Spiral arms

Before leaving the subject of spiral galaxies, we should address what is in fact probably the first question you'd like to know about them: why do they have spiral arms? So let's start by reviewing what we know about spiral arms.

Firstly, spiral arms are really evident when we look at massive stars and HII regions - these really delineate the spiral structure. But there is more: we also detect the arms in HI, and even better in molecular gas. In fact, GMCs are probably the best tracers of the pattern. So may be they have something to do with star formation?

However, they are also present in the K band where we are probing old stars. So first conclusion: it's really the whole galaxy that takes part in the spiral pattern. However, the density contrast (i.e. the relative difference in density at given $r$ from the centre, within vs outside of the arm) is not very large, probably less than a factor of two. The contrast in surface brightness can be quite a bit higher though, since the young stars in the arms are massive and hence bright.

The winding problem Given that the disk is in differential rotation, a spiral arm cannot be a material structure (meaning that it is always the same stuff in the arm rotating around the disk) - because of it were, we would have a winding problem. To realise why this is so, consider the following thought experiment.

Suppose you paint all stars along a radius in the disk green, and follow how those green stars move (see figure (5.2). If the circular velocity is a constant, $V_c$, then the period of an orbit is inversely proportional to its radius, $P\propto 1/R$. Now concentrate on two green stars, one at distance $R$ (star 1), the other at distance $2R$ (star 2), having periods $P$ and $2 P$. After a time $P$, star 1 will be at the original position, whereas star 2 will be at the other side of the galaxy. After time $2P$, both stars will be back at their original position, and so the green line of stars in between them will have circled the galaxy, i.e. the initially straight line of green stars now encircles the galaxy. Applying this to stars originally in a spiral arm, it is clear now that very quickly, the spiral arm will wind tighter and tighter. Considering how loosely some spiral arms are, this would imply they are all recently formed, placing us at a peculiar instant in time where spiral structure forms.

In cases where we were able to determine the sense of rotation of the pattern, it turned out that the spiral arms are trailing, that is, at least they are rotating in the same sense as the spiral pattern of our green stars.

Figure 5.2: A spiral pattern made out of stars will rapidly wind-up in a disk undergoing differential rotation.

So what's the solution? May be it's good to realise that there is quite a variety in spiral patterns. Grand Design spirals have two really well defined relatively open arms. Some spirals have flocculent arms, which are not very long (i.e. you can't trace them for very long), but often there are many in the disk. So may be we're looking at more than one possible origin.

The theory of spiral density waves suggest that a density wave rotates with a constant pattern speed in the disk. You can think of such a wave as a natural mode of oscillation of the disk, much as you have sound waves in air, or harmonic waves in a violin string. If the rotation period of a star is shorter than of the pattern, then the star will occasionally overtake the wave. The gravitational force of the matter in the wave will make the star linger a bit near the pattern, before it leaves the arm again. An analogy often made is that of a slow lorry on the motor way causing a pile-up of faster cars behind it. Although most cars go fast, the speed with which the pile-up moves is determined by the slow lorry.

Another process which we know to occur, is the triggering of spiral arms by galaxy encounters. When two galaxies come close together, they will exert tidal forces on each other.^5.5 This effect can be convincingly demonstrated with numerical simulations. And so, although these arms may quickly disappear when left on their own (winding problem), the satellite galaxy may continually re-excite the spiral arms. Another hint comes from the fact that in barred galaxies, the spiral arms emanate from the ends of the bar (have a look at NGC 1365 if you don't believe me). It's is thought that Grand Design spirals are either triggered by a tidal encounter, or by the rotating bar.

Goldreich and Lynden-Bell said about flocculent spirals: `a swirling hoch-potch of spiral arms is a reasonably apt description' . So here we're probably faced by some kind of gas-dynamical instability in the disk.

So the conclusion about spiral arms, is that there may be several processes that give rise to spiral arms, and depending on the particular spiral galaxy, one of these may dominate. So tidal encounters are probably responsible for the beautiful Grand Design spiral arms. Whereas the more messy pattern of flocculent spirals is probably due to a gas-dynamical instability in the disk.