Radiative feedback for supermassive star formation in a massive cloud with H2 molecules in an atomic-cooling halo

Recent three-dimensional cosmological simulations of protogalaxy formation have suggested that supermassive stars (SMSs) can form in gas clouds in which H$_2$ cooling is suppressed by dynamical heating prior to the activation of atomic cooling (Wise et al. 2019), but they stopped short of the following growth of a central protostar. Here we examine whether accretion on the protostellar core in this cloud is sufficiently rapid, in the face of the radiation feedback, to produce a SMS. We perform one-dimensional radiation-hydrodynamical simulations of the hot collapsing cloud with non-equilibrium chemical reactions directly adopting the cloud properties from Wise et al. (2019) as an initial condition. We find that the stellar Lyman-Werner (LW) radiation from the SMS dissociates H$_2$ in the inner regions of the gas flow, increasing gas temperature and thermal pressure, and temporarily stopping the accretion. However, this negative feedback ceases when the self-gravity and inward ram pressure force on larger scales push the gas inward. The central protostar is unable to expand an HII region due to the high density, and grows to a mass of $\gtrsim10^5\,{{\rm M}_\odot}$. Our results suggests the successful formation of SMSs, and resulting massive ($\sim10^5\,{{\rm M}_\odot}$) remnant black holes in the clouds, but need to be confirmed in two- or three-dimensional simulations.