Transcript from Epic of Evolution: Life, the Earth and the Cosmos (BEP 210A)
February 18, 2000 - Lecture by Claude Bernard
Okay, let’s get going. Last time, I described the chain of reactions that produce the energy of a
star like the sun. The net effect of these reactions is to convert four protons into one 4He
nucleus. The process includes a Weak Interaction, which is why it is slow. All normal stars (I’ll
say what I mean by normal stars in a bit) do the same thing -- convert protons, or hydrogen
(protons are hydrogen nuclei after all), into helium. This is known as “hydrogen burning.”
Burning is not the greatest term because you normally think of burning as a chemical process
that combines molecules with oxygen. The process in stars has nothing to do with that chemical
kind of burning. It is a nuclear process that changes one nucleus into another and gives out a
tremendous amount of energy.
If you compare the mass of a helium nucleus with the mass of four protons, the helium nucleus
has slightly less mass than the four protons that made it up. How could it have less mass?
Because some of the mass of the protons is converted into the energy that is released. That
energy goes off in photons and particles (positrons, neutrinos). It heats up the surroundings.
That’s where the energy that makes the sun shine is coming from. It’s described by the same
law, E=mc2, that we’ve talked about before. Because the speed of light (c) is so big, it doesn’t
take much difference in mass to produce a tremendous amount of energy.
Now the actual amount of energy being produced by the sun is enormous. Just to give you some
feeling, the sun produces about four times 1026 watts (that’s a 4 with 26 zeroes after it). It’d take
me a while to even work that out in trillion trillion billions or whatever (10,000 trillion trillions).
It’s an enormous amount of power .
[Ursula: Watts per day? Year? Hour?]
Watts already means energy per second: a watt is one joule per second. A joule is a certain
amount of energy (1 joule is about 1/4000 of a Calorie). So the sun is like a 4 times 1026 watt
light bulb up there, lighting the Earth. It’s like huge floodlight. (It’s not a spotlight because the
light is not directed specially towards us; it’s going in all directions.) The energy produced by
the sun is an enormous amount (4 times 1026 watts = 1023 Calories of energy per second). But if
you look at it in another way, it’s actually not much energy at all. The reason it’s such a big
number is because the sun has so much mass. Let’s compare it to the mass of the sun. The sun
has a mass of 2 times 1030 (a 2 with 30 zeroes) kilograms. In fact it’s such a standard number we
often give it a special symbol. Astronomers use a circle with a dot in it to indicate the sun. So
MO means the mass of the sun. [Note, the circle after the M should have a dot in the center of it,
but I am unable to make that in the web version of these notes.] When we talk about other stars
we’ll talk about stars that are twice the mass of the sun (2MO), or 8 times the mass of the sun
(8MO), or 11 times (11 MO), or half the mass of the sun (0.5 MO). So MO is just a nice unit to
measure things in. Yeah?
[Student: How do we go about determining mass of the sun?]
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Ah, good question. Well, it’s because we know how gravity acts. What you need to do to know
the mass of the sun is to find out how much gravitational force a given mass has. And the way
that’s done is by taking two known masses like two lead balls and putting them very close
together and seeing how much they attract each other. Once you know how much two lead balls
attract each other then you know how much mass produces how much gravitational force. The
next thing you have to know is how much force the sun exerts on the Earth to make Earth go in
its orbit (and not fly out in a straight line into space). You can calculate that. That’s what
Newton did. You always hear this story about Newton (which probably didn’t happen): He was
sitting under an apple tree, and an apple hit him on the head and gave him his great insight. In
any case, Newton realized that the force (gravity) that makes things (like the apple) fall to the
Earth is also the type of force which makes the Earth go around the sun, and the moon go around
the Earth. Once you realize that all those forces are gravitational --- and obey the same laws --then measuring the force between two lead balls and knowing the radius of the Earth’s orbit and
the time it takes to go around the sun (a year) allow you to compute the mass of the sun, to
“weigh” the sun. And by looking at the moon’s orbit you can “weigh” the Earth. Okay, so that’s
how we know these things. That’s a good question. You obviously can’t get up there with a
little scale and put the sun on the scale.
