Giant Stars

249-255

In the previous chapter you learned about star formation and the life of a main-sequence star. But, even with stars - all good things must come to an end! In this chapter we look at how stars age and begin to see the emergence of strange new properties in some stars. We will also encounter compelling evidence which suggests that our understanding of stars and the models we create is essentially correct.

Basic Facts About Giant Stars

Figure 10.1 shows the bright red star Aldebaran. Aldebaran is easy to spot in the late fall sky. It is the bright, red "eye" in Taurus the bull and is situated just below the Pleiades. Here are some basic "facts" about Aldebaran: visual magnitude mV = 0.85 parallax = 0.05" Spectral Type K5 Surface temperature 4100 K Binary system, Aldebaran's mass = 2.5 Mo; companion's mass = 0.15 Mo
	Figure 10.1 Aldebaran (a-Tauri) in the Hyades cluster is one of our nearest giant neighbours.

Example 10.1 How can we use the information about Aldebaran to conclude that it is much larger than our sun and cannot be a main-sequence star?

Solution: If we determine the luminosity of Aldebaran we can then use the temperature-radius-luminosity relation developed in section 8.3 to infer the size of Aldebaran. To determine the luminosity find the distance and then use the distance-modulus calculator (Chp 8.2).

Since the parallax is 0.05" we can conclude that the distance is 1/0.05 = 20 parsecs. Use the distance-modulus calculator to determine that the distance modulus m_V-M_V = 1.50 which absolute tells us that the absolute magnitude M of Aldebaran is -0.65.

Next, use the temperature-luminosity applet from Chp 8.3 and enter the appropriate temperature of 4100 K for one of the stars and then adjust the radius until the absolute magnitude matches that of Aldebaran. When you do this you discover that Aldebaran has a radius of just under 26 Ro and a luminosity of approximately 160 times that of the sun. If you put this on the HR diagram you will note that it is far off the main-sequence and is in the region we earlier classified as the "giant region" (Use "HR explorer to see this ). The red X marks the location of Aldebaran on the HR diagram.

Figure 10.2 Red X marks the location of Aldebaran on the HR diagram.

The HR Diagram - Luminosity Classes and Stellar Evolution

Example 10.1 tells you that Aldebaran is in some significant way "different" from a main-sequence type star. When we introduced the idea of stellar classification and the HR diagram we also introduced the concept of luminosity classes. Aldebaran and other stars are telling us that luminosity classes represent different epochs in the evolution of stars.

The challenge we now face is to understand how the changes that occur stars as they age will create the Giant (Luminosity III) region of the HR diagram as well as the other regions. There are a number of key ideas that will help do this:

1. In the core of a main-sequence star hydrogen is being steadily transformed into helium via fusion
2. As long as the star is able to produce enough energy in its core it can create enough pressure to support the weight of the layers above it (ie - Hydrostatic Equilibrium)
3. If a star begins to contract it will be able to "cash in" gravitational energy as heat

Start with the first idea listed above. As hydrogen is converted into helium in the core a "problem" begins to emerge for the star. Helium requires a temperature of over 100 million degrees K to undergo nuclear burning. The star is no where near this temperature and a inner core of "helium ash" begins to grow. Figure 10.3 shows a comparison of the hydrogen and helium content in the core of the sun over a 12 billion year span.

Figure 10.3 Hydrogen and Helium content in the solar core during a 12 billion year span.

Over the next 4 billion years the hydrogen fuel in our Sun's core will be used up so that by the time the sun is 9 billion years old it will have a central core of helium ash at a temperature of approximately 17 million K. SInce the helium ash is too "cold" to undergo fusion the core cannot produce energy and it is no longer able to support the weight of the star above it crushing down. The core starts to contract which increases both the density and the temperature. This is shown in Figure 10.4. Our sun's days are now numbered!

Figure 10.4 Graphing showing how a sun-like star's central temperature and density change over time.

During the first 10 billion years our sun (and stars similar to it) will undergo relatively mild outward changes. As the helium core begins to collapse however noticeable effects begin.

