  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 Msun $\lesssim M_*
\lesssim$ 1000 Msun. The formation of very massive ($\gtrsim$ 250 Msun) stars
is possible under weak UV feedback, whereas ordinary massive (a few x 10 Msun)
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 Msun/yr, 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.
