Clumpy Structures within the Turbulent Primordial Cloud

The primordial clouds in the mini-halos hatch the first generation stars of the universe, which play a crucial role in cosmic evolution. In this paper, we investigate how the turbulence impacts the structure of primordial star-forming cloud. Previous cosmological simulations of the first star formation predicted a typical mass of around $\mathrm{ 100 \, M_\odot}$, which conflicts with recent observations of extremely metal-poor stars suggesting a lower mass scale of around $\mathrm{25 \, M_\odot}$. The discrepancy may arise from unresolved turbulence in the star-forming cloud, driven by primordial gas accretion during mini-halo formation in the previous simulation. To quantitatively examine the turbulence effect on the primordial cloud formation, we employ the adaptive mesh refinement code $\mathtt{Enzo}$ to model the gas cloud with primordial composition, including artificial-driven turbulence on the cloud scale and relevant gas physics. This artificial-driven turbulence utilizes a stochastic forcing model to mimic the unresolved turbulence inside mini-halos. Our results show that turbulence with high Mach number and compressional mode effectively fragments the cloud into several clumps, each with dense cores of $\mathrm{22.7 - 174.9 \, M_\odot}$ that undergo Jeans instability to form stars. Fragmentation caused by intense and compressive turbulence prevents the runaway collapse of the cloud. The self-bound clumps with smaller masses in turbulent primordial cloud suggest a possible pathway to decrease the theoretical mass scale of first stars, further reconciling the mass discrepancy between simulations and observations.