On the Mass of Population III Stars
  Performing 1D hydrodynamical calculations coupled with non-equilibrium processes for H2 formation, we pursue the thermal and dynamical evolution of filamentary primordial clouds and attempt to make an estimate on the mass of population III stars. 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. 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). Applying a linear theory, we find that the spindle is unstable against fragmentation during the collapse. The wavelength of the fastest growing perturbation 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. 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. 
Fumitaka Nakamura, Masayuki Umemura