Energy- and momentum-conserving AGN feedback outflows
  It is usually assumed that outflows from luminous AGN are either in the
energy-conserving (non-radiative) or in the momentum-conserving (radiative)
regime. We show that in a non-spherical geometry the effects of both regimes
may manifest at the same time, and that it is the momentum of the outflow that
sets the $M_{\rm BH}-\sigma$ relation. Considering an initially elliptical
distribution of gas in the host galaxy, we show that a non-radiative outflow
opens up a wide ``escape route'' over the paths of least resistance. Most of
the outflow energy escapes in that direction. At the same time, in the
directions of higher resistance, the ambient gas is affected mainly by the
incident momentum from the outflow. Quenching SMBH growth requires quenching
gas delivery along the paths of highest resistance, and therefore, it is the
momentum of the outflow that limits the black hole growth. We present an
analytical argument showing that such energy-conserving feedback bubbles
driving leaky ambient shells will terminate SMBH growth once its mass reaches
roughly the $M_\sigma$ mass derived earlier by King (2003) for
momentum-conserving AGN outflows. Our simulations also have potentially
important implications for observations of AGN jet feedback and starburst
galaxy feedback. The collimation of the wide angle AGN outflow away from the
symmetry plane, as found in our simulations, indicates that credit for work
done by such outflows may sometimes be mistakenly given to AGN jets or star
formation feedback since wide angle $v \sim 0.1 c$ outflows are harder to
observe and the phase when they are present may be short.
