A Primer on Dark Matter Physics, Part 1

Every day, there are scientists who travel miles underground to tend to their dark matter detectors1. This may be old news to you; you may even, like me, be one of those scientists – nevertheless, I invite you to pause and consider for a moment just how science-fictional the preceding sentence sounds and how, like, cool and crazy this universe of ours is, man, – and, especially, how fun it is that we get to go deep beneath the earth’s surface and build things like this:

The DEAP-3600 dark matter detector

So, what on earth is that thing, and why did we build it (and why miles underground)? In the most recent “Introduce Yourself” thread, Megara Justice Machine suggested that I write a primer on dark matter, so let this be a lesson: Don’t ask me to do something unless you’re prepared to risk a slight chance that I might actually do it! I hope that what follows will be intelligible, and maybe even a little bit interesting. This ended up being longer than I’d intended, so I thought I’d split it into two parts. Today, I’ll give an overview of why we think dark matter exists and what it might be, as well as a brief summary of how we’re searching for it. Next time, I’ll go into a lot more depth about some of the methods being used to search for dark matter and talk a little bit about what we have – or haven’t – found so far, then wrap up with a slightly more philosophical discussion about where all this is going and whether we’ll ever find dark matter at all.

What Is Dark Matter?

The short answer is that we have a good deal of evidence from astronomical observations that there is a lot more matter out there in the universe than what we can see. We don’t know what this stuff is, but since (unlike stars, galaxies, nebulae, and whatnot) we can’t see it, we call it dark matter.

The first evidence for dark matter was observed in the early 1930s, when astronomers studied the velocities that stars are moving at in several nearby galaxies. Let’s look at, say, the Andromeda galaxy:

As you can see, the stars of this galaxy form something of a spiral disk, with a denser core at the center. (It’s harder to see, but there’s also a “stellar halo” of very sparse stars above and below that disk – but there are so few stars in the halo compared to core and the disk that they don’t really make much difference.) As you might guess from the picture, the galaxy is spinning; all the stars are orbitting the center of the galaxy, just as the planets in our solar system orbit the sun. Let’s say you want to predict how fast those stars are orbitting. Well, that should be pretty easy to do – the motion of objects on this scale is controlled by gravity, and we actually think we understand gravity pretty well. So, you just look at how the stars are distributed in the galaxy, do the math, and get an answer: within the dense core, you expect that the farther away from the center a star is, the faster it will be orbitting; once you get beyond the core, you expect that the stars’ velocities will gradually decrease again as you get farther and father away. A plot of velocity vs. distance from the center of the galaxy ought to look like this:

Plot of predicted star velocity versus distance from the center of the galaxy for the galaxy NGC 3198.

Without going into the math of this, it’s pretty easy to see that this prediction is directly related to the observed shape of the galaxy. The upward-sloping part at the left, where the velocities are increasing with radius, is the central core, and the downward-sloping part on the right, where they’re decreasing again, is the rest of the spiral disk.

So, let’s measure the velocities and see if our prediction was right. Uh oh:

Plot of predicted and observed star velocities versus distance from the center of the galaxy for the galaxy NGC 3198.

Well, we were right about the dense core, but it turns out that all the stars beyond the core are basically moving at the same speed, no matter how far away from the center they are. This discrepancy was discovered in the early 1930s and is called the “galactic rotation problem”.

Now, there were two assumptions that went into that prediction we made, so logically at least one of those two assumptions must be wrong. First, there’s the mass distribution of the galaxy, which we inferred by looking at where the starlight is coming from; second, there’s the theory of gravity that tells us how things should be moving given that mass distribution. Let’s set aside the second possibility for the moment (don’t worry, I’ll come back to it but probably not until part 2) and note that, yeah, it’s kind of plausible that maybe there’s some stuff out there that isn’t, you know, shining with the light of a billion suns, and that maybe we might have missed. And it actually turns out that the pattern of velocities that we do observe is just what you’d expect if that bulge/disk/halo of stars that we see were actually set within a bigger (and more massive) spheroid of invisible matter, which we call the “dark matter halo”. In other words, the velocities we observe are just what we’d expect if the galaxy looked like this:

Schematic of a typical galaxy including the hypothesized dark matter halo.