As the helium core collapses the density in the core grows enormously. Figure 10.6 shows the change in both core density and temperature over the next 2 billion years. By the time the sun is 12 billion years old the core density is an incredible 870 0000 g/cm³! When the core reaches densities of this magnitude a new and exotic effect begins.

Paradoxically, as the core is contracting the outer envelope of the star is expanding and cooling. As the sun-like star nears the 12 billion year mark its radius has ballooned to almost 170 times its current size and its surface temperature has dropped to about 3200 K. Table 10.1 shows a few values generated by the stellar model that we used in section 9.3. The age is measured in billions of years and the Luminosity and Radius are expressed in solar units.

Table 10.1 A small portion of output from a 1 solar mass stellar model for the first 12 billion years of a star's history

Example 10.2 Use the applet HR Explorer to plot the position of a sun-like star on the HR diagram during the first 12 billion years of its "life".

Solution: Open the applet and adjust the position on the HR diagram by dragging the mouse. Adjust the temperature and luminosity values to match those appearing in Table 10.1. Plot your results on an HR diagram. Your results should look something like the HR diagram shown on the right. If you do this exercise you will note how rapid the change is in the very last stages of the star's evolution.
	Figure 10.6 A plot of the change in position on the R diagram for a sun-like star over its lifetime.

Electron Degeneracy and the Failure of the Star's "Thermostat"

In sections 9.2 and 9.3 you saw that as a gas heats up it exerts more pressure. In a "normal" star an increase in pressure causes the star to expand and cool until equilibrium (balance) is achieved between the outward force exerted by the gas and the inward crush of gravity. We called this hydrostatic equilibrium and claimed that it operates in stars to control temperature and pressure in way analogous to how the thermostat in your house controls temperature. Something very strange, however, happens when you compress a gas too much. Normally a particle in a gas can collide with anther particle and lose some of its energy in the process. This why in a normal gas the expansion also leads to cooling and means that there is a very direct relationship between pressure and temperature.

Figure 10.7 The rapid increase in both density and temperature that occurs in the last phases of a sun-like star's life.

Inside a star pressure comes from three sources: electrons, protons (and other positively charged ions) and radiation (photons). As a star like our sun ages the pressure provided by electrons becomes increasingly important. BUT - electrons begin to behave "strangely" when you crowd them too closely. When electrons are packed too tightly they lose their ability to exchange energy with each other. This is a strange phenomenon that can only be understood by using the science of quantum mechanics. Quantum Mechanics tells us the "rules" of how particles can exchange energy and tells us that at extreme densities the relationship between pressure and temperature "breaks down". What this means is that the pressure exerted by the electrons no longer increases with temperature and this effect is called electron degeneracy. The central core of the star is now a degenerate gas. Another property of a degenerate gas is that it resists compression. So now the core of star has reached a peculiar state. Its pressure-temperature regulation has broken down and its temperature is rising rapidly. Something dramatic is about to occur!

The Helium Flash

Eventually the core temperature in the sun reaches 100 million degrees K and helium fusion begins. Helium fuses by the following two step procedure to produce carbon:

Two helium nuclei collide and produce the element Beryllium-8. This is an extremely unstable nucleus and normally "falls apart" in less than 10-12 s (a pico-second).
At the extreme densities in the core collisions occur so frequently that some of Beryllium-8 nuclei collide with another Helium nucleus to form Carbon-12 which is stable.

Because three helium nuclei are involved in this process and because a helium nucleus is the same thing as an alpha-particle this process is usually called the triple-alpha process.

The triple-alpha process begins explosively. A degenerate gas is able to conduct heat very effectively and when helium fusion begins the temperature rises rapidly everywhere in the core. The entire helium core begins burning at once for a matter of minutes to hours. A tremendous burst of energy is released and the inner core of the star expands explosively outward. As violent as this event is, however it produces only a minor change in the entire star. The overlying layers of the star absorb and quickly damp out the energy released during the helium flash. The applet shown in Figure 10.7 illustrates this.

