An estimate of the mass of zero metal stars

The temperature of a cloud of hydrogen–helium gas uncontaminated by metals is followed from post recombination conditions to hydrogen ionization, assuming the collapse takes place on a free-fall time-scale. Four characteristic masses are identifiable: 106M⊙ for a sufficiently hot cloud to allow H2 to form, 20M⊙ at H2 dissociation, 0.5M⊙ at optical depth unity, and 0.06M⊙ at H ionization. The initial cloud is of low enough density, ∼ 104 cm−3, that stellar winds will prevent the formation of stars heavier than 100M⊙. The characteristic masses 0.06M⊙ and 0.5M⊙ occur in environments with such high density, 10−2 and 10−8 g cm−3 respectively, that they are identified with a protostellar inner and outer core, and will continue to accrete material for a minimum stellar mass of a few solar masses. A metal production yield of 10 per cent combined with the minimum metal abundance for ordinary stars implies that the zero metal stars comprised at most 10−4 of the gas mass of the Universe. This small fraction of heavy stars would have been capable of re-ionizing the Universe at a z of 50–100.