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 (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 ~10⁵ 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, > 10³M_sun, consistently with previous studies; (ii) for Z>10⁻⁶ Z_sun a few clumps go through an additional high density (> 10¹⁰ 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 ~ 10⁻⁵Z_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 < Z/Z_sun < 0.1. (v) For > 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.