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Kinetic or thermal AGN feedback in simulations of isolated and merging disk galaxies calibrated by the M-sigma relation

(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.