For stars up to $8 M_{ ext{odot}}$, what is the fate of the resulting carbon core material?
Answer
They generally fail to reach the temperatures needed to burn the resulting carbon
Stars evolving through the red giant phase, specifically those with initial masses up to approximately $8$ solar masses, successfully fuse helium into carbon during the first red giant phase. However, they typically lack the necessary gravitational mass and resulting core temperatures required to initiate subsequent fusion reactions, such as burning the newly formed carbon into even heavier elements like oxygen or neon. Once the core helium is depleted, these stars often undergo instability, pulsate, and attempt fusion in surrounding shells, eventually leading to the expulsion of their outer layers.
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