One hundred first stars: Protostellar evolution and the final masses

We perform a large set of radiation hydrodynamic simulations of primordial star formation in a fully cosmological context. Our statistical sample of 100 First Stars shows that the first generation of stars has a wide mass distribution M _popIII = 10 ∼ 1000 M_·. We first run cosmological simulations to generate a set of primordial star-forming gas clouds. We then follow protostar formation in each gas cloud and the subsequent protostellar evolution until the gas mass accretion onto the protostar is halted by stellar radiative feedback. The accretion rates differ significantly among the primordial gas clouds that largely determine the final stellar masses. For low accretion rates, the growth of a protostar is self-regulated by radiative feedback effects, and the final mass is limited to several tens of solar masses. At high accretion rates the protostar's outer envelope continues to expand, and the effective surface temperature remains low; such protostars do not exert strong radiative feedback and can grow in excess of 100 solar masses. The obtained wide mass range suggests that the first stars play a variety of roles in the early universe, by triggering both core-collapse supernovae and pair-instability supernovae as well as by leaving stellar mass black holes. We find certain correlations between the final stellar mass and the physical properties of the star-forming cloud. These correlations can be used to estimate the mass of the first star from the properties of the parent cloud or of the host halo without following the detailed protostellar evolution.