Understanding rotation of spiral galaxies

[eaclou]

Hello all,

My first post here. I do CG animations, and am working on a project where two galaxies collide. It is important to note up front that my simulation will NOT be physically accurate - I don't have the tools, knowledge, or processing power for that, but I AM interested in getting the macro "look" correct, and so I had some questions for you guys.

In the videos of scientific simulations of galaxy rotation, the galaxy rotates at more or less a constant angular speed, regardless of distance from the galactic center. This means that for any star or object in the galaxy, its velocity is directly proportionate to its distance from the galactic center. However, because objects further away are pulled on with less gravitational force, (assuming constant mass) they shouldn't be able to orbit at such a speed (they would fly off into the universe). So this is where the subject of dark matter comes in, from what I've read, because with enough mass, an object at the edge of the galaxy could orbit at the required angular speed, given enough centripetal force from its mass.

Anyway, that is basically where I am in my understanding, which is woefully inadequate. Can someone explain how the rotation of these galaxies actually works? I don't understand how dark matter in the galaxies halo can allow a body of reasonable mass (because I'm assuming the mass of individual stars within the galaxy are evenly distributed, i.e. stars near the center are about equal mass on average to stars near the edge) on the edge of the galaxy to orbit so fast. I can see how a very massive ring of dark matter could orbit the galaxy at the same angular speed as the inner part of the galaxy, but how would that influence individual stars on the edge of the galaxy? The whole thing just seems weird. You would expect an even-ish mass distribution, or if anything, less density as you move away from the galactic center, which would mean that angular speed would decrease as you move out from the center.

Can anyone shed some light on this?

 

[Janus]

First off, the galaxies do not rotate with constant angular velocity as you move out from the center but with ~constant orbital velocity. Secondly, the dark matter halo is not a ring, but a spherical mass in which the disk of the galaxy is imbedded.

The stars are more concentrated in the central bulge, so if you were to just take the visible matter into account, objects should have slower orbital speeds as you move from the center. However, DM extends above and below the disk and this adds to the gravitational pull also, as any matter inside the spherical volume that is closer to the center than you are acts on you just the same as if it were all concentrated at the center. As you move further from the center, more and more of the DM is closer to the center than you are and adds its mass to the gravitational pull.

 

[eaclou]

Ok, the sphere of Dark Matter makes a lot more sense - for some reason I thought it was a ring.

Because the mass of dark matter is the same "above" and "below" the galactic ring, the net force orthogonal to the ring is ~zero, because the pull from both "sides" cancels out, leaving only the force component in the direction of the center of the galaxy.

So would it be fair to say that the galactic model is less like that of a solar system (where almost all the mass in the system is concentrated in a very small point, the "sun") and more like a cloud of matter with mass everywhere, but decreasing in density gradually as distance from the center increases?