The Lives of Stars: Stellar Evolution

So far this semester we have discussed the composition of the Earth, and the other planets in our solar system, and even life itself. Nearly all of the elements, besides hydrogen an helium, that we have encountered were created by stars. How do we know this? When the Universe came into existence, it was almost completely composed of hydrogen and helium--we know this because when we look at the oldest stars in our galaxy, they have almost none of the elements heavier than H or He. All of the other elements were created inside stars. This week, we will find out how stars create heavy elements. Today we want to begin our the discussion about how stars are born, how long they live, and what happens when they "die". This process is called "Stellar Evolution".

We have already talked about how stars generate energy, and how the energy generation in their cores balances gravity to keep stars from shrinking. We have also discussed how the Sun and our solar system came into being. This picture is valid for all other stars. In our galaxy (and other galaxies, we will talk about what a galaxy is soon), there are cold clouds of gas (and when I say cold, I mean cold: 10 to 30 K, -440 oF!) and dust. Inside these clouds there are slightly denser "sub-cloud" regions where gravity is strong enough to begin to collapse this sub-cloud down to form a star. Gravity is relentless, and tries to pull all mass in the Universe into a single point---fortunately there are forces which act to counter gravity so that this never happens.

Our cloud of gas and dust continues to shrink, as it does so its density and temperature continue to rise. Soon, this "proto-star" starts to glow softly in the far infrared. The heat at the center of this cloud is not sufficient yet to balance gravity, nor ignite hydrogen fusion-so the collapse continues. Eventually, the center of the cloud reaches a temperature of about 10 million degrees, and the fusion of hydrogen begins, and a star is born. This process is shown below:

Remember when we discussed the formation of the solar system? As the spherical cloud collapses it flattens out into a disk. In this disk planets form. In some proto-stellar systems, a high speed "jet" of material flows out perpendicular to the disk (where there is less material to block its flow), as shown on the right hand side of the artwork above, and in the actual photograph below:

In this photograph, we are seeing the disk of material edge-on, and it is so thick we cannot even see the young star at the center (the light we do see comes from material located above the disk that reflects a small amount of light from the central protostar). In a disk like this, planets will form, and a new solar system will be born. If you think about it, we can plot the birth of a star on an HR diagram. This is shown in the figure below. At first (#1), the collapsing cloud is very cold, and what little light it emits is far out into the infrared. As it collapses, however, it slowly gets hotter, and hotter. The star is now a big fluffy, warm ball of gas with a temperature of 2,000 K, and a luminosity that is 10X its main sequence luminosity (point #2). The star continues to collapse and get hotter (step #3). Eventually, it begins to fuse hydrogen at its center and is born as a main sequence star (step #4):

As we will find out today, the lifetime of various phases in the life of a star is governed by the mass of the star. This is also true for the process of star formation: high mass stars are formed more quickly than low mass stars. In a more massive sub-cloud, the gravity is stronger, and this forces the cloud to collapse much more quickly than a low mass sub-cloud. For a star with the mass of the Sun, the entire formation process takes about 50 million years. For a star that has a mass of three Suns this process only takes 3 million years. Figure 16.17 details the lifetime of the formation process for stars with different masses:

What is the mass range for stars? It is still uncertain what the highest mass a star can have, and still exist. As best we can tell, there are no stars with masses that are larger than 100X that of the Sun. There is no evidence for stars more massive than this existing anywhere in the Universe. The reason for this is unclear, but it probably has to due with the fact that as a very massive sub-cloud collapses, it might spin so rapidly that it breaks-up into two massive stars instead of a single one with twice that mass. We also know that very massive stars cannot generate enough energy in their cores in a stable way so that they can balance gravity. Such stars might form, but then blow themselves apart before reaching the main sequence.

On the other end of the scale, we have very low mass objects. There is a firm limit to the definition of what a star actually is: a star must be large enough to fuse hydrogen at its core. The smallest mass a true star can have is 0.08 solar masses. These are small objects, as this mass corresponds to 80X that of Jupiter. Objects with smaller masses than this form, but they never are able to fuse hydrogen in their cores, and thus can only shine by the energy generated by gravitational pressure (which causes them to shrink, get hot, and then slowly cool). These objects are called "brown dwarfs", and occupy a mass range between that of large (Jovian) planets, and true stars.

Because they do not fuse hydrogen, brown dwarfs do not emit very much light, thus they are extremely difficult to find, even if close by! The first true brown dwarf was not discovered until 1995. Once we knew what to look for, and several powerful all-sky photometric surveys were established, many more of these objects were found. We now have found many hundreds of these dim objects. Some of them are only 10X the mass of Jupiter, and have temperatures as low as 700 K! Such objects emit most of their luminosity in the infrared, and emit less than 1/100,000 the luminosity of the Sun! Because they have only recently been discovered, a large effort is currently underway to make sure we understand these curious objects.

