Sinusoidal dark matter: ANAIS Edition

Title: Annual Modulation Results from Three Years Exposure of ANAIS-112.


This is an exciting couple of months to be a particle physicist. The much-awaited results from Fermilab’s Muon g-2 experiment delivered all the excitement we had hoped for. (Don’t miss our excellent theoretical and experimental refreshers by A. McCune and A. Frankenthal, and the post-announcement follow-up.) Not long before that, the LHCb collaboration confirmed the R_K flavor anomaly, a possible sign of violation of lepton universality, and set the needle at 3.1 standard deviations off the Standard Model (SM). That same month the ANAIS dark matter experiment took on the mighty DAMA/LIBRA, the subject of this post.

In its quest to confirm or refute its 20 year-old predecessor at Brookhaven National Lab, the Fermilab Muon g-2 experiment used the same storage ring magnet — though refurbished — and the same measurement technique. As the April 7 result is consistent with the BNL measurement, this removes much doubt from the experimental end of the discrepancy, although of course, unthought-of correlated systematics may lurk. A similar philosophy is at work with the ANAIS experiment, which uses the same material, technique and location (on the continental scale) as DAMA/LIBRA.

As my colleague M. Talia covers here and I touch upon here, an isotropic distribution of dark matter velocities in the Galactic frame would turn into an anisotropic “wind” in the solar frame as the Solar System orbits around the center of the Milky Way. Furthermore, in the Earth’s frame the wind would reverse direction every half-year as we go around the Sun. If we set up a “sail” in the form of a particle detector, this annual modulation could be observed — if dark matter interacts with SM states. The amplitude of this modulation S_m is given by

R(t) = S_m \cos(\omega (t - t_0)) + R_0 \phi_{\rm bg}(t)~,


R(t) is the rate of event collection per unit mass of detector per unit energy of recoil at some time t,

\omega = 2\pi/(365 \ {\rm days}),

R_0 captures any unmodulated rate in the detector with \phi_{\rm bg} its probability distribution in time, and

t_0 is fixed by the start date of the experiment so that the event rate is highest when we move maximally upwind on June 02.

The DAMA/LIBRA experiment in Italy’s Gran Sasso National Laboratory, using 250 kg of radiopure thallium-doped sodium-iodide [NaI(Tl)] crystals, claims to observe a modulation every year over the last 20 years, with S_m = 0.0103 \pm 0.0008 /day/kg/keV in the 2–6 keV energy range at the level of 12.9 \sigma.

It is against this serious claim that the experiments ANAIS, COSINE, SABRE and COSINUS have mounted a cross-verification campaign. Sure, the DAMA/LIBRA result is disfavored by conventional searches counting unmodulated dark matter events (see, e.g. Figure 3 here or this recent COSINE-100 paper). But it cannot get cleaner than a like-by-like comparison independent of assumptions about dark matter pertaining either to its microscopic behavior or to its phase space distribution in the Earth’s vicinity. Doing just that, ANAIS (for Annual Modulation with NaI Scintillators) in Spain’s Canfranc Underground Laboratory, using 112.5 kg of radiopure NaI(Tl) over 3 years, has a striking counter-claim summed up in this figure:

Figure caption: The ANAIS 3 year dataset is consistent with no annual modulation, in tension with DAMA’s observation of significant modulation over 20 years.

ANAIS’ error bars are unsurprisingly larger than DAMA/LIBRA’s given their smaller dataset, but the modulation amplitude they measure is unmistakably consistent with zero and far out from DAMA/LIBRA. The plot below is visual confirmation of non-modulation with the label indicating the best-fit S_m under the modulation hypothesis.

Figure caption: ANAIS-112 event rate data in two energy ranges, fitted to a null hypothesis and a modulation hypothesis; the latter gives a fit consistent with zero modulation. The event rate here falls with time as the time-distribution of the background \phi_{\rm bkg} (t) is modeled as an exponential function accounting for isotopic decays in the target material.

The ANAIS experimenters carry out a few neat checks of their result. The detector is split into 9 pieces, and just to be sure of no differences in systematics and backgrounds among them, every piece is analyzed for a modulation signal. Next they treat t_0 as a free parameter, equivalent to making no assumptions about the direction of the dark matter wind. Finally they vary the time bin size in analyzing the event rate such as in the figure above. In every case the measurement is consistent with the null hypothesis.

