# Paper Explainer: Direct Detection Anomalies in light of Gaia Data

This is an explainer for my recent paper with Gopolang (Gopi) Mohlabeng and Chris Murphy on the implications of recent surveys of dark matter velocity distributions from the Gaia mission on dark matter direct detection. There are a bunch of moving parts in this paper, as we’re trying to tie together some new directions from astrophysics with a long-standing problem in particle dark matter.

Let’s start with the latter first. If you’ve been reading my work in the past, you know that we have pretty good evidence from cosmology that dark matter exists, but we have no idea what dark matter is, as a particle. There are many good ideas for a particle theory of dark matter, so many good ideas that ultimately I think at this point we are not going to resolve the issue without some new experimental evidence.

One of the longest running theoretical ideas for dark matter is called “weakly interacting dark matter” or WIMPs, where dark matter has a weak nuclear charge. The nice thing about this idea is that it naturally produces dark matter through “thermal freeze-out.” Basically, in the early Universe, when things were extremely hot and dense, dark matter was pair-produced through collisions of high-energy “normal” matter, and could pair-annihilate back.

As the Universe expanded and cooled, the rate of production decreased, but also the rate of annihilation decreased as well. The weaker the interaction between dark matter and other particles, the more dark matter would remain today (since the annihilation would stop earlier, leaving more dark matter behind). It turns out that the weak nuclear force is approximately the right interaction strength to produce the observed amount of dark matter. But more generally, we can have a new interaction between dark matter and normal matter and get the right result if the interaction is of the right strength. I call this type of dark matter “thermal dark matter,” since it was originally produced in the thermal bath of hot particles in the early Universe.

The point is that such well-motivated dark matter requires an interaction between dark matter and normal matter, and that interaction isn’t infinitesimally small. The weak nuclear force is weak sure, but we can measure it these days.

So how do you look for thermal dark matter?

One way is direct detection. If dark matter is a WIMP or thermal, then there is a lot of it moving through the Earth all the time. Rarely, one particle of dark matter will bash into a nucleus, and impart a tiny amount of energy. If you can build a detector with very low rates of radioactivity, and shield it from cosmic rays and anything else that could imitate a dark matter nuclear collision, then you can search for this kind of dark matter.

There are many such experiments; buried deep underground (for cosmic ray reduction). I got to visit one in Sudbury, Ontario: 2 km underneath the surface in a nickel mine. Almost all of them have seen nothing, and thus set very strong limits on the rate of dark matter-nuclei interactions.

There is one exception: the DAMA/Libra experiment in Gran Sasso (a car tunnel under a mountain in northern Italy, where the low-background lab is built on a side-tunnel halfway through). DAMA is unique in how it approaches searching for dark matter. Most direct detection experiments look for dark matter by having zero (or next-to-zero) background, and looking for a few scattering events over that background.

DAMA instead doesn’t seek zero background. Instead it looks for a modulation of the number of events they see over a year. Why do this?

A dark matter direct detection experiment is looking for a dark matter particle smashing into a nucleus and imparting some energy in the recoil. Think of it like two bowling balls hitting each other. The energy that the recoiling atom gets is set by the relative masses of the dark matter and nucleus and the momentum of the dark matter — that is, how fast the dark matter is moving through the experiment. No experiment can measure a recoiling nucleus with zero momentum, so there is always some experimental threshold of the minimum recoil energy that can be seen. Therefore, there is a minimum dark matter speed that could, even in principle, be measured by any experiment. This speed will vary from experiment to experiment, depending on the atomic mass of the target material and the experimental threshold.

So how fast is dark matter moving in the detector? Well, we don’t really know. We can make a simple assumption: this far from the Milky Way’s center, particles on orbits will be moving with an average speed of ~220 km/s or so, with some moving faster and some slower. This is the “Standard Halo Model” of dark matter. To that, we have to add the motion of the Sun through the cloud of dark matter — the cloud of dark matter isn’t rotating on average, but the Sun is moving at ~240 km/s through the rest frame of the Galaxy. So dark matter is moving through a direct detection experiment at incredible speeds: hundreds of km/s.

