  In the early Universe, while galaxies were still forming, black holes as
massive as a billion solar masses powered quasars. Supermassive black holes are
found at the centers of most galaxies today, where their masses are related to
the velocity dispersions of stars in their host galaxies and hence to the mass
of the central bulge of the galaxy. This suggests a link between the growth of
the black holes and the host galaxies, which has indeed been assumed for a
number of years. But the origin of the observed relation between black hole
mass and stellar velocity dispersion, and its connection with the evolution of
galaxies have remained unclear. Here we report simulations that simultaneously
follow star formation and the growth of black holes during galaxy-galaxy
collisions. We find that in addition to generating a burst of star formation, a
merger leads to strong inflows that feed gas to the supermassive black hole and
thereby power the quasar. The energy released by the quasar expels enough gas
to quench both star formation and further black hole growth. This determines
the lifetime of the quasar phase (approaching 100 million years) and explains
the relationship between the black hole mass and the stellar velocity
dispersion.
