Density wave theory
[1][2] The Lin–Shu theory introduces the idea of long-lived quasistatic spiral structure (QSSS hypothesis).
[3] Theoretically, the formation of a global spiral pattern is treated as an instability of the stellar disk caused by the self-gravity, as opposed to tidal interactions.
[4] The mathematical formulation of the theory has also been extended to other astrophysical disk systems,[5] such as Saturn's rings.
[7] Lin & 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.
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.
[7] For an m-armed spiral, a star at radius R from the center will move through the structure with a frequency
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:
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".
[8] The density wave theory also explains a number of other observations that have been made about spiral galaxies.
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.
Density waves have also been described as pressurizing gas clouds and thereby catalyzing star formation.
[6] Beginning in the late 1970s, Peter Goldreich, Frank Shu, and others applied density wave theory to the rings of Saturn.
The physics are largely the same as with galaxies, though spiral waves in Saturn's rings are much more tightly wound (extending a few hundred kilometers at most) due to the very large central mass (Saturn itself) compared to the mass of the disk.
[11] The Cassini mission revealed very small density waves excited by the ring-moons Pan and Atlas and by high-order resonances with the larger moons,[12] as well as waves whose form changes with time due to the varying orbits of Janus and Epimetheus.
