On the mass of Population III stars

Performing one-dimensional hydrodynamical calculations coupled with nonequi librium processes for hydrogen molecule formation, we pursue the thermal an d dynamical evolution of filamentary primordial gas clouds and attempt to m ake an estimate on the mass of Population III stars. The cloud evolution is computed from the central proton density n(c) similar to 10(2)-10(4) cm(-3 ) up to similar to 10(13) cm(-3) It is found that, almost independent of in itial conditions, a filamentary cloud continues to collapse nearly isotherm ally owing to H-2 cooling until the cloud becomes optically thick against t he H-2 lines (n(c) similar to 10(10)-10(11) cm(-3)). During the collapse th e cloud structure separates into two parts, i.e., a denser spindle and a di ffuse envelope. The spindle contracts quasi-statically, and thus the line m ass of the spindle keeps a characteristic value determined solely by the te mperature (similar to 800 K), which is similar to 1x10(3) M. pc(-1) during the contraction from n(c) similar to 10(5) cm(-3) to 10(13) cm(-3) Applying a linear theory, we find that the spindle is unstable against fragmentatio n during the collapse. The wavelength of the fastest growing perturbation ( lambda(m)) lessens as the collapse proceeds. Consequently, successive fragm entation could occur. When the central density exceeds n(c) similar to 10(1 0)-10(11) cm(-3), the successive fragmentation may cease, since the cloud b ecomes opaque against the H-2 lines and the collapse decelerates appreciabl y. Resultantly, the minimum value of lambda(m) is estimated to be similar t o 2 x 10(-3) pc. The mass of the first star is then expected to be typicall y similar to 3 M., which may grow up to similar to 16 M. by accreting the d iffuse envelope. Thus, the first-generation stars are anticipated to be mas sive but not supermassive.