Thermal and Fragmentation Properties of Star-forming Clouds in Low-Metallicity Environments

The thermal and chemical evolution of star-forming clouds is studied for different gas metallicities, Z, using the model of Omukai, 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 to 10^-3 Z_☉ and density ≈10⁵ cm^-3. Early on, CMB radiation prevents the gas temperature from falling 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 ≡ (b - a)/a > _NL ~ 1, where a (b) is the short (long) core axis length. The fragment mass is given by the thermal Jeans mass at = _NL. Given these assumptions and the initial (Gaussian) distribution of , we compute the fragment mass distribution as a function of metallicity. We find that (1) for Z = 0, all fragments are very massive, ≲10³ M_☉, consistent with previous studies; (2) for Z > 10^-6 Z_☉ a few clumps go through an additional high-density (≳10¹⁰ cm^-3) fragmentation phase driven by dust cooling, leading to low-mass fragments; (3) the mass fraction in low-mass fragments is initially very small, but at Z ~ 10^-5 Z_☉ it becomes dominant and continues to grow as Z is increased; (4) as a result of the two fragmentation modes, a bimodal mass distribution emerges in 0.01 < Z/Z_☉ < 0.1; and (5) for ≳0.1 Z_☉, the two peaks merge into a single-peaked mass function, which might be regarded as the precursor of the ordinary Salpeter-like initial mass function.