Properties of Stars: Tying Everything Together Chaisson & McMillan, Ch. 17

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.

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?

The first step is to graph the data (as for example, in homeworks 2 & 3). The reason we go through this exercise is because plots can indicate whether properties of different stars are correlated, that is, if there is seems to be a physical relationship (connection) between the different properties.

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 (Mochejska & Kaluzny, see APOD, 2001 Feb 23) is shown below

The Hertzsprung-Russell (HR) diagram is one of the most important astronomical discoveries of this 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.

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,

• The plot of weight versus IQ is a scatter diagram ===> there isn't a physical relationship between weight and IQ.

• The plot of weight versus height for a sample of people shows a correlation ===> that there is something in the structure of people which makes weight and height correlated.

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.

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?

• Let's address the names of the different groupings of stars, i.e.,, Main Sequence, Giants, Super-Giants,, and White Dwarfs. (By the way, these groups are also referred to as Luminosity Classes). Without having actually measured the radii of all of these stars, How did I know that the stars in the upper right hand corner of the diagram were big, while the stars in the lower left hand corner were small? (from Stefan-Blotzmann Law)

  Given a random sample of stars, we find that roughly 85-90 % of the stars fall along the Main Sequence and that the bulk of the other stars are White Dwarfs or Giants.

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 (assignments 2 & 3). 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.

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. The mass and luminosity are related in a well-defined manner, the Mass-Luminosity relationship for Main Sequence stars.