Formation of an embryonic supermassive star in the first galaxy

We studied the gravitational collapse of a warm (~8000 K) primordial-gas cloud as a candidate progenitor for a supermassive star (SMS; ≳10⁵M⊙) using a three-dimensional hydrodynamical simulation including all the relevant cooling processes of both H₂ and H, which can potentially induce cloud fragmentation. This is the first simulation of this kind to resolve protostar formation. We find that from a weakly turbulent initial condition, the cloud undergoes runaway collapse without a major episode of fragmentation. Although the H₂ fraction jumps by a large factor via the three-body reaction at ~10^-13 g cm^-3, its cooling remains inefficient due to the optical thickness, and the temperature remains ≳3000 K. When the central core of the cloud becomes opaque to continuum radiation at ~10^-8 g cm^-3, a hydrostatic protostar with ≃0.2M⊙ is formed. The protostar grows to the mass ≃1M⊙ and the radius ≃2 au within ~1 yr via rapid accretion of dense filamentary flows.With high accretion rate, ~2M⊙ yr^-1, the protostar is expected to turn into an SMS within its lifetime, eventually collapsing to a seed for the supermassive black hole observed in the early Universe at z ~ 7.