So the sun makes a lot of energy but the energy for each kilogram of the sun actually isn’t that
much. If you divide these two numbers, the sun makes about .0002 watts per kilogram. Every
kilogram of the sun produces about .0002 watts. So each kilogram of the sun (something about
this size [the size of a softball]) is a pretty dim bulb. It’s just because there’s so many kilograms
that the sun’s bright. And in fact, you could compare this amount of energy production by the
mass in the sun with the amount of energy produced by a living organism, let’s say a person. A
human produces 10,000 times more energy per kilogram than the sun. So every kilogram of us
is “burning” up fuel (food) and using that to keep us warm and to give us energy to move around.
Human metabolism produces about 10,000 times more energy per kilogram than the sun. On the
other hand, the sun is so enormous that even its small amount of energy per kilogram makes it
very bright and very, very hot.
Why would that be? Why does the sun produce so much less energy per kilogram than humans
do? Well, it’s due to something we’ve discussed before. We produce our energy by chemical
reactions. We burn food, using enzymes to catalyze the chemical reactions (to use some of
Ursula’s terms). So chemical forces are involved, and chemical forces are really electromagnetic
forces. The sun needs the Weak Force to make the nuclear reactions work, and it’s very slow
because the Weak Force is much, much weaker than the electromagnetic force. So the sun with
its Weak Process produces energy much less efficiently in this sense (energy per kilogram) than
humans do using chemistry, which is a manifestation of the electromagnetic force. Any
questions on that?
Okay, so we’ve got the sun making energy. As I said last time, the sun or any star requires all
four of the forces to shine. You need gravity to pull the gas together and condense it enough so
the center gets hot enough to allow these processes to take place. Once they’re hot enough you
have combining of nuclei because of the Strong Force, which allows you to get energy out.
There’s a barrier to combining the nuclei due to the electromagnetic force. That’s why you need
it to be hot in the first place. That’s why gravity is necessary. Clouds of gas that have not
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condensed are not stars. They don’t emit energy in this way because they’re not hot enough to
overcome the electromagnetic barrier. The energy that comes out is primarily energy due to the
Strong Force but you also need a Weak Process also to change protons into neutrons. So all of
the forces are important. The fact that it depends on the Weak Process is good for us because it’s
what makes the sun burn slowly, so there’s plenty of time for the Earth to have evolved and for
life to have evolved.
Now, let me back up a second. The heat, due to the energy produced inside the sun, creates
pressure, which pushes back against the gravity. So the sun is a very stable object, where the
heat produced by the nuclear processes counteracts the pull in by gravity. Just as Michael
described in the case of the Earth, there is a balance between gravity and heat in the sun. The
heat produces pressure, and the pressure is actually of two forms. One is just the motion of the
protons, neutrons, nuclei and electrons (i.e., the motion of the particles). In addition there’s
some pressure due to all the photons (the light and other forms of electromagnetic radiation)
emitted in these processes. The photons also push and help hold the sun up. It’s less than half
the total pressure. Most of the pressure is due to the motion of the particles, not the light. But
the light contributes, and it exerts a significant pressure on the particles in the sun, helping to
counteract gravity.
Now because of the heat, the electrons have been boiled off the atoms once again. It’s similar to
the early part of the Big Bang. No atoms can exist inside the sun; there are just protons, nuclei,
and electrons. The plus and minus charges are separated. So the photons bounce off them a lot,
just as they did in the very early universe before decoupling. And so the photons contribute to
the pressure. In fact, a photon bounces off the separate electrons, protons and nuclei so much
that a photon emitted in the center in the sun (by the energy-producing processes) takes about
50,000 years to get out. And remember it’s moving at the speed of light. But it keeps hitting
into electrons or protons and being absorbed and re-emitted so many times that it takes a really
long time just to get out to the surface. It’s like trying to get to the exit in a huge crowd of
people, with everybody pushing and shoving: You barely make any progress. Of course once
the photons get out to the surface they take only 8 minutes to get all the way to us. Yes, sir?
