What is the fate of the star after she leaves the main sequence? How is this determined?

After the star leaves the main sequence, the star turns into a red giant. This is due to the fact that the size of the core decreases, and the radius of the star itself increases. Subsequently, the star shrinks and its temperature increases greatly. Then, when all the elements for thermonuclear fusion run out, the star slowly extinguishes or explodes, or turns into a black hole. Its further fate depends on the mass of the star’s core.

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