The Life of a Low Mass Star

After the collapse of the proto-cloud that forms a low-mass star like the Sun (and we consider stars with masses of less than 2 solar masses to be "low mass stars"), what is the life of the Sun going to be like, and how long will the Sun be a main sequence star? The Sun fuses about 600 million tons of hydrogen into helium every second of its main sequence life. Let's look at this a little more closely. 600 million tons per second is the same as 6 x 1011 kilograms. Let's compare this to the mass of the Sun: Msun = 2 X 1030 kg. How long can the Sun keep this up? Well, we can guess by simply dividing the rate of hydrogen conversion into the mass of the Sun:

Msun/(mass fusion rate) = 2 X 1030/6 x 1011 = 3.33 X 1018 seconds = 100 billion years.

This is a large number, and is in fact 10X longer than the expected main sequence life time of the Sun. Why is this? Well, first off, the Sun is only 75% hydrogen, so at best, fusing every hydrogen atom to helium would supply energy for 75 billion years. The main problem with this estimate, however, is that only the hydrogen near the core of the Sun can actually take part in the fusion process--those regions outside the core (the radiative and convective zones) where it is not hot enough to fuse hydrogen, cannot supply fresh hydrogen to the core (remember that the energy generation in the core exerts an outwards pressure, so the low density material in the radiative zone does not move inwards). There just is no effective mixing process to supply the core with material from outside the core. Thus, only about 20% of the mass of the Sun can be involved with generating energy during its main sequence lifetime. As the core becomes "polluted" with helium, there are fewer protons around to ram into each other, so as the Sun turns its hydrogen into helium, it becomes harder and harder for hydrogen atoms to find each other, and thus the energy production rate begins to drop well before there is no hydrogen left. Therefore, the real liftime of the Sun is about 10 billion years. Note that because the Sun is already about 4.5 billion years old, it is about halfway through its main sequence life!

What happens when the core of the Sun runs out of hydrogen to fuse? If it is no longer able to generate energy through hydrogen fusion because it has exhausted its supply of hydrogen, the core of the Sun quickly stops generating energy. As we have discussed, the generation of energy in the core of the Sun and other stars is what keeps gravity at bay. As soon as the energy generation ceases, gravity takes over again--gravity always wins in the end. So, as soon as the hydrogen fusion stops, the core of the star begins to collapse. The core now is almost pure helium, so the density is higher, and the pressure from gravity makes this core of helium very hot. Around the collapsing core is still an atmosphere that is rich in hydrogen (remember that only about 20% of the Sun's mass was utilized during its main sequence lifetime). The density and temperature close to the collapsed core of helium is now so high that a shell, or envelope, of hydrogen starts to burn through fusion. The area/volume of this shell is actually larger than the old hydrogen burning core, and the temperatures are so high that hydrogen is now fused to helium at a much more rapid rate than before!

Now the energy generation rate is higher than when it was on the main sequence---it now exerts a larger pressure outwards than it did previously, and the star expands: it becomes a red giant. The structure of the star during this phase is shown in Figure 17.4 (note: this figure compares the relative sizes of the main sequence Sun and a subgiant---the eventual red giant is MUCH bigger):

The expansion process for stars like the Sun is relatively slow, as the core does not collapse in one big event--it slowly shrinks. Thus, stars like the Sun slowly get larger and more luminous as the core shrinks, and the hydrogen shell burning rate increases. A star that is expanding off of the main sequence is called a "sub-giant", a star that has a radius and luminosity between that of a main sequence star and a giant star. The entire process takes about 1 billion years for the Sun to become a red giant. We can plot this phase of the Sun's evolution in an HR diagram, such as figure 17.3:

It is during the expansion to a red giant when life on Earth will end. As the luminosity of the Sun grows, it will eventually get so hot on Earth that our oceans will boil, and our atmosphere will be removed. To survive, the distant descendants of humans (if there are any) will have to move elsewhere. For a brief time, the moons of the Jovian planets might become comfortable abodes for life---but events soon quicken, and our descendants won't be spending too much time there.

