What fate awaits stars below the minimum mass required to expand into a red giant phase, such as those around $0.5$ solar masses?
Answer
They contract until they become faint helium white dwarfs without expanding
The transition to a red giant requires sufficient gravitational force to generate the necessary core temperature following hydrogen depletion. Stars possessing mass near or below the minimum threshold, cited as about $0.5$ solar masses, lack the gravitational strength to ever reach the high temperatures required to ignite helium fusion, even in a degenerate state. Instead of expanding into a giant, these low-mass stars simply contract slowly over cosmological timescales, eventually fading away as faint helium white dwarfs, bypassing the dramatic red giant evolutionary stage entirely.
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