In the context of the star formation through the fragmentation of an extremely metal-deficient protogalactic cloud , the gravitational collapse of filamentary gas clouds is explored with H _ { 2 } and HD chemistry .
It is found by 1D hydrodynamical simulations that the cloud evolution is prescribed mainly by the initial density ( n _ { 0 } ) and H _ { 2 } abundance ( x _ { H _ { 2 } , 0 } ) .
In particular , it turns out that the evolution of low-density filaments ( n _ { 0 } \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } % } } 10 ^ { 5 } cm ^ { -3 } ) bifurcates at a critical H _ { 2 } abundance of x _ { H _ { 2 } ,cr } \simeq 3 \times 10 ^ { -3 } , beyond which HD cooling overwhelms H _ { 2 } cooling .
The numerical results indicate that the stellar IMF is likely to be double-peaked and deficient in sub-solar mass stars , where the high mass peak of the IMF is around 10 M _ { \odot } or 10 ^ { 2 } M _ { \odot } , dependently on the initial density and H _ { 2 } abundance .
If the gas in protogalactic clouds is photoionized by UV radiation or shock-heated , the H _ { 2 } abundance could exceed x _ { H _ { 2 } ,cr } \simeq 3 \times 10 ^ { -3 } by H ^ { - } reactions .
Then , the high mass peak would be O ( 10 ) M _ { \odot } .