Do Stellar Winds Prevent the Formation of Supermassive Stars by
  Accretion?
  Supermassive stars (SMS; ~ 10^5 M_sun) formed from metal-free gas in the
early Universe attract attention as progenitors of supermassive black holes
observed at high redshifts. To form SMSs by accretion, central protostars must
accrete at as high rates as ~ 0.1-1 M_sun/yr. Such protostars have very
extended structures with bloated envelopes, like super-giant stars, and are
called super-giant protostars (SGPSs). Under the assumption of hydrostatic
equilibrium, SGPSs have density inverted layers, where the luminosity becomes
locally super-Eddington, near the surface. If the envelope matter is allowed to
flow out, however, a stellar wind could be launched and hinder the accretion
growth of SGPSs before reaching the supermassive regime. We examine whether
radiation-driven winds are launched from SGPSs by constructing steady and
spherically symmetric wind solutions. We find that the wind velocity does not
reach the escape velocity in any case considered. This is because once the
temperature falls below ~ 10^4 K, the opacity plummet drastically owing to the
recombination of hydrogen and the acceleration ceases suddenly. This indicates
that, in realistic non-steady cases, even if outflows are launched from the
surface of SGPSs, they would fall back again. Such a "wind" does not result in
net mass loss and does not prevent the growth of SGPSs. In conclusion, SGPSs
will grow to SMSs and eventually collapse to massive BHs of ~ 10^5 M_sun, as
long as the rapid accretion is maintained.
