  Super-massive black holes, with masses larger than a million times that of
the Sun, appear to inhabit the centers of all massive galaxies.
Cosmologically-motivated theories of galaxy formation need feedback from these
super-massive black holes to regulate star formation. In the absence of such
feedback, state-of-the-art numerical simulations dramatically fail to reproduce
the number density and properties of massive galaxies in the local Universe.
However, there is no observational evidence of this strongly coupled
co-evolution between super-massive black holes and star formation, impeding our
understanding of baryonic processes within galaxies. Here we show that the star
formation histories (SFHs) of nearby massive galaxies, as measured from their
integrated optical spectra, depend on the mass of the central super-massive
black hole. Our results suggest that black hole mass growth scales with gas
cooling rate in the early Universe. The subsequent quenching of star formation
takes place earlier and more efficiently in galaxies hosting more massive
central black holes. The observed relation between black hole mass and star
formation efficiency applies to all generations of stars formed throughout a
galaxy's life, revealing a continuous interplay between black hole activity and
baryon cooling.