Exactly how far away is the ANAIS result from DAMA/LIBRA? There are two ways to quantify it. In the first, ANAIS take their central values and uncertainties to compute a 3.3 \sigma (2.6 \sigma) deviation from DAMA/LIBRA’s central values S_m^{\rm D/L} in the 1–6 keV (2–6 keV) bin. In the second way, the ANAIS uncertainty \sigma^{\rm AN}_m is directly compared to DAMA using the ratio S_m^{\rm D/L}/\sigma^{\rm AN}_m, giving 2.5 \sigma and 2.7 \sigma in those energy bins. With 5 years of data — as scheduled for now — this latter sensitivity is expected to grow to 3 \sigma. And with 10 years, it could get to 5 \sigma — and we can all go home.

Further reading.

[1] Watch out for the imminent results of the KDK experiment set out to study the electron capture decay of potassium-40, a contaminant in NaI; the rate of this background has been predicted but never measured.

[2] The COSINE-100 experiment in Yangyang National Lab, South Korea (note: same hemisphere as DAMA/LIBRA and ANAIS) published results in 2019 using a small dataset that couldn’t make a decisive statement about DAMA/LIBRA, but they are scheduled to improve on that with an announcement some time this year. Their detector material, too, is NaI(Tl).

[3] The SABRE experiment, also with NaI(Tl), will be located in both hemispheres to rule out direction-related systematics. One will be right next to DAMA/LIBRA at the Gran Sasso Laboratory in Italy, the other at Stawell Underground Physics Laboratory in Australia. ParticleBites’ M. Talia is excited about the latter.

[4] The COSINUS experiment, using undoped NaI crystals in Gran Sasso, aims to improve on DAMA/LIBRA by lowering the nuclear recoil energy threshold and with better background discrimination.

[5] Testing DAMA, article in Symmetry Magazine.

Maleficent dark matter: Part II

In Part I of the series we saw how dark matter could cause mass extinction by inducing biosphere-wide cancer, stirring up volcanoes, or launching comets from the Oort cloud. In this second and final part, we explore its other options for maleficence.

World-devouring dark matter

The dark matter wind that we encountered in Part I has yet another trick to bring the show on this watery orb to an abrupt stop. As J. F. Acevedo,  J. Bramante, A. Goodman, J. Kopp, and T. Opferkuch put it in their abstract, “Dark matter can be captured by celestial objects and accumulate at their centers, forming a core of dark matter that can collapse to a small black hole, provided that the annihilation rate is small or zero. If the nascent black hole is big enough, it will grow to consume the star or planet.” Before you go looking for the user guide to an Einstein-Rosen bridge, we draw your attention to their main text: “As, evidently, neither the Sun nor the Earth has suffered this fate yet, we will be able to set limits on dark matter properties.” For once we are more excited about limits than discovery prospects.

Limits on dark matter from its sparing our planet and star. Image source: Acevedo et al.

R-rated dark matter

Enough about destructions of life en masse. Let us turn to selective executions.

Macro dark matter” is the idea that dark matter comprises not of elementary particles but composite objects that weigh anywhere between micrograms and tonnes, and scatter on nuclei with macroscopic geometric cross sections. As per J. J. Sidhu, R. J. Scherrer and G. Starkman, since the dark wind blows at around 300 km/s, a dark macro encountering a human body would produce something akin to gunshot or a meteor strike, only more gruesome. Using 10 years of data on the well-monitored human population in the US, Canada and Western Europe, and assuming that it takes at least 100 J of energy deposition to cause significant bodily damage, they derive limits on dark matter cross sections and masses shown in the adjoining figure.

We’re afraid there’s nothing much you can do about a macro with your name on it.

Limits on dark matter from its sparing of human lives. Image source: Sidhu et al.

Inciteful dark matter

Dark matter could sometimes kill despite no interactions with the Standard Model beyond gravity. [Movie spoilers ahead.] In the film Dark Matter, a cosmology graduate student is discouraged from pursuing research on the titular topic by his advisor, who in the end rejects his dissertation. His graduation and Nobel Prize dreams thwarted, and confidante Meryl Streep’s constant empathy forgotten, the student ends up putting a bullet in the advisor and himself (yes, in that order). Senior MOND advocates, take note.

