And the Temperature of Dark Matter is...?

"A fact never went into partnership with a miracle. Truth scorns the assistance of wonders. A fact will fit every other fact in the universe, and that is how you can tell whether it is or is not a fact. A lie will not fit anything except another lie."
-Robert Green Ingersoll

One of the most amazing facts to comprehend about the Universe is that it actually is comprehensible! A few basic laws, properties and particles, given our current understanding, can take us from a hot, dense, nearly uniform Universe to the complexity of the billions of stars within the billions of galaxies we see today.

Image credit: NASA/CXC/M.Weiss.

One of the most surprising, but most robust, of results from our investigation of the Universe is the fact that dark matter -- some form of matter that does not interact with light, with atoms, or with itself except gravitationally -- not only exists, but makes up about five times as much of the Universe as atoms do!

There is a whole suite of evidence that points towards this conclusion, but the two best pieces of evidence are the fluctuations in the cosmic microwave background,

Image credit: WMAP team / NASA.

and the distribution of galaxies -- known as large-scale structure -- throughout the Universe.

Image credit: Sloan Digital Sky Survey.

Now, the thing we'd like to do next, given what we presently know, is to figure out how to directly create and/or detect this dark matter, so we can find out exactly what it is!

Unfortunately, because it doesn't interact with normal matter except gravitationally, and the gravitational force is something like a factor of 10³⁰ weaker than the other known forces, we haven't been able to do so, yet. (No disrespect to CRESST, DAMA or CoGeNT.)

But one of the questions we can ask that will have observable consequences is what kinetic energy this dark matter has relative to its mass!

Image credit: WMAP team, retrieved from Peter Coles' site.

The fluctuations in the microwave background, believe it or not, are completely insensitive to this! You could have dark matter that moves at ultrarelativistic speeds, or dark matter that barely moves at all, and the pattern of fluctuations wouldn't change at all.

But a number of things are sensitive to the speed of dark matter. As an analogy, think about it in terms of the molecules inside something like a balloon.

Image credit: UC Davis ChemWiki.

If the molecules are fast-moving, this corresponds to a high temperature, and the balloon would feel a significant pressure inside, and would therefore be large and the gas inside of it would be diffuse.

On the other hand, if the molecules are slow-moving, this corresponds to a low temperature, the balloon's pressure inside would be low and it would therefore be small, while the gas inside would be quite dense.

Now, if we apply this to dark matter, some parts of the analogy are no good. Molecules collide with one another and with the surface of the balloon; dark matter simply zips around with whatever speed it has in the expanding Universe. All it can do is either move slowly enough to help objects collapse gravitationally (and form stars, galaxies, clusters, etc.), or move quickly enough to hinder their formation.

So we look deep into the Universe's past to see what we have.

Image credit: NASA, ESA, S. Beckwith (STScI) and the HUDF Team.

We see lots of structure far enough back in the past to place limits on how hot -- or fast-moving -- this dark matter is allowed to be. And we not only find galaxies and quasars when the Universe is just a few hundred million years old, although we do find that, and that's very important.

Image credit: Bob Carswell.

We find, on even tinier scales, collapsed clumps of primordial hydrogen gas that are incredibly dense and incredibly cold. Because of how deep and narrow those lines above are -- absorption lines of cold hydrogen clumps in the early Universe -- we can place very good constraints on how slow-moving dark matter needs to be.

So we can rule out the picture known as hot dark matter, where something like a normal low-mass, relativistic neutrino makes up the bulk of the dark matter in our Universe.

But we can simulate different temperatures for this dark matter -- hot, cold, or somewhere in between -- and see what sort of predictions it gives.

From top: Cold, Warm, and Hot dark matter simulations, credit ITP, University of Zurich.

Now, this is where it gets interesting. Both Warm and Cold dark matter give results that generally agree with our observations of small-and-large-scale structure. From scales that are about a hundred thousand light years and larger, these two types of dark matter form structure that are virtually indistinguishable. But when we look at the smallest scales, scales smaller than that of a single, large galaxy, that's where the differences are the most evident between the two theories.

Image credit: R. Lehoucq et al.

One way to do this is to look is at individual galaxies themselves, and to reconstruct how the dark matter is distributed in them. Cold dark matter always gives predictions like the four upper lines, which are difficult to reconcile at their cores with observations. The isothermal model (the bottom line) has always given better fits, but has also always been chided as being ill-motivated, because there isn't a good particle candidate for it. (Unlike cold dark matter, which has WIMPs, axions, and a plethora of other candidates.)

But astronomers have been saying for a long time that if dark matter were warm, this fit would be much better. Physicists have preferred cold dark matter because of the possibilities of detection; indeed, that's where most of the efforts, including CDMS, XENON, Edelweiss, and the search at the LHC are sensitive.

But there has long been another puzzle. On the scale of individual galaxies, like our Milky Way, cold dark matter predicts a very large number of small, clumpy satellite galaxies. And although we find many in our local group, there aren't nearly enough.

Well, Carlos Frenk at the University of Durham -- the "F" in the NFW profile from the earlier images -- has been working for the last few years on a set of very sensitive simulations involving dark matter and the formation of structure, and he's got a very important result.

Image credit: C. Frenk.

Warm dark matter works! Dwarf galaxies around the Milky Way are less dense and less abundant than cold dark matter would give us, but the simulations using warm dark matter match up here, too!

And this is particularly amazing, because we can compare what cold dark matter and warm dark matter do, relative to one another, on the largest scales, where our observations have been very robust for a long time.

Image credit: V. Springel at Max-Planck-Institute at Garching.

They're the same! On large scales, cold dark matter and warm dark matter give identical results for clustering; this is great, because this is where our theory matches up with observation the best!

But going to smaller and smaller scales?

Image credit: Liang Gao and Tom Theuns.

Warm dark matter just works better. So if warm dark matter turns out to be the answer to our astronomy conundrums, what does this mean for the physics?

It means that we're not going to find dark matter where we're looking right now. Perhaps it's a sterile neutrino; a fourth family of neutrino that doesn't couple to the other ones the way we're accustomed to? Perhaps it's a new type of particle that we haven't considered before? Or perhaps it is something like an axion, only they aren't born either cold (like standard theory predicts) or hot (like a thermal relic would be), but warm, due to a new type of interaction or coupling?

Whatever the case may be, it's time to reopen the door for warm dark matter, and not to merely dismiss it because there are no satisfying particle candidates. Gravity and structure formation don't lie, so let's listen to what they're telling us!