What combination of measured properties operationally defines a star as belonging to the supergiant class?
Vast volume combined with thousands of times greater luminosity than the Sun
Astronomical classification relies on observable data, primarily luminosity (absolute magnitude) and temperature. A star that is merely larger than the Sun, even if it is a giant, occupies the standard giant branch on the Hertzsprung-Russell diagram. To be classified as a supergiant, a star must demonstrate both an enormous physical volume—as seen in its expanded atmosphere—and an intrinsically high power output. This massive energy output, often tens of thousands of times the Sun's luminosity, directly reflects the star's initial mass and its enhanced capacity for burning heavy elements in its core and shells. The combination of immense size (volume) and extreme intrinsic brightness (luminosity) is the key operational distinction separating giants from supergiants.

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How Do Stars Become Red Giants Or Supergiants? - Physics Frontier