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For the evolution of a star of one solar mass, about 80% of it’s time is spent on the main sequence of the HR diagram, burning it’s hydrogen into helium via the proton-proton chain. Once the hydrogen fuel begins to run out, the nuclear reactions inside the core stop. The core begins to collapse and heat up, which in turn causes the region just outside the core to heat up as well and expand outward. This is what causes the star to expand slightly. Fusion begins again in this thin shell surrounding the original core. This is called hydrogen shell burning. At this point, the star is called a red giant. At this point, it will begin to exhaust all of its remaining energy and slowly die.
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