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