Ann wrote:This is how I understand it (but I may very well be wrong, mind you).
Even though the star runs out of hydrogen in its core, and helium in its core, it still contains hydrogen and helium in shells around the core. So the stars fuse hydrogen or helium (not both at the same time, I think) in those shells. The fusion process takes place closer to the surface of the star, making it swell. It could be, too, although I'm not sure, that more of the mass of the star is being used for fusion when the fusion process "has moved outwards" in the star than when it was confined to the core.
Stars also swell and get very bright just when their cores "go dead", or stop fusing. Then the cores shrink, a lot of energy is released, and the stars swell and get brighter.
Sort of like being on it's 'last' gasps, then?