Final answer:
A helium flash does not occur in some stars because they cannot reach the necessary conditions for helium fusion within their cores. Initial mass is a key factor, as is the presence of helium from the Big Bang that impacts the evolutionary paths of stars. Mass loss during the red giant phase also plays a role in the ability of a star to undergo a helium flash.
Step-by-step explanation:
A flaheliumsh will never occur in some stars because these stars do not have sufficient mass to reach the extreme pressures and temperatures required for the triple-alpha process. In such stars, the core temperature will never reach the necessary 100 million K needed to slam three helium nuclei together to make them stick and produce a carbon nucleus. This process predominantly occurs in stars with an initial mass similar to or a few times larger than that of the Sun. Larger stars do not go through a helium flash because they ignite helium gradually in their cores, while smaller stars do not produce the necessary conditions for helium fusion to occur at all.
Furthermore, due to the Big Bang, there is an abundance of helium in the universe that cannot be explained solely by stellar processes like the helium flash. This suggests that a significant amount of helium was already present before stars began contributing to helium production through nuclear fusion. This pre-existing helium is a product of Big Bang nucleosynthesis.
Stars like the Sun are expected to lose a considerable amount of mass before reaching the red giant phase where the helium flash can occur. Such mass loss can limit the ability of a star to create the conditions under which a helium flash would take place, reinforcing the idea that not all stars will experience such an event.