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As a matter of fact, I was learning stellar astrophysics where I couldn't understand the chain of events at the time of death of stars,

Once the hydrogen fuel core is exhausted, the stars start shrinking until the helium nuclei starts fusing under immense gravitational pressure. Due to powerful radiation pressure the star starts expanding. Like our sun is expected to stretch 200 times it current radius, gobbling up the Mercury and Venus planets.

Here I couldn't understand that helium fusion starts when star is shrinking, but after star starts expanding, so how could star sustain fusion $?$ I mean helium fusion requires even more pressure or temperature than hydrogen, but once star starts expanding, it become cooler and less denser, which should make fusion impossible. And during this phase of Red giant, not only helium, but more heavier nuclei are formed like oxygen which should require even more pressure and temperature.

Is there any flaw in my understanding,then please tell$!$ Please help and thanks in advance $!$

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As the hydrogen fuel is exhausted, the core heat that resists gravity diminishes, so gravity takes over and compresses the star. If the star was big enough to start with, then the extra pressure from the compression is enough to enable helium fusion and the heat generated by that is enough to blow parts of the outer envelope off the star and expand it into an immense but cooler sphere. Meanwhile, the remaining inner core of the star continues to fuse helium and remains very hot, and all the heavier elements you mention get fused there as well.

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