A Comparative Study of AGN Feedback Algorithms
  Modelling AGN feedback in numerical simulations is both technically and
theoretically challenging, with numerous approaches having been published in
the literature. We present a study of five distinct approaches to modelling AGN
feedback within gravitohydrodynamic simulations of major mergers of Milky
Way-sized galaxies. To constrain differences to only be between AGN feedback
models, all simulations start from the same initial conditions and use the same
star formation algorithm. Most AGN feedback algorithms have five key aspects:
black hole accretion rate, energy feedback rate and method, particle accretion
algorithm, black hole advection algorithm, and black hole merger algorithm. All
models follow different accretion histories, with accretion rates that differ
by up to three orders of magnitude at any given time. We consider models with
either thermal or kinetic feedback, with the associated energy deposited
locally around the black hole. Each feedback algorithm modifies the gas
properties near the black hole to different extents. The particle accretion
algorithms usually (but not always) maintain good agreement between the mass
accreted by \dot{M} dt and the mass of gas particles removed from the
simulation. The black hole advection algorithms dampen inappropriate dragging
of the black holes by two-body interactions. Advecting the black hole a limited
distance based upon local mass distributions has many desirably properties. The
black holes merge when given criteria are met, and we find a range of merger
times for different criteria. Using the M_{BH}-\sigma relation as a diagnostic
of the remnants yields three models that lie within the one-sigma scatter of
the observed relation and two that fall below it. The wide variation in
accretion behaviours of the models reinforces the fact that there remains much
to be learnt about the evolution of galactic nuclei. (abridged)
