Does the CNO cycle play a role in stopping the collapse of solar mass stars after they have run out of Hydrogen?

Question

Wikipedia says about Stellar evolution:

Eventually the star's core exhausts its supply of hydrogen and the star begins to evolve off the main sequence. Without the outward radiation pressure generated by the fusion of hydrogen to counteract the force of gravity the core contracts until either electron degeneracy pressure becomes sufficient to oppose gravity or the core becomes hot enough (around 100 MK) for helium fusion to begin. Which of these happens first depends upon the star's mass.

However, when I look at the article about Triple-alpha process, I find the diagram below. It shows that the CNO cycle is activated at lower temperatures than the Triple Alpha process. During their main sequence life, CNO cycle was much less dominant than PP chain reactions, so if the star had at least some amount of C and H (the ingredients for CNO cycle), I would expect that to turn on before triple alpha process.

Given that collapse causes temperatures to rise, does the CNO cycle turn on when the temperature of the star is higher than what it was during its main sequence lifetime, when the CNO cycle is more energy efficient than both PP chain and Triple Alpha process? This is roughly in the middle of the diagram below.

I can see a few reasons why it wouldn't turn on:

• If the star runs out of H, it runs out of it so completely that even CNO cycle wouldn't ignite
• Collapse happens so quickly that temperatures reach the regime where the Triple Alpha process is much more energy efficient than CNO Cycle, so that will be activated.

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By energy efficient I mean producing more energy at that temperature.

Answer 1

Both the CNO cycle and p-p chain are different mechanisms for hydrogen fusion. For different masses (and hence internal temperatures), one or the other might be more dominant, or both may be present at the same time. But the common thing is that once a main sequence star exhausts the hydrogen fuel in its core, no more hydrogen fusion can occur, whether it is the CNO cycle or the p-p chain.

You are correct that the relative significance of the CNO cycle will increase throughout the Sun's main sequence lifetime. (It is already occuring now, to a small extent.) This is because helium ash will accumulate in the core, causing it to contract and increase in temperature, hence increasing the relative dominance of the CNO cycle. However this effect can be taken to be relatively insignificant.