We perform a large set of radiation hydrodynamics simulations of primordial star formation in a fully cosmological context. a Our statistical sample of 100 First Stars show that the first generation of stars have 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 which 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 to one hundred 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.

We perform a large set of cosmological simulations of early structure formation and follow the formation and evolution of 1540 star-forming gas clouds to derive the mass distribution of primordial stars. The star formation in our cosmological simulations is characterized by two distinct populations, the so-called Population III.1 stars and primordial stars formed under the influence of far-ultraviolet (FUV) radiation (Population III.2 D stars). In this work, we determine the stellar masses by using the dependences on the physical properties of star-forming cloud and/or the external photodissociating intensity from nearby primordial stars, which are derived from the results of 2D radiation hydrodynamic simulations of protostellar feedback. The characteristic mass of the Pop III stars is found to be a few hundred solar masses at z ∼ 25, and it gradually shifts to lower masses with decreasing redshift. At high redshifts z > 20, about half of the star-forming gas clouds are exposed to intense FUV radiation and thus give birth to massive Pop III.2 D stars. However, the local FUV radiation by nearby Pop III stars becomes weaker at lower redshifts, when typical Pop III stars have smaller masses and the mean physical separation between the stars becomes large owing to cosmic expansion. Therefore, at z < 20, a large fraction of the primordial gas clouds host Pop III.1 stars. At z 15, the Pop III.1 stars are formed in relatively cool gas clouds due to efficient radiative cooling by H 2 and HD molecules; such stars have masses of a few ×10 M ⊙ . Since the stellar evolution and the final fate are determined by the stellar mass, Pop III stars formed at different epochs play different roles in the early Universe.

We present coupled stellar evolution (SE) and 3D radiation-hydrodynamic (RHD) simulations of the evolution of primordial protostars, their immediate environment, and the dynamic accretion history under the influence of stellar ionizing and dissociating UV feedback. Our coupled SE-RHD calculations result in a wide diversity of final stellar masses covering 10 M M * 10 3 M . The formation of very massive ( 250 M ) stars is possible under weak UV feedback, whereas ordinary massive (a few ×10 M ) stars form when UV feedback can efficiently halt the accretion. This may explain the peculiar abundance pattern of a Galactic metal-poor star recently reported by Aoki et al. (2014), possibly the observational signature of very massive precursor primordial stars. Weak UV feedback occurs in cases of variable accretion, in particular when repeated short accretion bursts temporarily exceed 0.01 M yr −1 , causing the protostar to inflate. In the bloated state, the protostar has low surface temperature and UV feedback is suppressed until the star eventually contracts, on a thermal adjustment timescale, to create an Hii region. If the delay time between successive accretion bursts is sufficiently short, the protostar remains bloated for extended periods, initiating at most only short periods of UV feedback. Disk fragmentation does not necessarily reduce the final stellar mass. Quite the contrary, we find that disk fragmentation enhances episodic accretion as many fragments migrate inward and are accreted onto the star, thus allowing continued stellar mass growth under conditions of intermittent UV feedback. This trend becomes more prominent as we improve the resolution of our simulations. We argue that simulations with significantly higher resolution than reported previously are needed to derive accurate gas mass accretion rates onto primordial protostars.