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 mass (MBH) and host galaxy properties (sigma, M*,
and LV), finding good agreement with observational data, especially at the
high-mass end. The simulations have less intrinsic scatter than observations,
and the MBH-LV correlation has the largest scatter, suggesting it may the the
least fundamental of the three relations. We find Gaussian scatter about all
three relations, except among the highest mass galaxies, which host more
massive black holes. Below z~2 the slopes for the full population remain
roughly z-independent, and only steepen by 50% by z~4. The normalization of the
sigma, LV relations evolve by 0.3, 0.43 dex, while the MBH correlation does not
evolve to at least z~2. Testing for selection biases, we find samples selected
by MBH or M* have steeper slopes than randomly selected samples. If unaccounted
for, such a selection function would find faster evolution than inferred from a
randomly selected sample, as objects at the highend of the relation tend to
evolve more rapidly. We find a potential bias among high-LBH subsamples
(tending to reside in higher mass galaxies), but these bright-AGN exhibit no
intrinsic bias relative to fainter ones in equivalent-mass hosts, nor is there
a significant difference between active- and inactive-samples. Finally we
characterize the evolution of individual black holes along the scaling planes.
Below the local relation, black holes grow faster than their host (72% of black
holes 0.3 dex below the mean relation have a MBH-M* trajectory steeper than the
local relation), while those above have shallower trajectories (only 14% are
steeper than local). Black holes tend to grow faster than their hosts until
surpassing the local relation, at which point their growth is suppressed while
their hosts continue to grow, returning them to the mean relation.
