Posted by: Kash Farooq | April 18, 2012

Spiral Galaxies, Density Wave Theory and Dark Matter

Spiral Galaxies are very photogenic.

Whirlpool Galaxy M51 (NGC 5194)

Whirlpool Galaxy M51 (NGC 5194). Credit: Hubble Heritage Team (STScI/AURA) N. Scoville (Caltech)

See more fantastic images in Space Scenery: Spiral Galaxies.

As well as being very photogenic, they are also very puzzling: we don’t exactly know how they can keep those beautiful spiral arms.

Let’s imagine that the arms of a spiral galaxy were fixed in shape at the time of formation – i.e. they are composed of an unchanging set of stars. But we know that galaxies exhibit differential rotation; objects at different distances from the centre of the galaxy travel with different rates of rotation. Such differential rotation of the disc of the galaxy would cause the shape of the arms to alter with time. So any initially ‘realistic’ pattern of arms would soon cease to resemble any observed spiral arms.

However, spiral arms do appear to be a long lived feature. We’ve got images of loads of them! This is a puzzle known as the winding dilemma. Due to differential rotation, the arms of a spiral galaxy should wind around the galaxy in tighter and tighter formations. But we don’t see any evidence that this is happening. The winding dilemma suggests that there is in fact no permanent population of “spiral arm stars” and instead objects must move in and out of the arms.

This is what Density Wave Theory attempts to explain. Density Wave Theory proposes that a rotating disc of matter would naturally develop regions in which the density was enhanced relative to the surrounding material. These patterns of density enhancement are known as spiral density waves. A spiral density wave is expected to rotate rigidly about a galactic centre – not differentially. The differentially rotating matter (clouds of gas, stars, etc.) would rotate faster than the spiral density waves.

Density Wave Theory was proposed in the 1960s by  C.C. Lin and Frank Shu and is still the best explanation we have. The theory states that these spiral density wave structures are generally stable over long time periods.

As faster moving stars and gas approach the slowly moving denser region, they slow down as they pass through it, and then move ahead of the wave’s leading edge. Gas is compressed when it enters the density wave and this explains why we see lots of star formation in spiral arms – any giant molecular gas clouds on the verge of forming stars get that extra bit of compression as they hit the denser region and this may trigger star formation (specifically, the clouds may meet Jeans criterion). And therefore we see lots of young objects that trace the arm.

We can take this further. If star formation occurs when the faster differentially rotating gas clouds hits the spiral density wave, then there should be some sort of spatial ordering of objects in the arms. Very young objects should be observed at one edge, objects that are a bit older would be found in the middle and the oldest objects would be observed at the opposite edge of the arm.

This is something that is testable.

And here is a paper that looks for that evidence: “Observational Evidence Against Long-Lived Spiral Arms in Galaxies” by Foyle et al. (25 May 2011).

The authors looked at 12 nearby spiral galaxies. They failed to find such young-to-old ordering. They conclude:

“…result indicates that spiral density waves in their simplest form are not an important aspect of explaining spirals in large disk galaxies.”

I had to study and revise Density Wave Theory extensively during the Open University course S282 – Astronomy. Questions about Density Wave Theory frequently appeared in the exam past papers – the topic was one of my “banker” questions. It would be ironic if the theory may now have been disproved… (though, the study looked at only 12 galaxies – perhaps a bigger study is needed).

Now moving onto the other term in the title of this post: Dark Matter.

We know dark matter exists – there is something out there that is exerting gravity. One of the lines of evidence (yes evidence – the assertion that dark matter exists isn’t faith-based, as I’ve heard some people claim) is found in spiral galaxies.

If we measure the rotation velocities of spiral galaxies, we see that objects are moving at orbital speeds too fast for the amount of matter contained in the galaxy. This is simply because, according to how much matter we can see, there isn’t enough gravity generated to keep the objects in orbit at that speed. But, obviously, our observations tell us otherwise. The galaxies are happily rotating and not tearing themselves apart.

There are two ways of explaining this. Either Newtonian gravity behaves differently throughout the Universe (Modified Newtonian dynamics goes down this route) or at least 50% of the mass of galaxies is contained in something we cannot see – i.e. most galaxies were in fact dominated by “dark matter”. Dark matter is the widely accepted theory.

Related posts

Space Scenery: Spiral Galaxies.

Does Dark Matter Really Exist? – by Peter Hague.



  1. That’s pretty fascinating about the density wave theory. When I first heard about it, I remember thinking what an elegant, straightforward explanation it was for the spiral arm structure. It’d be a shame (in a way) if it turns out not to be accurate.

  2. Very interesting post. I have a general question about Dark Matter, which I hope you can answer. It is this: If DM pervades the Milky Way, why do we not see its influence, in terms of gravity, within the Solar System?

    • Thank you.

      Your question is answered in the quote below from Ethan Siegel, which is from this article. Basically, on such small scales, the effect on orbits would be too small to measure.

      Planetary orbits, if there were enough dark matter present, would have their perihelia precess faster than if there were no dark matter. The amount of dark matter allowed from these observations is considerably greater than the amount I predict. The errors on the measurements of perihelion precession are in units of hundredths of an arc second per century…Even if you assume the dark matter is at rest with respect to the galaxy that the Solar System moves through (which is the extreme example), the Sun is of order 10^30 kg; capturing a 10^20 kg clump of dark matter will slow you down by about 20 microns/second over the lifetime of the Solar System. So that would be small.”

  3. Thanks. That makes sense.


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