THE HR DIAGRAM

The HR Diagram was created simultaneously as separate discoveries by two astronomers (Hertzsprung and Russel) and was created on separate sides of the Atlantic ocean. These two astronomers plotted the luminosities of stars versus the temperatures of stars, and discovered some patterns on this diagram. (Consider the mock diagram for automobiles shown in lecture). For stars, note that the temperature is plotted so that cool stars are on the right and hot stars are on the left. Luminous stars are toward the top and low luminosity stars are toward the bottom.

The Spectral Sequence is a Temperature Sequence

Stars have been classified by their spectra in a spectral sequence . Stars with the strongest absorption lines were called "A" stars, those with the next strongest "B" stars, and so on. It got confusing after a while and it was soon realized that this was a temperature sequence.

The modern spectral types are "O", "B", "A", "F", "G", "K", "M" from the hottest stars to the coolest stars. See the diagram below.

Measuring Star Sizes

The HR diagram, among other things, provides indirect information on star sizes. This one is a bit involved, so pay attention. The idea is that luminosity depends upon the size and the temperature of the star.

The temperature determines the amount of light energy released by every square centimeter on the surface of the star. This is what we call the "Luminosity per Unit of Area". It scales with the fourth power of the temperature! That is,

The bigger the surface are of a star, the more area over which the light energy can be released (the greater the luminosity)! The surface area depends upon the square of the radius (size) of the star. For a fixed temperature, the bigger the radius, the greater the surface area, the greater the luminosity. Putting it altogether, we have or

So, if you know the luminosity and the temperature of a star, then you can solve the above equation for the radius and compute the value of R. As shown in the previous lectures, we easily can measure the luminosities and temperatures of stars. Solving the equation for R is the easy part! This relationship is why we know star in the upper right of the HR diagram are huge, and why star in the lower left are small (relatively speaking, of course!).

Mass-Luminosity Relation for Main Sequence Stars

For the following, what is stated is true only for Main Sequence stars (not Red Giants, Super Giants, White Dwarfs). The Main Sequence does include so-called Red Dwarfs!

The main sequence is, first and foremost, a mass sequence. Low mass stars are small and have low luminosity (lower right corner of HR diagram). As you go up in mass, the main sequence stars become larger, hotter, and more luminous. There is a mass-luminosity relationship... as mass goes up, the luminosity of the star is greater. This is called the mass--luminosity relations. In detail,

Main Sequence is a Temperature, Mass, Size, and Luminosity Sequence

As we can see from the above, the luminosity, temperature, size, and mass are all related to one another. Thus, the main sequence is also a sequence in these quantities. The more massive stars have larger luminosity (see above). They are also the hottest stars. Together this reveals that the most massive stars are the largest of the main sequence stars. That is in the end, the main sequence is a sequence of temperature, size, mass, and luminosity. However, mass rules all. It is the most important property of a star (details why in future lectures). We have the following relationships...

Broadening of Absorption Lines

(The following is only in the book, I did not lecture on this and it WILL NOT BE ON THE EXAM!) The pressure of the gas in the photosphere effects the shape of the absorption lines. Low pressure yields narrow lines, and high pressure yields broad lines. Big giant stars are all spread out and the gas in the photosphere is low pressure. Thus, giant stars have narrow lines, and smaller main sequence stars have broader lines.

Surveys of Stars: How Many of Each Type Are There?

(The following is only in the book, I did not lecture on this and it WILL NOT BE ON THE EXAM!) If you look in the night sky, you see the brightest stars, most of them very far away. This is not a fair sample of the population of stars. Most of the stars are too dim to see, so you miss them in your census. If you limit your survey by a volume of space and look for all stars above a certain brightness threshold, you get a fair representation of the stars in the galaxy. Most of the stars are low mass main sequence stars, the so-called red-dwarfs. Many of the stars are also so-called white dwarfs. We revisit why this is later.