Impact of the cosmic background radiation on the initial mass function of metal-poor stars

We study star cluster formation at low metallicities of $Z/Z_\odot=10^{-4}$--$10^{-1}$ using three-dimensional hydrodynamics simulations. Particular emphasis is put on how the stellar mass distribution is affected by the cosmic microwave background radiation (CMB), which sets the temperature floor to the gas. Starting from the collapse of a turbulent cloud, we follow the formation of a protostellar system resolving $\sim$au scale. In relatively metal-enriched cases of $Z/Z_\odot \gtrsim 10^{-2}$, where the mass function resembles the present-day one in the absence of the 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 $z\gtrsim10$. In lower-metallicity cases with $Z/Z_\odot \lesssim 10^{-3}$, 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 $Z/Z_\odot \lesssim 10^{-2}$ or at a high redshift $z\gtrsim10$, the mass spectrum consists of a low-mass Salpeter-like component, peaking at $0.1~M_\odot$, and a top-heavy component with $10$--$50~M_\odot$, with the fraction in the latter increasing with increasing redshift. In galaxies forming at $z\gtrsim10$, the major targets of the future instruments including JWST, CMB heating makes the stellar mass function significantly top-heavy, enhancing the number of supernova explosions by a factor of $1.4$ ($2.8$) at $z=10$ ($20$, respectively) compared to the prediction by Chabrier initial mass function when $Z/Z_\odot=0.1$.