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We address the question, "How do we know how stars evolve?" by having the student "review" the process of constructing what is known as a "color-magnitude diagram" of two clusters of stars. These diagrams reveal not only the ages of the clusters (and thus the way stars of different masses age) but also the relative distances to the clusters.
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After completing this lesson, you should be able to
You are at the point in your study of astronomy where you should be asking yourself: "How do we know all of this?" We cannot go to the center of the Sun, we cannot travel to the stars and grab a bit of plasma. We have been studying astronomy with large telescopes and at multiple wavelengths for only a few decades, using high-powered computers to model stars for even less time. Even the lives of the shortest-lived stars are a million times longer than any human life. As the text mentions, "we cannot hope to see the life story of any single star unfold before our eyes or telescopes."
When working with the classification of stars on the H-R Diagram, we assumed that if a star had nearly the same spectrum as another star, these stars were, in fact, nearly identical. When working with how stars live and die, we assume that if a star has nearly the same mass as another star, then those two stars will follow similar evolutionary paths. Well, we still cannot follow any given star for millions or billions of years. What we can do, however, is study clusters of stars—stars that we assume are of nearly the same age and chemical composition (having formed from the same giant molecular cloud). With these two variables taken care of, the differences we see in temperatures and luminosities for stars in a cluster must be due to differences in their masses.
Before going on with these notes, read carefully through Chapter 13, sections 13.1 through 13.3. This lesson uses our knowledge of stellar evolution at the end of a star's main sequence lifetime and color-magnitude diagrams to determine the ages of the stars in four open clusters of stars.
As we mentioned at the beginning of this lesson, our lifetimes are far too short to ever hope to see even the most massive stars go through their evolution. How have we arrived at what seems to be the complete story for the stars? We observe star clusters—open star clusters filled with mostly young stars, and globular clusters filled with mostly extremely old stars. Under the assumption that the stars in the individual clusters all condensed from the same interstellar giant molecular cloud, they would all have roughly the same age. Under this same assumption, the overall mix of elements in these stars would be nearly identical, leaving the only variable as the masses of the stars in the clusters. Then, by observing many, many clusters of different ages, we can plot the individual stars based upon their temperatures and luminosities and see just how the different H-R Diagrams compare.
Carefully read the sections in the text (13.2 and 13.3) concerning the types of clusters and their H-R Diagrams. Then, to continue our journey on becoming more familiar with our region of the Milky Way Galaxy, use the table showing each cluster along with actual data to get familiar with the open clusters (we investigate globular clusters in more depth in Lesson Eleven). You will be able to open a map of the clusters within 5000 light years along with viewing how the clusters look in the sky. We will be investigating how we determine the ages of the clusters, their distances, and other characteristics in Assignment 8.
Examine Fig. 13.4 of your text that shows the paths stars of various masses take as they age. These are stars that have finished or are nearly finished fusing hydrogen to helium in their cores. These are stars that are running out of time. Notice in all cases that at first the stars all increase in luminosity and eventually get cooler. These are stars that are increasing in size (their radii are increasing, not their masses). They increase in luminosity because of this increase in size; they get cooler and redder because their surfaces are now a long way from where energy is being generated and the energy is spread out over a much larger sphere.
If we could watch a cluster containing stars with a wide range of masses, we would see stars "peeling off of" the main sequence. Once again, since we can't wait around tapping our toes until stars start evolving off of the main sequence, we compare a number of different clusters of different ages. The following figures shows the color-magnitude diagram of the Hyades (black points), with an outline of the stars from other clusters. (See the link to the table of open clusters of the Galaxy above for the actual CMDs.) The colored outlines have been adjusted vertically until the main sequences matched at the same color (B-V). This adjustment is needed due to the fact that these clusters are all at different distances from us, and thus their apparent magnitudes are different. The adjustment in this case is equivalent to moving all of these clusters to the distance of the Hyades. Now that we have them all on a common basis (much like imagining the stars at 10 parsecs), we can do our comparisons.
Compare this diagram to Figures 13.12 to 13.14 of your text. Your text uses luminosity and temperature, but you should be able to notice that the overall characteristics of the plots are similar. (A color index (B-V) = 0 is equal to about 9,500 Kelvin.) Based upon stellar models, computer programs that calculate the pressure, temperature, and density at each point inside main sequence stars and the rate of nuclear fusion in their cores, we calculate approximate main sequence lifetimes for stars of different spectral types. (Recall, along the main sequence, the spectral type of a star is directly related to its mass.)
| Spectral Type | Color (B-V) | Lifetime (years) |
|---|---|---|
| O | –0.4 | < 106 |
| B | –0.2 | 3 × 107 |
| A | 0.2 | 4 × 108 |
| F | 0.5 | 4 × 109 |
| G | 0.7 | 1 × 1010 |
| K | 1.0 | 6 × 1010 |
| M | 1.6 | > 1011 |
Take a look at the following figure that shows the above CMDs, but now with arrows from the turn-off points of the main sequences for each cluster down to the color of that turn-off point. From these colors, you can determine the approximate age of each cluster, often times to within a few million years (and, that is good enough in astronomy!).
See if you can determine the age of each cluster, and then take a look at the answers.
The agreement between observations and theory for a huge range of stellar masses, encompassing luminosities from 100,000 times that of the Sun to 1/100 that of the Sun, from temperatures of over 40,000 Kelvin to under 3000 Kelvin tells astronomers that they are extremely close to understanding how stars are born, live, get old, and die.
From the textbook:
Learn more about the evolution of stars from a number of excellent sites:
