On the Mass of Population III Stars

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~10²-10⁴ cm^-3 up to ~10¹³ cm^-3. It is found that, almost independent of initial conditions, a filamentary cloud continues to collapse nearly isothermally owing to H₂ cooling until the cloud becomes optically thick against the H₂ lines (n_c~10¹⁰-10¹¹ 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 (~800 K), which is ~1×10³ M_☉ pc^-1 during the contraction from n_c~10⁵ cm^-3 to 10¹³ 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 (λ_m) lessens as the collapse proceeds. Consequently, successive fragmentation could occur. When the central density exceeds n_c~10¹⁰-10¹¹ cm^-3, the successive fragmentation may cease, since the cloud becomes opaque against the H₂ lines and the collapse decelerates appreciably. Resultantly, the minimum value of λ_m is estimated to be ~2×10⁻³ pc. The mass of the first star is then expected to be typically ~3 M_☉, which may grow up to ~16 M_☉ by accreting the diffuse envelope. Thus, the first-generation stars are anticipated to be massive but not supermassive.