Properties of Stars

Reading: Chapter 17

Russell-Vogt Theorem

Let me mention an important simplification before we go on:

The properties of a star are determined primarily by its mass.

This statement is so powerful that it has been codified as the Russell-Vogt theorem, although it is not really a theorem in the mathematical sense. We will explain why the Russell-Vogt theorem is true when we talk about stellar structure.

Hertzsprung-Russell Diagram

There is a bewildering array of catalogued properties of stars. We know their masses, radii, luminosities, surface temperatures, colors, distances, spectra, ... .

Question: How are we make sense of the data?

An obvious first step is to graph the data. For example, we could plot the radius versus the surface temperature. The reason we go through this exercise is because plots can indicate whether the two properties are correlated, that is, if there is a physical relationship (connection) between them.

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 result is amazing. A schematic Hertzsprung-Russell diagram 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) in their plots. They ordered the stars as O, B, A, F, G, K, and M. Since the O stars are the hottest, this means that in the HR diagram, the temperature axis is odd in that the temperature decreases as one moves to the right.

When luminosity versus temprature plots are made, stars are confined to specific regions. 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. So, we can plot properties of people and see what the plots look like. For example,

• 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 ===> something about the structure of a person in that the weight and height are connected.

This simple exercise taught us something about people. We did not learn how people are put together, but we learned that there is a correlation between height and weight. It is up to theorists to explain why height and weight are related.

Similarly, the HR diagram is telling us about how stars are put together (unfortunately, it is again up to theorists to tell us exactly what).

HERTZSPRUNG-RUSSELL DIAGRAM

Question: What can we deduce from the HR diagram?

• First, let me 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? Hmmmm, let's think.

  Given a random sample of stars, we find that 80-90 % of the stars fall along the Main Sequence and that the bulk of the other stars are either White Dwarfs or Giants.

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

  Answer: Many things

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 most stars in the 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? Theoretically, we believe that this is true and when we look at the Mass-Luminosity relationship this seems to be true.