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We consider the radiative feedback processes that operate during theformation of the first stars, including the photodissociation of H_2, Ly-alpharadiation pressure, formation and expansion of an HII region, and diskphotoevaporation. These processes may inhibit continued accretion once thestellar mass has reached a critical value, and we evaluate this mass separatelyfor each process. Photodissociation of H_2 in the local dark matter minihalooccurs relatively early in the growth of the protostar, but we argue this doesnot affect subsequent accretion since by this time the depth of the potentialis large enough for accretion to be mediated by atomic cooling. However,neighboring starless minihalos can be affected. Ionization creates an HIIregion in the infalling envelope above and below the accretion disk. Ly-alpharadiation pressure acting at the boundary of the HII region is effective atreversing infall from narrow polar directions when the star reaches ~20-30Msun,but cannot prevent infall from other directions. Expansion of the HII regionbeyond the gravitational escape radius for ionized gas occurs at masses~50-100Msun, depending on the accretion rate and angular momentum of theinflow. However, again, accretion from the equatorial regions can continuesince the neutral accretion disk has a finite thickness and shields asubstantial fraction of the accretion envelope from direct ionizing flux. Athigher stellar masses, ~140Msun in the fiducial case, the combination ofdeclining accretion rates and increasing photoevaporation-driven mass loss fromthe disk act to effectively halt the increase in the protostellar mass. Weidentify this process as the mechanism that terminates the growth of PopulationIII stars... (abridged)

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