The Final Fates of Accreting Supermassive Stars
  The formation of supermassive stars (SMSs) via rapid mass accretion and their
direct collapse into black holes (BHs) is a promising pathway for sowing seeds
of supermassive BHs in the early universe. We calculate the evolution of
rapidly accreting SMSs by solving the stellar structure equations including
nuclear burning as well as general relativistic (GR) effects up to the onset of
the collapse. We find that such SMSs have less concentrated structure than
fully-convective counterpart, which is often postulated for non-accreting ones.
This effect stabilizes the stars against GR instability even above the
classical upper mass limit $\gtrsim 10^5~M_\odot$ derived for the
fully-convective stars. The accreting SMS begins to collapse at the higher mass
with the higher accretion rate. The collapse occurs when the nuclear fuel is
exhausted only for cases with $\dot M \lesssim 0.1~M_\odot~{\rm yr}^{-1}$. With
$\dot{M} \simeq 0.3 - 1~M_\odot~{\rm yr}^{-1}$, the star becomes GR-unstable
during the helium-burning stage at $M \simeq 2 - 3.5~\times 10^5~M_\odot$. In
an extreme case with $10~M_\odot~{\rm yr}^{-1}$, the star does not collapse
until the mass reaches $\simeq 8.0\times 10^5~M_\odot$, where it is still in
the hydrogen-burning stage. We expect that BHs with roughly the same mass will
be left behind after the collapse in all the cases.
