Car analogy to density wave. (a) A truck (shaded) is broken down in the right lane. Far in front and behind the truck, cars have the normal speed and low density. Just behind the truck, the density of cars goes up, and their speed goes down. (b) As time goes on, cars slowly squeeze by the truck.The basic pattern is retained. However, as the numbers on the cars show, different cars are stuck behind the truck than in the earlier frame.We therefore have a density concentration along the highway while the individual cars are not permanently attached to the concentration. (c) This concentration can even move. Instead of being stuck, suppose the truck is moving slowly.The pattern moves along with the truck, while the individual cars move at higher speeds.

Now suppose the truck is moving at a slow speed. Again, there will be a buildup behind the truck as cars squeeze into one lane to move past the truck. As in the case of the stationary truck, we see the cars moving at their normal speed. However, now the pattern moves. The speed of the pattern is not related to the speed of the cars - it is determined by the speed of the truck. The truck is responsible for the pattern. The cars simply respond to the presence of the truck. This is the type of situation in which the pattern (the traffic jam) can move at one speed, and the matter (the cars) at another.

There is a theory that the same type of situation can occur in spiral galaxies. Since the matter moves at a different speed from a density buildup, the theory is called the density wave theory. In a galaxy, the dynamics is controlled by the halo, which contains most of the mass. The bright spiral arms contain a small fraction of the mass of the galaxy, and represent material which is orbiting at its normal speed, but responding to the gravitational effects of the asymmetric distribution of the stars in the halo. The mathematician C. C. Lin has shown that once a spiral pattern is established in a galaxy, it can sustain itself for a long time in this type of wave. Eventually, the wave will die out and a new one must be generated.

In the density wave picture, the visible arms are a result of a gathering of interstellar matter. When high enough densities are reached, star formation may take place. One scenario for this is illustrated in Fig. 17.17. A large HI cloud, or a group of small clouds, approaches an arm at a speed of about 100 km/s relative to the arm. (In this case, the arm may be moving at 100 km/s, and the matter overtaking it at 200 km/s.) The arm acts like a gravitational potential well, causing material to take more time to traverse the arm than a similar distance between arms. The matter entering an arm will leave its circular path, and have some motion along the arm, before finally emerging. It should be noted that, even if the density waves don't cause strong visible arms, they alter the orbits, resulting in noncircular motions. Some of the results of critical calculations of density waves are shown in Fig. 17.18.

HI Cloud with or without Small Molecular Clouds

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