Performing one-dimensional hydrodynamical calculations coupled with nonequilibrium processes for hydrogen molecule formation , we pursue the thermal and dynamical evolution of filamentary primordial gas clouds and attempt to make an estimate on the mass of population III stars .
The cloud evolution is computed from the central proton density n _ { c } \sim 10 ^ { 2 - 4 } cm ^ { -3 } up to \sim 10 ^ { 13 } cm ^ { -3 } .
It is found that , almost independent of initial conditions , a filamentary cloud continues to collapse nearly isothermally due to H _ { 2 } cooling until the cloud becomes optically thick against the H _ { 2 } lines ( n _ { c } \sim 10 ^ { 10 - 11 } cm ^ { -3 } ) .
During the collapse the cloud structure separates into two parts , i.e. , a denser spindle and a diffuse envelope .
The spindle contracts quasi-statically , and thus the line mass of the spindle keeps a characteristic value determined solely by the temperature ( \sim 800 K ) , which is \sim 1 \times 10 ^ { 3 } M _ { \odot } pc ^ { -1 } during the contraction from n _ { c } \sim 10 ^ { 5 } cm ^ { -3 } to 10 ^ { 13 } cm ^ { -3 } .
Applying a linear theory , we find that the spindle is unstable against fragmentation during the collapse .
The wavelength of the fastest growing perturbation ( \lambda _ { m } ) lessens as the collapse proceeds .
Consequently , successive fragmentation could occur .
When the central density exceeds n _ { c } \sim 10 ^ { 10 - 11 } cm ^ { -3 } , the successive fragmentation may cease since the cloud becomes opaque against the H _ { 2 } lines and the collapse decelerates appreciably .
Resultingly , the minimum value of \lambda _ { m } is estimated to be \sim 2 \times 10 ^ { -3 } pc .
The mass of the first star is then expected to be typically \sim 3 M _ { \odot } , which may grow up to \sim 16 M _ { \odot } by accreting the diffuse envelope .
Thus , the first-generation stars are anticipated to be massive but not supermassive .