[Student: Where do like solar winds and solar dust come from?]
Well, this pressure of photons coming out can push particles from near the sun’s surface out into
space, and that’s known as the solar wind. Some electrons and protons (and helium nuclei) are
pushed out by the photons, and they stream out away from the sun.
[Student: And that’s caused by this reaction?]
That’s right. The energy of the sun is coming from this reaction (as well as some very similar
ones that play a minor role). And it’s the energy produced by the sun that causes the photons to
be emitted that push out the solar wind.
Now, stars other than the sun work in basically the same way, but there’s one important
difference, which just depends on how big the star is, how much mass it has. If the star is a lot
bigger than the sun, if it weighs a lot more, it’s going to have much more pressure pushing things
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in due to gravity. Therefore the temperature in the middle is going to be a lot higher. And if the
temperature is a lot higher the nuclear processes will take place a lot more rapidly. It’ll be easier
to get over the Coulomb barrier. Remember that the Coulomb barrier is due to the
electromagnetic repulsion between positive charges. That makes it hard to combine protons or
simple nuclei into more complicated nuclei. But if you have a higher temperature it’s easier to
get over the barrier and the processes will take place much more quickly. So big stars are much
hotter than the sun and they burn more rapidly. Even though they’re bigger, the increased
temperature makes them burn their fuel so much more rapidly that they actually live for less time
than the sun. The bigger the star the shorter the amount of time it lives. It’s sort of counterintuitive: a bigger star has more fuel but it burns its fuel so much faster that it lives for less time.
(It’s sort of like dogs. Big dogs have much shorter lives than small dogs. As an owner of a big
dog that’s important to me.) What?
[Ursula: Big humans are also less likely to live long. If you go to a retirement community it’s
mostly little old men...]
…considering the male population...
[Ursula: Yeah.]
And even more little old women. That’s interesting.
So big stars live for a lot shorter time than the sun. A star of the mass of the sun it will live about
10 billion years (1010 years). A star 10 times the mass of the sun lives a mere 100 million years
(108 years), 100 times less. A star of mass 25 times the mass of the sun lives only 7 million
years. So it’s an amazing difference. Big stars live a short time. Since stars started to form
maybe a billion years or 2 billion years after the Big Bang, there’s been plenty of time for lots of
generations of big stars. A really big star only lives a few million years, so in the 12 or 14 billion
years since stars first formed there have been plenty of big stars forming, burning up, and --- as
we’ll see --- exploding when they’re finished. So then they send their material back out into
space and that material can recondense into new stars. I will explain in my next set of lectures
how these big stars make heavy elements and then explode. They produce the heavy elements
and send them out where they can recondense into new stars. That’s where all our heavy
elements came.
It also goes the other way: a star of one-half the mass of the sun would live 50 billion years (5
times 1010 years). That means that stars that are significantly smaller than the sun have had no
chance to die since the Big Bang. Any star that was formed early on that was half the mass of
the sun is still happily shining away. And ones that are the mass of the sun live about 10 billion
years, so if they were formed very early they have already died. But most of them are still also
happily shining away. Austin?
[Student: Is the sun a medium sized star compared to other stars?]
Yeah, a lot of stars are in the range of one-half to two solar masses. I don’t actually remember
the numbers but the sun is a pretty darn average kind of star. If you actually calculated the
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average, it wouldn’t be exactly the mass of the sun, but it’s in that range. The sun is pretty
ordinary.
[Student: Okay, I was trying to kind of envision it. When the stars are burning out it just gets
darker and darker and then it just explodes?]
Ah, that’s a good question. Well, I haven’t yet explained why it would explode. It’s a long story
and I see I’m not going to get there in this set of lectures; it will have to be the next set. There is
a reason and you will understand it, but I just haven’t gotten there yet. It’s not like a star just
winks out and gets all quiet and cold and then suddenly explodes.
