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Eventually all the hydrogen hot enough to undergo fusion is used up in a star. The core now only contains helium, contained by whatever small percentage of heavier elements the star had to begin with. Energy can no longer be generated by hydrogen fusion in this helium core.
With nothing more to supply heat to the central region of the star, gravity again takes over: after a long period of stability, the core begins to contract. Once more the star's energy is partially supplied by gravitational energy, in the way described by Kelvin and Helmholtz. As the star's core shrinks, the energy of the inward-falling material is converted to heat.
The heat generated in this way has an effect on the hydrogen that spent the whole long main-sequence time just outside the core. This hydrogen was almost (but not quite) hot enough to undergo fusion and take part in the main action that sustains the star. Now, the additional heat produced by the shrinking core puts this hydrogen over the limit, and a shell of hydrogen nuclei just outside the core becomes hot enough for hydrogen fusion to begin.
Energy now pours outward from this shell, flowing, as heat always does, to the cooler outer regions. This begins to heat up layers of the star farther out, causing them to expand a bit. Meanwhile the helium core continues to contract, producing more heat right around it, which leads to more fusion in the shell of fresh hydrogen. The fusion produces more energy, which also flows out into the upper layers of the star.
These changes result in a substantial and rather rapid readjustment of the star's entire structure, so that the star leaves the main sequence altogether. Most starst actually generate more energy in this stage than they did when hydrogen fustion was confined to the core; thus they increase in luminosity. The outer layers of the star begin to expand, and the star grows to enormous proportions -- it then becomes a giant.
Depending on their mass, these giant stars can become so large that if we were to replace the Sun with one of them, its outer atmosphere could extend to the orbit of Mars or even beyond. This is the next stage in the life of a star, as it moves from its long period of youth into middle age.
The expansion of the outer layers causes the temperature at the stellar surface to decrease. As it cools, the star's overall color becomes redder. So the star becomes simultaneously more luminous and cooler; on the H-R diagram this means it moves upward and to the right. The star becomes one of the red giants. You might say that these stars have "split personalities": their cores are contraacting while their outer layers are expanding.
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