  The formation of the first stars out of metal-free gas appears to result in
stars at least an order of magnitude more massive than in the present-day case.
We here consider what controls the transition from a primordial to a modern
initial mass function. It has been proposed that this occurs when effective
metal line cooling occurs at a metallicity threshold of Z/Z_sun > 10^{-3.5}. We
study the influence of low levels of metal enrichment on the cooling and
collapse of initially ionized gas in small protogalactic halos using
three-dimensional, smoothed particle hydrodynamics simulations with particle
splitting. Our initial conditions represent protogalaxies forming within a
previously ionized H ii region that has not yet had time to cool and recombine.
These differ considerably from those used in simulations predicting a
metallicity threshold, where the gas was initially cold and only partially
ionized. In the centrally condensed potential that we study here, a wide
variety of initial conditions for the gas yield a monolithic central collapse.
Our models show no fragmentation during collapse to number densities as high as
10^5 cm^{-3}, for metallicities reaching as high as 10^{-1} Z_sun in one
rotating case, far above the threshold suggested by previous work. Rotation
allows for the formation of gravitationally stable gas disks over large
fractions of the local Hubble time. Turbulence slows the growth of the central
density slightly, but both spherically symmetric and turbulent initial
conditions collapse and form a single sink particle. We therefore argue that
fragmentation at moderate density depends on the initial conditions for star
formation more than on the metal abundances present.
