What causes White Dwarfs to exhibit very low luminosity despite possessing extremely high surface temperatures?
Answer
Their minuscule radii result in a very small radiating surface area.
White Dwarfs represent the final stage for smaller stars, where the radius has contracted dramatically, often to only the size of Earth. While their cores are incredibly hot, exceeding $50,000$ K, the total area available for radiating this intense energy is extremely limited. According to the Stefan-Boltzmann relationship ($L Arr R^2 T^4$), the small radius term squared ($R^2$) severely limits the total luminosity output, causing these compact, hot objects to reside far below the Main Sequence on the H-R diagram.
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