Primordial supermassive stars (SMSs) formed in atomic-cooling halos at z ~ 15 - 20 are leading candidates for the seeds of the first quasars. Past numerical studies of the evolution of SMSs have typically assumed constant accretion rates rather than the highly variable flows in which they form. We model the evolution of SMSs in the cosmological flows that create them using the Kepler stellar evolution and implicit hydrodynamics code. We find that they reach masses of 1 - 2 x $10^5 M_{odot}$ before undergoing direct-collapse to black holes (DCBHs) during or at the end of their main-sequence hydrogen burning, at 1 - 1.5 Myr, regardless of halo mass, spin, or merger history. We also find that realistic, highly-variable accretion histories allow for a much greater diversity of supermassive stellar structures, including in some cases largely thermally relaxed objects, which may provide a significant source of radiative feedback. Our models indicate that the accretion histories predicted for purely atomic-cooling halos may impose a narrow spectrum of masses on the seeds of the first massive quasars, however further studies incorporating realistic feedback will be essential in order to confirm whether or not this holds true in all cases. Our results also indicate that multiple SMSs at disparate stages of evolution can form in these halos, raising the possibility of SMS binaries and supermassive X-ray binaries (SMXBs), as well as DCBH mergers which could be detected by LISA.
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