Hadron Collider as an attempt to recreate conditions that were last seen in the first moments after the Big Bang. A time machine for physics, if you will.

Now, imagine you have some new particle, one we haven't seen yet, and the Universe is hot enough so that pairs of this particle can be produced in the thermal bath. Now imagine what happens as the Universe starts to cool. Occasionally, two of these new particles (lets call them $X$ particles) will collide and annihilate into particles we know of in the Standard Model. That happened before, when the Universe was hotter. However, now that the Universe is cooler, it is harder and harder to find two Standard Model particles that have enough energy to combine to form new pairs of $X$ particles. So the number of $X$ particles will start to decrease.

You might think this will continue until there are no more $X$ particles left. However, as the density of $X$ particles decreases, it is harder and harder for $X$'s to find each other to smash into each other and annihilate away. The Universe is expanding after all, and $X$'s are getting rarer. Eventually, the rate of $X$-annihilation will drop essentially to zero; and the remaining $X$ particles are frozen out, and remain to the present day as a thermal relic. If $X$ doesn't interact with light or the strong nuclear force, this is a perfect dark matter candidate.

Thermal Freeze-Out, JungMan ET AL

But notice something strange: the easier it is for two $X$ particles to find each other, the longer they will continue to annihilate away, and the fewer we will have around today. Thus if the $X$ is "bigger," that is, has a bigger cross section, then we see less dark matter today. I show that in the picture here, where increasing the size of the dark matter keeps it annihilating longer, leaving fewer at the end of the day.

Strangely, we find that we would have approximately the "right" amount of dark matter today if the mass and cross section were approximately those of a particle that was at the scale of "electroweak symmetry breaking," the energy that the Higgs boson lives at, and that was already of interest to physicists because we knew something strange was going on here (that strange thing being the physics that allowed us to predict the Higgs, and why we built the LHC). This strange new physics has to do with the weak nuclear force. So, a very popular type of dark matter is a "Weakly Interacting Massive Particle" or WIMP.

One thing to remember is that "Weak" here means "the weak nuclear force," not "weak" in the colloquial sense. It's confusing for many physicists and astronomers too, since the weak nuclear force is certainly a (colloquially) weak force. We don't know that dark matter interacts via the weak nuclear force, this WIMP argument is just suggestive. Maybe this so-called "WIMP Miracle" is a coincidence, nothing more. But it is a place to start, and this idea gains more traction because many ideas for new physics at the interesting weak nuclear force scale include particles that can be dark matter. We haven't found them yet, though.

Non-Thermal Relics of the Early Universe

That thermal relic story I just told seems like a pretty solid story. After all, it just requires something we know to be true (Universe started hot and dense) and something that is not totally insane (there is at least one new particle we haven't discovered which was able to be produced in the early Universe). Then, one coincidence later, make the cross section the right size, and bam, dark matter.

However, when we look at the regular matter around us, the baryons, we don't see the visible Universe-version of that story. Baryons are not a thermal relic. We know that because there are no anti-baryons around, or at least, not in great numbers. For some reason, a reason we do not understand, the Universe choose early on to have an asymmetry between baryons and antibaryons. This requires violation of a symmetry called "charge-parity", and we don't know how it happened (which should make you say: New Physics. AWESOME). Something picked protons over antiprotons, and that's why we see matter today, not antimatter (though obviously, whichever bit "won" we call matter, since that's the stuff we're made out of)

So, maybe dark matter was born in the same way: some asymmetry between dark matter and dark antimatter. It's a very evoctive idea, clearly the Universe has chosen to do this once before when it got the baryon asymmetry, so maybe it did it again for dark matter. One of my early papers in my first postdoc was on this idea. We called it "xogenesis," but we were not the first to think of it by a long shot. In many cases, you can link the asymmetry in the dark matter with the asymmetry in the visible matter, explaining why we have more protons than antiprotons via dark matter. And it is always nice when one problem solves another problem

Now, one might worry that this means that we'll never see dark matter in a lab. At least thermal dark matter might have weak nuclear interactions, which are hard to see, but we can work to find them. But if there's just some asymmetry in the Early Universe, does dark matter need to interact with us in any way other than by gravity?

Turns out, for this idea to work, yes it does.

The only reason we know that we have more protons than antiprotons is that we got rid of most of the proton-antiproton pairs from the early hot plasma of particles after the Big Bang. Protons and antiprotons have a huge cross section to annihilate (they interact via a force we dubbed "strong," after all). They rode that annihilation curve I showed above all the way down to a tiny residual amount, meaning that the 1 extra proton that existed per 10 billion proton-antiproton pairs in the early Universe can be seen (and yes, that 1 extra part in 10 billion is what makes up everything you can see).

So if dark matter is to be made up some fundamental asymmetry, we would have to get rid of most of the thermal pairs of dark matter. Otherwise, we're just talking about thermal dark matter with a sprinkling of a few extra particles without their parnter antiparticles around. And that's not very interesting. It turns out, when you do the math, the cross section you need for this "asymmetric" dark matter is about the same (or larger) as you need for thermal dark matter. Which gives us hope that we can still see it in our labs.

Something else

There are not quite as many hypothetical particles which could be dark matter as theoretical physicists, but it's not a small number of possibilities. You need to imagine a particle which doesn't interact with light, doesn't interact with nuclei, and doesn't get overproduced in the early Universe. If you want people to take your idea seriously, it better be more than a minor variation on our old favorites. I won't go through all the possibilities here though.

I will leave with a mention of the "best" of these other types of possible dark matter candidates, a particle called the axion. This idea is at least as compelling as the idea of WIMPs. It certainly deserves to be taken seriously, at any rate, but to do it justice will require a bit of background. So I'll leave it to another blog post.