Can supermassive stars form in protogalaxies due to internal Lyman-Werner feedback?

Population III stars are possible precursors to early supermassive black holes (BHs). The presence of soft UV Lyman–Werner (LW) background radiation can suppress Population III star formation in minihaloes and allow them to form in pristine atomic-cooling haloes. In the absence of molecular hydrogen (⁠H2⁠) cooling, atomic-cooling haloes enable rapid collapse with suppressed fragmentation. High background LW fluxes from preceding star-formation have been proposed to dissociate H2⁠. This flux can be supplemented by LW radiation from one or more Population III star(s) in the same halo, reducing the necessary background level. Here, we consider atomic-cooling haloes in which multiple protostellar cores form close to one another nearly simultaneously. We assess whether the first star’s LW radiation can dissociate nearby ⁠, enabling rapid accretion on to a nearby protostellar core, and the prompt formation of a second, supermassive star (SMS) from warm, atomically-cooled gas. We use a set of hydrodynamical simulations with the code enzo, with identical LW backgrounds centred on a halo with two adjacent collapsing gas clumps. When an additional large local LW flux is introduced, we observe immediate reductions in both the accretion rates and the stellar masses that form within these clumps. While the LW flux reduces the H2 fraction and increases the gas temperature, the halo core’s potential well is too shallow to promptly heat the gas to >1000 K and increase the second protostar’s accretion rate. We conclude that this internal LW feedback scenario is unlikely to facilitate SMS or massive BH seed formation.