Cosmological simulations of the growth of supermassive black holes and
  feedback from active galactic nuclei: method and tests
  (Abridged) We present a method that tracks the growth of supermassive black
holes (BHs) and the feedback from AGN in cosmological simulations. Our model is
a substantially modified version of the one by Springel et al. (2005). Because
cosmological simulations lack both the resolution and the physics to model the
multiphase interstellar medium, they tend to strongly underestimate the
Bondi-Hoyle accretion rate. To allow low-mass BHs to grow, it is therefore
necessary to increase the predicted Bondi-Hoyle rates in dense gas by large,
ad-hoc factors. We explore the physical regimes where the use of such factors
is reasonable, and through this introduce a new prescription for gas accretion.
Feedback from AGN is modeled by coupling a fraction of the rest-mass energy of
the accreted gas thermally into the surrounding medium. We describe the
implementation as well as the limitations of the model and motivate all the
changes relative to previous work.
  We investigate the robustness of the predictions for the cosmic star
formation history, the redshift zero cosmic BH density, BH scaling relations,
and galaxy specific star formation rates. We find that the freedom introduced
by the need to increase the predicted accretion rates, the standard procedure
in the literature, is the most significant source of uncertainty. Our
simulations demonstrate that supermassive BHs are able to regulate their growth
by releasing a fixed amount of energy for a given halo mass, independent of the
assumed efficiency of AGN feedback, which sets the normalization of the BH
scaling relations. Regardless of whether BH seeds are initially placed above or
below the BH scaling relations they grow onto the same relations. AGN feedback
efficiently suppresses star formation in high-mass galaxies.
