BlueTides simulation: establishing black hole-galaxy relations at
  high-redshift
  The scaling relations between the mass of supermassive black holes
($M_{\bullet}$) and host galaxy properties (stellar mass, $M_{\star}$, and
velocity dispersion, $\sigma$), provide a link between the growth of black
holes (BHs) and that of their hosts. Here we investigate if and how the
BH-galaxy relations are established in the high-$z$ universe using
\textsc{BlueTides}, a high-resolution large volume cosmological hydrodynamic
simulation. We find the $M_{\bullet}-M_{\star}$ and $M_{\bullet}-\sigma$
relations at $z=8$: $\log_{10}(M_{\bullet}) = 8.25 + 1.10 \
\log_{10}(M_{\star}/10^{11}M_{\odot})$ and $\log_{10}(M_{\bullet}) = 8.35 +
5.31 \ \log_{10}(\sigma/200kms^{-1})$ at $z=8$, both fully consistent with the
local measurements. The slope of the $M_{\bullet}-\sigma$ relation is slightly
steeper for high star formation rate and $M_{\star}$ galaxies while it remains
unchanged as a function of Eddington accretion rate onto the BH. The intrinsic
scatter in $M_{\bullet}-\sigma$ relation in all cases ($\epsilon \sim 0.4$) is
larger at these redshifts than inferred from observations and larger than in
$M_{\bullet}-M_{\star}$ relation ($\epsilon \sim 0.14$). We find the
gas-to-stellar ratio $f=M_{\rm gas}/M_{\star}$ in the host (which can be very
high at these redshifts) to have the most significant impact setting the
intrinsic scatter of $M_{\bullet}-\sigma$. The scatter is significantly reduced
when galaxies with high gas fractions ($\epsilon = 0.28$ as $f<10$) are
excluded (making the sample more comparable to low-$z$ galaxies); these systems
have the largest star formation rates and black hole accretion rates,
indicating that these fast-growing systems are still moving toward the relation
at these high redshifts. Examining the evolution (from $z=10$ to 8) of high
mass black holes in $M_{\bullet}-\sigma$ plane confirms this trend.
