What Has Dark Matter Ever Done For Us ?

Well I suppose even Albert Einstein must have had an off-day, because if you ask me, a Universe full of giraffes and supernovae doesn't score highly on list of "things I definitely understand". In fact I wouldn't put it on the list at all.

I mean, Albert, what the hell were you thinking/drinking/smoking ? In what possible way is a Universe containing armadillos and exploding stars and porridge and black holes the slightest bit comprehensible ? Even very senior astronomers still insist on the old cliché that a frog is far more complicated than, say, a star or a galaxy. Which is a little bit weird considering just how little we understand about galaxies, and makes me wonder if biologists are all in the wrong profession.

ALL GLORY TO THE HYPNO-TOAD... but is he really more complicated than a galaxy ? I think not.

Nothing in astronomy seems to anger People On The Internet quite so much as the apparently simple notion of dark matter. Popular articles are universally greeted with a chorus of "scientists don't understand everything !" and "they're only looking for dark matter to keep themselves employed !" The sociology of this anti-science movement, even though dark matter is about as detached from any political or ethical concerns as it's possible to be, is almost as interesting as the physics itself. But today, let's stick to the science as much as possible.

(To digress from that just for a moment, I get kind of cheesed off when I read things like, "physicists who don't believe in dark matter are wrong." Such a level of certainty is not warranted. I do believe dark matter is the most likely explanation, but to claim that all other explanations have been falsified seems a bit strange.)


I've written about dark matter many times before, but to sum up : galaxies appear to be spinning too fast. Without some extra mass to hold them together, they should just fly apart.

Explanatory blog post.

My third-year undergraduate project has earned me a small degree of internet fame in some circles, while my fourth year project has never, until now, got a look in*. Today, in an effort to demonstrate how science is really done (and hopefully convince you that dark matter isn't such a crazy notion after all), I shall try and redress the balance.

* Unfortunately at the time I had yet to learn Python, which was a shame because it would naturally have lent itself to some pretty animations.

This was a project to try and simulate the formation of a disc galaxy without dark matter. Back then I was far less convinced about dark matter : probably, I would say, only at the 50:50 level. These days I'm more at the 75:25 level in favour - good enough to work with, but not nearly enough to bet my life on.

In my report, I described several arguments against the existence of dark matter. There are plenty more, of course, but these will do for now :


1) Halo conspiracy
Why are rotation curves* of galaxies flat as opposed to some other shape ? These days I'm a lot less convinced that this is really a problem - curves are seldom truly flat. They vary considerably, sometimes always rising, sometimes weakly declining (though not as much as if there was no dark matter). The only sense in that there's a "conspiracy" is that the curves don't agree with predictions from Newtonian dynamics. That's a lot less interesting than if they really did all have very similar shapes. Actually the details of this turn out to be very interesting, but I'll save that for a future post.

* A rotation curve just measures the speed at which a galaxy  is rotating at different distances from its center (usually by measuring its gas). That the speed doesn't drop with distance was the key piece of evidence in the discovery of dark matter.

If you're wondering about the name, dark matter clouds are usually known as halos, hence the "halo conspiracy" term - the idea being that the halo is somehow conspiring with the normal matter to always produce rotation curves of roughly the same shape.

Source - rotation curves of a sample of spiral galaxies. Irregular galaxies tend to show curves which never flatten off but just keep rising.

2) Surface brightness conspiracy
Surface brightness just means how bright galaxies are per unit area  - or to put it another way, some galaxies of a given size have more stars than others. Strangely, this doesn't seem to make much difference - it's only the total brightness that determines how fast the galaxy is rotating. But it's quite easy to show that surface brightness should make a difference. It's as though the dark matter and luminous matter are connected, and it isn't at all obvious why that should be.

The low surface brightness VCC 975 (left) compared with the normal VCC 1555 (right).

Similarly, dark matter "halos" (i.e. clouds) always seem to contain the same fraction of luminous matter, no matter their size. Galaxy formation theory says that ordinary matter falls into dark matter halos, so there's no obvious reason why the fraction of ordinary matter should be constant.


3) Dark matter inside galaxies is inferred from a single measurement - rotation curves.
If there were several observations that dark matter existed this would be a lot more convincing, but as far as we can tell dark matter does one thing, and one thing only : it keeps galaxies rotating more quickly. Even on scales just a bit smaller than the galaxy it doesn't appear to have much of an effect. And it seems a bit strange that 90% of the galaxy should do nothing very much except keep it spinning round a bit faster than it otherwise would.

Of course there are other observations in other situations where dark matter is also very important, like galaxy clusters and the large-scale structure of the Universe. But on scales smaller than galaxies, this is apparently not the case. Yes, even though galaxies come in many different sizes - dark matter only appears to be important over the whole galaxy. You may have heard recent reports to the contrary, but in my opinion that press release was actually pretty awful.

Shamelessly plugging my own work again.

It was that third point that motivated my undergraduate project - what would happen if we tried to simulate the formation of a spiral galaxy but without the dark matter ? Does the dark matter really do nothing at all except change the rotation curve ? If so, that would be a bit suspicious. You'd think that 90% of the mass of a galaxy ought to play some role beyond gathering the gas together and making it spin faster.

Yes, I know there are a whole bunch of other reasons to believe dark matter exists. But trying to test the entire dark matter paradigm at once is a monumental undertaking - so daunting a prospect that there's a risk no-one* will check it at all, thus establishing a false consensus. A much better approach is to break it down into smaller, manageable chunks. If we can say, "dark matter doesn't do anything expect make things spin faster", then we might want to start questioning other aspects of the paradigm. If, on the other hand, we can show that dark matter has some other essential role, then that strengthens the case for its existence.

