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? 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 He-burning 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?