Fragmentation induced starvation in Population III star formation: a
  resolution study
  The Population III initial mass function (IMF) is currently unknown, but
recent studies agree that fragmentation of primordial gas gives a broader IMF
than the initially suggested singular star per halo. In this study we introduce
sink particle mergers into Arepo, to perform the first resolution study for
primordial star formation simulations and present the first Population III
simulations to run up to densities of 10-6g cm-3 for hundreds of years after
the formation of sink particles. The total number of sinks formed increases
with increasing sink particle creation density, without achieving numerical
convergence. The total mass in sinks remains invariant to the maximum
resolution and is safe to estimate using low resolution studies. This results
in an IMF that shifts towards lower masses with increasing resolution. Greater
numbers of sinks cause increased fragmentation-induced starvation of the most
massive sink, yielding lower accretion rates, masses and ionising photons
emitted per second. The lack of convergence up to densities 2 orders of
magnitudes higher than all relevant chemical reactions suggests that the number
of sinks will continue to grow with increasing resolution until H2 is fully
dissociated and the collapse becomes almost adiabatic at 10-4g cm-3. These
results imply that many Population III studies utilising sink particles have
produced IMFs which have overestimated the masses of primordial stars, and
underestimated the number of stars formed. In the highest resolution runs,
sinks with masses capable of surviving until the present day had an ejection
fraction of 0.21.
