We measure and analyze the energy , momentum , and mass feedback efficiencies due to radiation from active galactic nuclei ( AGN ) in relatively large scale outflows ( from \sim 0.01 to \sim 10 pc ) .
Our measurements are based on the two-dimensional ( axisymmetric ) and time-dependent radiation-hydrodynamical simulations recently presented in Kurosawa & Proga .
In that paper , we studied outflows from a slowly rotating ( sub-Keplerian ) infalling gas driven by the energy and pressure of the radiation emitted by the AGN .
These simulations follow dynamics of gas under the influence of the gravity of the central 10 ^ { 8 } ~ { } M _ { \odot } black hole on scales from \sim 0.01 to \sim 10 pc .
They self-consistently couple the accretion-luminosity with the mass inflow rate at the smallest radius ( our proxy for the mass-accretion rate , \dot { M } _ { \mathrm { a } } ) .
Over thirty simulations have been performed to investigate how the results depend on the gas density at the outer radius , \rho _ { \mathrm { o } } .
A key feature of these simulations is that the radiation field and consequently the gas dynamics are axisymmetric , but not spherically symmetric .
Therefore , the gas inflow and outflow can occur at the same time .
We compare our \dot { M } _ { \mathrm { a } } - \rho _ { \mathrm { o } } relation with that predicted by the Bondi accretion model .
For high luminosities comparable to the Eddington limit , the power-law fit ( \dot { M } _ { \mathrm { a } } \propto \rho _ { \mathrm { o } } ^ { q } ) to our models yields q \approx 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 \sim 10 ^ { -2 } and \sim 10 ^ { -1 } , respectively .
However , the outflows are much less important energetically : the thermal and kinetic powers in units of the radiative luminosity are \sim 10 ^ { -5 } and \sim 10 ^ { -4 } , respectively .
In addition , 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 .