Now there’s a minimum mass for a star and a maximum mass for a star. The minimum is really
easy to see. If the glob of gas doesn’t have enough mass, when it compresses by gravity it’s
never going to get hot enough in the center for the nuclear reactions to start. Remember, these
are thermonuclear reactions; it has to be hot to get over the barrier. If it’s not hot enough, the
reactions won’t occur and it won’t emit light and be a star. It might reflect light like Jupiter.
Jupiter is similar to a star. It has a lot of hydrogen and helium gas. It’s highly compressed
because of gravity, but it’s just not compressed enough to be hot enough to turn on and emit light
of its own. The minimum mass ---- this is something that physicists have to calculate --- is 0.08
times the mass of the sun. About a 12th or a 13th of the mass of the sun is the minimum mass
that a star can have, because if it’s lighter than that it won’t get hot enough in the middle to turn
on.
There’s also a maximum mass for a star. The reason there is a maximum is a little bit subtle.
When a star gets too big, it gets so hot in the middle that it emits so much light that the pressure
of the light gets too great. It blows itself apart. And it’s related to the fact that no stars and
galaxies could form before the time of matter domination. Matter domination was the time when
the energy that was in matter got to be bigger than the energy in photons. That’s the first time
you can start getting condensation of matter into galaxies and stars. Because before that the
photons bouncing around create so much pressure that they don’t allow things to condense. And
the same thing happens if the star is too big. It gets too hot and you get too many photons and
the photons won’t allow the star to condense. And they just blow it apart. So the maximum
mass is about 100 times the mass of the sun.
Now I don’t envision asking you questions on the exam, “What is the maximum mass of a star,
how many times the mass of the sun?” I do envision asking you questions like, “What’s the role
of electromagnetic and Strong Forces in the nuclear reactions that power a star?” Very quick
answer: “Strong Forces trying to pull things together; electromagnetic creating the barrier.” The
issues that I would put on an exam are qualitative, but are more important than memorizing some
numbers. As usual I’ll put some study questions on the Web to help you see what I think is
important.
Now let’s look at some slides. I have a lot of nice, pretty pictures. We may not look at all of
them for that long, but some of them are really neat and they tell you a lot. [slide 1.] On the left
is the view from a ground-based telescope; on the right is a Hubble Space Telescope photograph.
I actually meant to show this on Wednesday or Monday, but I forgot. It’s two colliding galaxies.
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You can see their spiral shapes. This is like the picture in the movie from Monday (2/14), or the
simulation of galaxies colliding on that web site I recommended. By the way, that site is really
neat --- look at it if you can. In that simulation on the web, you can see spiral galaxies collide
with each other and go through each other and come back and smash into a big mush (an
elliptical galaxy). The real collision actually takes billions of years; the simulation is highly
speeded up. This slide is an example of two colliding galaxies. And it also is relevant for us
today because when galaxies collide, the gas from one galaxy is pushed together with the gas of
the other and makes highly compressed regions. The gas in those regions will condense into
many stars. In this slide you can see a lot of star formation where gas and dust from one galaxy is
meeting gas and dust from another.
[slide 2.] This is a small galaxy that’s actually in our local group with us and Andromeda and a
few other little ones. It’s called the Small Magellanic Cloud. It’s about 200,000 light-years
away. In the middle, you can see a lot of bright points. Those are new, bright, hot stars. They’re
emitting enough energy to light up the gas around them. In fact, this whole red region is gas that
is being heated up by these bright, big stars. And the whole thing glows with this nice red glow.
[slide 3.] This is another galaxy. On the left is a view from the Mt. Palomar telescope. And on
the right is a close-up by the Hubble, which shows a region of gas that is collapsing into stars.
The stars are big --- bright enough to light up the gas. So it’s a lot like the other one, but I
included it because it’s a pretty picture. Some of these stars are as big as 60 times the mass of
the sun. So they’re quite hot and quite young, because a star that’s 60 times the mass of the sun
lives a very short time --- probably less than a million years. So these were formed fairly
recently.
[slide 4.] This is yet another galaxy. You can see some very bright regions where big new stars
have been formed.
