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 H-2 in the local dark matter minihalo occurs early in the growth of the protostar but does not affect subsequent accretion. (2) Ly alpha 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 similar to 20-30 M-circle dot 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 similar to 50-100 M-circle dot. 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, similar to 140 M-circle dot 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 Ly alpha 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.