$\mathrm{H_2}$ cooling and gravitational collapse of supersonically induced gas objects

We study the formation and gravitational collapse of supersonically induced gas objects (SIGOs) in the early universe. We run cosmological hydrodynamics simulations of SIGOs, including relative streaming motions between baryons and dark matter. Our simulations also follow nonequilibrium chemistry and molecular hydrogen cooling in primordial gas clouds. A number of SIGOs are formed in the run with fast-streaming motions of 2 times the rms of the cosmological velocity fluctuations. We identify a particular gas cloud that condensates by H$_2$ cooling without being hosted by a dark matter halo. The SIGO remains outside the virial radius of its closest halo, and it becomes Jeans unstable when the central gas-particle density reaches $\sim 100~{\rm cm}^{-3}$ with a temperature of $\sim$ 200 K. The corresponding Jeans mass is $\sim 10^5 M_{\odot}$, and thus the formation of primordial stars or a star cluster is expected in the SIGO.