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Thermal and chemical evolution of primordial gas clouds irradiated with far-ultraviolet (FUV; < 13. 6 eV) radiation is investigated. In clouds irradiated by intense FUV radiation, sufficient hydrogen molecules to be important for cooling are never formed. However, even without molecular hydrogen, if the clouds are massive enough, they start collapsing via atomic hydrogen line cooling. Such clouds continue to collapse almost isothermally owing to successive cooling by H^- free-bound emission up to the number density of 10^16 cm^-3. Inside the clouds, the Jeans mass eventually falls well below a solar mass. This indicates that hydrogen molecules are dispensable for low-mass primordial star formation, provided fragmentation of the clouds occurs at sufficiently high density.
Kazuyuki Omukai (2001) studied this question.