Low-metallicity protostars and the maximum stellar mass resulting from radiative feedback: Spherically symmetric calculations

The final mass of a newborn star is set at the epoch when the mass accretion onto the star is terminated. We study the evolution of accreting protostars and the limits of accretion in low-metallicity environments under spherical symmetry. Accretion rates onto protostars are estimated via the temperature evolution of prestellar cores with different metallicities. The derived rates increase with decreasing metallicity, from at Z = Z to 10 ^-3 M yr^-1 at Z = 0. With the derived accretion rates, the protostellar evolution is numerically calculated. We find that, at lower metallicity, the protostar has a larger radius and reaches the zero-age main sequence (ZAMS) at higher stellar mass. Using this protostellar evolution, we evaluate the upper stellar mass limit where the mass accretion is hindered by radiative feedback. We consider the effects of radiation pressure exerted on the accreting envelope, and expansion of an H II region. The mass accretion is finally terminated by radiation pressure on dust grains in the envelope for Z ≳ 10^-3 Z and by the expanding H II region for lower metallicity. The mass limit from these effects increases with decreasing metallicity from M _* ≃ 10 M at Z = Z to ≃300 M at Z = 10^-6 Z. The termination of accretion occurs after the central star arrives at the ZAMS at all metallicities, which allows us to neglect protostellar evolution effects in discussing the upper mass limit by stellar feedback. The fragmentation induced by line cooling in low-metallicity clouds yields prestellar cores with masses large enough that the final stellar mass is set by the feedback effects. Although relaxing the assumption of spherical symmetry will alter feedback effects, our results will be a benchmark for more realistic evolution to be explored in future studies.