What is the fundamental determinant for a star achieving supergiant status?
Answer
The star's initial mass
The fundamental determinant is the star's initial mass. Stars destined to become supergiants are typically born with masses exceeding about eight times the mass of the Sun.

Frequently Asked Questions
What two combined characteristics are essential for a star to be classified as a supergiant?What is the fundamental determinant for a star achieving supergiant status?In the Yerkes system, which Roman numeral class is specifically assigned to supergiants?If a Red Supergiant like Betelgeuse were placed at the center of our Solar System, where might its outer layers extend?Which evolutionary phase is characterized by incredibly hot surface temperatures up to 50,000 Kelvin?Why are red supergiants generally observed more frequently than blue supergiants at any given time?What process causes the dramatic mass loss observed in supergiants?What is the approximate surface temperature of a cooler Red Supergiant star?If a massive star's remnant core mass after a supernova exceeds roughly $3 ext{M}_ ext{odot}$, what object forms?What type of explosive event marks the dramatic demise of a star that has gone through the supergiant phase (initial mass $> 8 ext{M}_ ext{odot}$)?