Cosmological DCBH formation sites hostile for their growth
  The direct collapse (DC) is a promising mechanism that provides massive seed
black holes (BHs) with $\sim 10^{5}~M_{\odot}$ in the early universe. To study
a long-term accretion growth of a DCBH thus formed, we perform cosmological
radiation-hydrodynamics simulations, extending our previous work where we
investigated its formation stage. With a high spatial resolution down below the
Bondi radius, we show that the accretion rate onto the BH is far below the
Eddington value. Such slow mass growth is partly because of the strong
radiative feedback from the accreting BH. Moreover, we find that the BH has a
large velocity of $\sim 100~{\rm km~s^{-1}}$ relative to the gas after it falls
into the first galaxy, which substantially reduces the accretion rate. The
latter effect stems from the fact that the DCBHs form in metal-free
environments typically at $\sim 1~$kpc from the galaxy. The BH accelerates as
it approaches the galactic center due to the gravity. The relative velocity
never damps after that, and the BH does not settle down to the galactic center
but continues to wander around it. An analytic estimate predicts that the DCBH
formation within $\sim 100$~pc around the galactic center is necessary to
decelerate the BH with dynamical friction before $z=7$. Since metal enrichment
with $Z \sim 10^{-5} - 10^{-3}~Z_\odot$ is expected in such a case, the
formation of DCBHs in the metal-poor environments is preferable for the
subsequent rapid growth.
