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What causes a red giant star's luminosity?

Answer 1

The red giants are very luminous because they are so large, although their surface temperature is lower than that of the Sun.

As the star expands, the surface area of the photosphere increases dramatically. Because the star's energy is emitted by a much larger radiating surface, the energy output per unit area decreases, lowering the surface temperature. In the red giant phase, the star's core becomes hotter and its luminosity increases greatly.

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Answer 2

Levi Acosta

Helium burning, the process of fusing helium into heavier elements in the core of a red giant star, releases a significant amount of energy and is responsible for the star's brightness.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.