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We study the influence of low levels of metal enrichment on the cooling andcollapse of ionized gas in small protogalactic halos using three-dimensional,smoothed particle hydrodynamics simulations. Our initial conditions representprotogalaxies forming within a fossil HII region -- a previously ionized HIIregion which has not yet had time to cool and recombine. Prior to cosmologicalreionization, such regions should be relatively common, since thecharacteristic lifetimes of the likely ionizing sources are significantlyshorter than a Hubble time. We show that in these regions, H_2 is the dominantand most effective coolant, and that it is the amount of H_2 formed thatdetermines whether or not the gas can collapse and form stars.  At the low metallicities (Z < 10^{-3} Z_sun) thought to be associated withthe transition from population III to early population II star formation, metalline cooling has an almost negligible effect on the evolution of low densitygas, altering 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 temperaturesabove 2000 K. Although there is evidence that metal line cooling becomes moreeffective at higher density, we find no significant differences in behaviourfrom the metal-free case at any density below our sink particle creationthreshold at n = 500 cm^{-3}. Increasing the metallicity also increases theimportance of metal line cooling, but it does not significantly affect thedynamical evolution of the low density gas until Z = 0.1 Z_sun. This resultholds regardless of whether or not an ultraviolet background is present.Comment: 38 pages, 8 figures, AASTex. Accepted by ApJ. Corrected typos and  reference

Star Formation at Very Low Metallicity. II. On the Insignificance of Metal‐Line Cooling During the Early Stages of Gravitational Collapse