Make a histogram of the w
(up/down) velocities
of stars of different spectral type:

Remember also that different groups of stars had
different
disk thicknesses:

(km/s) 
(pc) 















Question #1: Why does dispersion increase with spectral type?Question #2: Why do dispersion and scale height increase together?
The disk is not perfectly smooth  there are "lumps" of matter (what kind of lumps?)As stars move through these lumps, they scatter gravitationally, increasing their random velocities and moving from circular orbits to elliptical orbits. As a group, their velocity dispersion increases.
Why are they born on circular orbits?
Imagine the disk as a plane parallel slab of mass. Gravity pulls stars towards the disk, their velocities can carry them away. We want to balance these two effects:
First, think of balancing KE with PE for a small mass m orbiting a big mass M: So we can solve for the big mass M: Now, instead of a big mass M, think of a circular patch of radius r and surface density Sigma (in M_{sun}/pc^{2}). It has a total mass: So plug that in and get Or, now thinking about a group of stars:So if we measure velocity dispersions and scale heights for groups of stars, we can measure the mass density of the Galaxy's disk. This was first done in the early 1930s by Jan Oort and is called the Oort limit. Modern analyses gives ~ 75 M_{sun}/pc^{2} or so.
Now let's just add up all the mass we see:
Stars 30 M_{sun}/pc^{2} Stellar remnants
(mostly WDs)5 M_{sun}/pc^{2} Brown Dwarfs
2 M_{sun}/pc^{2} Gas (HI+H_{2}) 13 M_{sun}/pc^{2} Total 50 M_{sun}/pc^{2} Hmm. What's going on??