Evolution and Final Fates of Rapidly Accreting Supermassive Stars

The formation of supermassive stars (SMSs) is a possible pathway to seed supermassive black holes in the early universe. This chapter summarizes recent theoretical efforts to understand their evolution, highlighting effects of very rapid accretion at the rates of $\dot{M}_* \gtrsim 0.1~$M$_\odot$ yr$^{-1}$. Stellar evolution calculations predict that such an accreting SMS has a characteristic feature, i.e., a very large radius that monotonically increases as the stellar mass increases. The radius exceeds $7000$ R$_\odot$ (or $30$ AU) after the star accretes the gas of more than $10^3$ M$_\odot$. We show that the emergence of the "supergiant protostar" stage is a key for the formation of SMSs, because resulting radiative feedback against the accretion flow is substantially weakened during this stage. We also show that these SMSs end their lives while the accretion continues, and that their final fates vary with different accretion rates.