Density wave theory

Density wave theory or the Lin-Shu density wave theory is a theory proposed by C.C. Lin and Frank Shu in the mid-1960s to explain the spiral arm structure of spiral galaxies. Their theory introduces the idea of long-lived quasistatic density waves (also called heavy sound), which are sections of the galactic disk that have greater mass density (about 10–20% greater). The theory has also been successfully applied to Saturn's rings.

Originally, astronomers had the idea that the arms of a spiral galaxy were material. However, if this were the case, then the arms would become more and more tightly wound, since the matter nearer to the center of the galaxy rotates faster than the matter at the edge of the galaxy. The arms would become indistinguishable from the rest of the galaxy after only a few orbits. This is called the winding problem.

Lin and Shu proposed in 1964 that the arms were not material in nature, but instead made up of areas of greater density, similar to a traffic jam on a highway. The cars move through the traffic jam: the density of cars increases in the middle of it. The traffic jam itself, however, does not move (or not a great deal, in comparison to the cars). In the galaxy, stars, gas, dust, and other components move through the density waves, are compressed, and then move out of them.

More specifically, the density wave theory argues that the "gravitational attraction between stars at different radii" prevents the so-called winding problem, and actually maintains the spiral pattern.

The rotation speed of the arms is defined to be $\Omega _{gp}$ $\Omega _{{gp}}$ , the global pattern speed. (Thus, within a certain non-inertial reference frame, which is rotating at $\Omega _{gp}$ $\Omega _{{gp}}$ , the spiral arms appear to be at rest). The stars within the arms are not necessarily stationary, though at a certain distance from the center, $R_{c}$ $R_{{c}}$ , the corotation radius, the stars and the density waves move together. Inside that radius, stars move more quickly ( $\Omega >\Omega _{gp}$ $\Omega >\Omega _{{gp}}$ ) than the spiral arms, and outside, stars move more slowly ( $\Omega <\Omega _{gp}$ $\Omega <\Omega _{{gp}}$ ). It is easy to see that for an m-armed spiral, a star at radius R from the center will move through the structure with a frequency $m(\Omega _{gp}-\Omega (R))$ $m(\Omega _{{gp}}-\Omega (R))$ . So, the gravitational attraction between stars can only maintain the spiral structure if the frequency at which a star passes through the arms is less than the epicyclic frequency, $\kappa (R)$ $\kappa (R)$ , of the star. This means that a long-lived spiral structure will only exist between the inner and outer Lindblad resonance (ILR, OLR, respectively), which are defined as the radii such that: $\Omega (R)=\Omega _{gp}+\kappa /m$ $\Omega (R)=\Omega _{{gp}}+\kappa /m$ and $\Omega (R)=\Omega _{gp}-\kappa /m$ $\Omega (R)=\Omega _{{gp}}-\kappa /m$ , respectively. Past the OLR and within the ILR, the extra density in the spiral arms pulls more often than the epicyclic rate of the stars, and the stars are thus unable to react and move in such a way as to "reinforce the spiral density enhancement".

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