Primordial protostars accreting beyond the ΩΓ-limit: Radiation effect around the star-disc boundary

We consider whether the maximum mass of first stars is imposed by the protostellar spin (i.e. by the so-called ΩΓ-limit), which requires the sum of the radiation and centrifugal forces at the stellar surface to be smaller than the inward pull of the gravity. Once the accreting protostar reaches such a marginal state, the star cannot spin up more and is not allowed to accrete more gas with inward angular momentum flux. So far, however, the effect of stellar radiation on the structure of the accretion disc has not been properly taken into account in discussing the effect of the ΩΓ-limit on the formation of the first stars. Here, we obtain a series of steady accretion-disc solutions considering such an effect, and we find solutions without net angular momentum influx to the stars with arbitrary rotation rates, in addition to those with finite angular momentum flows. The accretion of positive angular momentum flows pushes the star beyond the ΩΓ-limit, which is allowed only with the external pressure provided by the circumstellar disc. However, the accretion with no net angular momentum influx does not result in the spin-up of the star. Thus, the existence of the solution with no net angular momentum influx indicates that protostars can keep growing in mass by accretion, even after they reach the ΩΓ-limit.