密度波的由來
spiral arms 只在 flattened 或是 disks 的星系中發現。
differential rotation: the time to complete a full rotation increases with distance from the center.
所以 inner/outer 此2者的速度差造成了 winding(纏繞) 的現象，consequently 纏繞的結果會造成纏繞很多圈 (many turns) 的現象，與所觀測的結果不符合。
因為現在的星系大約年齡為 10 billions，但是星系中，環繞一次所花的時間為 .1 billion，所以可以知道應該星系己經繞了約 100 次，但是現在所觀測的 spiral arms，大約只有 1-2 turns，所以differentai rotation的預測與觀測結果，此2者並不吻合。
The second important piece of physics for understanding spiral structure is that the stars and gas in the disk of the galaxy exert an appreciable gravitational force, which helps maintain the spiral structure form against the tendency to wind up.
其實星系本身因為重力吸引的緣故，傾向於 winding up tightly，但由於 spiral arms 的結構提供了 appreciable gravitaional force，來對抗彼此重力的吸引。
that gravitational systems act to increase their central binding energy. Spiral arms remove angular momentum from the center of the galaxy, allowing it to achieve a state of higher binding energy. There are two main versions of the theory of spiraling: one in which the waves are steady and long-lived, the other in which spirals are transient features that come and go. The natural, but not very easy, test is to observe spiral galaxies for a few hundred million years and see what happens.
星系本身因為重力的吸引，就會傾向於binding，亦即會increase binding energy，而由於spiral arms會從galaxy中心移走角動量，造成binding energy的增加，也就造成winding的困難。有2種模型來解釋spiral arms結構的成因:
- spiral arms本身是wave, 但此wave是steady and long-lived
- spiral arms結構只是過渡(transient)性結構
藉由觀測一些年輕星系(只有數百萬年)的 spiral structure ，來推論 spiral 的穩定性，及其 spiral structure的理論，何者為正確的。
"Most spiral arms in galaxies are density waves, which are compression waves (like sound) that travel through the disk and cause a piling-up of stars and gas at the crest. The wave is temporarily sustained by the force of its own gravity, but it eventually wraps up or gets absorbed at orbital resonances, places where random stellar oscillations have the same period as the local wave. "In some galaxies, a large central bulge can prevent the wave from reaching a resonance; the wave then reflects off the bulge, giving rise to a giant standing spiral wave with a uniform rotation rate and a lifetime of perhaps 5 to 10 disk rotations (roughly one to two billion years). In all cases, the stars and gas rotate around the galaxy's center faster than the wave in the inner parts of the disk, and slower than the wave in the outer parts. This differential rotation forces gas to enter the wave at a high speed in the inner regions, causing it to shock and form long, thin dust lanes in each spiral arm.
spiral arms 的形成是由於密度波造成的，密度波可以想像類似音波的概念，密集的波峰部份，就是星球聚集產生的地方。
