The fragmentation process in collapsing clouds with various metallicities is studied using three-dimensional nested-grid hydrodynamics. Initial clouds are specified by three parameters: cloud metallicity, initial rotation energy and initial cloud shape. For different combinations of these parameters, we calculate 480 models in total and study cloud evolution, fragmentation conditions, orbital separation and binary frequency. For the cloud to fragment during collapse, the initial angular momentum must be higher than a threshold value, which decreases with decreasing metallicity. Although the exact fragmentation conditions depend also on the initial cloud shape, this dependence is only modest. Our results indicate a higher binary frequency in lower metallicity gas. In particular, with the same median rotation parameter as in the solar neighbourhood, a majority of stars are born as members of binary/multiple systems for <10-4 Z⊙. With initial mass <0.1 M⊙, if fragments are ejected in embryo from the host clouds by multibody interaction, they evolve to substellar-mass objects. This provides a formation channel for low-mass stars in zero- or low-metallicity environments.
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