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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 spiral arm structure of certain galaxies. Their theory introduces the idea of long-lived quasistatic density waves, which are sections of the galactic disk that have greater mass density (about 10-20% greater^[1]).

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^[2].

Lin and Shu proposed 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, Lin and Shu argued that within a certain non-inertial reference frame which is rotating at Ω_gp, the global pattern speed, the spiral arms appear to be at rest. The stars within the arms are not necessarily stationary; at a certain distance from the center, R_c, the corotation radius, the stars and the density waves move together. Within that radius, stars move more quickly (Ω > Ω_gp) than the spiral arms, and outside, stars move more slowly (Ω < Ω_gp)^[3].

The Density Wave Theory also explains a number of other observations that have been made about spiral galaxies. For example, "the ordering of H I clouds and dust bands on the inner edges of spiral arms, the existence of young, massive stats and H II regions throughout the arms, and an abundance of old, red stars in the remainder of the disk"^[4]. Basically, when clouds of gas and dust enter into a density wave and are compressed. The rate of star formation increases as some clouds meet the Jeans criterion, and collapse to form new stars. Since star formation does not happen immediately, the stars are slightly behind the density waves. The hot OB stars that are created ionize the gas of the interstellar medium, and form H II regions. These stars have relatively short lifetimes, however, and expire before fully leaving the density wave. The smaller, redder stars do leave the wave, and become distributed throughout the galactic disk.

C.C. Lin, Yuan, C., and F.H. Shu, "On the Spiral Structure of Disk i Galaxies III. Comparison with Observations", Ap.J. 155, 721 (1969). (SCI)

Yuan, C.,"Application of Density-Wave Theory to the Spiral Structure of the Milky Way System I. Systematic Motion of Neutral Hydrogen", Ap.J., 158, 871 (1969). (SCI)