Transition of the initial mass function in the metal-poor environments

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 $0.1~Z_{\odot}$. The cooling induced by dust grains promotes fragmentation at small scales and the formation of low-mass stars with $M_{*} \sim 0.01$--$0.1~M_{\odot}$ when $Z/Z_{\odot} \gtrsim 10^{-5}$. While the number of low-mass stars increases with metallicity, the stellar mass distribution is still top-heavy for $Z/Z_{\odot} \lesssim 10^{-2}$ compared to the Chabrier initial mass function (IMF). In these cases, star formation begins after the turbulent motion decays and a single massive cloud core monolithically collapses to form a central massive stellar system. The circumstellar disk preferentially feeds the mass to the central massive stars, making the mass distribution top-heavy. When $Z/Z_{\odot}=0.1$, collisions of the turbulent flows promote the onset of the star formation and a highly filamentary structure develops owing to efficient fine-structure line cooling. In this case, the mass supply to the massive stars is limited by the local gas reservoir and the mass is shared among the stars, leading to a Chabrier-like IMF. We conclude that cooling at the scales of the turbulent motion promotes the development of the filamentary structure and works as an important factor leading to the present-day IMF.