  (Abridged) We investigate two modes of coupling the feedback energy from a
central AGN to the neighboring gas in galaxy simulations: kinetic - velocity
boost, and thermal - heating. We formulate kinetic feedback models for
energy-driven wind (EDW) and momentum-driven wind (MDW), using two free
parameters: feedback efficiency epsilon_f, and AGN wind velocity v_w. A novel
numerical algorithm is implemented in the SPH code GADGET-3, to prevent the
expansion of a hole in the gas distribution around the BH. We perform
simulations of isolated evolution and merger of disk galaxies, of Milky-Way
mass as well as lower and higher masses. We find that in the isolated galaxy BH
kinetic feedback generates intermittent bipolar jet-like gas outflows. We infer
that current prescriptions for BH subgrid physics in galaxy simulations can
grow the BH to observed values even in an isolated disk galaxy. The BH growth
is enhanced in a galaxy merger. Comparing the [M_BH - sigma_star] relation
obtained in our simulations with observational data, we conclude that it is
possible to find parameter sets for a fit in all the models, except for the
case with MDW feedback in a galaxy merger, in which the BH is always too
massive. The BH thermal feedback implementation of Springel, Di Matteo &
Hernquist (2005) within the multiphase star-formation model is found to have
negligible impact on gas properties; and the effect claimed in all previous
studies is attributed to gas depletion around the BH by the creation of an
artificial hole. The BH mass accretion rate in our simulations exhibit heavy
fluctuations. The star formation rate is quenched with feedback by removal of
gas. The CGM gas at galactocentric distances (20 - 100)/h kpc are found to give
the best metallicity observational diagnostic to distinguish between BH models.
