An Observational Determination of the Bolometric Quasar Luminosity   Function
  We combine a large set of quasar luminosity function (QLF) measurements from the rest-frame optical, soft and hard X-ray, and near- and mid-infrared bands to determine the bolometric QLF in the redshift interval z=0-6. Accounting for the observed distributions of quasar column densities and variation of spectral energy distribution (SED) shapes, and their dependence on luminosity, makes it possible to integrate the observations in a reliable manner and provides a baseline in redshift and luminosity larger than that of any individual survey. We infer the QLF break luminosity and faint-end slope out to z~4.5 and confirm at high significance (>10sigma) previous claims of a flattening in both the faint- and bright-end slopes with redshift. With the best-fit estimates of the column density distribution and quasar SED, which both depend on luminosity, a single bolometric QLF self-consistently reproduces the observed QLFs in all bands and at all redshifts for which we compile measurements. Ignoring this luminosity dependence does not yield a self-consistent bolometric QLF and there is no evidence for any additional dependence on redshift. We calculate the expected relic black hole mass function and mass density, cosmic X-ray background, and ionization rate as a function of redshift and find they are consistent with existing measurements. The peak in the total quasar luminosity density is well-constrained at z=2.15+/-0.05. We provide a number of fitting functions to the bolometric QLF and its manifestations in various bands, and a script to return the QLF at arbitrary frequency and redshift from these fits, as the most simple inferences from the QLF measured in a single band can be misleading. 
Philip F. Hopkins (1), Gordon T. Richards (2), Lars Hernquist (1) ((1)   Harvard/CfA, (2) Johns Hopkins)