Galaxies come in different shapes and sizes, but pretty much all galaxies we can see follow this same pattern. That is, based on the velocities of their stars, they all look like they have big halos of invisible mass around them. And it’s not just galaxies. Most galaxies are found in gravitationally-bound groups called clusters, with the galaxies in a cluster circling its center just like stars circle the center of a galaxy, or planets circle a star. If we look at the velocities of the galaxies in a cluster, we see the same thing as when we look at the velocities of stars in a galaxy: the galaxies are moving faster than we’d expect, but the observations would make perfect sense if we also assume that the clusters contain halos of stuff we can’t see. In 1933, the Swiss astronomer Fritz Zwicky noticed this effect when he was looking at the Coma Cluster, and he was the first to suggest that if there were some invisible mass out there, that would explain things very nicely. He called that invisible stuff “dark matter”.  (Well, actually he called it “dunkle Materie”, but what can you expect, he was one of them foreigners.)

So, that’s nice and all, but what could that invisible stuff be? At first glance, it seems that it needn’t be anything particularly special. After all, all that we’re hypothesizing is that there’s a lot of stuff out there that we can’t see from millions of light years away. You can’t see me (or Mt. Everest, or Jupiter) from millions of light years away, and I’m not made of some mysterious unknown substance. Granted, I also don’t weigh very much – and for that matter, neither do Mt. Everest or Jupiter. In fact, 99.8% of the mass of the solar system is contained in the sun, which is why it seemed at first like a pretty good assumption that we could just look at where the stars are and that’s all the matter that, well, matters. So you need to assume that there’s something in that dark matter halo more than just a bunch of rogue planets or asteroids or anything like that. But you could imagine that somehow that space is filled with some kind of dead stars, or supergiant planets, or something along those lines – exotic, perhaps, by local standards, but ultimately just made out of the same protons, neutrons, and electrons as you, me, and the sun. The other possibility is that the dark matter halos are made of some unknown kind of particle, something that’s very heavy but that doesn’t have strong interactions with other matter. For years, these were the two main hypotheses as to what dark matter was and these were dubbed Massive Compact Halo Objects (i.e. objects like planets or dead stars, made of normal matter) and Weakly Interacting Massive Particles (i.e. some unknown kind of particle, not your usual protons, neutrons, and electrons). That is, MACHOs and WIMPs. Physicists are a silly bunch.

Sadly for this silly joke, it turns out that MACHOs can’t be the answer. It turns out that most of that mysterious missing mass has to be something other than your standard protons and neutrons. The reasoning behind this is a bit more complex and requires more understanding of cosmology than the galactic rotation curves, so I won’t go into great detail here. But it comes from observations of the Cosmic Microwave Background. What is the Cosmic Microwave Background, you ask? Well, to put it briefly: after the Big Bang, the universe was very hot and it’s been continually cooling down ever since. For a long time, the particles in the early universe had too much energy to form atoms – the electrons were essentially zipping around too quickly for the protons to capture them. But as the universe cooled, it rather suddenly crossed a threshold to the point where protons could capture electrons, and the first hydrogen atoms were formed. Every time an electron was captured in an atom, that process involved the release of a photon2. And most of those photons that were released when this happened are still out there, flying in all directions through the universe. This means that if you look at an empty portion of the sky, someplace where there are no visible stars or galaxies, with a very sensitive telescope, you’ll see an extremely faint background of light (mostly in the microwave range) – that’s the Cosmic Microwave Background.

The CMB is useful because it gives us a sort of snapshot of the universe about 400,000 years after the Big Bang, when those first hydrogen atoms formed. Now, obviously there were no stars, or planets, or even garbage apes, around back then; there was just a sort of gas of various particles. But it wasn’t perfectly homogeneous – there were spots where that gas was a little denser, spots where it was a little less dense. In the denser spots, more atoms were formed, so more background radiation was given off. So if you look at that background radiation in the sky, you’ll see slightly brighter spots and slightly fainter spots – and what you’re really seeing is the density patterns of that primordial gas from 13.8 billion years ago. And this what it looks like:

Image of the Cosmic Microwave Background across the sky from the Planck cosmology probe.

What does any of that have to do with dark matter? Well, we can use that snapshot of the primordial gas to measure what the density of protons and neutrons was in the early universe. And ever since that time, the universe has been too cold to produce protons and neutrons in large quantities, so (once we account for the expansion of the universe), we can deduce the average density of protons and neutrons in the universe today. And that number turns out to be significantly smaller than the density of dark matter that we deduce from astronomical observations.  Thus, the dark matter must not consist of protons and neutrons.

