Why is Dark Matter Cold?

[dibs_and_dlas]

First off, for all those interested in the “what is a planet?” debate, I suggest checking out this paper. A good read, and a good take on the subject.

So now, cold dark matter, via gravitational lensing, neutrinos, relativistic free-streaming, and structure formation. Basically, all the neat stuff that turned the universe from a photon-baryon coupled fluid into the mostly-isotropic-but-with-some-structure (galaxies, clusters, and so forth) thing it is today.

So previously I had shown how some very good research had led to the conclusion that there was definitely some dark matter out there. Now, the power spectrum of the cosmic microwave background (basically analysing the size and distribution of the temperature fluctuations) implies that there is definitely non-baryonic matter out there, but we’ll ignore that for now (it’s a fairly recent result). Instead, we’ll first look at the various types of baryonic particle which have been proposed for dark matter.

First up, we have MACHOs (MAssive Cosmic Halo Objects). These are brown dwarfs (~0.1 M⊙ 1, “stars” too small to initiate fusion), free Jupiters (gas giants which aren’t orbiting around stars), white dwarfs (burned-out stars <1.4M⊙ which are no longer emitting light since they’ve fused all they can), and black holes (do I really need to explain what these are?). So one theory was that there were a whole bunch of these things floating around the galaxies (especially in the galactic halos), and that they were the dark matter.

Of course, once these ideas were proposed, they had to be tested. So a search had to be mounted for MACHOs, with the usual difficulties inherent in looking for things that are, well, invisible (or pretty much so). Hubble is able to see white dwarfs fairly well, but the others are essentially impossible to see with telescopes. So, enter gravitational lensing.

Gravitational lensing comes as a result of the theory of relativity. If, as Einstein suggested, gravity is a distortion of the geometry of space (rather than a force), it should act on light as well as on matter, because light passes through the space between the source and the observer (Newtonian gravity could have been defined as a force acting on light as well as matter, but then light would have to be given a mass for the purposes of calculating the force, and the equivalence of mass and energy is another of those relativity things you may have heard of). In Astronomy, lensing is divided into “microlensing” and “macrolensing” 3, of which microlensing is the important one here (macrolensing also is very useful, but it would add a bit too much to this discussion to mention it here).

So, gravity bends light. Now, imagine a heavy (but not too heavy) object passing between us an a distant light source (a star, a galaxy, whatever). Since the light source emits light in all directions, for every light ray that goes directly towards us, there are several that are aimed slightly away from us, and so we just barely don’t see them. Now, when the object moves directly between us and the source, it bends some of those rays a little bit towards us. Sure, it blocks out the rays that we were seeing before, but it bends even more rays from “just missing” to “just hitting”, so we see the light source get brighter for a moment (with a slight dip to “fainter” (not as faint as at the start, but a bit fainter than the maximum brightness) right when the object crosses the line of sight. On the off chance that the explanation was a bit confusing, it’s figure time. The first figure is taken from the University of Oregon, the second from UBC.





So, as you can see, even if a MACHO is “invisible” (not emitting light), it can still be detected if it passes in front of something. And, if there are enough of them in the galactic halo to act as dark matter, then if we monitor a bunch of stars in a nearby galaxy (let’s say one of the Magellanic clouds), we should see a few lensing events. And we do, but not nearly enough. So, while there are definitely large massive objects in the galactic halo, there aren’t enough of them to be dark matter.

