Early in the 20th century, Danish astronomer Einar Hertzsprung and American astronomer Henry Norris Russell independently looked at a possible relation between luminosity and temperature. That was a very significant research question. The result is shown in figures 10.12, 10.13, 10.14 and 10.15. Figure 10.15 shows the obvious relationship that ultimately appeared. The band running from upper left to lower right is the Main Sequence; it clearly reveals the relationship. The hottest (type O) stars are also the most luminous while the coolest (type M) are the least luminous (dimmest). This graphic shows the H-R Diagram quite nicely.
Main sequence stars are "normal" stars which are burning hydrogen as their fuel.
There are two other regions of the diagram to note: the red giant and white dwarf regions. The red giants are found in the upper right. These are very cool (3,000 K) stars which are VERY luminous. Their excuse for this is that they are VERY large. Each square meter doesn't emit a lot of energy as stars go, but the huge star has a LOT of surface area, so it is quite bright. The white dwarfs are found in the lower left. These objects are quite hot and very dim. Each square meter emits a lot of energy but the star is small and has a small surface area to radiate, so it is dim. See More Precisely 10-2. Here's a H-R plot of nearby stars using data from the Hipparcos spacecraft.
Spectroscopic parallax isn't exactly a parallax (angle) measurement, but it does present a means of getting a distance estimate for a star that is too far away for actual parallax measurement. You do it by examining the spectrum of a star and determining its spectral type. Looking at the Main Sequence band at that type allows you to look to the left of the diagram and get an estimate of the absolute magnitude. Since you always can find m (apparent magnitude) and you have an estimate of M (absolute magnitude), the formula will yield a distance. The Main Sequence does have some width (is not a thin line), so the estimate of M, and therefore the distance, is somewhat uncertain (has an error bar). That is, however, a LOT better than knowing nothing about the distance.
There's only one way to determine the mass of a star directly - measure its gravitational influence on something else. For the Sun it's easy; use the orbits of its planets to find its gravity. For other stars that do not have planets we can see it is a problem. The only thing we are likely to be able to use in finding the star's gravitational influence is another star, and that requires having two stars orbiting each other in a binary star system. Fortunately, over half the stars in the Galaxy are in binary systems, so there are a lot of opportunities.
The masses are determined by studying the orbit of the binary system. Remember that the two stars orbit around the common center of mass (CM). Astronomers will determine the following.
Once masses have been determined for a significant number of stars, we find that mass and luminosity are related. See Figure 10.21 for an indication of the Mass-luminosity relationship (or use this graphic); type O stars are the most massive and type M stars (red dwarfs) are the least massive.
Also note that stellar radius and spectral type are related. The more massive stars are the largest, while the least massive stars are smallest.
Be sure you understand this chapter. Use the questions at the end of the chapter for practice.