Why do stars become red giants? Disclaimer: I’m not a career astronomer.  I don’t own a telescope.  I have no professional credentials.  But I do find this stuff fascinating, and I consume all the astronomy documentaries I can.  



So, I’ve watched lots of documentaries describing stellar evolution.  I understand that below a certain threshold, stellar death does not involve supernovae.  I understand that above that threshold, supernovae may create neutron stars, magnetars, or (if the supernova qualifies as a hypernova) black holes.

However, for a long time, I was curious about why stars below the supernova threshold—like our own Sun—become Red Giants.



From documentaries, I have been instructed that (for stars below the supernova threshold), when the star’s core’s fusion cannot continue…fusion ceases, and the star begins to collapse under gravity.  

As gravity crushes the star, I understand that the star heats up as gravity crushes it.  As a result, although the stellar core remains “dead” (no fusion occurs), a “shell” of gas around the stellar core becomes hot enough to begin fusing helium.  Since the fusion occurs as a “shell” around the stellar core, the outward-push from the fusion is what pushes the star’s outer layers further.  The result is that the star grows into a Red Giant.



My question is this:  Why does fusion cease in the core?!  It seems to me that as gravity crushes the star, stellar fusion would reignite in the core itself—not in a sphere around the core.  Why does the stellar core remain “dead” while its “shell” begins fusion???
(This is somewhat simplified but I hope it gets the idea across.)

The reactions stop in the core because it runs out of fuel. During the main sequence, the star is supported by the fusion of hydrogen into helium. Eventually, the hydrogen runs out at the centre, so hydrogen fusion is no longer possible there.

Why doesn't it start fusing helium into carbon right away? That's because the core isn't hot or dense enough yet. Different reactions broadly rely on the presence of different resonant states in the nuclei and, in the case of helium, such a state cannot be reached often enough until the core temperature is about $10^8$ kelvin.

In order to get that hot, the core has to contract and heat up. It eventually does (if the star is massive enough) but it doesn't happen instantaneously. Remember that the gas is still hot and at high pressure, which it exerts on itself and its surroundings.

Meanwhile, at the edge of the core, the star (partly as a result of said contraction) is hot enough to turn hydrogen into helium, so it does so. This is exactly the nuclear-burning shell that distinguishes the internal structure of a red giant.

So maybe think of it this way. Imagine a star at the end of the main sequence. Where is it hot enough to fuse hydrogen into helium? Everywhere up to the edge of the core! Does it fuse in the core? No, because it's out of fuel. So where does it fuse? At the edge of the core, which we recognize as the shell.