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} Z_sun and density ~10^{5} cm^{-3}. Early on, CMB radiation
prevents the gas temperature to fall below T_CMB, 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 > E_NL ~ 1, where a (b) is the short (long) core axis
length. The fragment mass is given by the thermal Jeans mass at E = E_NL. 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^{3}M_sun, consistently with previous
studies; (ii) for Z>10^{-6} Z_sun 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^{-5}Z_sun 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 0.1Z_sun,
the two peaks merge into a singly-peaked mass function which might be regarded
as the precursor of the ordinary Salpeter-like IMF.Comment: 38 pages, 16 figures, ApJ in pres