Spiral Density Waves

How does the spiral structure in galaxies like the Milky Way originate, and what maintains it? To be honest, we don't know completely, but there are two ideas that at least partially explain it. The first is that spiral arms are really indications of density waves (slowly moving regions of higher density) in the disk of the galaxy. The second is that the spiral structure is generated by self-sustaining star formation, coupled with the differential rotation of the galaxy. Let's discuss the spiral density wave idea first.
Differential Rotation of the Galaxy
The spiral arms of the Milky Way, or any other spiral galaxy, cannot be rigid structures that simply rotate like a pinwheel because the galaxy exhibits differential rotation: the stars in its inner part revolve around the center faster than those further out. This is reminiscent of the Solar System, where the inner planets must revolve faster than the outer ones, and for the same reason: gravitational forces, as embodied in the third law of Kepler. The following diagram illustrates.

(Actually, the differential rotation of the galaxy is more complex than this, as we will discuss in a subsequent module. But the above picture is approximately true near the Sun's distance from the center.)

So even if we started with a well-defined spiral structure, the spiral arms would get wound up tighter and tighter with each turn of the galaxy until they would finally no longer be distinguishable. Because we see so many spiral galaxies, we conclude that they can sustain spiral structure over long periods, certainly longer than the time for several rotations of the galaxy. Thus, the actual stars and dust and gas that make up a spiral arm change over time, but the spiral structure itself persists, at least for billions of years (see the right panel for an analogy).

An Example: A Traffic Density Wave
Density waves are an example of the structures discussed above that can maintain themselves even as the individual pieces that make them up change. A common example of a density wave concerns traffic flow. A slow-moving vehicle on a narrow two-lane road causes a high density of cars to pile up behind it. As it moves down the highway the "traffic density wave" moves slowly too. But (assuming it is possible for cars to pass the slow-moving vehicle at a slow rate) the density wave of cars does not keep the same cars in it. Instead, old cars leave the density wave when they pass the slow vehicle and continue on at a more normal speed (we assume these are law-abiding citizens!) and new ones are added as they approach the density wave from behind.

Also notice that the speed with which the density wave moves is lower than the average speed of the traffic and that the density wave can persist well after its original cause is gone. If the slow-moving car backs up a high density region that is large, the congestion (density wave) will remain for some time after the slow car that caused it turns off the road.

Spiral Density Wave Theory
The spiral density wave theory extends that analogy to a more complex set of density waves in the disk of a spiral galaxy. These density waves have a slowly rotating spiral structure (just as the traffic density wave of the above example moves slowly down the road). As the density waves rotate, they are overtaken by the individual stars and nebulae that are rotating around the galaxy at a higher rate (like the motorists overtaking the traffic density wave). The molecular clouds passing through the density wave are subjected to compression because it is a region of (somewhat) higher density. This triggers the formation of clusters of new stars, which continue to move through the density wave. The adjacent animation illustrates.

Density in Spiral Density Waves

Do not be mislead by the current discussion into believing that the density in the spiral density waves is very high compared with the rest of the galaxy. It is higher, but perhaps only by 10% or so. Nevertheless, that increase in density is thought to be sufficient to initiate star formation in large molecular clouds. It is not the density of the spiral arms directly that makes them prominent; it is the star formation triggered by the increased density that is responsible.

The short-lived stars die, most likely as supernovae, before they can leave the spiral density wave. But the longer-lived stars that are formed pass through the slower density wave and eventually emerge on its front side and continue on their way as a slowly dissipating cluster of stars (like the motorists who finally pass the slow-moving car responsible for the traffic density wave).

Star formation persists in the spiral density wave because other molecular clouds are continually overtaking the density wave and initiating a new round of star formation. This continual manufacturing of new stars in the density wave causes it to emit bright light and marks the region of the spiral density wave as bright spiral arms.

Problems with the Density Wave Theory
Density wave theory explains much of the spiral structure that we see, but there are some problems. First, computer simulations with density waves tend to produce very orderly "grand design" spirals with a well-defined, wrapped 2-arm structure. But there are many spiral galaxies that have a more complex structure than this. Second, density wave theory assumes the existence of spiral density waves and then explores the consequences. But what produced the density waves to begin with?

Origin of Density Waves
We shall address an alternative theory of spiral formation that may help with the first problem in the next module. Several ideas have been proposed to help with the second problem of how density waves originate in spiral galaxies:

  • A spiral galaxy may be naturally unstable with respect to the formation of spiral density waves. Thus, even small disturbances can cause them to form and persist.
  • If the center of the galaxy has a bar shaped and rotating mass distribution, it could cause enough gravitational disturbance in the disk to produce density waves. We shall see later that some spiral galaxies do have prominent bars across their middle regions.
  • The gravitational perturbation of an encounter with another galaxies could be sufficient to produce spiral density waves.

    • Because there is strong independent evidence that many galaxies interact with each other, the last idea is particularly attractive. However, this would not explain spiral structure in a truly isolated galaxy. Perhaps all of these ideas have some influence on the formation of spiral structure in various galaxies.