What is the critical density threshold called, beyond which gravity starts to win the local battle against outward pressure?

Answer

Jeans mass

When the force of a trigger compresses a section of the cloud past this specific critical density threshold, gravity begins to dominate the local pressure forces.

What is the critical density threshold called, beyond which gravity starts to win the local battle against outward pressure?

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Birth of a star - from nebula to main sequence - YouTube

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