Tying Everything Together: Hertzsprung-Russell Diagram, Mass-Luminosity Relation, ....

A Limited Russell-Vogt Theorem

This statement is so powerful that it has been given the name the Russell-Vogt theorem (although it is not really a theorem in the mathematical sense). Why the Russell-Vogt theorem in the above form is true will be explained when we talk about stellar structure.

Hertzsprung-Russell Diagram

We know masses, radii, luminosities, surface temperatures, colors, distances, spectra, ... of many stars.

Question: How do we make sense of the plethora of available data?

H-R Diagram

In the early 1900's, Ejnar Herstzprung and Henry Norris Russell independently made the discovery that the luminosity of a star is related to its surface temperature. The resulting plot is amazing. A schematic Hertzsprung-Russell diagram is shown to the right. A Hertzsprung-Russell diagram for the old cluster M55 (Mochejska & Kaluzny, see APOD, 2001 Feb 23) is the top panel on this page. The Hertzsprung-Russell (HR) diagram was one of the most important astronomical discoveries of the twentieth century.

Hertzsprung and Russell used the spectral class (which is related to the temperature, and color of the star [which is related to B-V]) in their plots. They ordered the stars as O, B, A, F, G, K, and M. Since O stars are the hottest stars, this means that the temperature axis in the HR diagram is odd in that the temperature decreases as one moves to the right. The veritcal axis is the luminosity of the star, it increases upward. The axis is logarithmic (it mimics the human eye).

Stars are confined to specific regions in the HR diagram. This tells you that there is some physical relationship between the luminosity and temperature of a star. To make this point clear, let's look at people. People have many defining characteristics, not all of which are related. Let's plot some properties of people and see what they look like. Consider,

This simple exercise taught us something about people. We did not learn in detail how people are put together; we learned that the height and weight of people are somehow related. It is up to theorists to explain the how and why of the physical connection between the height and weight of the people population.

Similarly, the HR diagram is not telling us about how stars are put together. It is, again, up to the theorists to tell us what is going on. However, for now, let's ignore the role of the theorist and just examine the HR diagram to see what we can deduce about stars.

Some Inferences Based on the Hertzsprung-Russell Diagram

Luminosity Classes

    I -- Super-Giants
    II -- Bright Giants
    III -- Normal Giants
    IV -- Sub-Giants
    V -- Main Sequence Stars

Question: What can we deduce from the HR diagram?

Question: What is this be telling us about stellar evolution?

Luminosity Function

Even along the Main Sequence, stars are not distributed smoothly. There are many more low luminosity stars than there are high luminosity stars. A plot of this distribution is referred to as the Luminosity Function. The plot is for the Solar Neighborhood, but it is representative of stars in our Galaxy. Note that for stars the luminosity of our Sun, that there is around 1 stars every 1,000 cubic parsecs. That is, there is one Sun-like star in every cube whose sides are 10 pc long. Sun-like tars are roughly 10 parsec apart (30 light years) in the Solar Neighborhood. The number of stars increases strongly with decreasing luminosity. We find stars around 1 % the luminosity of the Sun, are separated by distances of around 1 parsec (3.3 light years).

Mass-Luminosity Relation for Main Sequence Stars

When we consider Main Sequence stars, is there any hint about whether an individual star evolves along the Main Sequence or whether a star once on the Main Sequence does not change its position? We believe that stars do not move along the Main Sequence. That is, Main Sequence stars with particular L have the same properties. This can be seen from the Mass-Luminosity relationship for Main Sequence stars.