The Polytropic Equation of State of Primordial Gas Clouds

The polytropic equation of state (EOS) of primordial gas clouds with modest enrichment is computed, motivated by the recent observations of very Fe-deficient stars, [Fe/H]~10^{-3.5}-10^{-5}, such as HE 0107-5240 and CS 29498-043. These stars are overabundant, relative to Fe, in C and O. We assume that the observed abundances of species like C, O, Si and Fe are representative of the gas from which the currently observed metal-deficient stars formed. Under this assumption, we find that this primordial metal abundance pattern has profound consequences for the thermal balance and chemical composition of the gas, and hence for the EOS of the parental cloud. The polytopic EOS is soft for low, [O/H]<10^{-3}, oxygen abundances, but stiffens to a polytropic index gamma large than unity for [O/H]>10^{-2} due to the large opacity in the CO and H2O cooling lines. It is further found that a regulating role is played by the presence and temperature of the dust, even when the overall carbon abundance is only [C/H]~10^{-2}. When the dust is warmer than the gas, a region with gamma~1.2 results around a density of ~10^4 cm^{-3}. When the dust is colder than the gas, a region with gamma~0.8 is found for a density of ~10^6 cm^{-3}. Implications for the primordial initial mass function (IMF) as well as the IMF in starburst galaxies, where the metallicity is super-solar, are explored and related to processes that influence the temperature of the ambient dust.