On the Feedback Efficiency of Active Galactic Nuclei
  (Abridged) We measure and analyze the energy, momentum, and mass feedback
efficiencies due to radiation from AGN in relatively large scale outflows. Our
measurements are based on the axisymmetric and time-dependent
radiation-hydrodynamical simulations recently presented in Kurosawa & Proga.
These simulations follow dynamics of gas under the influences of the AGN
radiation and the gravity of the central 10^8 Msun black hole on scales from
~0.01 to ~10pc. We compare our Mdot_a-rho_o relation with that predicted by the
Bondi accretion model. For high luminosities comparable to the Eddington limit,
the power-law fit (Mdot_a ~ rho_o^q) to our models yields q=~0.5 instead of
q=1.0 which is predicted by the Bondi model. This difference is caused by the
outflows which are important for the overall mass budget at high luminosities.
The maximum momentum and mass feedback efficiencies found in our models are
~10^-2 and ~10^-1, respectively. However, the outflows are much less important
energetically: their thermal and kinetic powers in units of the radiative
luminosity are ~10^-5 and ~10^-4, respectively. The efficiencies do not
increase monotonically with the accretion luminosity but rather peak around the
Eddington limit beyond which a steady state disk-wind-like solution exists. Our
energy feedback efficiencies are significantly lower than 0.05, which is
required in some cosmological and galaxy merger simulations. The low feedback
efficiencies found here could have significant implications on the mass growth
of super massive black holes in the early universe. We stress however that we
have not considered the innermost parts of the accretion and outflow where
radiation and matter interact most strongly. The feedback from this region
could have efficiencies significantly above the low values found here.
