Terrible Ideas I've Had

I just got back from a two week workshop on dark matter hosted by the Aspen Physics Center. Aspen Physics is a really special place to think: the workshops are limited to only a few planned meetings per week. You’re supposed to just talk and work and think. So I took this trip as an opportunity to take a bit of a vacation from my existing projects, and try to think about interesting things that I wasn’t working on, but maybe should.

Is this dark matter? I legitimately have no idea. (Daylan et al)

The thing that could my attention was the saga of the Goodenough-Hooperon. Ten years ago, Lisa Goodenough and Dan Hooper noticed that there were slightly too many gamma rays coming from the Galactic Center (as measured by the Fermi Gamma-Ray Space Telescope) than one might expect from known astrophysical sources. Interestingly, these gamma rays had a spatial distribution around the center of the Galaxy as a function of distance from the center that went approximately like one would expect from the square of a Navarro-Frenk-White (NFW) density profile. This NFW profile is what we generically expect dark matter to have in a galaxy, and if dark matter was annihilating with itself into gamma rays, the distribution of resulting photons should go like the square of the density (since you need two particles to find each other to annihilate).

In many follow-up studies, it is now pretty clear that there is in fact an excess of gamma rays coming from the Galactic Center. This excess is consistent with the distribution one would expect from dark matter annihilation, and can be well-fit by very simple dark matter models where dark matter has a mass of roughly 50 GeV, annihilating into some pair of Standard Model particles ($b$-$\bar{b}$ quarks is the canonical choice, but not the only one), that decays into a shower of short-lived particles, which themselves decay into particles including gamma rays (as per the usual naming scheme for particles, this dark matter candidate is often dubbed the Hooperon or the Gooperon).

As Dan Hooper said at a talk once, there is $40\sigma$ evidence for the Galactic Center excess. To which I gather Tim Tait responded “Dan, you don’t know we are having this conversation at $40\sigma$.” (this is absolutely true: there’s always the chance someone slipped you some hallucinogens, and your brain has decided to invent a rather boring conversation out of whole cloth.)

The sage of the Hooperon hit a bit of a snag in 2015, when a paper came out demonstrating that the signal from the Galactic Center was consistent with coming from a number of point sources that are just below the Fermi detection threshold, rather than a smooth distribution as one would expect from dark matter annihilation. This suggested that the gamma rays were coming from some non-dark matter astrophysical sources; the leading candidate being gamma rays generated by millisecond pulsars.

Millisecond Pulsars are so boring.

Artists Impression of a Millisecond Pulsar and Binary Companion (Credit: NASA)

This of course is tremendously disappointing. I want to find something cool, like dark matter, not something boring, like the corpses of dead stars that spun themselves up to tremendous speeds by consuming another star and which are now using magnetic fields powerful enough to kill you from across a star system to accelerate subatomic particles to unimaginable energies. Pulsars, man. I hate ‘em.

Now, even with this result — that the Galactic Center excess was point-sourcy — this didn’t necessarily kill the dark matter interpretation. Indeed, we have no reason to suspect that there should be enough millisecond pulsars in the Galactic Center to fit the excess, or that the distribution of such pulsars (if they exist) should be approximately NFW-squared. But the sociology of the field moved on, for a number of reasons, some good, some bad. In the end, the real problem is that the simplest models of dark matter that fit the excess don’t predict any other signals that are easily measured. When building models of dark matter, it is trivial to make your dark matter as dark as you like — to avoid existing experimental bounds. But in the case of the Galactic Center excess, I don’t even need to appeal to what I refer to as “stupid theorist tricks” to evade other limits: just build the dumbest model of dark matter and you get the Galactic Center excess but should not have expected to find a signal in direct detection, or be terribly surprised that the LHC hasn’t seen it yet. So, without much else to say, the field moved on.

But recently, one of the authors of the original paper (Tracy Slatyer) indicating a preference for point-sources has put out a new paper (along with a postdoc, Rebecca Leane) suggesting that the evidence for point sources might be due to issues with the modeling of other sources of gamma rays in the Galactic Center. Rebecca was at Aspen Physics, along with other authors of the original paper, and there were a lot of really interesting discussions as to what we know from the Fermi data. There are a lot of differing views, set forth by people whose scientific opinions I hold in extremely high regard. My current view is that the Fermi data cannot distinguish between the point-source and non-point source options. I might be wrong, but I’m not sure there will be resolution that I feel very confident in.

This makes me really concerned. My (somewhat self-assigned) job is to find dark matter. I’ve spent a lot of time on it, and so have many others. The entire conference I was just at was about finding dark matter. Now here’s a signal that might be dark matter. And I don’t know what to do with it. Moreover, the signal would be from a completely standard WIMP-type dark matter candidate — no stupid-clever theorist tricks. If we can’t “find” this kind of dark matter, despite what might an actual signal of it, what does that mean about this whole effort?

