Supermassive star formation via episodic accretion: Protostellar disc instability and radiative feedback efficiency

The formation of supermassive stars (SMSs) is a potential pathway to seed supermassive black holes in the early universe. A critical issue for forming SMSs is stellar UV feedback, which may limit the stellar mass growth via accretion. In this paper, we study the evolution of an accreting SMSand itsUVemissivity with realistic variable accretion from a circumstellar disc. First we conduct a 2D hydrodynamical simulation to follow the protostellar accretion until the stellar mass exceeds 104M⊙. The disc fragments by gravitational instability, creating many clumps that migrate inward to fall on to the star. The resulting accretion history is highly timedependent: short episodic accretion bursts are followed by longer quiescent phases. We show that the disc for the direct collapse model is more unstable and generates greater variability than normal Pop III cases. Next, we conduct a stellar evolution calculation using the obtained accretion history. Our results show that, regardless of the variable accretion, the stellar radius monotonically increases with almost constant effective temperature at T_eff ≃ 5000 K as the stellar mass increases. The resulting UV feedback is too weak to hinder accretion due to the low flux of stellar UV photons. The insensitivity of stellar evolution to variable accretion is attributed to the fact that time-scales of variability, ≲10³ yr, are too short to affect the stellar structure.We argue that this evolution will continue until the SMS collapses to produce a black hole by the general relativistic instability after the mass reaches ≳10⁵M⊙.