Arms of the Milky Way

1.4 GHz line

Using a radio telescope we can detect the H 21 cm line which is produced by the spin-flip transition in atomic hydrogen. As this line is not attenuated by interstellar dust or by the earth's atmosphere, we can detect it using ground-based telescopes.
 
The probability of the spin-flip transition is low (lifetime of an excited state t~ 3.5 x 10^14 seconds), meaning that a single hydrogen atom might undergo this transition only once in 11 million years! 

But if we point our radio telescope at the sky we do see this transition. Why?

Well, because of the vast abundance of hydrogen in the galaxy. If a chance of transition is 10^(-14) but you got around 10^57 hydrogen atoms, then a simple multiplication might give you an idea of how many HI atoms are emitting this transition. This makes it possible to detect the 1.4 GHz line and use it for astronomy.
Scanning the galaxy in steps of 5 degrees of galactic latitude you can see the structure of the galaxy pretty easily. Here I have constructed a latitude-velocity plot of the Milky Way Galaxy. I have fixed the galactic longitude for observation at l=120 degrees. 
If all the HI atoms were emitting at the same frequency then we would have observed the emission at the same velocity. (Doppler effect). But instead of the emission being all concentrated at v=0 km/s. We see some at negative(blue shift) while others at positive(red shifted) velocities.

These "other" emissions are the different arms of the Milky Way. The Perseus is at -50 km/s and the Outer is at -100 km/s.The arm at 0 km/s is the Local arm of the galaxy which we reside in although there is much debate in the community whether it's an arm on its own or just a spur from the Perseus Arm. From the Doppler-shifted velocities, we can determine the rotational velocities of the HI gas in the galaxy. Using a bit of trigonometry the positions of the HI gas can also be determined enabling us to construct a map of the galaxy (How cool is that!!)

Below is a polar plot of the Galaxy from the data I obtained where the HI clouds' galactocentric distance has been plotted to show the arms of the galaxy. I have superimposed logarithmic spirals to highlight the arms.

Rotation Curve of the Milky Way

The rotation curve remains 'flat' instead of falling inversely proportional to distance, what we would expect if Newtonian Physics was right. But instead, we see an almost constant rotational velocity.

Using a 3 part mass model to construct the rotation curve obtained(in light green). The analytical formulas of the Galactic bulge, Stellar Disk, and the Dark Matter halo. Keep in mind that the first two, the Bulge and the Stellar disk are visible while the other is hypothetical.

We see that the 3 part model including the Dark Matter Halo gives us a great match with the observed data. So is this the whole story? Our galaxy is enshrouded in a vast envelope of some stuff we can't observe??? No Dark matter particle has been detected yet. So the mystery deepens.

MOND or Dark matter?

There is another paradigm to explain the flatness of the rotation curve. While the DM model invokes the existence of some strange unseen stuff akin to Pokemon abilities. The MOND model (Modified Newtonian dynamics) explains the apparent "missing mass" by postulating that the gravitational force falls off more slowly at large distances or more accurately at lower accelerations.

The fact that MOND gives us the rotation curve with only the baryonic matter (the stuff we can see stars , gas, and dust) without hypothesizing the existence of a completely new form of matter is remarkable.Although its still has its own demerits much like the Dark Matter paradigm. The battle continues on......