Formation of Supersonic Turbulence in the Primordial Star-forming Cloud

We present new simulations of the formation and evolution of the first star-forming cloud within a massive minihalo of mass of $1.05 \times 10^7\, M_{\odot}$, carried out using the GIZMO code with detailed modeling of primordial gas cooling and chemistry. Unlike previous studies that simulated the formation of the first stars within a smaller cosmological boxsize of $\sim 1-2$ Mpc, our work adopts initial conditions from the large-scale cosmological simulations, IllustrisTNG spanning $\sim 50$ Mpc to study the formation of primordial clouds that give birth to the first stars. We increase the original resolution of IllustrisTNG by a factor of $\sim10^5$ using a particle-splitting technique, achieving an extremely high resolution that allows us to resolve turbulence driven by gravitational collapse during early structure formation. We find that strong supersonic turbulence with a characteristic Mach number of $\sim 5.2$ naturally develops within the collapsing halo. This turbulence efficiently stirs the gas, promoting fragmentation of the star-forming cloud into multiple dense clumps. Among them, we identify a gravitationally bound core with a mass of $8.07\,M_{\odot}$ and a size of $0.03$ pc, which exceeds its local Jeans mass and is on the verge of collapsing into a star. Our results indicate that supersonic turbulence may be common in primordial halos and can play a crucial role in cloud-scale fragmentation, potentially lowering the characteristic mass scale of the first stars.