The other category of dark matter is so-called WIMPs (Weakly Interacting Massive Particles). Now, there’s one possible WIMP that’s actually known to exist now, and that’s the neutrino. Neutrinos are (almost) massless particles which were first invented to deal with problems that were found in nuclear reactions, and have since been detected. In particular, let’s look at a couple of decay reactions and show where the neutrino belongs:

167N → 168O + e−

127N → 126C + e+

Each of these reactions has a slight problem. The first problem is that, well, mass-energy isn’t conserved. When you add up the total mass-energy of the products, it’s lower than the mass-energy of the reactants. The second problem is that particle number isn’t conserved. The electron (e−) has a baryon number of 1, while the positron (e+) has a baryon number of −1 (it’s antimatter, which is defined as having a negative baryon number). So, in the first case you’re creating a particle from nowhere, and in the second destroying a particle. Not a good thing to do. As a result, the neutrino was created to “balance out” the equation (and then, eventually, detected). Now, things look like:

167N → 168O + e− + νe

127N → 126C + e+ + νe

Incidentally, the overlined text indicates that the particle in question is antimatter, here an electron anti-neutrino (now, neutrinos and anti-neutrinos are effectively the same, but the important thing is making the particle number come out right). Lots of nuclear reactions (including the fusion reactions that happen inside stars) emit neutrinos, so there are a lot of them around, and they don’t interact with much. They can be detected, however, and scientists were actually quite quick to detect solar neutrinos &emdash; there just weren’t enough of them. While many theories were created to explain this, the answer turned out to be that neutrinos change type. In theory there are three types &emdash; electron (νe), muon (νμ) and tau (ντ). And the early experiments could only detect electron neutrinos (which should have been the ones the Sun was producing). Instead, though, some were changing type on the way, and thus weren’t being detected. What this type-changing (“oscillating”) means is that neutrinos have mass. 4 Unfortunately, they don’t have enough mass to be dark matter. The electron neutrino has a mass <2.2 eV, the muon neutrino <170 keV, and the tau neutrino <28 MeV. 5 Considering that an electron has a mass of 0.51 MeV, and the proton 938 MeV, you’d need a lot of neutrinos to be six times as heavy as the rest of matter combined. Not to mention, of course, that neutrinos would be hot dark matter (and next I’ll tell you what the difference is).

Whether dark matter is “cold” or “hot” depends on the mass of whatever particle(s) make up dark matter. Heavy particles are “cold”, while light particles are “hot” (except axions, which I believe are both light and cold, because they work very oddly). What the distinction means is that, essentially, dark matter particles start out moving at relativistic speeds (near the speed of light), and eventually slow down, and heavier particles slow down sooner. The reason that this is important is that dark matter is most of the matter in the universe. Now, relativistic free-streaming dark matter tends to “smooth out” normal matter, getting rid of structure (like, say, galaxies or clusters) on a size scale that gets bigger for lighter particles (that stay relativistic longer). Cold dark matter is thus the currently accepted default, because hot dark matter wouldn’t have allowed galaxies to form at all.

Of course, cold dark matter has its problems. Specifically, the models predict that there should be dozens of dwarf companion galaxies around every regular galaxy (like, say, the Milky Way), and instead there are two. Three if you count the one currently being digested. Well, a few more than that, really, but not as many as there should be. This has led some physicists to speculate on the possibility of “warm” dark matter, which is hot enough to have smoothed out most of the companion galaxies, but cold enough to have left everything else in place. Of course, balancing things just right is difficult to do, and simulating warm dark matter is much more difficult than simulating the cold stuff. And, since no one knows what dark matter is yet, there’s no real way to resolve the debate either.

This has gotten to be a really long article, so I think I’m going to close things here, at least for now. Hope it was entertaining, and at least somewhat comprehensible. Next time, I might even talk about what it is that I, personally, do in Astronomy.

1. 
   Where the ⊙ (Odot, or circled dot symbol) refers to the Sun, so M⊙ refers to the mass of the Sun. ↩ 2
   
2. 
   Note that the “↩” symbol for “go back from the footnote” was stolen as a really good idea from the Daring Fireball web site. ↩
   
3. 
   Innovative names, aren’t they? ↩
   
4. 
   And I bet you didn’t even know they were Catholic. ↩
   
5. 
   The eV is the electron volt (the energy gained by accelerating one electron through a 1-volt electric field). Particle physicists measure masses in units of energy, and rely on E=mc2 to convert to a mass (if, for some reason, you need a mass). ↩