What happens at the edge of a galaxy What happens at the edge (around the optical radius) of a galaxy when it has a flat rotation curve? After some length scale: does the velocity start to decrease or is there a phase-transition-like that keeps the galaxy being finite in size?
 A: Eventually the rotation curves do decrease to smaller velocities.  The problem is that this usually happens well outside of the characteristic radii (like the "half-light" radius) after which point it is very difficult to get good measurements.
The velocity as a function of radius is roughly,
$$v_{rot} \approx \left(\frac{G M_{enc}(r)}{r}\right)^{1/2}$$
where $M_{enc}$ is the total mass enclosed out to that radius $r$.  The distribution of dark matter extends to much larger radii than that of stars, so the mass enclosed tends to increase roughly as fast as the radius does, until you get out to near the "virial radius" (well outside the half-light radius).  Eventually the mass enclosed becomes almost constant (because the density gets lower and lower at large radii) and the velocity starts to decrease as $1/r$.
A: If a star passes the edge with a velocity greater than the local escape velocity $\sqrt{\text{2GM/r}}$ it will leave the galaxy, and if the velocity is smaller it will catch an elliptic orbit. If the velocity is exactly the orbital velocity $\sqrt{\text{GM/r}}$ the orbit will be circular. For $\text{M}$ just use the mass inside the shell (see the shell theorem and the density profiles). So at farther distances where the density sinks the velocities of orbiting objects start to decrease, since all objects travelling with higher velocities would get ejected from the galaxy.
A: Regarding my question, I went to a conference with Dr. Asimina Arvanitaki, and she answered by saying that there are no compelling data to be sure what happens at the edge, so this is still a mystery.
