This is an introductory astronomy survey class that covers our understanding of the physical universe and its major constituents, including planetary systems, stars, galaxies, black holes, quasars, larger structures, and the universe as a whole.
Energy Generation in Stars
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The Evolving Universe
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Week 4
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S. George DjorgovskiProfessor
Astronomy
All right, let's now talk how stars make energy.
We do it through fusion of lighter elements into heavier.
That's mostly hydrogen to helium.
This cartoon is actually what people aspire to do in a lab.
To do controlled thermonuclear fusion in reactors like Tocamax or with lasers.
We're still a little far away from that.
But stars know how to do it.
And the ultimate physical reason why stars can shine
is that nuclei of atoms have binding energy,
because there is a strong force that binds protons and neutrons together.
And the difference between all those particles separately and
then bound together in a nucleus corresponds
to energy that can be taken away, if you can make nuclei.
So if you go from 4 hydrogens into helium, you
just add up the mass and you find out that there is a little bit of an excess and
so that corresponds to the change of energy of 27,
almost 28 mega electron volts per one of these fusions,
or about 7 mega electron volts per nucleon.
And since the rest mass of a proton is a little shy of one giga electron volt,
that means that 0.7% of the rest mass
is converted into energy during fusion of hydrogen into helium, Mc squared.
So how does that happen?
The dominant process is the chain
of nuclear reactions called the proton-proton chain.
And it begins indeed with two protons, which get captured together and
then one of them does beta decay, releasing
charge in the form of a positron, and there is anti-neutrino that comes out.
I'm sorry, neutrino comes out.
And then that positron then can annihilate what electron that was left
over from these hydrogens and create gamma rays,
which again are downgraded in energy to something different.
So that way you get deuterium.
Then, deuterium can accrete another hydrogen,
another proton, and become helium three isotope, and missing one neutron.
Similar thing happens here, some energy has been released,
now charge is conserved so there no neutrino emission.
And then turns out that 2 helium 3 nuclei can fuse much more easily
than hydrogen and helium 3.
That makes the regular helium 4 release its two
extra protons that can participate in the nuclear fusion again.
And so that's sort of the basic fuse step reaction.
People who try to do this in thermonuclear reactors on planet Earth
actually bypass a lot of the hardest initial steps and
try to fuse deuterium and tritium because that still be the easiest part.
So in reality this is a little more complicated, and
you don't have to remember this, but
I have to show it to show you what is the real chain of reactions.
Sometimes other like nuclei, like lithium or beryllium, play the role catalyzers,
just like chemical reactions can be catalyzed by some additional compound, so
it can happen in thermonuclear reactions.
So you can fuse hydrogen to helium,
then you can fuse helium into heavier stuff like carbon and
oxygen and so on and so forth, and the question is how far does this go?
Well the answer is, it will go as high as it's profitable to do in terms of energy.
So it turns out, if you plot the binding energy per unit nuclei
for different nuclei, the number increases all the way up to iron,
iron 56, and then starts dropping.
That means, fusing things up to iron generates energy.
Beyond that you actually have to put in energy to generate heavier elements.
So what happens in stars, they create chemical elements all the way up iron.
And where do the heavier ones come from?
They come from supernova explosions.
That's the extra energy that you need in order to fuse
things all the way up to uranium.
And so this is why nuclear
fission is done with uranium and plutonium and heaviest elements you can find.
Whereas nuclear fusion is most efficiently done with light nuclei.
But even for light nuclei this was not an easy thing to do.
And that is because protons are all charged positive.
Electrons are irrelevant here.
So if you have a nucleus could be a single proton, could be two,
in helium it doesn't matter.
Another proton's coming in.
There is an electrostatic repulsive force.
And if you were just to look at electrostatic repulsive force,
there would be sort of hyperbola going up to infinity particles at zero size.
And most particles cannot come close enough for
the nuclear forces that can grab them in and then they're purely attractive.
So once you get past that barrier, it's fine.
So if classical physics were working all the way down
to the nuclear world, this will never happen.
But there is a phenomenon of quantum tunneling that this is
intrinsic to quantum physics.
That sometimes particle can go through some barrier that normally wouldn't go,
that can tunnel through walls, so to speak.
This is really a tiny wall, and
three is probability it can be computed, how to do this.
And it's highest for the highest energy particles.
And so this very specifically quantum effect is what enables occasional
proton to actually pass through this electrostatic barrier and
fuse with whatever's inside the nucleus.
Now, that led to the concept of so-called Gamow Peak.
The theory of thermonuclear reactions in stars was worked out in 1940s, more or
less, by Hans Bethe, George Gamow, and their collaborators.
And Gamow peak comes from competition of two different distributions.
You need fastest particles you can get,
highest energy particles you can get in a thermal distribution,
the tail of the Maxwellian, because those are the ones that can do anything.
The probability of them actually interacting to
profusion increases dramatically with the range.
So those are two opposing trends and you have to multiply the two.
It turns out, when you multiply the two,
there is a maximum where those two trends kind of intersect.
So there is a particular energy for a given plasma where
particles are most likely to interact and fuse into something heavier.
Now that also should be somewhere there is available energy states for
the product nuclei.
That actually turns out to be important for some of the heavier elements so
this is the mechanism but quantitatively this happens very, very rarely.
Nevertheless, there are so
many particles there, that even with the very low probability for
any one of them doing it, there is still plenty of them fusing together.
So to recap, just thermonuclear reactions.
The burning of hydrogen into helium is the main source of energy in stars.
And it's the only source of energy in stars for most of their life.
Also called Main Sequence of HR diagram, which we'll cover next time.
And then heavier elements fusion happens in advanced evolutionary states for
stars that are sufficiently massive, they can do this.
Now, solar luminosity, if you divide it by the yield of reactions,
corresponds to turning 4.3 million tons of hydrogen into helium every second.
And that's a lot of MC squared.
This is why you get sunburn even though you're an astronomical unit out.
So it's impressive, actually.
And proton-proton cycle that I described to you is the dominant,
but not the only way in which hydrogen can fuse into helium.
There is a whole another set of nuclear reactions that involve carbon,
nitrogen, and oxygen as catalyzers for nuclear reactions.
And they can add additional hydrogen to helium production.
No matter what, all of these reactions are very steeply dependent on temperature,
because temperature is proportional to angioparticles and
probabilities of fusion or tunneling rise steeply with energy.
So they're very, very sensitive to the temperature in stellar cores, and
the density helps of course.
The higher the density the more targets you have.
Now by and large, more massive stars tend to achieve higher densities and
temperatures in the middle, that's kinda intuitively clear.
And because of that it's the higher mass stars that can push fusion reactions
beyond helium all the way up to iron and then they explode.
So, this strong dependence of nuclear reactions
on temperature is what actually establishes stability of stars.
This is sort of the opposite of the core collapse effect that we discussed for
collapsing protostars.
So imagine you turn on the nuclear reactions.
Temperature goes up, pressure goes up, temperature goes up.
Then core will expand.
Because it expanded, the density drops and
temperature will drop, and fusion rate will go back down.
And so that there is a self-regulating cycle for a given star.
Because of that feedback mechanism, stars exist for a long time and
don't just explode.
All right.
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