On top of which, the Earth orbits the Sun with a speed of 30 km/s. But here’s where things get interesting. Half the year, the Earth’s orbit causes us to move “with” the motion of the Sun around the Galaxy. The other half of the year, we are moving “against” that motion. Around June, more of the dark matter is moving faster relative to an experiment built on Earth than there is in December. So, if you measure the rate of scattering, you should see more events in June than December, because more dark matter can surpass your detector’s energy threshold.

So this is what DAMA/Libra has been looking for: a yearly modulation in the number of events, peaking around the date predicted by the models of the dark matter motion in the Galaxy. And they see such a modulation: now at nearly $13\sigma$ significance.

Great! Discovery of dark matter!

Limits on dark matter elastic spin-independent scattering from XENON1T, CDMSlite, and Cosine-100 assuming the Standard Halo Model, contrasted with the best-fit regions from DAMA/Libra. Fits to the recoil spectrum are shown in orange, and to the daily modulation in yellow.

Unfortunately, no other experiment sees the same signal. Even though the other experiments don’t look for modulation, you can, if you know the dark matter velocity distribution, predict how many events other experiments should see if DAMA/Libra is measuring real dark matter modulation. Experiments such as Xenon-1T (that’s Xenon-1-ton: a ton of liquid xenon instrumented to detect dark matter scattering) rule out the DAMA/Libra signal region by four or five orders of magnitude.

Now, you can appeal to a bunch of possible explanations to save the DAMA signal: you can try to make dark matter that scatters with the sodium-iodide crystals of DAMA and not with xenon (or the many other target materials used by other experiments). Given the strength of the negative results, that doesn’t seem to work anymore.

Or you can say that the Standard Halo Model is wrong, and the real velocity distribution of dark matter is such that other experiments get suppressed rates while DAMA gets an enhanced rate. I’ve written papers on this idea. Again, given the strength of the Xenon-1T limits, the plausible variations on the dark matter velocity distribution don’t seem like they could rescue DAMA.

So for the last few years, I’d been saying that, in order to get the DAMA signal from changing the dark matter velocity distribution, you’d need to do something very extreme. You’d need the Earth to be passing through a very fast-moving stream of dark matter — then if the dark matter mass was just right, you could get a greatly increased modulation rate in DAMA as the Earth went from going “with” the wind of dark matter to “against” the wind while not really changing the yearly average rate.

Further, you’d need this stream to be oriented pretty much exactly so it was pointed in exactly the opposite direction of the Sun’s motion through the Milky Way. Because DAMA isn’t just seeing a modulating rate: it’s seen a modulation that peaks when the Standard Halo Model predicts it should peak. A random stream of dark matter coming from a random direction in the sky would shift the modulation peak day.

So DAMA could only be saved by a very special stream of dark matter, and how likely was that?

Modulation of amount of dark matter capable of causing a dark matter scattering event for the Standard Halo Model (black), the Gaia model for the halo (red), and the S1 stream (blue).

Then Gaia came along.

Gaia is a space telescope run by the European Space Agency that is measuring the position and motion of 1.4 billion stars in the Milky Way. Now, Gaia can’t see dark matter, because dark matter is… dark (or, more precisely, it is invisible).

But Gaia can identify kinematic structures in the stars. Combined with measures of the age of stars, one can use this data set to find groups of stars that are statistically unlikely to be just due to chance. In particular, Myeong et al found a number of stars that were consistent with being “streams” or “tidal debris:” the relics of dwarf galaxies that were long ago absorbed by the Milky Way. Such ancient streams of stars are expected to have dark matter with them, though getting an idea of the amount of dark matter is difficult (and something I’m very interested in).

One of these streams, called S1, is extremely high velocity. It is also counter-rotating to the Sun. It coincidentally is pointing more or less exactly in the direction needed to result in a peak-day for a modulation experiment that would be the same as if there was no stream.

Limits and Best-fit regions assuming 100% of local dark matter is in the S1 stream and spin-independent Elastic scattering.

Basically, if you wanted to build a stream of dark matter that could boost the signal that DAMA/Libra sees while not changing other experiments’ sensitivities by much, you couldn’t do better than S1. Since I’d been going around saying “look, the only way to save DAMA is to have a stream that’s fast and counterrotating and how likely is that?” I sort of felt obligated to go and do the very time-consuming task of checking to see if S1 (or similar streams) can get a DAMA signal without being ruled out by any other experiment.

