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 $\text{textsc}BlueTides$, 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 ($ϵ\sim 0.4$) is larger at these redshifts than inferred from observations and larger than in $M_{\bullet }-M_{\star }$ relation ($ϵ\sim 0.14$). We find the gas-to-stellar ratio $f=M_{\mathrm{g}\mathrm{a}\mathrm{s}}\mathrm{/}{M}_{\star }$ 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 ($ϵ=0.28$ 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.