  In cold dark matter cosmological models, the first stars to form are believed
to do so within small protogalaxies. We wish to understand how the evolution of
these early protogalaxies changes once the gas forming them has been enriched
with small quantities of heavy elements, which are produced and dispersed into
the intergalactic medium by the first supernovae. Our initial conditions
represent protogalaxies forming within a fossil H II region, a previously
ionized region that has not yet had time to cool and recombine. We study the
influence of low levels of metal enrichment on the cooling and collapse of
ionized gas in small protogalactic halos using three-dimensional, smoothed
particle hydrodynamics (SPH) simulations that incorporate the effects of the
appropriate chemical and thermal processes. Our previous simulations
demonstrated that for metallicities Z < 0.001 Z_sun, metal line cooling alters
the density and temperature evolution of the gas by less than 1% compared to
the metal-free case at densities below 1 cm-3) and temperatures above 2000 K.
Here, we present the results of high-resolution simulations using particle
splitting to improve resolution in regions of interest. These simulations allow
us to address the question of whether there is a critical metallicity above
which fine structure cooling from metals allows efficient fragmentation to
occur, producing an initial mass function (IMF) resembling the local Salpeter
IMF, rather than only high-mass stars.
