  One of the central features of the last 8 to 10 billion years of cosmic
history has been the emergence of a well-populated red sequence of
non-star-forming galaxies. A number of models of galaxy formation and evolution
have been devised to attempt to explain this behavior. Most current models
require feedback from supermassive black holes (AGN feedback) to quench star
formation in galaxies in the centers of their dark matter halos (central
galaxies). Such models make the strong prediction that all quenched central
galaxies must have a large supermassive black hole (and, by association, a
prominent bulge component). I show using data from the Sloan Digital Sky Survey
that the observations are consistent with this prediction. Over 99.5% of red
sequence galaxies with stellar masses in excess of 10^{10} M_{\sun} have a
prominent bulge component (as defined by having a Sersic index n above 1.5).
Those very rare red sequence central galaxies with little or no bulge (n<1.5)
usually have detectable star formation or AGN activity; the fraction of truly
quenched bulgeless central galaxies is <0.1% of the total red sequence
population. I conclude that a bulge, and by implication a supermassive black
hole, is an absolute requirement for full quenching of star formation in
central galaxies. This is in agreement with the most basic prediction of the
AGN feedback paradigm.