After a few hours the core becomes hot enough for the gas to return to a non-degenerate state and the temperature-pressure thermostat operates normally. The star now reaches a new equilibrium state with a very hot core fusing helium into carbon and a surrounding shell of hydrogen fusing into helium. This will become a common motif for the structure of most stars in the later stages of stellar evolution and we will return to this in a later section.

Why Should You Believe This?

Discussions of events occurring billions of years from now, or temperatures of hundreds of millions of degrees or of violent explosions that you can't really see should be met with a healthy dose of skepticism and raise the question "How do we know this?". How can we talk about how a star will change over millions to billions of years when astrophysics, as we know it, is barely 200 years old? It turns out that astronomers can offer quite compelling evidence to support the ideas developed in this chapter and to also explain why we are so confident that our understanding of how stars work is very good.

The evidence for all of this is provided by star clusters. In a future unit we will address the different types of star clusters in detail but for now consider the following two clusters:

The open cluster M67 is shown in Figure 10.9. This is a family of about 500 stars located about 2700 light years away. An important assumption is made when we look at an object like this: These stars all formed at essentially at the same time. If that is the case and because we expect there to be a range in the masses of the stars we should expect to see evolutionary effects if we plot each of these stars on a HR diagram. This is because we know that the rate at which a star evolves depends very strongly on mass. The more massive stars should lie well away from the main-sequence on the HR diagram while the lowest mass stars should still be on the main sequence. Our stellar models allow us to predict where stars of varying masses fall on the R diagram for the cluster. If you position the mouse over the image of M67 its HR diagram (more technically its "colour-magnitude" diagram) will appear.
	Figure 10.9 The open cluster M67 located in the constellation Cancer
The globular cluster M15 is located about 34 000 light years away in the direction of the constellation Pegasus. It is a very different object than M67 but can still be thought of as a family of about 200 thousand stars that orbit our galaxy in a tight ball or globule. Again we assume that the stars are "coeval" or that they formed at essentially the same time. The HR diagram constructed here is from data from a sample of nearly 20 000 stars obtained with the Hubble Space Telescope. Again, roll-over the image to see the HR diagram for M15. In both cases the HR-diagrams are precisely what our models predict.
	Figure 10.10 The globular cluster M15 located in the constellation Pegasus (Image courtesy of The King's University Observatory)

Example 10.3 Use the HR diagram for M67 provide in Figure 10.9 to estimate the "age" of this cluster.

Solution: By inspecting the HR diagram it is evident that stars of spectral type mid to late-F are just beginning to evolve off the main sequence. This is called the "turn-off" point. This suggests that stars of mass M = 1.4 Mo are evolving off the main sequence.This is shown in Figure 10.11. If you use the Main-sequence age calculator you will conclude that M67 is approximately 4.3 billion years old.

Figure 10.11 HR diagram for the open cluster M67 showing the turn-off point at spectral-type F5 - F9.5

Practice

1. The star Procyon (alpha Canis Minoris) has an absolute magnitude of 2.65 and a surface temperature of about 6600 K. Is this star a member of the giant luminosity class? Explain.
2. Explain why giant stars are less dense than main sequence stars.
3. Two stars have identical surface temperatures but one is a supergiant and the other is a dwarf star. How could you tell which is which just by looking at the spectrum?
4. Explain how we can find the age of a star cluster.
5. What is the "Helium-Flash"?
6. True or false - All stars will eventually undergo a Helium Flash.

To understand the processes that lead to the evolution of a main-sequence star into a giant star

Chp 12.2

The Arabic name "Aldebaran" means "the follower" - Aldebaran is seen "following" the Seven-Sisters or Pleiades.

Remember that parallax can be used to determine distance by using the simple relation:
d = 1/p
where p is measured in seconds of arc and d is in parsecs.

Electron degeneracy occurs when electrons are packed too tightly. The "normal" relationship between pressure and temperature no longer holds for a degenerate gas.

Electron degeneracy is not entirely foreign to your life! Metals contain electrons that behave very much like a degenerate gas. You can't compress metals easily and the electrons in metals are very good at conducting heat and electrical energy.

The Helium Flash is the explosive onset of helium fusion that occurs in the degenerate core of a star