Where does hydrogen ignition begin after the core runs out of hydrogen fuel?
Answer
In the layer of fresh hydrogen surrounding the inert helium core
When the hydrogen in the central region is exhausted, the gravitational collapse of the now-inert helium core causes extreme increases in pressure and temperature. This intense heating doesn't confine itself to the contracting center; rather, it superheats the adjacent layer composed of fresh, unburnt hydrogen that surrounds the helium ash core. This superheated shell ignites, leading to a process known as hydrogen shell burning, which becomes the star's new, albeit less stable, energy mechanism.
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