Galileo's Pendulum

Last year, scientists looking at data from the orbiting Fermi gamma ray observatory announced they found a possible signal of dark matter particles annihilating each other near the center of the Milky Way. The signal consisted of a spike in the number of gamma ray photons around 130 billion electron volts (130 GeV) in energy. The analysis was based on nearly 4 years of observation, and looked very promising. At the Phenomenology 2013 conference I recently attended, several people based their talks on the specific premise that the 130 GeV signal was not only real, but from dark matter annihilation.

However, not everyone was equally excited. There were a few caveats even in the original analysis: for example, the signal was offset from the galactic center by a few degrees, which would be hard to explain based on the expected distribution of dark matter in the Milky Way. Others focused on the problem of dark matter annihilation producing that particular energy of gamma-ray photons, and still others were concerned about the statistical significance of the signal.

The last concern turns out to be the most valid. Astronomers directly involved with the Fermi observatory’s Large Area Telescope (LAT) performed their own analysis of the same data, and found the significance of the gamma ray excess nearly vanished. Their conclusions highlight how complicated the hunt for dark matter signals can be, but also how probability and statistics work when looking for a signal we can’t describe in advance.

Operation Annihilate!

Dark matter helps shape galaxies and influenced the fluctuations in the early Universe that led to the structures we see today. Based on detailed analysis of galaxies, galaxy clusters, and the cosmic microwave background, we know dark matter comprises about 80% of all the mass in the Universe. However, we still don’t know exactly what it’s made of. We have good hints that it’s a type of particle (or possibly more than one type), and it obviously exerts a gravitational influence — since that’s the way we know it exists. We know it doesn’t interact with light, it’s not made of the same particles that comprise atoms, and that it’s not neutrinos. Beyond that, we have to make educated guesses, based on what we know about normal matter.

One popular conjecture is that dark matter is a WIMP: a weakly interacting massive particle. The “weakly” bit refers to the weak force, one of the four fundamental interactions. “Massive” hints that it’s relatively heavy, at least compared to neutrinos (which have very tiny masses), so they move fairly slowly compared to the speed of light. One general class of WIMPs predicts that each type of particle is its own antiparticle, so if a WIMP meets another WIMP, they mutually annihilate.

However, unlike an electron meeting a positron, the result of WIMP annihilation isn’t automatically a pair of gamma rays. Recall that dark matter doesn’t interact with light (I’ve said before that a better term for it is “invisible matter”), so it can’t annihilate directly into photons: the reaction has to produce something else that will eventually produce gamma rays. In symbolic form (using the standard symbol χ for dark matter),

meaning that two dark matter particles collide, then annhilate into something else. That something else produces a gamma ray photon (γ) and another particle X, which might be another gamma ray, a Z boson, a Higgs boson, or something more exotic. (Particle physicists know I’m lying slightly on this, but as the saying goes, it’s complicated. I’d rather not talk about loop corrections today.)

That’s what researchers using Fermi were hunting for: gamma rays that were the result of WIMP mutual annihilation. However, according to WIMP models, the “something” in the reaction above doesn’t always produce photons. Depending on which particular theory, maybe only 1 WIMP collision in 10 will make a photon, or even 1 collision in 10,000. If WIMP collisions are fairly rare — and they likely are, based on the density of dark matter in most of the Universe — then it’s going to be hard to find the gamma rays they produce. The best hope is to look at regions where dark matter is more dense, such as the center of the Milky Way or other galaxies. Even then, a knowledgeable physicist I spoke with at VERITAS is skeptical we’ll ever see a WIMP annihilation signal if it’s there: it’s too easy to confuse it with something else.

However, let’s assume for a moment the signal exists, and we can find it if we look. Theoretical models say that the energy of a single photon from WIMP annihilation (or WIMP decay, if the particles are unstable) has the form
where E_γ is the gamma ray energy, m_χ is the WIMP mass, and M_X is the mass of whatever other product comes out of the annihilation. (My apologies for using both X and χ in the same equation; it’s not my fault.) (If X is a second gamma ray, then the energy of the photon is the same as the rest energy of the WIMP.) In other words, seeing a gamma ray with a given energy doesn’t automatically give us the WIMP mass, but plugging in (say) the Higgs boson mass for M_X would tell us whether the dark matter particle corresponds to anything in an existing model.

However, we don’t necessarily know in advance how much energy the gamma ray should carry — or perhaps more to the point, we have too many possible predictions to choose from. WIMPs are predicted in several different versions of supersymmetry (SUSY), as well as other extensions to the Standard Model. We are still very much in the dark (ha!) about dark matter’s identity, though we’re doing better at ruling out possibilities. Which brings us to….

Looking for car keys under the wrong lamppost

The new analysis of Fermi data took several steps to make sure the potential annihilation signal was real. First, the researchers removed events that could be possibly due to cosmic rays hitting Earth’s atmosphere. Cosmic rays are high-energy particles from a variety of sources, and when they reach Earth, they can produce a cascade of gamma rays that can mimic a signal. The new analysis was particularly careful to trim any potential stray events from the data.

Next, the researchers divided the sky into five overlapping “regions of interest” (ROIs) centered on the galactic center. These were chosen based on several well-known models for the dark matter distribution (which in turn were developed for understanding the structure of spiral galaxies like ours). The authors of the study also split Fermi’s very broad energy range (5 to 300 GeV) into overlapping “bins”. Combining the predicted dark matter profile and other gamma ray sources, both known and modeled, they developed a good heuristic for looking for annihilation signatures — assuming nothing either way about the prior detection claims.

The result: the new analysis found no significant excess of gamma rays that could be attributed to WIMP annihilation anywhere in the data. As I pointed out in the previous section, that doesn’t mean WIMPs aren’t destroying each other all over the place — just that any gamma ray signal is too small or too rare (since photons are necessarily a byproduct) to be seen. However, the researchers did find a small bump at the same location as the earlier analysis, but too small to be considered a real signal. One problem with interpreting it as WIMP annihilation is something known as the “look-elsewhere” effect, where if you consider all the possibilities for where a gamma ray line could be, it’s particularly unlikely this specific bump is real.

Interestingly, they found that the gamma-ray signature from cosmic rays interacting with Earth’s atmosphere — which should contain no bumps — also had a slight excess at 133 GeV. That weird result indicated there may be a systematic problem that boosted the photon count near the galactic center enough to make it look like a signal. However, that isn’t enough by itself to explain the slight bump in the adjusted data. It will be interesting to see what happens with that later: if it’s an instrumentation problem, or something else going on.

What does this mean? First, a small excess of gamma rays could still mean WIMP annihilation, but it could also mean something else — another type of signal or a systematic effect of unknown origin. The low statistical significance of the bump means that it’s just barely above a fluctuation in noise, which means it could become more prominent with more data, if it really is a tiny excess…or vanish entirely.

References

• Fermi-LAT collaboration, Search for Gamma-ray Spectral Lines with the Fermi Large Area Telescope and Dark Matter Implications. arXiv:1305.5597
• Meng Su and Douglas P. Finkbeiner, Strong Evidence for Gamma-ray Line Emission from the Inner Galaxy. arXiv:1206.1616