why is there a lower limit on the mass of a star?

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(what cant happen in a lower mass accumulation of hydrogen atoms and other instellar material?)
 
Nuclear fusion can't occur at the core if there isn't enough mass (which means gravity, which means pressure) to fuse two hydrogen nuclei together.
 
All new stars begin by fusing hydrogen into helium. To start this fusion process, a forming star must have enough mass to gravitationally compress its core enough to generate a temperature of at least 10-million degrees Kelvin. Jupiter is a good example of a "failed" star. It had plenty of helium, but not enough mass to generate the required temperature in its core to set off nuclear fusion.
 
below a certain mass, the collapsing object doesn't attain high enough temperature and pressure to initiate and sustain hydrogen fusion. this mass is about 8% of the solar mass, with typical elemental abundances.

the rate determining step is deuterium production - objects just below the critical mass (brown dwarfs) can initiate fusion but only of relatively rare deuterium and lithium isotopes. this fuel is quickly consumed, whereas at slightly higher temperatures, deuterium is formed from hydrogen and then is immediately consumed. but there is plenty of hydrogen, so the reaction is self-sustaining for long periods - maybe up to a trillion years for low-mass red dwarfs.
 
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