The Formation of the First Stars. II. Radiative Feedback Processes and Implications for the Initial Mass Function

We consider the radiative feedback processes that operate during the formation of the first stars. (1) Photodissociation of H₂ in the local dark matter minihalo occurs early in the growth of the protostar but does not affect subsequent accretion. (2) Lyα radiation pressure acting at the boundary of the H II region that the protostar creates in the accreting envelope reverses infall in the polar directions when the star reaches ~20-30 M_☉ but cannot prevent infall from other directions. (3) Expansion of the H II region beyond the gravitational escape radius for ionized gas occurs at masses ~50-100 M_☉. However, accretion from the equatorial regions can continue since the neutral accretion disk shields a substantial fraction of the accretion envelope from direct ionizing flux. (4) At higher stellar masses, ~140 M_☉ in the fiducial case, photoevaporation-driven mass loss from the disk, together with declining accretion rates, halts the increase in the protostellar mass. We identify this process as the mechanism that determines the mass of Population III.1 stars (i.e., stars with primordial composition that have not been affected by prior star formation). The initial mass function of these stars is set by the distribution of entropy and angular momentum. The Appendix gives approximate solutions to a number of problems relevant to the formation of the first stars: the effect of Rayleigh scattering on line profiles in media of very large optical depth, the intensity of Lyα radiation in very opaque media, radiative acceleration in terms of the gradient of a modified radiation pressure, the flux of radiation in a shell with an arbitrary distribution of opacity, and the vertical structure of an accretion disk supported by gas pressure with constant opacity.