Why isn't this so?
If the mass of the star is about 1/4 the mass of our sun, then the core's (where fusion occurs) temperature and pressure will never be enough to fuse anything other than hydrogen into helium. The death of this star may be something like a fire dying. The flames disappear for a while, then you may get one or 2 popping back into existence.
Our sun will start to fuse helium into carbon before all the hydrogen in the core is used. In the description of a heavy star, it is described as a onion with its layers with the higher fusion products occurring in the lower layers. They use this model since the iron fusion requires temperature and pressures above a certain level. Neon has lower requirements, but still greater than carbon fusion, and so on. What is not mentioned, is that there is still hydrogen fusion occurring in the center, as well as all the other fusion, helium, carbon, neon, etc.
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