At the same time, the CMB also provides more evidence that the total amount of matter in the universe is greater than what we can see. This comes from looking at the density fluctuations of the CMB. Based on our theory of gravity, plus an assumption about how much matter and radiation there is (and was) in the universe, we can predict what those density fluctuations will look like – i.e., will the CMB be mostly homogeneous, with just small differences in density between different parts of the sky? Will the dense and sparse regions be big, or will there be lots of little fluctuations? Physicists ask these questions in a more quantitative way, of course, but that’s the gist of what is being predicted and measured. And, as it turns out, to correctly predict the density fluctuations that we see, you need to assume a lot more matter than what we see, and in fact a lot more matter than what the neutrons and protons in the universe can account for. If our theory of gravity is correct, then it looks like some 80% of the mass in the universe is some kind of particle we don’t know about, which we call “non-baryonic dark matter” (“baryon” being the general class of particle that both protons and neutrons fall under). And we can go further and say, again, based on the sizes of these density fluctuations, that these non-baryonic dark matter particles must be “cold” – that is, they don’t have a lot of kinetic energy. (To be slightly more precise, they are moving slowly enough compared to the speed of light that relativistic effects are negligible). If you ever see the acronym “CDM” in a physics context, this is what it refers to – Cold Dark Matter.

A Little Bit of Theory

Let’s step back for a minute and talk about particles. The current best description of the universe that we have is what’s called the “Standard Model”3. The Standard Model is essentially a list of allowed particles and a set of rules governing how they can interact. Each type of particle in the Standard Model has certain definite properties – so, for example, every electron everywhere has the same mass and the same charge. The Standard Model includes not just the familiar particles but also some unusual ones. So there’s the electron, which we all know and love, and there are the up and down quarks, which make up protons and neutrons. But there are also muons and tau leptons (basically, heavier versions of the electron) and four more “flavors” of quark (strange, charmed, bottom, and top quarks). These particles are all more massive than the familiar ones, and as a rule of thumb in quantum field theory, the more massive a particle, the less stable it is. So, the massive tau lepton4, for example, can only exist for less than a trillionth of a second before it decays into other particles (and the “rules” of the Standard Model tell us what other particles it can decay into).

Heavier particles are also harder to produce than light ones, because mass is a form of energy, and their mass has to come from somewhere. This is why it takes high-energy particle colliders to discover massive particles – to have a chance of producing a top quark, for example, you not only have to smash two protons together; you have to smash them together with more total energy than the mass of the top quark (plus the masses of whatever other particles are created in the collision).

The Standard Model is not some a priori theory. The list of particles included in the Standard Model is basically just the list of particles that we’ve been able to create and observe in particle colliders, and as far as we currently know there’s no fundamental reason that those particles, with those specific properties, have to be the particles that exist in this universe. And we don’t know that the particles we’ve observed are the only particles that can exist in this universe, either – in fact, most people would agree that there are probably other particles out there that we haven’t seen yet simply because they are too massive to be created with the particle colliders we’ve built so far. And there are various theories that extend the Standard Model, predicting the existence of new particles that (hopefully) we might one day be able to detect. So, if we think that there’s some unknown kind of particle out there making up the invisible mass of the universe, then that might provide some support for these extensions of the Standard Model; and conversely, extensions of the Standard Model can provide some suggestions as to what those unknown particles are.

One idea that comes up in many of these extensions of the Standard Model is something called supersymmetry. According to supersymmetry, every fundamental particle we know about has a corresponding “superpartner” that is presumably much more massive. These superpartners are named things like sneutrinos, selectrons, squarks, and neutralinos (I swear I’m not making this up). Now, as I said, the rule of thumb in quantum field theory is that the more massive a particle is, the less stable it is – but that’s only true if the rules of the theory allow it to decay into other particles. The lightest of these superpartners, if they exist, are expected to be stable, even though they’re very massive, because there simply aren’t any combinations of other particles that they are allowed to decay into.5 In particular, the sneutrino, the neutralino, and the gravitino look like good candidates for a massive, stable particle that could constitute the dark matter.

As an aside, there are other hypothetical particles that are predicted by various theories that could constitute dark matter but that are not classified as WIMPs. The one that’s most talked about is the axion, but there are also ideas for things like “hidden photons”. These differ from WIMPs in that they are not massive and not necessarily “weakly interacting”, and the approach to detecting them is quite different. I’m not going to say much more about these, because it’s not my field of expertise. The upshot, though, is that they would still be unknown particles that we haven’t detected yet, just with different properties.

