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Abstract Supermassive primordial stars with masses exceeding ∼10⁵M_⊙that form in atomically cooled halos are the leading candidates for the origin of high-redshift quasars atz> 6. Recent numerical simulations, however, find that multiple accretion disks can form within a halo, each of which can potentially host a supermassive star. We investigate the formation and evolution of secondary supermassive stars in atomically cooled halos, including strong variations in their accretion histories driven by gravitational interactions between their disks and those surrounding the primary supermassive stars in each halo. We find that all secondary disks produce long-lived supermassive stars under sustained rapid accretion. We also find, however, that the majority of secondary supermassive stars do undergo at least one protracted quiescent accretion phase, during which time they thermally relax and may become powerful sources of ionizing feedback. In many halos, the two satellite disks collide, suggesting that the two stars can come into close proximity. This may induce additional mass exchange between them, leading to a great diversity of possible outcomes. These range from coevolution as main-sequence stars to main sequence—black hole pairs and black hole—black hole mergers. We discuss the likely outcome for these binary interactions based on the evolutionary state of both supermassive stars at the end of our simulations, as well as prospects for their future detection by current and next-generation facilities. 

ABSTRACT Supermassive stars are Population III stars with masses exceeding $$10^4\, {\rm M}_{\odot }$$ that could be the progenitors of the first supermassive black holes. Their interiors are in a regime where radiation pressure dominates the equation of state. In this work, we use the explicit gas dynamics code ppmstar to simulate the hydrogen-burning core of a $$10^4\, {\rm M}_{\odot }$$ supermassive main-sequence star. These are the first three-dimensional hydrodynamics simulations of core convection in supermassive stars. We perform a series of 10 simulations at different heating rates and on Cartesian grids with resolutions of 7683, 11523, and 17283. We examine different properties of the convective flow, including its large-scale morphology, its velocity spectrum, and its mixing properties. We conclude that the radiation pressure-dominated nature of the interior does not noticeably affect the behaviour of convection compared to the case of core convection in a massive main-sequence star where gas pressure dominates. Our simulations also offer support for the use of mixing-length theory in one-dimensional models of supermassive stars.