The disk

Most of the MW's stars are in a thin disk, which represents about 70 per cent of the total star light of the MW. The centre of the disk is in the direction of Sagittarius, $\alpha=17^h 42^m 29.3^s$, $\delta=-29^{o} 59'$, at a distance of $R_0$. The latter is called the solar galacto-centric distance, and there is quite some discussion to how large it really is. $R_0=8.5{\hbox{\rm kpc}}$ is usually quoted, but some studies find $R_0=8.0{\hbox{\rm kpc}}$. These studies try to determine the centre of a set of objects, for example globular clusters, variable stars such as RR Lyrae or Mira variables, or O and B stars. An $H_2O$ maser source is located near the centre of the MW. The maser emission is thought to come from a spherical shell, and one can measure both the radial and transverse speed of the shell. If the shell is expanding spherically, then one can determine its distance.

Apart from stars, the disk also contains gas and dust. On top of the smooth disk are spiral arms, traced by young stars, molecular clouds, and ionised gas. The disk stars are in (nearly) circular motion around the centre. For the sun, the circular velocity is $\approx 220{\hbox{\rm km s$^{-1}$}}$.

How old is the disk? We don't really know. But we can put limits on the ages of the stars in the disk, but have to keep in mind that the stars could possibly be older than the disk (i.e., they have formed somewhere else). One neat age estimator are White Dwarfs. As you recall, these don not undergo nuclear fusion anymore, but are presently just cooling down. So, by measuring their current temperatures, and cooling rates, we can compute how old they are. Some of the older White Dwarfs are thought to be $\sim 10-12\times 10^9$ years old.

Let's describe the position of a star in the MW using cylindrical coordinates $(R,\varphi,z)$, where $R$ is the distance to the centre, $z$ the distance to the plane, and $\varphi$ an angle. The density of stars in the disk goes approximately like $n(R,\varphi,z)\propto \exp(-R/R_h)\exp(-z/z_h)$. Since the disk is (nearly) axis-symmetric, $n(R,\varphi,z)$ is independent of $\varphi$. Away from the centre, $n$ decreases exponentially, and at distance $R_h\approx 3.5{\hbox{\rm kpc}}$, it has fallen to $1/e$ of it's central value. Also perpendicular to the disk, the fall-off is exponential, with $z_h\approx 0.3{\hbox{\rm kpc}}$. $R_h$ and $z_h$ are called the scale length and scale height of the disk, respectively. These scale lengths really depend on the type of star you're using. Young stars are born out of gas, which is much more concentrated toward $z=0$. And so the scale height of young stars is much smaller than of older stars.

Note that there isn't really an edge to the disk. It can be traced to a distance of around 30kpc. With a height of 0.3kpc, this is a ratio 100:1, which is thinner than a compact disc!

Given the exponential distribution in $n$, the luminosity profile (in $L_\odot$ per unit volume) of the disk is often modelled as

$$L(R,z)=L_0 \exp(-R/R_h) {2\over \exp(z/z_h)+\exp(-z/z_h)} ,$$ (3.1)

where $L_0$ is some normalisation constant. In the B-band, the total luminosity is $\sim 2\times 10^{10}\hbox{$L_\odot$}$.

Because of the component I'll describe next, the disk is also sometimes called the thin disk.