Searching for Dark Matter

OK, so how do we actually look for dark matter? Well, that depends on what we think it might be. I mentioned MACHOs earlier, and though we no longer think that these can account for all or even most of the universe’s missing mass, they could still make up some of it, and it’s worth looking for them. The main way this is done is through gravitational lensing. General Relativity predicts that massive objects should bend light around them, functioning like, well, a lens – and this has by now been observed plenty of times. If there were a massive, invisible object like a black hole or a neutron star out there in the sky, then light coming from any star or galaxy more or less directly behind it would bend around the massive object, and would look distorted, as if we were literally looking at it through a glass lens.  Now, this of course will only happen if, by coincidence, a MACHO is directly along the line of sight between us and a source of light; most of them won’t be, so most of them can’t be found this way.  But if there are enough MACHOs, some of them should happen to be between us and something bright.  So the search for MACHOs is about looking at as many stars and galaxies as we can to see if the light coming from them is being distorted by an in-between massive object. And plenty of MACHOs have been found! But, as we already expected for cosmological reasons, these searches have shown that there are not enough of these objects to make up the missing mass of the universe.

I mentioned axions and hidden photons above, and there are specialized experiments looking for these, which I honestly know very little about. But one approach to searching for the latter is trying to “shine light through a wall”. The idea is that these particles would couple to the photon, the particle that makes up light, meaning that if you have a lot of photons, some tiny fraction of them could spontaneously transform into hidden photons. And if you have enough hidden photons, some tiny fraction of them could spontanteously transform into photons. Now, hidden photons would not interact with normal matter (that’s what makes them hidden), so if you shine a really, really intense laser at a wall, there is some probability of a few of the photons in that laser turning into hidden photons, passing through the wall, and then turning back into normal photons (i.e. into light, which we can see!) on the other side. So, yes, there are actually physicists who are shining light at walls and looking to see if any is coming out the other side.

It’s fair to say, though, that most of the efforts to find dark matter are focused on WIMPs, and since this is the kind of experiment I work on, I’m going to go into some more detail here. All searches for WIMPs are based on that “W”. WIMPs, by definition, would be weakly interacting – and in physics that isn’t just a qualitative statement; it means that according to the “rules” of the theory governing WIMPs’ behavior, they would be allowed to interact via the weak nuclear force, but not via the electromagnetic or strong nuclear forces. This is in contrast the quarks (and the particles made of quarks, like protons and neutrons), which interact through all three of those forces, or to the electron, which interacts through electromagnetism and the weak force.6 The weak force is, well, weaker than electromagnetism or the strong force, meaning that weakly interacting particles mostly just go about their business and rarely even notice the existence of other matter.

We have, in fact, already detected one weakly interacting particle – the neutrino. Like WIMPs, neutrinos do not experience the strong or electromagnetic forces, and as a result, they mostly just pass through other matter, barely noticing that it’s there. If you or I smashed into a rock wall, the electric fields of all our atoms would be repelled by the electric fields of all the atoms in the rock, and would stop us (and probably hurt us). Something tiny, like, say, a proton, could maybe penetrate a few meters into the wall before stopping (depending on how fast it’s moving when it hits). But a neutrino is so oblivious to other matter that it would take, on average, a light-year’s thickness of lead to stop one.

Incidentally, let me digress for a moment – you might be saying, “Hey Aiwendil, these neutrinos sound like a tricksy sort of particle – couldn’t they be the dark matter?” And it’s not a ridiculous suggestion. For a long time, neutrinos were thought to be massless particles, like the photon, but it was discovered about twenty years ago that they do have a very small mass. So, if there were enough neutrinos in the universe, they could in principle have enough mass to account for the missing mass of the universe. The problem with that is that neutrinos, since their masses are so small, move very close to the speed of light, which means that they would constitute “hot” dark matter. As I mentioned earlier, the density fluctuations in the CMB show that the missing mass must be “cold”. So the neutrinos we know and love can’t explain the missing mass. (Though in extensions of the Standard Model, there could be additional, heavier neutrinos, which could be candidates for WIMPs).

