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The thermal and chemical evolution of star-forming clouds is studied for different gas metallicities, Z, using the model of Omukai (2000), updated to include deuterium chemistry and the effects of cosmic microwave background (CMB) radiation. HD-line cooling dominates the thermal balance of clouds when Z \\~ 10^-5-10^-3 Zₛun and density ~10^5 cm^-3. Early on, CMB radiation prevents the gas temperature to fall below TCMB, although this hardly alters the cloud thermal evolution in low-metallicity gas. From the derived temperature evolution, we assess cloud/core fragmentation as a function of metallicity from linear perturbation theory, which requires that the core elongation E: = (b-a) /a > ENL ~ 1, where a (b) is the short (long) core axis length. The fragment mass is given by the thermal Jeans mass at E = ENL. Given these assumptions and the initial (gaussian) distribution of E we compute the fragment mass distribution as a function of metallicity. We find that: (i) For Z=0, all fragments are very massive, > 10^3Mₛun, consistently with previous studies; (ii) for Z>10^-6 Zₛun a few clumps go through an additional high density (> 10^10 cm^-3) fragmentation phase driven by dust-cooling, leading to low-mass fragments; (iii) The mass fraction in low-mass fragments is initially very small, but at Z ~ 10^-5Zₛun it becomes dominant and continues to grow as Z is increased; (iv) as a result of the two fragmentation modes, a bimodal mass distribution emerges in 0. 01 0. 1Zₛun, the two peaks merge into a singly-peaked mass function which might be regarded as the precursor of the ordinary Salpeter-like IMF.
Omukai et al. (Wed,) studied this question.