Shut up and simulate. (In which I try to understand how dark matter forms galaxies, and end up very confused.)

Galactic structures.
Illustris Simulation.
[Image Source]

Most of the mass in the universe isn’t a type of matter we are familiar with. Instead, it’s a mysterious kind of “dark matter” that doesn’t emit or absorb light. It also interacts rarely both with itself and with normal matter, too rarely to have left any trace in our detectors.

We know dark matter is out there because we see its gravitational pull. Without dark matter, Einstein’s theory of general relativity does not predict a universe that looks like what we see; neither galaxies, nor galaxy clusters, nor galactic filaments come out right. At least that’s what I used to think.

But the large-scale structure we observe in the universe also don’t come out right with dark matter.

These are not calculations anyone can do with a pen on paper, so almost all of it is computer simulations. It’s terra-flopping, super-clustering, parallel computing that takes months even on the world’s best hardware. The outcome is achingly beautiful videos that show how initially homogeneous matter clumps under its own gravitational pull, slowly creating the sponge-like structures we see today.

Dark matter begins to clump first, then the normal matter follows the dark matter’s gravitational pull, forming dense clouds of gas, stars, and solar systems: The cradles of life.

structure formation, Magneticum simulation
Credit: Dolag et al. 2015

It is impressive work that simply wouldn’t have been possible two decades ago.

But the results of the computer simulations are problem-ridden, and have been since the very first ones. The clumping matter, it turns out, creates too many small “dwarf” galaxies. Also, the distribution of dark matter inside the galaxies is too peaked towards the middle, a trouble known as the “cusp problem.”

The simulations also leave some observations unexplained, such as an empirically well-established relation between the brightness of a galaxy and the velocity of its outermost stars, known as the Tully-Fisher-relation. And this is just to mention the problems that I understand well enough to even mention them.

It’s not something I used to worry about. Frankly I’ve been rather uninterested in the whole thing because for all I know dark matter is just another particle and really I don’t care much what it’s called.

Whenever I spoke to an astrophysicist about the shortcomings of the computer simulations they told me that mismatches with data are to be expected. That’s because the simulations don’t yet properly take into account the – often complicated – physics of normal matter, such as the pressure generated when stars go supernovae, the dynamics of interstellar gas, or the accretion and ejection of matter by supermassive black holes which are at the center of most galaxies.

Fair enough, I thought. Something with supernovae and so on that creates pressure and prevents the density peaks in the center of galaxies. Sounds plausible. These “feedback” processes, as they are called, must be highly efficient to fit the data, and make use of almost 100% of supernovae energy. This doesn’t seem realistic. But then again, astrophysicists aren’t known for high precision data. When the universe is your lab, error margins tend to be large. So maybe “almost 100%” in the end turns out to be more like 30%. I could live with that.

Eta Carinae. An almost supernova.
Image Source: NASA

Then I learned about the curious case of low surface brightness galaxies. I learned that from Stacy McGaugh who blogs next door. How I learned about that is a story by itself.

The first time someone sent me a link to Stacy’s blog, I read one sentence and closed the window right away. Some modified gravity guy, I thought. And modified gravity, you must know, is the crazy alternative to dark matter. The idea is that rather than adding dark matter to the universe, you fiddle with Einstein’s theory of gravity. And who in their right mind messes with Einstein.

The second time someone sent me a link to Stacy’s blog it came with the remark I might have something in common with the modified gravity dude. I wasn’t flattered. Also I didn’t bother clicking on the link.

The third time I heard of Stacy it was because I had a conversation with my husband about low surface brightness galaxies. Yes, I know, not the most romantic topic of a dinner conversation, but things happen when you marry a physicist. Turned out my dear husband clearly knew more about the subject than I. And when prompted for the source of his wisdom he referred to me to no other than Stacy-the-modified-gravity-dude.

So I had another look at that guy’s blog.

Upon closer inspection it became apparent Stacy isn’t a modified gravity dude. He isn’t even a theorist. He’s an observational astrophysicist somewhere in the US North-East who has become, rather unwillingly, a lone fighter for modified gravity. Not because he advocates a particular theory, but because he has his thumb on the pulse of incoming data.

I am not much of an astrophysicist and understand like 5% of what Stacy writes on his blog. There are so many words I can’t parse. Is it low-surface brightness galaxy or low surface-brightness galaxy? And what’s the surface of a galaxy anyway? If there are finite size galaxies, does that mean there are also infinite size galaxies? What the heck is an UFD? What means NFW, ISM, RAR, and EFE?* And why do astrophysicists use so many acronyms that you can’t tell a galaxy from an experiment? Questions over questions.

