Spiral structure

I’m not entirely sure why, but recently, in various forums I hang out on, I’ve been seeing a particular creationist argument pop up that’s fairly annoying. The argument is that the universe can’t be as old as astronomers say it is because, if it were, the spiral arms in galaxies would “wind up”.

This argument is pretty convincing at first, because it plays on the expectation that galaxies are fairly straightforward systems without dirty little tricks up their sleeves. If this were the case, galaxies would behave like the solar system wherein the things towards the center go around quickly and objects towards the edges slowly work their way around. Thus, if you started everything on a straight line, the inner part would have orbited several times while the outer edges would barely have budged thanks to the fact that those inner bits not only move faster, but have a shorter distance to travel in their smaller orbits.

Expectation wise, galaxies shouldn’t have graceful arms that tend to only go about half a full turn. Unless, of course, those expectations are wrong. And I’m sure by now most readers are anticipating what should be the obvious answer: They are.

The first thing that’s wrong is that galaxies don’t behave like our solar system. This was first realized in 1959 in the galaxy M33 by Louise Volders. In the 1970’s, this non-Keplarian motion was discovered in more and more galaxies by Vera Rubin, which is one of the foundations for the need for Dark Matter. Instead of velocities trailing off in an exponential decay like we see in the solar system, most galaxies tend to have fairly flat velocity curves as shown in the figure. A flat rotation curve means that galaxies don’t wind up and if they do, it would be very slowly.

Of course, this raises an even more interesting question. Even though we’ve established that these arms could be very old, it still doesn’t say anything about why you have regions in the galaxy where they exist in the first place. What’s so special about spiral structure!?

The answer to this question is profound because it gets to the very nature of what spiral arms are and, as with before, it’s something that completely defies what you’re probably thinking if you’re not already familiar with this topic: Spiral structure is the result of spiral density waves...

Whatever the hell that means.

Unfortunately, there’s no real good way I’ve yet come across to explain this. Silly analogies with traffic jams tell you what is going on, but says nothing of why it happens. And that “why” is fairly important, lest we be accused of making up just-so stories.

I’m going to skip the math since it requires a course in mechanics and quite a bit of calculus to go through and I’ll just get to the heart of what it reveals.

Let’s start off with an idealized galaxy in which we have everything as simple as we can get it. Let’s pretend the galaxy is a perfectly uniform distribution of gas and dust in perfectly circular orbits around the center. Yeah right. No galaxy really starts off that way. Galaxies are in clusters and being acted on by one another. Many galaxies have satellites that perturb them and they were formed from smaller lumps that have gotten cannibalized. They’re dynamic places, so if we introduce some perturbations to the system, we can ask what happens then.

No need to really do this for the whole galaxy at this point. We can just look at the case of what would happen to any single star. It ends up that if you knocked a star out of its ideal orbit, the combined forces of the rest of the galaxy would work to try to restore its ideal position. But as with most restorative forces, it will tend to overshoot. Thus, you get harmonic motion. Not only do you get this towards and away from the center of the galaxy though, you also get it in the direction of motion. The combination of these two motions means that the star would make little orbits about its idealized location. The Sun does this too. Its motion in relation to the idealized point it should be (known as the Local Standard of Rest or LSR) is known as “Peculiar Motion”.

So let’s try to picture what that looks like. In this image, I’ve drawn the idealized LSR for our star in green. On top of that, I’ve sketched the path it would travel around an idealized point in red at four different points in the full orbit. The extent of this is grossly exaggerated of course, but it will illustrate the point.

Now let’s have the star make an integer number of rotations around its small circle every time it goes around the full big circle. If we take the star to be at its furthest from the center of the galaxy at point a, then it would be at its closest at b, furthest again at c, and closest again at d. Now putting the overall true motion of the star (in blue) in with the smaller wobbles, the true motion becomes apparent: Stars have elliptical orbits.

What’s more, the way these elliptical orbits line up isn’t the same at all distances from the center of the galaxy. Rather, the orientation of the major axis of the ellipse will rotate as you move out. That means that if we drew is successive ovals, each one would be slightly skewed resulting in a pattern like the one I’ve shown here.

The result of these skewed orbits is that at some points around the galaxy, stars tend to all bunch up more than at other places. And what happens when you get a bunch of massive things bunching up? It creates a gravitational potential. The result is that stars will speed up as they fall in making a lack of stars on the trailing edge but then be slowed down again as they exit, creating a pile up on the front edge. If spiral arms really were some magical place that could get wound up, we shouldn’t expect to see this. But we do, which suggests that the Creationist version of spiral arms doesn’t fit reality.

And this is what a spiral arm is. It’s the crowding together of a bunch of stuff as its slowed down exiting the potential well caused by the spiral wave. And it turns out these things are very stable. So the Creationist claim that they must be very young because galaxies should “wind up” is just wrong. It’s using a horribly outdated idea of what spiral structure is. Not that this is surprising.

But how robust is this explanation? Turns out it does very well to explain not just the very nice two armed spirals like M51, but it also can explain the not so neat spiral galaxies like M101. It just takes a different number of orbits around the small path per full orbit. And even the flocculent spirals with patchy arms can be explained through this, using non-integer numbers of rotations or linear combinations of many states.

I hope that clears up what’s really going on with spiral structure. If you’re really interested in seeing the math behind this, it should be in most junior/senior level astronomy texts.