# My favorite dark matter experiment

Physicists have a lot of ways we can look for the unknown particles which must make up dark matter. Since we don't know what this mysterious stuff is, we don't know how (or really if) it interacts with the normal matter that makes up the stuff we are made out of. We of course have a number of ideas of what is possible, and there are actually really good arguments as to why we expect dark matter to have some small - but non-zero - interaction with normal matter. Basically, it comes down to the fact that if dark matter has no interactions with the normal matter, there tends to be too much dark matter produced in the first moments of the Universe's life. You can of course find theoretical ways to avoid this argument, but it's a pretty generic result, so it's a good starting point

But that said, we don't know what dark matter is, so it is important that we look for it in as many ways as possible. As a theorist, part of my job is to synthesize these distinct experimental strands, and try to see whether there is a consistent story (in the case of possible signals), or what sort of dark matter is still not ruled out (in the case that we don't see anything). So I keep my eye on the results of a lot of experiments. But there is one type of experiment that is my favorite. Not because necessarily because it yields the strongest bounds, or has the most interesting possible signals or anything, but because the physics behind it is so much fun.

Dark matter (called a "WIMP" in this example) scattering with the nuclei of atoms. IMage from University of California, Berkeley

The type of experiment I want to talk about is called a bubble-chamber. The original version I heard about was COUPP, and the current version is PICO. It's a type of "direct detection" experiment. That is, it is an experiment that looks for dark matter smacking into atoms of normal matter in a lab (thus: a "direct" interaction with dark matter).

Right now, the Earth is moving through the halo of dark matter that is part of the Milky Way: we know this halo is there because it is what is providing the mass whose gravity keeps the stars spinning in the beautiful spiral. Thus, there is a wind of invisible dark matter passing through the Earth, the room you are sitting in, and through you right now. Whatever dark matter is, it rarely interacts with normal matter, so most of it passes straight through you without any interaction. Rarely though, a dark matter particle could smack into one of the atomic nuclei in normal matter and impart some energy to that nuclei, causing it to ricochet away. If that happens inside you, no one would notice: there are a lot of sources of radiation around that can cause nuclear scatterings that would look a lot like a dark matter scattering, and these events cause no appreciable damage to the larger structure the atoms are embedded in.

So if you want to look for dark matter, you have to get clever. You need to build an experiment which not only can see these rare dark matter scattering events (which occur at a rate of less than 1 event per 100 days per kilogram of normal matter), but can distinguish them from the far more common non-dark matter scattering events (the "background"). One way to do this is to reduce the background by going deep underground, with many hundreds or thousands of meters of rock overhead blocking the high energy cosmic rays which can induce dark-matter-like scatterings. Another thing you can do is build your detector out of materials which are very low radioactivity; some experiments have gone so far as to use Roman Empire-era lead that spent 2000 years underwater, since that lead had a lower radiation level than lead that has spent time on the surface of the Earth getting bombarded by cosmic rays. Or, you get clever by figuring out ways to get a slightly different signal from dark matter than from your background events.

The reason I like the bubble chamber experiments so much is that they have a very clever way of trying to look for the interesting physics (dark matter) and rejecting the "uninteresting" physics (random cosmic rays and other radiation). To explain how it works, I need to explain about bubbles.

Take a bottle of carbonated soda, and pour it into a glass. You'll see bubbles form, these are bubbles of CO$_2$. When soda is stored in a sealed container, the internal pressure is high enough that the CO$_2$ is forced to mix with the liquid; once the pressure is released (by opening the bottle or can), the gas wants to come out of solution by forming bubbles. But look at your glass, and look where the bubbles are coming from. Typically, you'll find bubbles forming at particular points on the wall of the glass. Why is that?

It turns out it is sort of hard for a gas bubble to form in a liquid. To say that a gas bubble "wants" to form, we're saying that it is energetically favorable for the substance to exist in a gaseous, rather than liquid form. That is, if you have some volume $V$ of material, you'll release energy if it was a gas rather than a liquid. We could write that energy release as $\Delta E_{\rm volume} = -\rho V$ where $\rho$ is some energy density that will depend on exactly which material you're talking about (and what the pressure and temperature are). So great, things tend to want to move to the lowest available energy state (that's why things roll downhill), so this material finds its energetically favorable to be a gas rather than a liquid, and bubble forms. What's the problem?

The problem is that bubbles have walls - the boundary between the liquid and the gas - and those walls have a surface tension. Again, you've likely seen surface tension: it's the skin of water that allows you to slightly overfill a glass without the water spilling over. We can think of that surface tension as containing energy, it's like a stretched spring in some sense. So when you have a bubble with surface area $A$, the energy in the wall is $\Delta E_{\rm wall} = +\sigma A$ where $\sigma$ is some surface tension parameter that again will depend on exactly what material you're working with. So having a bubble costs you energy, since it has to have surface tension. Incidentally, minimizing this energy is why a bubble is generally spherical: a ball has the lowest surface area $A$ per volume $V$ of any shape, and so it minimizes the energy in the surface tension.

