In the relationship $L ext{ propto } R^2 T^4$, what factor dominates the luminosity increase when a star transitions from main sequence to red giant?
Answer
The immense increase in the star's radius ($R$)
Although the temperature ($T$) decreases, the corresponding massive increase in the radius ($R$), squared ($R^2$), overwhelmingly drives the overall luminosity ($L$) upward, making the star much brighter despite its cooler skin.
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