The First Stars: Mass Growth Under Protostellar Feedback
  We perform three-dimensional cosmological simulations to examine the growth
of metal-free, Population III (Pop III) stars under radiative feedback. We
begin our simulation at z=100 and trace the evolution of gas and dark matter
until the formation of the first minihalo. We then follow the collapse of the
gas within the minihalo up to densities of n = 10^12 cm^-3, at which point we
replace the high-density particles with a sink particle to represent the
growing protostar. We model the effect of Lyman-Werner (LW) radiation emitted
by the protostar, and employ a ray-tracing scheme to follow the growth of the
surrounding H II region over the next 5000 yr. We find that a disk assembles
around the first protostar, and that radiative feedback will not prevent
further fragmentation of the disk to form multiple Pop III stars. Ionization of
neutral hydrogen and photodissociation of H_2 by LW radiation leads to heating
of the dense gas to several thousand Kelvin, and this warm region expands
outward at the gas sound speed. Once the extent of this warm region becomes
equivalent to the size of the disk, the disk mass declines while the accretion
rate onto the protostars is reduced by an order of magnitude. This occurs when
the largest sink has grown to ~ 20 M_sol while the second sink has grown to 7
M_sol, and we estimate the main sink will approach an asymptotic value of ~ 30
M_sol by the time it reaches the main sequence. Our simulation thus indicates
that the most likely outcome is a massive Pop III binary. However, we simulate
only one minihalo, and the statistical variation between minihaloes may be
substantial. If Pop III stars were typically unable to grow to more than a few
tens of solar masses, this would have important consequences for the occurence
of pair-instability supernovae in the early Universe as well as the Pop III
chemical signature in the oldest stars observable today.
