How do galactic rotation curves suggest the need for dark matter?

Question posed by Sven.

I guess the first question we should ask here is:

What is a galactic rotation curve?
It's a graph.

All graphs show the relationship between two things, and a galactic rotation curve shows the relationship between how fast a star is moving in its orbit around the centre of whichever galaxy it's in, and its distance away from that centre. To produce one, astronomers choose a galaxy and look at the stars in it. for each star (or each group of stars*) and measure the speed and distance of its orbit. When they have enough data, they plot this information on a graph with the distance on the horizontal axis and the velocity on the vertical axis.

It's pretty easy, if you know how graphs and gravity work (which we do) to make a guess as to how the graph should work. Thanks to Newton, we know that the effect of gravity decreases as we move away from a lump of mass (i.e. a star, planet, galaxy, moon, etc), and thanks to pictures we know that galaxies generally have a big lump of stuff in the middle which thins out towards the edges.

This means that we would expect our graph to show the stars close to the central bulge moving pretty quickly, with stars further out moving correspondingly more slowly because 1, the distance from the big lump in the middle is increasing, so its attraction becomes weaker, and 2, the rest of the matter is thinning out towards the edges. This makes sense when we look at another model: our own solar system. In it, planets that orbit further away from the Sun do so more slowly than those closer in.

For those of you of a more visual persuasion, that means that the graph should look like this:

Actually grab a telescope and do it, though, and you get something that looks more like this:

The left of this graph is pretty much what we'd expect, but as we look to the right it's easy to see that it's wrong and just keeps on getting wronger**.

This means one of two things:

1. What we know is wrong
When observations don't fit the theory, it's usually an indication that the theory is wrong. In this case, however, Newton's theories about gravity fit perfectly everywhere else we look; even the planets in our own solar system do what we expect them to do. Galactic rotation curves are pretty much the only observation we make that doesn't fit with what we 'know' about gravity. Many scientists, however, think that this is enough evidence to suggest that there's something wrong with our understanding and are working on ways of modifying the theory to account for this. The most well-known of these is called Modified Newtonian Dynamics, or MOND to its mates, though there are a number of other adjusted theories of gravity that have been proposed to solve this problem.

2. What we see is wrong
If our current theories about gravity are right (and there's a lot of evidence to support them), then something else must be wrong. The galactic rotation curves that we observe can only fit the theories we have for gravity if there's a lot more stuff there than we can see or detect with any of our current methods. The prevailing theory is that there must be some kind of matter in the universe that we don't know about because we can't detect it. This matter is known as 'dark matter' because, if it's there, we can't see it.

This second theory is currently the more widely accepted of the two because it generally makes better predictions than any of the modified gravity theories. It is still, however, far from being a closed case!

* Or, more accurately, each cloud of gas, but I'm simplifying here...
** Yes, grammar nuts... I know. Call it artistic licence.


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