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Existing models of galaxy formation have not yet explained strikingcorrelations between structure and star-formation activity in galaxies, notablythe sloped and moving boundaries that divide star-forming from quenchedgalaxies in key structural diagrams. This paper uses these and other relationsto ``reverse-engineer'' the quenching process for central galaxies. The basicidea is that star-forming galaxies with larger radii (at a given stellar mass)have lower black-hole masses due to lower central densities. Galaxies crossinto the green valley when the cumulative effective energy radiated by theirblack hole equals $\sim4\times$ their halo-gas binding energy. Sincelarger-radii galaxies have smaller black holes, one finds they must evolve tohigher stellar masses in order to meet this halo-energy criterion, whichexplains the sloping boundaries. A possible cause of radii differences amongstar-forming galaxies is halo concentration. The evolutionary tracks ofstar-forming galaxies are nearly parallel to the green-valley boundaries, andit is mainly the sideways motions of these boundaries with cosmic time thatcause galaxies to quench. BH-scaling laws for star-forming, quenched, andgreen-valley galaxies are different, and most BH mass growth takes place in thegreen valley. Implications include: the radii of star-forming galaxies are animportant second parameter in shaping their black holes; black holes areconnected to their halos but in different ways for star-forming, quenched, andgreen-valley galaxies; and the same BH-halo quenching mechanism has been inplace since $z \sim 3$. We conclude with a discussion of black hole-galaxyco-evolution, the origin and interpretation of BH scaling laws.

Quenching as a Contest between Galaxy Halos and their Central Black Holes