Download PHYSICS 015

The Fate of the Sun
– What Will Happen?
Within the Sun
The sun starts out as a ball of
completely uniform composition.
In the outermost parts, there are no nuclear reactions
at all: it’s not hot enough! So nothing changes.
At the very center, there are very vigorous reactions:
it is extremely hot there. A bit removed from the
center, where it is not quite so hot, reactions occur
at more moderate rates.
After About
10 Billion Years
At the very center, all the H has
turned to He. The core is now
essentially pure Helium – the “ashes” of the p-p cycle. (Not
literal “ashes” like a wood fire leaves behind, of course.) Nuclear
reactions cease!
At intermediate zones, only some of the H has turned to He. So
reactions continue there, at a moderate pace, because there
is some H fuel still left to consume.
In the outer parts, the composition stays unchanged.
The Structure
Becomes ‘Stratified’
[but note that there are
no ‘sharp’ boundaries]
Note that this happens because He forms at the
center, where it is hot enough for that to take
place. It is NOT because the heavier He nuclei
settled to the center.
(We will encounter this important point again with respect
to later stages of stellar evolution.)
Why Do The Central Reactions Cease?
Why Don’t He Nuclei Fuse Together?
The He nuclei have two protons each, and repel
one another very strongly.


It is not hot enough to force the He nuclei to merge
(That requires a temperature of ~100 million degrees!)
“Shell Burning”
The central reactions cease completely, but
4 H  He continues in the surrounding
shell, where the H has not yet been totally
consumed.
What Happens at the Core?
1.
2.
The central heat diffuses outward, and is
radiated away, so the sustaining pressure is
reduced. The sun’s gravity will start to win.
Consequently, the central parts of the sun will
contract.
This contraction leads to the release of
gravitational potential energy. So, the central
parts will get hotter.
(This is the paradoxical behaviour we described earlier: as
the Sun radiates away its central energy, it eventually
gets hotter rather than cooling off.)
Our Simple Expectation –
with One Surprise
The Sun should shrink and get hotter. Indeed, it
does so – but only in the inner parts.
Amazingly, the outer parts of the Sun swell up
enormously: it gets very much bigger. The
outermost material also cools off, so the Sun
becomes a RED GIANT.
Deceptive Behaviour!
This Great Expansion Takes
A Fantastic Amount of Energy!
The Sun will, in effect, ‘lift’ trillions of tons of
material up, through a distance of millions of
kilometers, against the pull of gravity!
The collapse of the core releases a lot of energy,
but only some of it goes into heating up the
core. A lot of it goes into ‘puffing up’ the outer
layers of the Sun!
But This Does Not
Go On Forever!
The core is shrinking and getting progressively
hotter. Eventually, the central parts reach a
temperature of ~ 108 (one hundred million)
Kelvin – about 10x as hot as the sun’s core is
right now.
This is hot enough for Helium nuclei to fuse
together, so nuclear reactions start again.
Stability is Restored!
In the new reactions
He + He  heavier elements,
(mainly carbon)
This releases energy, keeping the core hot and
stopping any further contraction. The Sun attains a
new stable structure, now as a red giant – no longer
a main sequence star.
But its potential lifetime is now quite limited.
Why a Limited Lifetime?
Binding Energy Again
An Unceasing Fight
The inward pull of gravity is unceasing, and enough energy
must be generated to support the star.
The new He  C reactions do that, but the He fuel
cannot last as long as the H  He phase did because

there are fewer possible reactions (fewer particles)

and each reaction produces less energy than H  He
Let’s Do an Example Calculation
[I won’t ask you to repeat this – but do learn from it!]
Suppose we started with 12 gazillion protons in the hot central
core of the Sun. [Note that “gazillion” is not a real word!]
They fuse (in groups of 4) to form 3 gazillion He nuclei.
That is, 3 gazillion ‘completed reactions’ have occurred.
Each one produces some amount of energy (call it X).
The total energy released is 3 gazillion X.
This maintains the Sun on the main sequence for 1010 yrs.
Now, As a Red Giant
The center contains 3 gazillion He nuclei
They can combine (3 at a time) to form 1 gazillion Carbons,
through a total of 1 gazillion completed reactions.
But each one of these ‘completed reactions’
produces quite a bit less than X amount of energy.
(This is because of the Binding Energy curve!)
The total energy released is considerably less than 1
gazillion X.
How Long Can it Last?
Detailed calculation show that the Heburning stages will last no more than about
10% of the lifetime that the Sun enjoyed as
a main-sequence star.
So we are now on the ‘slippery slope’ to
stellar death.
A Human Analogy:
Keeping Warm!
After He Burning?
By the same reasoning:
When He runs out, leaving Carbon ‘ash’ in the core, we
expect that the sun will:


cease producing energy, lose pressure support, and
contract in the core
get still hotter in the middle, and ignite some new fusion
reaction that creates progressively heavier nuclei.
(Fusing C nuclei together will require very high
temperatures indeed.)
How Long
Can This Last?
(nothing is forever)
As each fuel source is used up, a less efficient one might
be expected to kick in, but for a dramatically shorter
period of time. However, the ‘peak’ of the binding
energy curve means that eventually there will be no
further energy supply to be tapped at all.
Stars seem to be doomed. Will gravity inevitably win??
Will every star, including the sun, become a black hole?