  There is strong evidence that supermassive black holes reside in all galaxies
that contain a stellar spheroid and their mass is tightly correlated with
properties such as stellar bulge mass and velocity dispersion. There are also
strong theoretical arguments that feedback from supermassive black holes plays
an important role in shaping the high mass end of the galaxy mass function,
hence to accurately model galaxies we also need to model the black holes. We
present a comparison of two black hole growth models implemented within a
large-scale, cosmological SPH simulation including star formation and feedback.
One model is a modified Bondi-Hoyle prescription that grows black holes based
on the smooth density of local gas, while the other is the recently proposed
Accretion Disc Particle (ADP) method. This model swallows baryonic particles
that pass within an accretion radius of the black hole and adds them to a
subgrid accretion disc. Black holes are then grown by material from this disc.
We find that both models can reproduce local scaling relations, although the
ADP model is offset from the observed relations at high black hole masses. The
total black hole mass density agrees between models to within a factor of
three, but both struggle to reproduce the black hole mass function. The
simulated mass functions are too steep and underestimate the number of
intermediate and high mass black holes. In addition, the ADP model swallows
excessive amounts of material at the resolution of large-scale, cosmological
simulations producing unrealistically large accretion discs. Future work needs
to be performed to improve the black hole mass function within simulations.
This should be done through the mass growth and feedback as they are strongly
coupled and should not be treated as separate entities.
