[Physicist]

If the line height at a given radius is linear velocity, that would mean that the outer parts of a galaxy (with its flat rotation curve) are indeed rotating much slower (angular velocity) than the inner parts after all,

That's right. The speed of the stars is constant throughout much of the galaxy, unlike a record album, in which the outer edge moves at a faster speed than the innermost groove.

which doesn't sound like the problem befuddling astronomers at all.

It's a huge problem, as according to Kepler's laws, the speed should be inversely proportional to the square root of the radius. It's not.

[VadeRetro]

Thanks again. Wasn't modeling out the implications well at all.

[AndrewC]

It's a huge problem, as according to Kepler's laws, the speed should be inversely proportional to the square root of the radius. It's not.

I concur. Thanks, Herr Physiker, it is wise to get out of the way of the pros so I can add nothing. I also found another paper on the calculation of galactic angular velocity. The Disk Rotation of the Milky Way Galaxy

[PatrickHenry]

It's a huge problem, as according to Kepler's laws, the speed should be inversely proportional to the square root of the radius. It's not.

Yet another question revealing my ignorance: Kepler described the orbits of the planets around our sun. Do Kepler's laws hold for stars orbiting the galaxy? Wouldn't you need a solid rotating disk of a galaxy to perform that way? Well, maybe not.