Quasars: What turns them off?

(Abridged) We explore the idea that the anti-hierarchical turn-off observed in the quasar population arises from self-regulating feedback, via an outflow mechanism. Using a detailed hydrodynamic simulation we calculate the luminosity function of quasars down to a redshift of z=1 in a large, cosmologically representative volume. Outflows are included explicitly by tracking halo mergers and driving shocks into the surrounding intergalactic medium. Our results are in excellent agreement with measurements of the spatial distribution of quasars, and we detect an intriguing excess of galaxy-quasar pairs at very short separations. We also reproduce the anti-hierarchical turnoff in the quasar luminosity function, however, the magnitude of the turn-off falls short of that observed as well as that predicted by analogous semi-analytic models. The difference can be traced to the treatment of gas heating within galaxies. The simulated galaxy cluster L_X-T relationship is close to that observed for z~1 clusters, but the simulated galaxy groups at z=1 are significantly perturbed by quasar outflows, suggesting that measurements of X-ray emission in high-redshift groups could well be a "smoking gun" for the AGN heating hypothesis.