[slide 5.] This was in Time and Newsweek magazines. These are regions of cold, dark gas,
which are condensing at the points into new stars. The gas forms this kind of shape because the
light from bright new stars (out of the picture, at the top) is blowing the gas towards the bottom
of the picture. Only near places where stars are beginning to form --- at the little fingertips at the
top edges of the pillars --- is the gas being held by the gravity of the forming stars. The rest is
being blown downward. They are like the erosion pillars that you might see in Utah, where
some hard rocks at the top of the pillars protect them from the erosion that has carried away the
stuff between pillars. And here what correspond to the hard rocks are these stars forming at the
fingers at the top of the pillars. Those proto-stars are big enough to hold some gas in the
neighborhood and protect the gas underneath them.
[slide 6.] The next two slides are two more views of the same thing. This is a close-up of one of
the pillars. And then the next one [slide 7] is a still closer view.
[Ursula: So each one of those little fingers is making a star?]
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Right, wherever you have a little projection. You can see a couple of the proto-stars pretty well.
In some cases the dark finger has a little round tip at the end of it. That round tip is a star
beginning to form. Any questions on the slides?
Up to now I’ve described the main process of energy production in a star. But eventually all the
raw material for this process will be used up. When all the protons have been turned into helium,
what is going to happen? Well, once it’s used up the protons, it can’t make any more heat this
way. Therefore it can’t make the pressure necessary to oppose the gravitational force, which is
squeezing everything together. So after the protons are used up, the pressure in the middle of the
star initially decreases, and so the whole thing collapses to a much smaller size. And in the
collapsing it heats up again --- just like the initial collapse heated up the gas to start the star
burning hydrogen. In fact, it now gets even hotter than it was before, since it’s much more
compressed than it was before. So it’s almost counter-intuitive: By using up the fuel it starts to
get cooler and have less pressure in the center, but then, because it collapses to a much smaller
size than before, and it ends up more dense, and hotter.
When it gets hot enough in the center, a new process can start. The new process is very similar
to the old one. Recall that the old process, called “hydrogen burning,” resulted in four protons
forming a helium nucleus. It went through various intermediate stages and the same will be true
of the new process, and I’ll say some more about the stages of the new process in my next
lecture. The new process is called “helium burning.” Three helium nuclei come together and
become a carbon nucleus, and release energy in the process. The helium nucleus involved here
is 4He, which has two protons and two neutrons, and which is the end result of the previous stage
of burning. The carbon nucleus produced is 12C, made out of 6 protons and 6 neutrons. As in
the previous stage, energy is released because the mass of the product is less than the mass of the
raw materials: One carbon nucleus has slightly less than three times the mass of a helium
nucleus. So there’s some mass left over, which is turned into energy (E=mc2 again).
Helium burning requires a higher temperature than hydrogen burning. That’s why it doesn’t
occur at the same time as hydrogen burning. Hydrogen burning will start when the central
temperature of the star gets to 10 million degrees. Helium burning only will occur if the
temperature is 100 million degrees, i.e., 10 times hotter. So while hydrogen burning is taking
place helium burning can’t occur at all. In the former process, you just take protons and make
helium, and the helium just sits there. Only when hydrogen burning is completed and the core
shrinks and gets much hotter can the helium can combine to make carbon.
Why does helium burning need a higher temperature? We have the basics to understand it.
Helium burning is basically a two-step process. First two helium nuclei combine (to make
beryllium-8: 8Be) and then 8Be combines with the third helium nucleus to make a carbon
nucleus. In each of those steps, you’re combining things that have more positive charge than
single protons. A helium nucleus has two positive charges. So the force of electromagnetic
repulsion between two helium nuclei is much greater [four times greater] than it is between two
protons. Therefore the Coulomb barrier between two helium nuclei is greater than the barrier
between two protons. And the Coulomb barrier between a helium nucleus and a beryllium
nucleus is even greater. So it takes more initial energy, and hence higher temperature, for helium
burning than for hydrogen burning.
