What initial mass range (relative to the Sun) often leads a star through the Bright Giant phase?
Answer
Roughly between 2 and 8 times the mass of the Sun
The evolutionary pathway a star takes after exhausting core hydrogen is heavily dependent on its initial mass. For stars that are significantly heavier than the Sun but not massive enough to immediately evolve into the highest luminosity classes, the path involves traversing the bright giant phase. Specifically, stars beginning their lives with masses estimated to be roughly between two and eight times the mass of the Sun frequently follow this specific evolutionary track before proceeding to become red giants or true supergiants, depending on nuances of their mass and evolutionary path.

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