The main observables

Star clusters Two types of star cluster were (and are) known. We already described Globular Clusters (GCs), spherical, bound systems of $10^5-10^6$ stars. The MW has about 150 GCs, which are spherically distributed around the MW. Stars form in the MW disk out of large molecular clouds. Sometimes, after the gas has been dispersed, the newly formed stars are gravitationally bound to each other, in what is called an Open Cluster. These typically contain of order $10^4$ stars. They are of great importance for studies of stellar evolution, since we know all the stars in such a cluster have (more or less) the same age, distance and initial composition, and hence they provide us with a sample of stars in which the only (or at least the main) difference is the stellar mass.

Star counts Previously we described how star counts can be used to probe the number density of stars as a function of position. In the early days, William Herschel and his sister counted the numbers of stars as function of their magnitude in many (700!!) directions in the sky, by spending (most?) nights gazing through his telescope! Later, photographic plates were used for the same purpose. These confirmed that the stars around the Sun are distributed in a disk, with axes ratio about 5:1.

Standard candles are objects with a known absolute property, for example a known size, or known luminosity. So measuring their angular size size, or apparent luminosity, you can determine their distance. A most important example is that of Cepheid variables. Henrietta Leavitt studied variable stars in the Magellanic Cloud in 1912. She found a relation between the period $P$ of the variation $\Delta m$ and the magnitude $m$ of these Cepheids. Since all these stars are at (nearly) the same distance, this must mean it is actually a relation between the absolute magnitude $M$ and $P$. There are many types of variable stars, but Cepheids have many advantages (a) the shape of their light curve (i.e. luminosity as function of time) is a very characteristic sawtooth pattern, (b) they are luminous - and so can be seen out to large distances and (c) the $P(M)$ relation has little scatter. Unfortunately, they are also relatively rare. RR Lyrae are similar to Cepheids, but occur in a different type of star. They are also used as standard candles. Of course, to get an absolute distance, we need somehow to find the distance to some Cepheids or RR Lyrae using another method, for example using the parallax.

Parallax Stretch your arm, point your index finger upward, and look with your left eye alone toward a distant wall. Now, look with your right eye alone: your finger seems to have moved with respect to the background. You've done (your first?) parallax measurement. If the wall is sufficiently distant then there is a relation between how much your finger appeared to have moved (in degrees, say), the length of your arm, and the distance between your eyes.

For astronomical measurements, you can increase the distance between your eyes to twice the distance earth-Sun, by looking at the same object half a year apart. Since one can relatively easily measure angles to a fraction of an arcsec ^2.1, we have a new distance unit: the . An object at 1 distance has a parallax of 2arcsec. Let's compute how much this really is. Consider an equi-lateral triangle, with two sides of length 1 third side 1AU. By definition 1/1AU=1arcsecin radians^2.2 Hence

$$1\pc ={180\times 3600\over \pi}{\hbox{AU}}\approx 206265{\hbox{AU}} .$$ (2.1)

Unfortunately, this literally doesn't get use very far: the distance to even the nearest stars is of this order. We'll come back to the distance scale later.