$\mathrm{H_2}$ 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.
