Formation of first star clusters under the supersonic gas flow -- I. Morphology of the massive metal-free gas cloud
We performed $42$ simulations of the first star formation with initial supersonic gas flows relative to the dark matter at the cosmic recombination era. Increasing the initial streaming velocities led to delayed halo formation and increased halo mass, enhancing the mass of the gravitationally shrinking gas cloud. For more massive gas clouds, the rate of temperature drop during contraction, in other words, the structure asymmetry, becomes more significant. When the maximum and minimum gas temperature ratios before and after contraction exceed about ten, the asymmetric structure of the gas cloud prevails, inducing fragmentation into multiple dense gas clouds. We continued our simulations until $10^5$ years after the first dense core formation to examine the final fate of the massive star-forming gas cloud. Among the $42$ models studied, we find the simultaneous formation of up to four dense gas clouds, with a total mass of about $2254\,M_\odot$. While the gas mass in the host halo increases with increasing the initial streaming velocity, the mass of the dense cores does not change significantly. The star formation efficiency decreases by more than one order of magnitude from $ε_{\rm III} \sim 10^{-2}$ to $10^{-4}$ when the initial streaming velocity, normalised by the root mean square value, increases from 0 to 3.