So myself, Gopi, and Chris recast DAMA/Libra’s results along with the leading experiments that don’t see dark matter: Xenon-1T, CDMSlite (a germanium-based detector), PICO-60 (a fluorine-based detector that is very sensitive to dark matter that couples to nuclear spin), and COSINE-100 (an experiment built out of the same target material as DAMA). In addition to the stream data, we used the best models of the “bulk” dark matter velocity distributions also derived from Gaia data.

While we couldn’t check every type of scattering of dark matter against nuclei, we checked a number of possibilities: spin-independent and spin-dependent, elastic (i.e., bowling ball hitting bowling ball type scattering), and inelastic (where some of the recoil energy is absorbed internally during the scattering).

Overall, we found that the stream can do exactly what we’d expect. It has a peak-day nearly the same as that predicted by the Standard Halo Model. It allows dark matter of lower mass than we’d normally expect to give a viable DAMA/Libra signal, and since low mass is where Xenon-1T has the least sensitivity, this moves things in the right direction to evading the null results.

Energy Spectrum of DAMA/Libra observed modulation signal (black), along with S1-only best-fit (Red), and S1+halo best fit (blue).

Additionally, overlaying the stream with the background halo of dark matter allows one to fit the DAMA results much better. DAMA, in addition to measuring the modulation of scattering per day also measures their spectrum: how many events are modulating per energy. One problem with the Standard Halo Model predictions for DAMA is that the lowest energy bins don’t seem to be showing the decrease in modulation that the models predict. A stream added to the halo changes the spectrum enough to greatly improve the statistical fit.

That said, for most every parameter point we considered, DAMA continues to be ruled out by the other experiments. There are a few exceptions though. For one, if dark matter scatters elastically and spin-independently, and the S1 stream is over 80% of the local density, then DAMA can be well-fit and no other experiment should have seen it yet. However, this amount of stream density is, to put a technical term on it, completely bonkers. My naive expectation is that S1 could be 10-20% of the local density. 30% would be “wow, but ok.” 80-90% seems implausible. But we don’t know for sure, and I’d like to find some way to check.

Best-fit regions to DAMA/Libra Recoil Spectrum as a function of mass and stream density fraction for spin-independent elastic scatter (yellow, green, orange are 1,2,3 sigma fits). Grey shaded region are parameter points ruled out by null results of other experiments. Note a very small allowed region at 3 sigma near 30 GeV and >80% stream fraction.

The other option is that the modulation rate seen by DAMA is right, but the recoil energy spectrum is way off. Then we can fit the signal with a stream scattering elastically and spin-dependently without being ruled out. However, at this point you’d be arguing that the experiment you want to be right is in fact sort of wrong (its spectrum would be incorrect), wrong in just the right way. Such arguments tend to be come across as a bit grasping at straws, but I mention it for completeness.

So, this was a lot of work to prove that DAMA is, for the most part, still ruled out. I think it was useful though, for a couple of reasons. First: I convinced myself that this stream that was perfect to “help” DAMA is just not enough to easily explain the positive signal while not being in tension with everyone else’s negative results. DAMA is a difficult signal to explain, and it seemed necessary to me to do the work to figure out if it could be understood through this new stream. It can’t, outside of some unlikely caveats, but if I didn’t check, I wouldn’t know. DAMA is still unexplained, but it once again seems, to me at any rate, that it isn’t something that can be easily fit by dark matter. Experiments like COSINE and similar sodium-iodine targets in the southern hemisphere (like SABRE) will probably tell us more about what’s really going on, but as of right now, I don’t see a clear way for this signal to be dark matter.

Second, I found out how much a stream like S1 can change direct detection results. The answer is “a surprising amount.” Even with reasonable stream densities, you can get pretty significant changes to the recoil spectrum, and some pretty wild changes in expectations from the Standard Halo Model. We know these streams exist, we will learn more and more about them as our ability to model the dark matter halo improves. Direct detection assumes something about the motion of dark matter, so as our knowledge of this motion improves, so will out ability to extract signals and limits.