As a red giant expands to its very large size, the gravity at the photosphere of the red giant becomes very weak. So weak, in fact, that much material in the photosphere can escape from the star. This process is similar to the solar wind--in the case of the solar wind, only the highest speed (hottest) particles can escape from the Sun's gravity. For a red giant, the gravity is so weak that an enormous solar wind develops. In fact, a red giant can lose as much as half of its atmosphere through this wind! We call this the "red giant mass loss phase". Meanwhile, the pressure in the core of the red giant increases as more helium is added to the non-fusing core from the hydrogen fusing shell. This added pressure causes the core to get hotter, and hotter. Eventually, the temperature reaches 100 million degrees. At this high temperature, helium can be "burned". What happens is that three helium nuclei can collide to form carbon (carbon has an atomic mass of 12, while helium has an atomic mass of four, 3 X 4 = 12). The ignition of helium is like a little explosion---it happens very quickly, and this phase is sometimes called the "helium flash" (as noted in Figure 17.6):

Helium fusion:

Due to the rapid burning (fusing) of helium, this phase is short-lived, probably only a million years at most. Oddly, now the total luminosity of the star goes down, and the star becomes smaller and hotter. What is happening is that the energy generation rate is now lower than when it was a red giant, thus it shrinks in total size, and the smaller, hotter star gradually moves to the lower left in the HR diagram (as shown above). As you can guess, the star cannot fuse helium into carbon forever, there is only a limited supply. The core eventually becomes nearly pure carbon, and begins to shrink (as it no longer is generating much energy as the helium gets used-up). This of course, makes the core become hotter again--so hot that the star now starts fusing hydrogen and helium in shells around the core. The luminosity now skyrockets, as does the size of the star, and it evolves back into an even larger red giant than before. At this stage, the Earth will be reduced to a hot cinder (if it isn't completely obliterated), as the photosphere of the red giant Sun reaches all the way out to the Earth's orbit (or even further!):

Now the gravitational pressure is so weak, and there is so much energy being generated at the core, that the entire outer atmosphere of the star is shed. This process is shown in Figure 17.8:

As the atmosphere expands outwards, the extremely hot central core now becomes visible. The outer parts of the core of this red giant are close to 1 million degrees, and this hot core now heats the low density, expanding atmosphere to temperatures where it now glows. This phase is called the planetary nebula phase, and only lasts for a few tens of thousands of years. Here are some images of actual planetary nebulae (or see Fig. 17.7):

Planetary nebulae are both beautiful and complex. Most of the material seems to flow out along the poles of the star, creating the cylindrical shapes of many planetary nebulae. If you look at a planetary nebula along the axis of the cylinder, it can look nearly round.

Eventually, the red giant core runs out of fuel, and it collapses to a very small size. Because of this collapse, and from all of the heating during the red giant phase, it is very hot. During this phase it is called a white dwarf--an object about 50% larger than the Earth, but containing about 60% of the mass of the Sun! The density of a white dwarf is enormous, we have packed 1.2 x 1030 kilograms into a sphere that has a radius of 8,000 km! As we have often done, lets examine a white dwarf's density: Mass/Volume. Changing kilograms to grams (multiply by 1,000) and km to cm (multiply by 105), we get that the density of a white dwarf is 1.2 x 1033gm/6.4 x 1027 cm3 = 186,500 gm/cm3!!!!!! One cubic centimeter of white dwarf material has a mass of 186 kg (one cubic inch would weigh 3,000 lbs on the Earth)! Here is a linear version of the evolution of the Sun:

A white dwarf no longer has an energy source---why doesn't it keep collapsing forever? What force can act to stop gravity? This is more difficult to explain---the force is something called "degeneracy pressure". It is briefly discussed on page 484.

To explain degeneracy pressure adequately requires an understanding of quantum mechanics. The analogy the book uses is an auditorium. A normal star is like an enormous auditorium containing hundreds of seats, but few patrons. The auditorium isn't crowded, because there are plenty of seats available. As you try to pack more, and more people into the auditorium it soon runs out of seats. When every seat is taken, there is no more room for additional people. This happens at a quantum mechanical level. In this case, the people are replaced by electrons, and the seats by "quantum mechanical states". Electrons do not like to get very close to each other, as unlike protons and neutrons, there is no "strong force" to stick them together. Thus, as you squeeze mass to higher, and higher densities, the electrons eventually fill up all of the allowed quantum mechanical states that are available---they refuse to sit on top of each other. When this happens we term the matter to be in a "degenerate state". There are no more places for electrons to exist without sitting on top of each other--and they will refuse to sit on top of each other until you add lots, and lots of additional pressure! We say that a white dwarf is "electron degenerate".

A star like the Sun ends its life as a white dwarf, slowly cooling with time. Eventually, the white dwarf will cool to the point where it is no longer emitting any light, and we will have a burnt-out core of a star that floats through space that emits no light. In the next class, we will examine the life and evolution of a high-mass star. Their lives are even more eventful, but much shorter.