Vital dark matter

Lest we suspect by now that dark matter has a hotline to the Grim Reaper’s office, D. Hooper and J. H. Steffen clarify that it could in fact breathe life into desolate pebbles in the void. Without dark matter, rocky planets on remote orbits, or rogue planets ejected from their star system, are expected to be cold and inhospitable. But in galactic regions where dark matter populations are high, it could capture in such planets, self-annihilate, and warm them from the inside to temperatures that liquefy water, paving the way for life to “emerge, evolve, and survive“. The fires of this mechanism would blaze on long after main sequence stars cease to shine!

And perhaps one day these creatures may use the very DNA they got from dark matter to detect it.



[6] Dark Matter, Destroyer of Worlds: Neutrino, Thermal, and Existential Signatures from Black Holes in the Sun and Earth, J. F. Acevedo,  J. Bramante, A. Goodman, J. Kopp, and T. Opferkuch, arXiv: 2012.09176 [hep-ph]  

[7] Death and serious injury from dark matter, J. J. Sidhu, R. J. Scherrer and G. Starkman, Phys. Lett. B 803 (2020) 135300  

[8] Dark Matter and The Habitability of Planets, D Hooper & J. H. Steffen, JCAP 07 (2012) 046  

[9] New Dark Matter Detectors using DNA or RNA for Nanometer Tracking, A. Drukier, K. Freese, A. Lopez, D. Spergel, C. Cantor, G. Church & T. Sano, arXiv: 1206.6809 [astro-ph.IM]  

Maleficent dark matter: Part I

We might not have gotten here without dark matter. It was the gravitational pull of dark matter, which makes up most of the mass of galactic structures, that kept heavy elements — the raw material of Earth-like rocky planets — from flying away after the first round of supernovae at the advent of the stelliferous era. Without this invisible pull, all structures would have been much smaller than seen today, and stars much more rare.

Thus with knowledge of dark matter comes existential gratitude. But the microscopic identity of dark matter is one of the biggest scientific enigmas of our times, and what we don’t know could yet kill us. This two-part series is about the dangerous end of our ignorance, reviewing some inconvenient prospects sketched out in the dark matter literature. Reader discretion is advised.

[Note: The scenarios outlined here are based on theoretical speculations of dark matter’s identity. Such as they are, these are unlikely to occur, and even if they do, extremely unlikely within the lifetime of our species, let alone that of an individual. In other words, nobody’s sleep or actuarial tables need be disturbed.]

The dark matter wind could blow in mischief. Image source: Freese et al.

Carcinogenic dark matter

Maurice Goldhaber quipped that “you could feel it in your bones” that protons are cosmologically long-lived, as otherwise our bodies would have self-administered a lethal dose of ionizing radiation. (This observation sets a lower limit on the proton lifetime at a comforting 10^7 times the age of the universe.) Could we laugh similarly about dark matter? The Earth is probably amid a wind of particle dark matter, a wind that could trigger fatal ionization in our cells if encountered too frequently. The good news is that if dark matter is made of weakly interacting massive particles (WIMPs), K. Freese and C. Savage report safety: “Though WIMP interactions are a source of radiation in the body, the annual exposure is negligible compared to that from other natural sources (including radon and cosmic rays), and the WIMP collisions are harmless to humans.

The bad news is that the above statement assumes dark matter is distributed smoothly in the Galactic halo. There are interesting cosmologies in which dark matter collects in high-density “clumps” (a.k.a. “subhalos”, “mini-halos”,  or “mini-clusters”). According to J. I. Collar, the Earth encountering these clumps every 30–100 million years could explain why mass extinctions of life occur periodically on that timescale. During transits through the clumps, dark matter particles could undergo high rates of elastic collisions with nuclei in life forms, injecting 100–200 keV of energy per micrometer of transit, just right to “induce a non-negligible amount of radiation damage to all living tissue“. We are in no hurry for the next dark clump.

Eruptive dark matter

If your dark matter clump doesn’t wipe out life efficiently via cancer,  A. Abbas and S. Abbas recommend waiting another five million years. It takes that long for the clump dark matter to gravitationally capture in Earth, settle in its core, self-annihilate, and heat the mantle, setting off planet-wide volcanic fireworks. The resulting chain of events would end, as the authors rattle off enthusiastically, in “the depletion of the ozone layer, global temperature changes, acid rain, and a decrease in surface ocean alkalinity.”

