Spiral arms

Why do a galaxy's spiral arms not wind themselves into a blur after a few rotations?

Let us start with an arithmetic problem that ought to destroy every spiral galaxy in the sky. A disc galaxy does not turn like a gramophone record. Out beyond the central bulge its rotation curve is roughly flat: material at 4 kiloparsecs from the centre and material at 16 kiloparsecs are both moving at something like 200 to 230 kilometres per second. Same speed, very different circumference.

So ask the obvious question. If the inner material completes a lap in a fraction of the time the outer material takes, what happens to a straight line of stars drawn from the centre outwards? It shears. After one full outer rotation the inner end has gone round several times, and the line has become a tightly coiled spiral. After ten it is wound so tight it is indistinguishable from a smooth disc.

The Sun takes roughly 230 million years to orbit, and the galaxy is about 13 billion years old — some fifty laps, with the inner disc having done many times that. Bertil Lindblad set this out in the 1920s and it has been called the winding problem ever since. Yet we look out and see open, two-armed spirals everywhere. So one of our assumptions is wrong. Which one?

Notice that the whole argument rests on a single unstated premise: that an arm is made of particular stars, the way a queue is made of particular people. Drop that premise and the arithmetic stops applying, because the shearing calculation only tells you what happens to a fixed set of material.

So consider the alternative. Suppose the arm is not an object but a place — a region where the disc is temporarily crowded, which stars and gas clouds move through and out of again. Then the pattern can rotate at its own rate, quite independent of how fast any individual star is going. That is the core of the density wave picture, worked out by C. C. Lin and Frank Shu in 1964 from Lindblad's earlier ideas.

Now, how does a crowd hold itself together instead of dispersing? Here gravity is doing something a traffic jam cannot do. A slight overdensity in the disc pulls on nearby stars; they linger a little as they pass through it, which deepens the overdensity, which pulls harder. The crowd is self-reinforcing. What you get is a wave pattern turning at a single pattern speed while the stars slide through it.

That gives a clean prediction. If the pattern has one angular speed and the stars have an angular speed that falls with radius, the two must be equal at exactly one radius — corotation. Inside it, stars overtake the arms from behind; outside it, the arms overtake the stars. Estimates of the Milky Way's pattern speed cluster loosely around 20 to 25 kilometres per second per kiloparsec, though different methods disagree.

But if stars merely pass through, why are the arms so bright? Ask what happens to gas rather than stars. Gas, unlike stars, can collide with itself. Piling into the arm it shocks and compresses, and compressed molecular gas collapses into new stars. The most massive of those, the hot blue O and B stars, live only a few million years — far less time than it takes them to cross to the next arm. So they are born in the arm and die in it, and the arm is permanently outlined in fresh blue light and glowing hydrogen. Measured in old red starlight instead, the arm-to-disc contrast is much more modest, often only a tens-of-percent enhancement.

Here I should flag what is not settled, because the textbook version overstates its case. Whether grand-design spirals really carry a long-lived, rigidly rotating wave is still argued about. Many N-body simulations instead produce transient, recurrent arms that form, shear, dissolve and reform — these ones genuinely do wind up, they are simply replaced. Some patterns look more like material arms whose speed falls with radius than like a rigid wave. And many of the most striking grand-design spirals, M51 being the classic, are plainly being driven by a bar or a passing companion rather than sustaining themselves. The winding problem is solved; the exact machinery differs from galaxy to galaxy.

The misconception to dislodge is that a spiral arm is a thing you could point at and follow. It is better understood as a standing pattern in a rotating medium — a property of the disc as a whole rather than of any of its members. Once you accept that, the winding argument does not fail, it simply becomes irrelevant: it was a correct calculation applied to the wrong object.

Two refinements worth keeping. First, the arms are not empty of old stars and full of new ones; they contain a mild excess of everything, and a dramatic excess only of the short-lived bright stars that make the excess visible. Second, "solved" here means the paradox is dissolved, not that one mechanism has won. Grand-design, flocculent, barred and tidally driven spirals may not all be doing the same thing.

• Why bars form in disc galaxies at all, and how a bar drives a spiral pattern in the gas outside it.
• How astronomers try to measure a pattern speed directly, and why the answers scatter so widely.

Every term the collection defines is gathered in the glossary.