So I decided to spend most of my Aspen stay thinking about ways to prove or disprove the dark matter interpretation of the Galactic Center excess. Obviously, this isn’t the first time I’ve thought about it, or others, and so I didn’t expect necessarily to succeed. I came up with a number of ideas, some of which might work (though don’t get your hopes up), and some would definitely work, if we had experimental facilities that are optimistically ten years away (if not further).

Two of them are terrible ideas that won’t work, which are the ones I’ll tell you about now. I’ll tell you because the proof they won’t work are examples of “Fermi problems” so beloved by theorists. And because sometimes seeing why ideas are won’t work can be useful. And who knows, maybe I’m missing something.

The Moon: What a Useless Rock

pokes Moon with Stick Come ON Moon, do something.

Apollo 11, Image Credit: NASA (Also Going-to-the-moon-credit: NASA)

Gamma rays similar to the Galactic Center excess have actually been seen in a number of places. I found it in the Large Magellanic Cloud, and it’s been seen in the core and outskirts of the Andromeda Galaxy. But the problem in every case is that we can’t say for sure that there aren’t non-dark matter sources in those locations too. Millisecond pulsars can lurk everywhere.

Those jerks.

So I starting thinking about what line of sight in the sky could I be pretty sure didn’t have a millisecond pulsar hiding. One came to mind: I’m reasonably sure there isn’t a pulsar between me and the Moon. There are certainly pulsars far beyond the Moon, but since the Moon is opaque to gamma rays, any contribution such sources have to gamma ray signal from the Moon would be completely negligible. So the idea is to look at the gamma ray signal from the direction Moon, and see if there’s any evidence of the dark matter between us and the Moon annihilating. This seems vaguely plausible: a rough estimate of the number of annihilations (for a Galactic Center-like dark matter candidate) in the volume of space occupied by the cone that stars at your eye and ends on the Moon’s surface is 100,000 annihilations per second. That’s not bad!

Unfortunately, reality ensues quickly. The energy from those annihilations goes out in all directions, only a very few of which end on the surface of the Fermi telescope. We classify the potential strength of a dark matter signal as seen by Fermi using a number called the $J$-factor. The bigger this number, the easier it is to see the dark matter signal. The $J$-factor for the Galactic Center is $\sim 10^{24}~{\rm GeV^2/cm^5}$. A good-sized dwarf galaxy has a $J$-factor of $10^{19}$ in these units.

The dark matter between the Earth and the Moon? It has a $J$-factor of $10^5~{\rm GeV^2/cm^5}$. So any signal is 1/100,000,000,000,000,000 as strong as the Galactic Center. This is because the Moon is not very far away, so there’s not much dark matter between us and it.

As a result, despite my best efforts, the Moon continues to not pull its weight around here, particle physically speaking.

Space: Too Damn Empty

Shown: Not at all what a Interstellar Gas Cloud Looks like

Image Credit: Paramount Pictures

My next idea was at least not as dumb as the previous. The problem with the previous thought was that all those annihilations of dark matter weren’t visible because the energy is flying off into space, and not ending up in our detector. So let’s find some system which somehow responds to that annihilation energy. But how?

In space there are these clouds of cold gas. We can see how cold they are, and (assuming they are in thermal equilibrium), that means we can determine how much energy they are radiating per second. If dark matter was somehow dumping energy into such a cloud, it would heat up, and thus reveal the presence of dark matter. (Well, really, we wouldn’t be able to tell if the dark matter was doing the heating, or some unseen star, but at least we could set a bound.)

If you estimate how much energy dark matter annihilation will be producing per second per volume, you should take the number density squared, multiply it by the energy each annihilation produces (roughly twice the mass), and then by the “velocity-averaged cross section” (which gives you an estimate of how likely an annihilation is). For Galactic Center-excess compatible dark matter near the Earth, assuming a mass of 50 GeV, this is:

\[ \left(\frac{0.3~{\rm GeV/cm^3}}{50~{\rm GeV}}\right)^2 \times 100~{\rm GeV} \times 3\times 10^{-26}~{\rm cm^3/s} \sim 10^{-28}~{\rm GeV/cm^3/s} ~ 10^{-31}~{\rm erg/cm^3/s} \]

Put that gas cloud in the Galactic Center, and the increased density of dark matter gains you 2-3 orders of magnitude. Now, this energy deposition is tiny, but it is also about the energy loss rate of cold gas clouds in the Galaxy. So there’s a potential limit to be extracted here!

Unfortunately, the energy is coming out in the form of hard radiation: high energy gamma rays very fast electrons, and the like. Interstellar dust clouds are very diffuse, and they don’t interact very much with such energetic particles. So the dark matter annihilation products won’t heat the gas, but rather speed through it effortlessly. Some tiny amount would be measured here on Earth by telescopes like Fermi, but the whole point is that I don’t know the source of such gamma rays. So I’m stymied by the fact that space, in case you hadn’t heard, is very empty. Damn.