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The fate of a star depends not so much on its size (diameter), but on its mass.Low-mass stars (up to about 1.4 times the mass of our Sun) will become white dwarves.

Above that, and the star will become a neutron star.

Somewhere between 2-3 solar masses another limit is reached, where a neutron star isn't stable; instead, the star becomes a black hole.

The masses mentioned refer to the mass that remains once the star runs out of energy.

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