But back to the issue of detecting these slippery particles. If neutrinos and WIMPs are so oblivious to other matter, then how can we detect them at all? Fortunately, they do interact through the weak force, which means that if you have a lot of these particles passing through some other matter, every once in a while one of them will collide with the nucleus of an atom. What happens next depends on the energy of the colliding particle, but in the case of a WIMP, they will generally just recoil like billiard balls, the WIMP and the nucleus each flying off in a different direction. The nucleus loses energy as it travels, colliding with other atoms, until it eventually stops – but that deposited energy is something we can detect in various ways. So the most obvious strategy for detecting WIMPs is to create a target mass surrounded by instrumentation, the idea being that if you let it sit there long enough, a few WIMPs will collide with nuclei in the target, and your instrumentation will then see the energy deposited by the recoiling nuclei.7 This is called a direct search – you are looking for WIMPs passing through your lab to actually interact inside your detector.

I’ll come back to direct searches in part 2 and go into some more depth, but let me conclude here by talking briefly about the two other ways of looking for WIMPs. These don’t get as much press because instead of building dedicated experiments, these are things that can be done opportunistically using detectors that are primarily interested in other physics topics.

In addition to colliding/interacting with other particles, the weak interaction allows two other things to happen to WIMPs: they can be annihilated and they can be created. Annihilation would be a WIMP-WIMP interaction – that is, two WIMPs could annihilate each other and turn into other particles. So in principle, you could search for WIMPs indirectly, by looking for the particles produced by their annihilation. Exactly what those other particles might be depends on the unknown nature of the WIMP, but there’s pretty much no way you can imagine WIMPs annihilating without producing, among other things, neutrinos.

Now, two WIMPs interacting with (and annihilating) each other would be an even rarer process than a WIMP interacting with normal matter. Think of it this way if you like: protons, neutrons, atomic nuclei, and the like are extroverts and WIMPs are shy, retiring introverts. An extrovert starting a conversation with another extrovert is something that happens pretty easily. An extrovert and an introvert striking up a conversation is less likely. But two introverts starting a conversation is even less likely than that. So if you want to have any hope of seeing WIMPs annihilate, you’ll need to look in places where you expect there to be a lot of WIMPs (throw enough introverts together in a room and chances are some of them will talk to each other). Fortunately, there are such places; WIMPs should congregate in greater numbers at strong centers of gravity. So there should be more WIMPs in and around the sun than out in the far reaches of the solar system, for instance, and there should be more near the center of the galaxy than out in the periphery. An indirect search for WIMPs, then, means looking for an excess of neutrinos coming from places like the sun and the galactic center. And fortunately, there are already a lot of neutrino detectors studying neutrinos from other sources, so doing an indirect WIMP search is a bonus feature of those detectors.

The third way you can look for WIMPs is by trying to create them, by smashing together other particles with sufficient energy. This is something we’re already doing anyway with particle colliders like the LHC, so a collider search for WIMPs is a bonus feature of those experiments. But wait – if you do manage to create a WIMP by smashing together a couple of other particles, how will you know? After all, the WIMP you created will, in all likelihood, pass right through your detector without even noticing it. Well, you won’t be able to detect that WIMP you created, but you will be able to look for its missing energy. Energy cannot be created or destroyed, which means that whatever energy is in the particles you collide has to equal the total energy of the particles that are created by the collision. So if you know the energy of the particles you started with and measure the energy of the particles you created, they should be the same. If the particles you created have less total energy than the particles you started with, that means that the collision must also have created one or more particles that you weren’t able to detect. Now, we already know about one such particle – the neutrino. In fact, this is how neutrinos were first discovered – it was noticed that when a neutron decays, the energies of the resulting particles don’t add up to the original mass of the neutron. Long before the neutrino was ever detected, its existence was posited as an explanation for this missing energy. Fortunately, we’ve studied neutrinos pretty extensively now, so we know what reactions can produce them and we can predict the range of energies the neutrinos created in such interactions will have. So, very roughly, collider searches for dark matter involve looking for more missing energy than the missing energy that we already expect due to neutrinos.

So those – direct, indirect, and collider searches – are the three ways of looking for WIMPs, the prime candidate for dark matter.  Many searches of all three types have been done and, spoiler alert, we haven’t found them yet.  But (and this is something I’ll talk about more in part 2) it should be noted that this in no way means that those experiments were failures.  Every search that doesn’t find WIMPs tells us more about what they are not, and puts tighter constraints on what sort of particles they could be.

I’m going to cut off there for now, but in part 2 I’ll talk more about direct searches for WIMPs and then about the results so far from all these searches.  I hope to get part 2 up a week from today, though there is some chance it could get delayed.  If you’ve stayed with me this far, thanks for reading, and I hope something in there was of some interest to somebody.