In large spaces where there is a lot of dark matter, Stars are born in groups and not alone, so what is the minimum amount of dark matter to start controlled nuclear fusion in nature?
2 Answers
Stars are often produced in groups, when a large cloud of gas collapses under its own gravity and splits up. Sometimes stars are born solo, when a small cloud collapses and doesn't split up. Neither of these processes have anything to do with dark matter. It is the gravity of the gas and dust, not dark matter that causes the collapse.
The initial formation of large scale structure was guided by dark matter. If you change the amount of dark matter and visible matter, you will get a different universe. In some universes, spacetime will collapse before stars can form. But dark matter is not required to achieve sustained nuclear fusion in stars.
So the answer is "None". And, indeed, there are galaxies with stars that have very little dark matter (how they formed is a bit of a conundrum)
The average dark matter density in the Galactic plane (where stars are born) near the Sun is about $10^{-21}$ kg/m$^3$ (Salucci et al. 2010) and should be evenly spread (it doesn't clump on scales smaller than galaxies).
In contrast, the density of normal matter in a star-forming molecular cloud at the start of its collapse is about 1000 times larger (and gets bigger as the cloud collapses).
Thus dark matter plays no role in star formation at level of a cluster of stars

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1More precisely, the dark matter doesn't form clumps within galaxies (since it was heated by the infall). In the conventional CDM picture, DM should form clumps at scales smaller than galaxies, but only in the extragalactic field (and while those clumps could persist in galaxies, they wouldn't be expected to accrete the gas to form stars). – Sten Jun 05 '23 at 16:54
and the dark matter acts a large scale between stars so I wanted to know the minimum amount of this matter that is there when the stars begins to be born
– z.10.46 Jun 04 '23 at 21:01