So here's the problem: to create a bubble, you need to have a large enough volume so that the energy you gain from the liquid turning into a gas is enough to make up for the energy you have to pay in terms of the surface tension. Which means really small bubbles can't form easily. We can do some simple math to see this. A spherical bubble with $r$ will have volume $V = 4\pi/3 r^3$ and surface area $4\pi r^2$. In order for a bubble to form, you need $\Delta E_{\rm volume} +\Delta E_{\rm wall} < 0$ Which is to say $-\frac{4\pi}{3} r^3 \rho + 4\pi r^2 \sigma < 0.$ This defines some critical radius, the smallest bubble that can form for this particular material: $r_c = \frac{3\sigma}{\rho}.$ Bubbles smaller than this radius will find it energetical favorable to collapse: the surface tension wins and the bubble is pulled back into nothingness. Bubbles larger than this find it energetically favorable to keep growing. But then, how does a bubble start? A bubble starting at zero size will find it impossible to grow, since $0 < r_c$.

So that seems to say that no material can every boil: a bubble can't grow from nothing. Now, a bubble can form by just waiting long enough for a random confluence of events to bring enough extra energy into a small enough region to provide enough of an energetic kick to start the bubble formation rolling. But that takes time; depending on the material (that is, on the precise values of $\rho$ and $\sigma$), it might be a long wait for that first bubble to form. Better if something else was around to help with that energetic kick.

And that's why the bubbles of CO$_2$ in your Coke form on specific spots on the wall: at those spots, there's some microscopic defect in the glass: a chip or a dent or a speck of dirt. Something that changes the argument I just laid out above. The defect allows the bubble to grow by modifying the price the bubble pays in surface tension, allowing that initial tiny bubble to grow to size $r_c$, and then can expand from there. This is also why the Diet Coke and Mentos trick works: Mentos have a lot of nooks and crannies that allow for bubbles to form without paying as large of a price in surface tension energy. So when you throw a Mentos into a bottle of Diet Coke, all the CO$_2$ finds it energetically favorable to form a bubble. Rapidly.

So what does this story have to do with dark matter?

Well, take a container filled with a superheated fluid: a liquid that really wants to start boiling, but every nascent bubble lacks enough energy to make it to size $r_c$ and start growing. Make sure your pressure vessel holding that liquid has no defects or dust or anything that can act a nucleation site (like the walls of a glass of Coke). Then wait.

Eventually, some nuclear interaction will occur in your liquid: some cosmic ray, some radioactive decay, something. That something will give a tiny amount of extra energy in a small region of liquid. If you set things up right, that energy is enough to create a tiny bubble with $r > r_c$. So, you can cause the superheated fluid to suddenly explode from liquid into gas.

Superheated fluid undergoing bubble nucleation. Movie from Juan Collar.

If you set things up right, that nuclear interaction could be a dark matter scattering event. So essentially you can search for dark matter by setting a big tank of liquid, and waiting for it to boil. When I worked at Fermilab, the experimentalists next door working on the test-version of COUPP just had a video camera pointed at their clear pressure vessel. So they could sit up in their office and know an "event" had occured by literally seeing the liquid in the vessel erupt in a big boiling mess. Then they'd reset the chamber by lowering the temperature and bringing it back up to being superheated, and start waiting for another event again. The results look something like the gif playing here (though in the actual experiment they usually don't get the bubble get that big before resetting).

But remember, seeing a possible dark matter event is only part of the equation for a direct detection search. If a dark matter particle can give enough energy to the liquid to cause a bubble nucleation event, then so could a regular boring nuclear scattering from an alpha particle or a neutron. And this is 2nd clever bit.

Since dark matter is so weakly interacting with normal matter, a scattering event is rare. But a dark matter hitting two atoms in your detector in quick succession is (rare)$^2$. So rare you can ignore the chance of it happening. So every signal event in a bubble chamber is a bubble nucleated at single location. If a background event is instead kicked off by a strongly interacting neutron or alpha particle, it will likely hit multiple nuclei in a row. So instead of one bubble, you'll get two or three. As these bubbles expand, they'll merge, but as they expand, they'll send a pressure wave out through the unboiled liquid.

That pressure wave is just sound. And just as you can tell the difference from sound coming from one speaker versus the sound of multiple speakers, the sound of a single bubble nucleating is different than multiple bubbles nucleating. So you can look for dark matter by listening: if the bubble sounds like it came from one place, it might be dark matter, and if it came from multiple locations, it's not.

And I think that's a pretty cool way to look for dark matter.