Asymptote of expected rotation curve velocities

[Buckethead]

Can someone tell me why the expected velocity of the outer most stars of spiral galaxies has an asymptote quite a bit greater than zero? For example NGC 3198 at a radius of 50 kpc appears to be reaching it's asymptote at about 40-50 km/s which seems illogical.

 

[Matterwave]

This is part of the rotation curve problem in Astrophysics. The rotation curve of galaxies do not drop off as expected by applying known laws of gravity on the observable matter. Thus, there is hypothesis of "dark matter halos" that exist all around galaxies. This extra matter (which extends quite far out) can flatten out rotation curves to significant distances from the center of the galaxy.

 

[Buckethead]

This is part of the rotation curve problem in Astrophysics. The rotation curve of galaxies do not drop off as expected by applying known laws of gravity on the observable matter. Thus, there is hypothesis of "dark matter halos" that exist all around galaxies. This extra matter (which extends quite far out) can flatten out rotation curves to significant distances from the center of the galaxy.

I was actually referring to the expected velocity curve, not the observed velocity curve. For example if you look at the graph here:

http://w3.iihe.ac.be/icecube/3_Activities/1_WIMPs%20Analysis/fig1.bmp

It appears that the expected rotation curve has an asymptote at about 35-40 km/s

 

[Matterwave]

Oh, well, that's because velocity only goes down as the square root of r at large distances (outside where luminous matter appear).

Out at very large distances, one could approximate the galaxy as a point source of gravity. In that case, for circular orbits:

$$v=\sqrt{\frac{GM}{r}}$$

As r goes up, v goes down, but only as a square root. This function is asymptotic to 0 as r goes to infinity, but is very slowly doing so. At distances that the graph has, the function doesn't approach zero quickly.

 

[Buckethead]

Oh, well, that's because velocity only goes down as the square root of r at large distances (outside where luminous matter appear).

Out at very large distances, one could approximate the galaxy as a point source of gravity. In that case, for circular orbits:

$$v=\sqrt{\frac{GM}{r}}$$

As r goes up, v goes down, but only as a square root. This function is asymptotic to 0 as r goes to infinity, but is very slowly doing so. At distances that the graph has, the function doesn't approach zero quickly.

Excellent! That was the answer I was looking for. Thank you!