Lecture #24: the future of the Sun
The Sun is now in an equilibrium where the heat it loses to space in the form
of sunlight is replaced by nuclear fusion of hydrogen into helium. However, that cannot last forever, eventually the core runs out of hydrogen!
What happens then?
Some major surprises. The core loses heat (because it's still hot), but
it is not replaced, so the core shrinks and gets hotter still. There is
no hydrogen to fuse, and the helium requires even higher temperatures to fuse,
so nothing much different happens to the core for awhile. But something very
important happens to the shell around the core, which has also shrunk and gotten
hotter-- it will get hot enough to fuse the hydrogen that it still has plenty of because it didn't used to be hot enough to fuse it! (Ask yourself: why does it have to be hot to fuse hydrogen to helium?)
I. Shell fusion
Shell fusion is a completely different animal, because it cannot self-regulate
its temperature the way core fusion does (if a core fuses too fast because the
temperature is too high, the heat it releases cause expansion, which causes cooling, which lowers the fusion rate like the thermostat and furnace does in your apartment). Thus its fusion tends to go a bit nuts as the temperature goes
way up, and the only way it can self-regulate that is by lowering its pressure
rather than its temperature. It does that by dumping heat into the envelope
around the core, which causes the envelope to expand (why?), which causes it
to have less weight (gravity gets weaker at larger radius), which presses
down less on the shell, which lowers the shell pressure and keeps the
fusion rate under control. Hence, the star as a whole must expand a lot as
fusion initiates in a shell around the core instead of in the core itself.
It's a huge difference, and eventually makes a huge star, called a "red giant."
II. The core of a red giant
Meanwhile, in the core, we have something very interesting going on. It
loses heat and contracts, but eventually it has lost so much heat it does
the same thing an individual atom does when it loses heat: it approaches
a state called the "ground state", where it can lose no more energy so it
ceases to lose heat. The core is now in a state called "degenerate," where
it cannot contract because it cannot lose any more heat.
The reason a "ground state" cannot lose heat is because to do so would
cause the waves that tell the free electrons in the core what to do would destructively
interfere, and that's generally what prevents things from happening in our
universe. So yes, this means the core of an entire star begins to act a
bit like an atom in its ground state, and this is only true because
the electrons are indistinguishable particles (technically, they are "fermions"), so they obey the "Pauli exclusion principle." That says they begin to
destructively interfere with each other if they get too close together, and
that's what prevents the core from losing any more heat and shrinking
any more (the same thing is happening to essentially all the material that
is around you right now, including metals, which have very high energy
free electrons zooming around in them but cannot burn you because they are
not allowed to lose any more heat than they have already).
III. Core helium burning
As helium "ash" is added to the core by the hydrogen shell burning
above it, the core mass grows, and its gravity increases. This
squeezes it into an even smaller volume, releasing energy and raising
the core temperature further. Eventually the core temperature reaches
the 100 million Kelvin level necessary for the helium to start fusing
(remind yourself why helium nuclei, which contain two positively charged
protons to repel the other helium nuclei, would require higher temperature
to fuse). This returns the fusion of the star to the "core burning"
geometry, which is fundamentally different from shell burning because
it is able to self regulate its temperature like a thermostat, whereas
shell burning cannot do that, it can only self regulate its pressure
by dumping heat into the stellar envelope and causing it to expand.
Also, the helium fusion causes the core to expand until it is no
longer "degenerate" (meaning the electrons in the core are no longer
anywhere near their ground state, so behave like an ideal gas once again,
obeying what you might have learned about in high school science, the ideal
gas law). All this means is the core expands to something close to the
size it is now in the Sun (since the gas in there is an ideal gas now), and
that tames the shell burning of the hydrogen (which continues to happen
even after the core starts fusing helium) such that the envelope of the star
no longer needs to be puffed out, and it sinks back down to a size roughly
similar to what the Sun is now. So the connection in your head should be,
if something is fusing in the core, then the Sun is about the size it is
now, if nothing is fusing in the core then the core goes degenerate and
the shell burning goes nuts, causing the envelope to expand to about 100
times what it is now.
IV. Red giant for the second time
The helium in the core fuses into carbon (which takes 3 helium nuclei to
make 1 carbon nuclei, see the periodic table), and of course, eventually
the helium in the core runs out, just as the hydrogen did. And the
same thing happens as a result, nothing is fusing in the core, the
core shrinks and goes degenerate, and the helium fusion in the shell
around the core goes nuts, dumps heat into the envelope to expand it
and lift off weight from the shell. So once again, the Sun expands to
about 100 times (closer to 200 this time) its current size, and we have
a red giant for the second time.
V. planetary nebulae and the white dwarf final state
You might now expect the carbon in the degenerate core to start fusing just
as the helium did, but the core never gets hot enough to do that. Which
is a good thing, because it would cause an explosion called a type Ia
supernova! But the Sun will never go supernova, because something else
happens first: it will blow off its whole envelope into space, creating
what is called a "planetary nebula" (even though it has nothing to do
with planets). The naked carbon core is left behind, but it can never
get anough mass added to it to start fusion (which actually takes a little
more mass than the Sun has in it even now). So instead, it just
gradually (very gradually) cools down. It is still about the size of
the Earth, so it is not very bright, even though it starts out much
hotter than the surface of the Sun, and gradually just cools away into
darkness. Since it is very small and starts out very hot, it is called a
"white dwarf."
New topic: The solar wind
The Sun has a large convection zone which stirs up magnetic fields at
its surface, creating magnetic heating and a very hot low density cloud
around the Sun called the solar corona. This is what you will see when
there is a total eclipse of the Sun on April 8! (In Iowa it will not be
total enough to see the corona, you'll still see part of the Sun's surface.)
The gas in the corona is as hot as the core of the Sun, but the density is
too low to undergo fusion fast enough to matter at all. Still, the high
temperature does matter because it causes the gas to essentially evaporate
from the surface, which leads to the solar wind.
To be moving fast enough to escape, even at a very slow rate, the protons
in the solar corona need to be about ten million Kelvin. The reason they
get that hot is they are so low density that they cool very inefficiently
by radiation, but they can shed the heat they are given via thermal
conduction, like when you touch a hot oven, but that only works once they
get really hot. So when an astronomer named Parker found out about this
hot gas, he realized that the gas pressure in the interstellar medium could
not hold this gas in, it would have to "leak out" in the form of a solar
wind that passes by Earth. So he predicted that wind even before it was
observed. Today the University of Iowa has scientists that study the solar
wind and the famous aurora borealis that it produces.
The solar wind also carries particles in bursts, if there is a solar flare
and a kind of plasma eruption called a "coronal mass ejection" (very
imaginative name). These can affect power grids on Earth, and can even
knock out satellites. There was a huge one of these in 1859 called the
"Carrington event" that was stronger than any we've seen since, and would knock out essentially all our GPS and communications satellites if it happened again.