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 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 _ { \sun } ) and \log _ { 10 } ( M _ { \bullet } ) = 8.35 + 5.31 \log _ { 10 } ( \sigma / 200 kms ^ { -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 _ { 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 .