[exe34]

The up down oscillation is completely decoupled from the orbit itself, assuming the orbital potential is uniform. It's like the galaxy wasn't rotating at all. You put something above the disk, and it gets accelerated downwards, but doesn't stop at the disk, it keeps going, until it gets dragged back up. Think of it like a pendulum.

[truculent]

Would we expect the oscillation to get smaller over time, like a pendulum, or is that stretching the analogy too far?

[exe34]

There might be some gas in the way that would slow it down slightly, but I expect that to be a very long time scale compared to other things like interactions with other systems and even the upcoming collision with Andromeda.