Dark matter settling in the Earth’s core could spell doom. Image source: J. Bramante & A. Goodman.

Armageddon dark matter

If cancer and volcanoes are not dark matter’s preferred methods of prompting mass extinction, it could get the job done with old-fashioned meteorite impacts.

It is usually supposed that dark matter occupies a spherical halo that surrounds the visible, star-and-gas-crammed, disk of the Milky Way.  This baryonic pancake was formed when matter, starting out in a spinning sphere, cooled down by radiating photons and shrunk in size along the axis of rotation; due to conservation of angular momentum the radial extent was preserved. No such dissipative process is known to govern dark matter, thus it retains its spherical shape. However, a small component of dark matter might have still cooled by emitting some unseen radiation such as “dark photons“. That would result in a “dark disk” sub-structure co-existing in the Galactic midplane with the visible disk. Every 35 million years the Solar System crosses the Galactic midplane, and when that happens, a dark disk of surface density of 10 M_\odot/pc^2 could tidally perturb the Oort Cloud and send comets shooting toward the inner planets, causing periodic mass extinctions. So suggest L. Randall and M. Reece, whose arXiv comment “4 figures, no dinosaurs” is as much part of the particle physics lore as Randall’s book that followed the paper, Dark Matter and the Dinosaurs.

We note in passing that SNOLAB, the underground laboratory in Sudbury, ON that houses the dark matter experiments DAMIC, DEAP, and PICO, and future home of NEWS-G, SENSEISuper-CDMS and ARGO, is located in the Creighton Mine — where ore deposits were formed by a two billion year-old comet impact. Perhaps the dark disk nudges us to detect its parent halo.

A drift (horizontal passage) in Creighton Mine, 2.1 km underground. Around the corner is SNOLAB, where several experiments searching for dark matter are located. The mine owes its existence to a meteorite impact — perhaps triggered by a Galactic disk of dark matter. Photo: N. Raj.

In the second part of the series we will look — if we’re still here — at more surprises that dark matter could have planned for us. Stay tuned.


[1] Dark Matter collisions with the Human Body, K. Freese & D. Savage, Phys.Lett.B 717 (2012) 25-28.

[2] Clumpy cold dark matter and biological extinctions, J. I. Collar, Phys.Lett.B 368 (1996) 266-269.

[3] Volcanogenic dark matter and mass extinctions, S. Abbas & A. Abbas, Astropart.Phys. 8 (1998) 317-320

[4] Dark Matter as a Trigger for Periodic Comet Impacts, L. Randall & M. Reece, Phys.Rev.Lett. 112 (2014) 161301

[5] Dark Matter and the Dinosaurs, L. Randall, Harper Collins: Ecco Press‎ (2015)

Adjectivous dark matter

How would you describe dark matter in one word? Mysterious? Ubiquitous? Massive? Theorists often try to settle the question in the title of a paper — with a single adjective. Thanks to this penchant we now have the possibility of cannibal dark matter. To be sure, in the dark world eating one’s own kind is not considered forbidden, not even repulsive. Just a touch selfish, maybe. And it could still make you puffy — if you’re inflatable and not particularly inelastic. Otherwise it makes you plain superheavy.

Below are more uni-verbal dark matter candidates in the literature. Some do make you wonder if the title preceded the premise. But they all remind you of how much fun it is, this quest for dark matter’s identity. Keep an eye out on arXiv for these gems!

anapole, asymmetric, atomic, brane-world, charged, co-interacting, coloured, cryptobaryonic, disformal, fluid, freeze-twin, gluequark, GUTzilla, homeopathic, impeded, inflaxion, Kaluza-Klein, luminous, macro, minimal, monodromy, \nu-inflaton, parafermionic, relaxion, resonant, self-destructing, self-interacting, singlet-doublet, spectator, super-cool, technicolor, topological, undulating, unparticle, wave.

This image has an empty alt attribute; its file name is cannibnoun.png
Dark matter, in addition to consuming physicists, could also be cannibal. Image: Gan Khoon Lay, Noun Project.