* Especially a fourth-year undergraduate.

Neither scenario makes for a revolutionary breakthrough, but as I've tried to stress again and again and again : that's not how science usually works. What we'll get from the investigation is only one piece of the puzzle - nothing more, nothing less. Take enough baby steps and eventually you'll get to Outer Mongolia, write a novel, learn to play the piano, bring dinosaurs back to life, or whatever the heck else it is you want out of life.

Of course, some of us have more cerebral goals than others.

With that in mind, the simulations we ran were anyway somewhat unorthodox. Mainstream cosmology says that galaxies form by the merging of smaller galaxies. The model we used was much simpler : the collapse of a big cloud of gas straight into a rotating disc. It's called a monolithic collapse, though actually the process is a lot more complicated than a big hunk of gas suddenly turning into a galaxy.

More here. Dark matter is purple, gas yellow, and stars are red. The particles are initially in a 3D grid (filling a spherical volume), with small random motions. That's why at the start it looks like there are lots of discrete purple and yellow clouds - actually they are long columns.

I'm not sure why this approach doesn't get more attention. While dark matter is usually taken for granted, the idea of hierarchical merging is very much more openly controversial. In fact, pretty much every conference I've ever been to has left me with the distinct impression that it's only really a few prestigious diehards who actually believe it.

To me, the collapse of a single giant cloud into a galaxy - which quantitatively resembles actual spiral galaxies - seems like a much simpler idea than trying to build up a disc by lots of small galaxies that all collide in just the right way as to form a neat disc. It also has the advantage of not producing a "missing satellite" problem - unlike most other simulations, this one produces a spiral galaxy with about the same number of orbiting satellite dwarf galaxies as we observe in reality*. Unfortunately their orbits are all wrong, but meh. You can't have everything.

* That is no small achievement, but for some reason - God knows why - the paper has only 15 citations in 14 years.

The satellite galaxies of the Milky Way orbit at right-angles to
the disc, whereas the simulation predicts they should orbit in
the same plane. Ah, well, whatever, never mind.

Anyway, what you can't see too well in the gif is that on the large scale, the dark matter tends to fragment before it completely collapses. Any part of the halo which happens to become slightly denser than the rest (just through the small random motions of the particles) will have more gravity and tend to collapse faster. Remember that the gif is showing several billion years of simulation time - there's plenty of time for parts of the halo to fragment before the whole thing collapses.

Fragmentation of the collapsing dark matter (left) and gas (right). Both images are about 85 kpc across (280,000 light years).

Since the dark matter is collisionless - it doesn't interact with itself - these condensations tend to be pretty diffuse, but they're still quite massive. This means the dark matter fragments draw in some of the surrounding gas, which makes the whole collapse process very messy. Instead of a uniform sphere that just shrinks, you get a load of different clouds all heading only roughly toward the center of the cloud.

In the gif you can see a giant purple shockwave - after the dark matter collapses, most of it re-expands. That means the gravity near the center is reduced, and what you get is a bunch of gas fragments all sort of milling about, which eventually turn into a nice happy galaxy.

But... take the dark matter away and that early fragmentation doesn't happen. Instead, the gas just collapses uniformly until it reaches a very small size indeed, at which point it does, eventually, fragment*. But the final result looks nothing like a galaxy - what we found was a ring about 10% the diameter of the galaxy that formed in the case of dark matter, with the gas density being very much higher.

* The gas is much hotter than the dark matter. Temperature is basically velocity dispersion, i.e. random motions. For fragmentation to occur, gravity has to be strong enough to overcome these random motions. For the hotter gas, this means it only happens when the density is very high.

With dark matter, a galaxy around 50 kpc (163,000 light years) across is formed. Without it, what we got was this itty-bitty ring about 3 kpc (9,700 light years) across.

This lack of pre-collapse fragmentation was certainly important, but there was also another problem. The simulation lost angular momentum (which breaks physics - simulations do that all the time but usually just by a negligible amount), so everything was spinning more slowly than it should. The resulting ring was therefore smaller than it should have been. However, fourth-year undergraduate me neglected to write down exactly how much angular momentum was lost, so I can't tell you how much bigger the ring may have been if the code wasn't bugged. Well, we live and learn.

(all I did write was that while normally it's conserved to within 1% or less, in this run it was losing 8% per timestep - which is nothing short of catastrophic)

Of course we didn't just do one simulation - more like a couple of dozen, each taking a few days to run. We varied a whole bunch of parameters, which I won't go into here. Nothing worked. The one time we managed to create something that did resemble a galaxy, it was spinning much too fast - more than twice as fast as anything ever observed, and for once that's well above any measurement errors.


So, another triumph for the dark matter model then ? Heck no ! That's how the popular press would spin it... but I'm trying really hard to convince you that just because a result doesn't have Earth-shattering implications doesn't mean it's not interesting. The obsession in the media for decisive results is pretty damaging for science communication, but that's another story...

What we showed was that in this unconventional model, dark matter was necessary to forming the galaxy - it's not a case of it doing nothing much except making the gas spin faster. It doesn't merely help galaxies form more rapidly - it's essential for them to form at all. I don't know of anyone who's tried to do a more conventional galaxy formation simulation but with the dark matter simply turned off, but it would make for a fascinating comparison.

So we found one small piece of evidence in favour of dark matter. It's through a series of these small, incremental findings that I've become convinced that dark matter is the most likely explanation for what we observe. But that in no way means that there aren't still other problems, or other ways to form a galaxy without dark matter. I'll take a look at why I'm still not a True Believer in dark matter next time.