Though I barely understood what the man was saying, it was also clear why other people thought I may have something in common with him. Even if you don’t have a clue what he’s on about, frustration pours out of his writing. That’s a guy shouting at a scientific community to stop deluding themselves. A guy whose criticism is totally and utterly ignored while everybody goes on doing what they’ve been doing for decades, never mind that it doesn’t work. Oh yes, I know that feeling.

Still, I had no particular reason to look at the galactic literature and reassess which party is the crazier one, modified gravity or particle dark matter. I merely piped Stacy’s blog into my feed just for the occasional amusement. It took yet another guy to finally make me look at this.

I get a lot of requests from students. Not because I am such a famous physicists, I am afraid, but just because I am easy to find. So far I have deterred these students by pointing out that I have no money to pay them and that my own contract will likely run out before they have even graduated. But last year I was confronted with a student who was entirely unperturbed by my bleak future vision. He simply moved to Frankfurt and one day showed up in my office to announce he was here to work with me. On modified gravity, out of all things.

So now that I carry responsibility for somebody else’s career, I thought, I should at least get an opinion on the matter of dark matter.

That’s why I finally looked at a bunch of papers from different simulations for galaxy formation. I had the rather modest goal of trying to find out how many parameters they use, which of the simulations fare best in terms of explaining the most with the least input, and how those simulations compare to what you can do with modified gravity. I still don’t know. I don’t think anyone knows.

But after looking at a dozen or so papers the problem Stacy is going on about became apparent. These papers typically start with a brief survey of other, previous, simulations, none of which got the structures right, all of which have been adapted over and over and over again to produce results that fit better to observations. It screams “epicycles” directly into your face.

Now, there isn’t anything scientifically wrong with this procedure. It’s all well and fine to adapt a model so that it describes what you observe. But this way you’ll not get a model that has much predictive power. Instead, you will just extract fitting parameters from data. It is highly implausible that you can spend twenty or so years fiddling with the details of computer simulations to then find what’s supposedly a universal relation. It doesn’t add up. It doesn’t make sense. I get this cognitive dissonance.

And then there are the low surface-brightness galaxies. These are interesting because 30 years ago they were thought to be not existent. They do exist though, they are just difficult to see. And they spelled trouble for dark matter, just that no one wants to admit it.

Low surface brightness galaxies are basically dilute types of galaxies, so that there is less brightness per surface area, hence the name. If you believe that dark matter is a type of particle, then you’d naively expect these galaxies to not obey the Tully-Fisher relation. That’s because if you stretch out the matter in a galaxy, then the orbital velocity of the outermost stars should decrease while the total luminosity doesn’t, hence the relation between them should change.

But the data don’t comply. The low surface brightness things, they obey the very same Tully-Fisher relation than all the other galaxies. This came as a surprise to the dark matter community. It did not come as a surprise to Mordehai Milgrom, the inventor of modified Newtonian dynamics, who had predicted this in 1983, long before there was any data.

You’d think this would have counted as strong evidence for modified gravity. But it barely made a difference. What happened instead is that the dark matter models were adapted.

You can explain the observations of low surface brightness galaxies with dark matter, but it comes at a cost. To make it work, you have to readjust the amount of dark matter relative to normal matter. The lower the surface-brightness, the higher the fraction of dark matter in a galaxy.

And you must be good in your adjustment to match just the right ratio. Because that is fixed by the Tully-Fisher relation. And then you have to come up with a dynamical process for ridding your galaxies of normal matter to get the right ratio. And you have to get the same ratio pretty much regardless of how the galaxies formed, whether they formed directly, or whether they formed through mergers of smaller galaxies.

The stellar feedback is supposed to do it. Apparently it works. As someone who has nothing to do with the computer simulations for galaxy structures, the codes are black boxes to me. I have little doubt that it works. But how much fiddling and tuning is necessary to make it work, I have no telling.

My attempts to find out just how many parameters the computer simulations use were not very successful. It is not information that you readily find in the papers, which is odd enough. Isn’t this the major, most relevant information you’d want to have about the simulations? One person I contacted referred me to someone else who referred me to a paper which didn’t contain the list I was looking for. When I asked again, I got no response. On another attempt my question how many parameters there are in a simulations was answered with “in general, quite a few.”

But I did eventually get a straight reply from Volker Springel. In the Illustris Simulation, he told me, there are 10 physically relevant parameters, in addition to the 8 cosmological parameters. (That’s not counting the parameters necessary to initialize the simulation, like the resolution and so on.) I assume the other simulations have comparable numbers. That’s not so many. Indeed, that’s not bad at all, given how many different galaxy types there are!

Still, you have to compare this to Milgrom’s prediction from modified gravity. He needs one parameter. One. And out falls a relation that computer simulations haven’t been able to explain for twenty years.

And even if the simulations would get the right result, would that count as an explanation?

From the outside, it looks much like dark magic.

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* ultra faint dwarfs, Navarro-Frenk-White, interstellar medium, radial acceleration relation, external field effect