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

The thermal and chemical evolution of star-forming clouds is studied fordifferent gas metallicities, Z, using the model of Omukai (2000), updated toinclude 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 radiationprevents the gas temperature to fall below T_CMB, although this hardly altersthe cloud thermal evolution in low-metallicity gas. From the derivedtemperature evolution, we assess cloud/core fragmentation as a function ofmetallicity from linear perturbation theory, which requires that the coreelongation E := (b-a)/a > E_NL ~ 1, where a (b) is the short (long) core axislength. The fragment mass is given by the thermal Jeans mass at E = E_NL. Giventhese assumptions and the initial (gaussian) distribution of E we compute thefragment mass distribution as a function of metallicity. We find that: (i) ForZ=0, all fragments are very massive, > 10^{3}M_sun, consistently with previousstudies; (ii) for Z>10^{-6} Z_sun a few clumps go through an additional highdensity (> 10^{10} cm^{-3}) fragmentation phase driven by dust-cooling, leadingto low-mass fragments; (iii) The mass fraction in low-mass fragments isinitially very small, but at Z ~ 10^{-5}Z_sun it becomes dominant and continuesto grow as Z is increased; (iv) as a result of the two fragmentation modes, abimodal 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 regardedas the precursor of the ordinary Salpeter-like IMF.Comment: 38 pages, 16 figures, ApJ in pres