What initial mass threshold roughly determines whether a star avoids the red giant path described and instead faces a supernova explosion?
Answer
Roughly $8$ times the Sun's mass or more
The ultimate fate of a star is fundamentally determined by its initial mass, which dictates the internal pressures and temperatures achievable in its core. Stars in the solar mass range follow the path of red giant expansion, Helium Flash, and eventual planetary nebula formation. However, stars that are significantly more massive—estimated to be around $8$ times the Sun's mass or greater—have enough gravitational power to compress their cores beyond the point where degeneracy pressure halts the collapse. These massive stars bypass the gentle Helium Flash, continue fusing heavier elements past carbon and oxygen, and ultimately meet a much more catastrophic end involving a supernova explosion.
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