The Relation between Quasar and Merging Galaxy Luminosity Functions and the Merger-driven Star Formation History of the Universe

Using a model for the self-regulated growth of supermassive BHs in mergers involving gas-rich galaxies, we study the relationship between quasars and the population of merging galaxies and predict the merger-driven SFR density of the universe. Mergers drive gas inflows, fueling starbursts and ``buried'' quasars until feedback disperses the gas, allowing the quasar to be briefly visible as a bright optical source. By simulating the evolution of such events, we demonstrate that the observed statistics of merger rates/fractions, luminosity and mass functions, SFR distributions, quasar (and quasar host) luminosity functions, and elliptical/red galaxy luminosity and mass functions are self-consistent. We use our simulations to deconvolve quasar and merger luminosity functions and determine the birthrate of BHs and merger rates as a function of mass. From this, we predict the merging galaxy luminosity function in various observed wavebands, color-magnitude relations, mass functions, SFR distributions and density, and quasar host galaxy luminosity function, as a function of redshift from z = 0 to 6. We invert this to predict quasar luminosity functions from observed merger luminosity functions or SFR distributions. Our results show good agreement with observations, but idealized models of quasar light curves give inaccurate estimates and are ruled out at >99.9% confidence, provided that quasars are triggered in mergers. Using only quasar observations, we estimate the contribution of mergers to the SFR density of the universe to high redshifts, z ~ 4, and constrain the evolution in the characteristic initial gas fractions of quasar and spheroid-producing mergers.