In this talk I will present an overview of recent simulations of Population
III star formation in a cosmological context. Recent published and
unpublished work by multiple groups of authors using fundamentally
different computational methods appears to have converged to give a
consistent view of Population III star formation. In the absence of a
photodissociating background, Population III protostellar cores form within
small (5x105 - 106 solar mass) cosmological
halos. Due to the relatively poor cooling properties of molecular
hydrogen, collapse of the halo core occurs quasistatically until high
densities (on the order of 108 cm-3) are reached, at
which point 3-body molecular hydrogen formation takes place and the
collapse accelerates. The collapsing core finally forms a hydrostatic
protostar with mass of ~0.001 Msun. At this point, cosmological
simulations do not have sufficient physics to continue the calculations
(and to determine the Population III IMF) and different methods must be
considered.
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