What is the designation for a fragment that fails to reach the temperatures needed for hydrogen fusion?
Answer
A brown dwarf
The final mass accumulated by the initial core fragment is the single most important factor determining a star's entire life history. If a fragment accumulates significantly less mass—specifically, less than about 0.08 times the mass of the Sun—it will never generate enough core pressure and temperature to initiate the sustained nuclear fusion of hydrogen. Such an object is classified as a brown dwarf. Although they are often termed 'failed stars,' brown dwarfs do exist and shine faintly due to residual heat left over from their initial gravitational collapse, but they cannot sustain core burning like true stars.

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