Radiative feedback from primordial protostars and final mass of the first stars

In this contribution, we review our efforts toward understanding the typical mass-scale of primordial stars. Our direct numerical simulations show that, in both of Population III.1 and III.2 cases, strong UV stellar radiative feedback terminatesmass accretion onto a protostar. An HII region formed around the protostar expands very dynamically into the accreting envelope, and cuts off the gas supply to a circumstellar disk. The disk is exposed to the stellar UV radiation and loses its mass by photoevaporation. The derived final masses are 43 M_⊙ and 17 M_⊙ in our fiducial Population III.1 and III.2 cases. Much more massive stars, however, should form in other exceptional conditions. In atomic-cooling halos where H₂ molecules are dissociated, for instance, a protostar grows via very rapid mass accretion with the rates M_*∼0.1-1M_⊙yr^-1. Our new stellar evolution calculations show that the protostar significantly inflates and never contracts to reach the zero-agemain-sequence stage in this case. Such "supergiant protostars" have very low UV luminosity, which results in weak radiative feedback against the accretion flow. In the early universe, supermassive stars formed through this process might provide massive seeds of supermassive black holes.