If a main sequence star runs out of hydrogen fuel in the core, the core collapses because of its own gravity, but what exactly leads to the expansion of the outer layers of the star when it is becoming a red giant?
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3Possible duplicate of What causes the dimensions of a star increase when its hydrogen fuel is exhausted? – John Rennie Jan 30 '18 at 09:29
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1Have a look at dmckee's answer to the question I've linked above. Basically the core gets hotter as the hydrogen runs out and this heats up the rest of the star. Since gas expands as it gets hotter this increases the size of the star. It seems odd that the core should be getting hotter as its fuel runs out, but dmckee nicely explains why this happens. – John Rennie Jan 30 '18 at 09:33
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It's interesting to look at variable stars, as a case where they repeatedly expand in this way – CriglCragl Jan 30 '18 at 13:37