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