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So helium burning occurs only when the hydrogen burning is finished, and the core collapses
further and heats up to 100 million degrees. Once helium burning starts it gives off a tremendous
amount of energy. Again, you have to put in energy to get out energy. Here we’re starting with
more energy, and you also get out a lot more. Chemical reactions often behave in a similar way:
if you want to burn something, you have to heat it up first (with a match, say) --- it doesn’t just
start to burn by itself. Once it starts burning, though, it emits lots of energy. In other words,
chemical reactions have barriers that you have to overcome to make the reaction go. Similarly,
the nuclear reactions in a star need to be ignited before they will proceed. You have to overcome
the barriers --- and in the case of helium burning that requires a temperature of 100 million
degrees --- but once it goes it emits an enormous amount of energy.
So with helium burning you have a small, very hot core of the star. And because the core gets so
hot --- shooting out huge number of high-energy photons and hot particles --- it actually pushes
the outer layers of the star outward. The outer layers expand to an enormous size. So again it’s
sort of counter-intuitive: The process starts with collapse of the core. As the core collapses it
gets a lot hotter than before. Then, once helium burning starts, the outer layers get blown out to
enormous size. And as the outer layers expand they begin to cool. After they cool, the photons
they emit have less energy than before, in other words, lower frequency. And lower energy
photons have lower frequency, which means redder. So you’ve got these huge outer layers
emitting relatively low energy (redder) photons, and you’ve got a small but very hot core
emitting very high-energy stuff (the core is getting its energy from helium burning). Since the
outer layers are enormous and red, such a star is called a Red Giant.
Normally stars will go through a Red Giant phase after they use up their protons in the center.
There’s one Red Giant that you may have seen with your naked eyes. The brightest star in the
constellation Orion is called Betelgeuse and that star is a Red Giant. And here’s a picture of it.
[slide 8.]
[Student: The brightest star in Orion is called...?]
“Betelgeuse.” Betelgeuse is the one in the upper left corner of the constellation. Orion is
supposed to be the hunter, and Betelgeuse is his left shoulder (he’s facing away from us).
I had to look up the pronunciation: BEE-tuhl-jooz. The dictionary said it came from an Arabic
term, but then it didn’t say what the Arabic term was. [I’ve since found it in another dictionary.
The Arabic name means “shoulder of the giant.”] Here is a close-up of Betelgeuse. [slide 9.]
You can see a comparison of the size of the star with the sizes of the Earth’s and Jupiter’s orbits
around the sun. So Betelgeuse is bigger than the distance from Jupiter to our sun.
[slide 10.] I’ll probably show this one again; it’s a little bit ahead of my story. This was a Red
Giant. Look at the small white dot a little off center in the blue region that looks like the CBS
eye. That was the central core of a Red Giant. After the helium burning is finished, the central
core becomes what’s called a “White Dwarf.” I haven’t mentioned that yet. When the helium
burning is over you end up with a huge cloud formed from the outer layers, and the core
collapses further and can become a White Dwarf, a very dense object. In this slide the cloud has
a double-lobed shape, and it’s called the Hourglass Nebula. (Nebula is another word for cloud.)
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Okay, maybe I’ll stop now because the next slide is just about White Dwarves, and I haven’t
explained them yet.
[Ursula: Am I right that when the sun finishes it’s going to become a Red Giant?]
Yes, absolutely. Maybe I’ll say a few additional things while you’re filling out your Friday
questionnaires. The sun is going to become a Red Giant more or less like Betelgeuse. I think it
will not be quite as big, because Betelgeuse was a bigger star to begin with. Even so, the Earth
will be inside the sun when the sun becomes a Red Giant. The sun will be bigger than the
Earth’s orbit, so Earth as we know it will not exist past that time. And that should occur in about
5 billion years when the sun uses up its hydrogen and starts burning helium. But not to worry.
Well before that Andromeda is going to hit us so all bets are off. The gravity of a star from the
Andromeda galaxy might throw us someplace else. You can always hope.
[end of lecture]
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