Recent galaxy formation models have revealed that feedback from
supermassive black holes plays an important role in the shaping the
properties of massive galaxies. In particular, such feedback seems
necessary to explain the well-known correlation between supermassive
black hole mass and the velocity dispersion of its host galaxy's stellar
bulge (the M-sigma relation). However, as important as black hole
feedback is for galaxy formation, it cannot be said that we understand
how it works. Indeed, the standard approach to modelling black hole
feedback in galaxy formation simulations is highly unsatisfactory,
assuming a model of thermal (i.e. energy-driven) feedback that cannot
work in real galaxies.

In this talk I will describe my recent work on developing a numerical
momentum-driven outflow model for black hole feedback using idealised
simulations. I will discuss the motivation for such an approach and
describe analytically why such momentum-driven outflows can provide an
elegant explanation for the M-sigma relation. I will show that the
numerical model of momentum-driven outflow can recover the expected
M-sigma relation, whilst highlighting the importance of comptetition
between timescales for gas infall and for black hole growth. Finally, I
will discuss those situations in which the model fails and why this
might provide an important clue to how supermassive black holes and
their galaxies grow.