We study star cluster formation in a low-metallicity environment using three-dimensional hydrodynamic simulations. Starting from a turbulent cloud core, we follow the formation and growth of protostellar systems with different metallicities ranging from 10-6 to 0.1 Z?. The cooling induced by dust grains promotes fragmentation at small scales and the formation of low-mass stars with 0.01-0.1 M?. While the number of low-mass stars increases with metallicity, when Z/Z? ? 10-5, the stellar mass distribution is still top-heavy for Z/Z? ? 10-2 compared to the Chabrier initial mass function (IMF). When Z/Z? = 0.1, a highly filamentary structure develops owing to efficient fine-structure line cooling and the mass is shared among the stars, leading to a Chabrier-like IMF.
We also study how the stellar mass distribution is affected by the cosmic microwave background radiation (CMB), which sets the temperature floor to the gas. In relatively metal-enriched cases of Z/Z? ? 10-2, where the mass function resembles the present-day one in the absence of CMB, high-temperature CMB suppresses cloud fragmentation and reduces the number of low-mass stars, making the mass function more top-heavy than in the cases without CMB heating at z ? 10. In lower-metallicity cases with Z/Z? ? 10-3, where the gas temperature is higher than the CMB value due to inefficient cooling, the CMB has only a minor impact on the mass distribution, which is top-heavy, regardless of the redshift. In cases either with a low metallicity of Z/Z? ? 10-2 or at a high redshift z ? 10, the mass spectrum consists of a low-mass Salpeter-like component, peaking at 0.1 M?, and a top-heavy component with 10-50 M?, with the fraction in the latter increasing with increasing redshift.
In addition, we discuss the radiative feedback effects from the forming stars on their final mass distribution.