The deposition of mechanical feedback from a supermassive black hole (SMBH)
in an active galactic nucleus (AGN) into the surrounding galaxy occurs via
broad-line winds which must carry mass and radial momentum as well as energy.
The effect can be summarized by the dimensionless parameter
η=dotMoutflow/dotMaccretion=(2ϵwc2)/vw2 where
(\epslion_w \equiv dot{E}_w/(dot{M_accretion} c^2)) is the efficiency by
which accreted matter is turned into wind energy in the disc surrounding the
central SMBH. The outflowing mass and omentum are proportional to η, and
many prior treatments have essentially assumed that η=0. We perform one-
and two-dimensional simulations and find that the growth of the central SMBH is
very sensitive to the inclusion of the mass and momentum driving but is
insensitive to the assumed mechanical efficiency. For example in representative
calculations, the omission of momentum and mass feedback leads to an hundred
fold increase in the mass of the SMBH to over 10^{10} \Msun. When allowance
is made for momentum driving, the final SMBH mass is much lower and the wind
efficiencies which lead to the most observationally acceptable results are
relatively low with ϵw≲10−4.Comment: 10 pages, 8 figures, resubmitted to ApJ, added reference