Central velocity dispersion vs rotation cuves for estimating galactic mass

[Simfish]

Okay, so, say, you're trying to measure the mass of the very center of the Andromeda galaxy (within 1 arcsecond of the center). You have a central velocity dispersion of 250 km/s and a rotation curve of 100 km/s (1 arcsecond away from the center). Now, from the virial equilibrium equation, M(r) = 5*sigma^2*R/G, where sigma is velocity dispersion. From the rotation curve equation, M(r) = v^2*R/G.

Now, from this, I get that the mass in the center is much higher using the dispersion equation. Is this expected? Dispersion velocities tend to be higher in ellipticals than in spirals, and the centers of spiral galaxies (with the bulge) tend to be more elliptical in nature than the lobes of spiral galaxies.

 

[gtoguy97]

This is why the mass is higher in the center when using the dispersion equation. Also, note that both equations are used to measure the mass of the galaxy, but they are not necessarily measuring the same thing. The dispersion equation measures the total mass within a given radius, while the rotation curve equation measures the mass enclosed within the same radius (as determined by the rotation curve).