Primordial protostars accreting beyond the $\Omega\Gamma$-limit: radiation effect around the star-disk boundary

Abstract

We consider whether the maximum mass of first stars is imposed by the protostellar spin, i.e., by the so-called $\Omega\Gamma$-limit, which requires the sum of the radiation and centrifugal forces at the stellar surface 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 disk has not been properly taken into account in discussing the effect of $\Omega\Gamma$-limit on the first star formation. Here, we obtain a series of the steady accretion-disk solutions considering such effect and 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 $\Omega\Gamma$-limit, which is allowed only with the external pressure provided by the circumstellar disk. On the other hand, 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 the protostars can keep growing in mass by accretion even after they reach the $\Omega\Gamma$-limit.