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

Using a model for the self-regulated growth of supermassive black holes in mergers involving gas-rich galaxies, we study the relationship between quasars and the population of merging galaxies and, as a consequence, predict the merger-induced star formation rate density of the Universe. These mergers drive nuclear inflows of gas, fueling starbursts and “buried” quasar activity until feedback energy from black hole growth expels the gas, rendering the quasar briefly visible as a bright optical source. As black hole accretion declines, the quasar dies, and the stellar remnant relaxes as a passively evolving spheroid with properties and correlations typical of red, elliptical galaxies. Based on the time history of these events in our simulations, we demonstrate that the observed statistics of merger rates/fractions, luminosity functions, mass functions, star formation rate distributions, specific star formation rates, quasar luminosity functions, quasar host galaxy luminosity functions, and elliptical/red galaxy luminosity and mass functions are self-consistent and follow from one another as predicted by the merger hypothesis. We use our simulations to de-convolve both the quasar and merging galaxy luminosity functions to determine the birthrate of black holes of a given final mass and merger rates as a function of the total stellar mass and the mass of new stars formed during the merger. We use this to predict the merging galaxy luminosity function in several observed wavebands (e.g. UV, optical, and near-IR), color-magnitude relations, mass functions, absolute and specific star formation rate distributions and star formation rate density, and quasar host galaxy luminosity function, as a function of redshift from z = 0 − 6. We invert this prescription and predict e.g. quasar luminosity functions from observed merger luminosity functions or star formation rate distributions. Our results show good agreement with observations, but idealized models of quasar lightcurves give inaccurate estimates and are ruled out by comparison of merging galaxy and quasar observations at > 99.9% confidence, provided that quasars are triggered in mergers. Using only observations of quasars, we estimate the contribution of mergers to the star formation rate density of the Universe even to high redshifts z ∼ 4 and constrain the evolution in the characteristic initial gas fractions of quasar and spheroid-producing mergers. Subject headings: quasars: general — galaxies: active — galaxies: evolution — cosmology: theory