The Hertzprung-Russell Diagram

Ejnar Hertzprung (1905) published tables of luminosities and colors of stars, noting certain correlations. In 1913, Henry Norris Russell presented similar data in a diagram (now known as the Hertzprung-Russell diagram)

The H-R diagram turns out to be perhaps the most important tool in astronomy. It helps us determine ages, distances, and chemical composition (metallicity), of stars and nearby galaxies.

A more modern (observer's) H-R diagram looks something like this:
An ultramodern observer's H-R diagram (called a Hess diagram) from Dennis Zaritsky:
Note that the vertical axis here is apparent magnitude. For this to make sense, all stars on this plot must lie at roughly the same distance (why?). That is the case here: this is a hess diagram for the Large Magellenic Cloud, a small dwarf galaxy which is about 50 kiloparsecs away...

We can also make a theorist's H-R diagram which looks something like this:

Where do those lines of stellar radius come from?