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Observations of spiral galaxies reveal that objects within the same arm of a spiral galaxy move at around the same speeds, regardless of their distance from the center of the galaxy. Conversely, the speed of points on a fan blade vary with their distance from the center, such that the outside of the blade is rotating faster than the inside of the blade. This would be required for the blades of a fan to remain rigid and extending along a radius of the fan.

I imagine the curved shape of spiral galaxy arms is due to the points along the arm remaining at the same speed. However, I am curious what this phenomenon does to the shape of spiral galaxies and objects within them over long periods of time.

Let's take two arms of a hypothetical spiral galaxy, and two points within each arm. The arms extend straight along a radius from the center at 0° and 270°. The galaxy is rotating clockwise. The closest two points in arms 1 and 2 are ~0.159 from the center of the galaxy where they rotate along a circumference of 1 , at a velocity of 0.25. The outer two points in arms 1 and 2 are ~0.318 from the center of the galaxy, where they rotate along a circumference of 2, at a velocity of 0.25:

The table below describes their positions at time-steps 0 to 4:

enter image description here

At the end of time-step 4, points 1 and 3 have gone through one full rotation, while points 2 and 4 will have gone through one half of a rotation. This means that points that originally started along the same radius (within the same arm) are now at the opposing ends of the galaxy.

How does this play out in our current models galaxy dynamics? Do spiral arms eventually dissipate? Do objects at the outer edge of spiral arms fall into the arms adjacent to them?

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I think you have the wrong idea about spiral arms. They are density waves that do not necessarily move with the same velocity as the objects that coincide with the wave peak at any instant in time.

The waves have a "pattern speed", which to first order corresponds to a fixed angular speed multiplied by the galactocentric radius. Meanwhile, as you rightly point out, stars have (on average) a "flat rotation curve" such that their tangential orbital speeds in the Galactic disc are roughly constant from a few kpc and outwards from the Galactic centre.

What this means is that in the inner parts of the Galaxy stars overtake the spiral arms, whereas in the outer parts the spiral arms overtake the stars. By coincidence(?), The cross-over point where the pattern speed and average stellar orbital speed are equal is around where the Sun is.

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  • $\begingroup$ Also those density waves cause dust to become more dense which accelerates star birth on the fronts of the arms. $\endgroup$ Commented Aug 2, 2023 at 14:04
  • $\begingroup$ @shaihorowitz that is a reasonable hypothesis. $\endgroup$
    – ProfRob
    Commented Aug 2, 2023 at 14:05
  • $\begingroup$ What i learned in astro at least. This seems to back it up cns.utexas.edu/news/research/…. $\endgroup$ Commented Aug 2, 2023 at 14:08
  • $\begingroup$ @shaihorowitz that's a bit "chicken and egg" if spiral arms are identified as places where dust gathers and young stars are formed. As I say, it's a reasonable and likely hypothesis but quite difficult to prove in practice. $\endgroup$
    – ProfRob
    Commented Aug 2, 2023 at 14:19
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    $\begingroup$ @shaihorowitz That's an effect which enhances the visibility of spiral arms. But the arms are clearly present if you look in the infrared, where the light mostly doesn't come from newly formed massive stars. $\endgroup$ Commented Sep 11, 2023 at 14:54

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