A Cosmological Framework for the Co-Evolution of Quasars, Supermassive Black Holes, and Elliptical Galaxies: II. Formation of Red Ellipticals

(Abridged) We develop and test a model for the cosmological role of mergers in the formation and quenching of red, early-type galaxies. Making the ansatz that star formation is quenched after a gas-rich, spheroid-forming major merger, we demonstrate that this naturally predicts the turnover in the efficiency of star formation at ~L_star, as well as the observed mass functions/density of red galaxies as a function of redshift, the formation times of spheroids as a function of mass, and the fraction of quenched galaxies as a function of galaxy and halo mass, environment, and redshift. Comparing to a variety of semi-analytic models in which quenching is primarily driven by halo mass considerations or secular/disk instabilities, we demonstrate that our model and different broad classes of models make unique and robust qualitative predictions for a number of observables, including the red fraction as a function of galaxy and halo mass, the density of passive galaxies and evolution of the color-morphology-density relations at high z, and the fraction of disky/boxy spheroids as a function of mass. In each case, the observations favor a model in which galaxies quench after a major merger builds a massive spheroid, and disfavor quenching via secular or pure halo processes. We discuss a variety of physical possibilities for this quenching, and propose a mixed scenario in which traditional quenching in hot, massive halos is supplemented by the feedback associated with star formation and quasar activity in a major merger, which temporarily suppress cooling and establish the conditions of a dynamically hot halo in the central regions of the host, even in low mass halos.