Study Guide for Section 7: Spiral Structure

Section 7.1

• In this section we begin by considering whether an explanation of spiral structure that assumes each arm contains essentially the same material at different times matches what we know about the rotational behaviour in spiral galaxies. So, we propose a hypothesis for the nature of the arm-like structure, and then use observational evidence to confirm or refute it. Our main piece of evidence is the form of rotation curves of spiral galaxies.

• Rigid-body rotation: does the whole galaxy rotate rigidly, maintaining its shape (and the arm like structure) as it rotates? We know from galaxy rotation curves that this behaviour is not observed.
• We know that over much of a spiral, the rotational velocities are roughly constant as a function of radius. However, we show here that this would imply that spiral arms would tighten up over time, or `wind up'. Galaxies have ages in excess of 10 Gyr, a figure far in excess of the typical rotation periods of stars and clouds. So why aren't all arms tight?
• Does this instead mean that some arms could be very young? Observational evidence shows that arm-like structure is still present (albeit less noticeably) when filtered observations of old stars are made. We are therefore forced to look for an alternative explanation.

Section 7.2
 

• The density-wave explanation assumes that at different times, different stars and clouds make up the structure of a given arm.
• It is the passage of a density wave through the stars and clouds in a given part of the galaxy that compresses the material locally, thereby giving the appearance of an arm-like structure.
• The density wave rotates around the galaxy, and so the `arms' move with it.
• We discussed qualitatively the origin of the density wave by looking at the problem in two ways:

We noted that the distribution of matter in the galaxy is not smooth, but `lumpy'. The resulting gravitational `anomalies' will influence the paths followed by stars, i.e., their orbits will be shifted or perturbed. This will give rise to a knock-on effect, as perturbed stars affect their neighbours. The resulting perturbations of position give shifts in mass and the formation of a density wave.

We also considered the torques that are generated by the gravitational clumpiness. Torques will be applied that do not lie parallel to the orbital angular momentum vectors of the stars. We saw in Section 2 (in the case of a spinning top, and the planet Earth) that this will lead to precession of the angular momentum vector. The orbits of our stars therefore precess, so that star orbits are tilted slightly with respect to one another (see Figure 7.02). This gives increased density in those regions where the paths of many orbits are pulled closer to one another by the precession.