We have a hard time mapping the Milky Way Galaxy because we are inside it! There is no way to get a look at it from outside. All we can do is look around from our place in it. We run into a basic problem - the ISM. There is enough of it in the disk of the Galaxy that we can't see very far. Remember that we can't see the galactic center 8 kpc away. Same reason. The only way to do it is to use wavelengths longer than visible light, which means infrared and radio.
There are two ways we can find out something about the structure of the Galaxy. One involves the very luminous O and B type stars. Because they are so bright, they can be observed at distances greater than the size of our Galaxy. Their distribution is clumpy as we look out from here; the clumps correspond to the spiral arms of the Galaxy.
The other method of mapping makes use of the 21-cm radiation from hydrogen to map the location of hydrogen clouds in the Galaxy. Figure 14.10 on page 372 shows how this is done. The clouds have different radial velocities, which means that the Doppler shift of the 21-cm radiation is different for each cloud. This allows the clouds to be distinguished from each other. Note that this method doesn't work when looking across the galactic center or directly outward from it; in these directions the motion of the clouds is entirely transverse and there is no significant Doppler shift to separate the clouds.
Here's a radio image made in 21-cm. Notice the indications of spiral arms. The original article is found here.
Check out Figure 14.12 and Table 14.1 on page 374. They describe the orbital motions in the Galaxy. Note that everything in the Galaxy must be orbiting; if it wasn't, everything would have piled up in the center long ago. Note that halo stars actually orbit THROUGH the disk. Stars are so far apart in relation to their size that collisions are very rare.
The Sun orbits the center (of mass) of the Milky Way. Notice how it passes through spiral arms as it goes around.
Disk stars (like the Sun) have circular orbits. At its distance from the center, the Sun takes roughly 250,000,000 years to make one trip around.
The Milky Way Galaxy is made of three main components: the central bulge, the disk and the halo, or spherical component. The bulge and disk are the "fried eggs" shape, while the halo is a spherically distributed population of stars and globular clusters. Star formation is going on in the disk and near the center of the bulge, while the outer bulge and halo have little star formation happening. An illustration clearly shows the components.
How can we know that there are stars in the halo? We can look at their motion. If the motion of a star can be measured AND it is not parallel to the disk but is at a steep angle to it, that is a halo star. Its orbit is NOT in the disk. These stars are old and have less of the heavy elements than disk stars.
How can we tell where stars are forming? Simple - look for type O and B stars. We know that they have relatively short lifetimes, so when we see them, we know that they are quite young. They must have formed only a short time (astronomically speaking) ago. We used an example of some peculiar type of moth (what type doesn't matter). This moth leaves its cocoon, mates, reproduces, then dies in 2 days maximum. Suppose you are wandering around some evening and see one of these moths. You immediately know two things about it - it is less than 2 days old and it is not far from where it emerged from the coccoon. So it is with the O and B type stars. They are young, and as a result have not had time to move very far from where they formed. This star forming area is the disk of a spiral galaxy. You can see that in photos because the spiral arms look distinctly bluish.
Astronomers use a simple notation to refer to the abundance of elements in stars.
Look at Figure 14.12 to see an illustration of the two distinct types of orbital motion - disk and halo - found in the Galaxy. Note that the halo stars can pass right through the disk; star collisions are VERY rare. Here's an example. Imagine that the Sun is represented by a basketball right here in Dallas. On that scale the nearest other star is another basketball in southern California! The space between stars is VERY large compared to the sizes of the stars, making collision unlikely.
Knowledge of galaxy formation is relatively recent and is still incomplete. Earlier ideas involved a VERY large colud of material collapsing to form a galaxy. Recent work by the Hubble Space Telescope has provided evidence for another description. At extreme distances, Hubble images show LOTS of blue star-forming clouds; they're called blue galaxies. The idea is that several of these irregularly-shaped aggregations would merge into a large object. The relative motion of the clumps would cause the combined mass to rotate. Stars which formed early on would have more or less random orbits. As the process continued, the gas and dust would collapse to the equatorial plane of the rotation and form a disk. This would form the star-forming disk of the galaxy; those orbits would be circular. The stars formed BEFORE the disk formed would have orbits distributed in 3 dimensions, like today's halo stars.
A spiral galaxy is at once a beautiful sight and a physical puzzle. The problem is understanding how the arms remain as stable long-term features.
The term was coined by Dr. Vera Rubin, the astronomer who gathered the data and showed that there was something strange going on with the matter distribution in spiral galaxies. This result was first published in 1970. Dark matter is simply matter, detectable by its gravity, that is not visible in any wavelength band. Somewhere around 90% of the matter in the Galaxy is composed of this stuff. It would be nice if we knew what it was.
The dark matter shows in the rotation (stars orbiting) of a galaxy. The galaxy M33 shows it clearly. Star velocities do not drop off with distance from the center as wold be the case if the matter that we can see was all that existed in the galaxy.
Here's an excellent page covering galaxies.