Scaling relations between black holes and their host galaxies: comparing theoretical and observational measurements, and the impact of selection effects

We use the high-resolution simulation MassiveBlackII to examine scaling relations between black hole (BH) mass and host galaxy properties (σ, total M_* and L_V), finding good agreement with recent observational data, especially at the high-mass end. We find Gaussian intrinsic scatter (∼half the observed scatter) about all three relations, except among the most massive objects. Below z ∼ 2 the slope of the relations remain roughly z-independent, and only steepen by 50 per cent by z ∼ 4. The normalization of the σ, L_V relations evolve by 0.3, 0.43 dex, while the M_* correlation does not evolve out to at least z ∼ 2. Testing for selection biases, we find M_BH- or M_*-selected samples have steeper slopes than random samples, suggesting a constant-mass selection function can exhibit faster evolution than a random sample. We find a potential bias among high-L_BH subsamples due to their more massive hosts, but that bright (active) active galactic nuclei exhibit no intrinsic bias relative to fainter (inactive) BHs in equivalent-mass hosts. Finally, we show that BHs below the local relation tend to grow faster than their host (72 per cent of BHs >0.3 dex below the mean relation have an M_BH-M_* trajectory steeper than the local relation), while those above have shallower trajectories (only 14 per cent are steeper than local). Thus BHs tend to grow faster than their hosts until surpassing the local relation, when their growth is suppressed, bringing them back towards the mean relation.