An Observational Determination of the Bolometric Quasar Luminosity Function

TLDR: In this paper, the authors combine a large set of quasar luminosity function (QLF) measurements from the rest-frame optical, soft and hard X-ray, and near and mid-IR bands to determine the bolometric QLF in the redshift interval z = 0-6.

Abstract: 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-IR 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 SED shapes, as well as 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 (10 σ) 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 that 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, as well as a script to return the QLF at arbitrary frequency and redshift from these fits.

Figures

FIG. 5.— The observedB-band QLF (points) atz∼ 1, and that determined from the best-fit bolometric QLF in Figure 4 (solid line) ignoring contributions to the observed luminosity from quasar host galaxies.Also shown is the B-band QLF determined from the same bolometric QLF, but including the expected host galaxy contribution to the observed luminosities (normalized for a given Eddington ratio with the observed relation between black hole mass and host galaxyB-band luminosity from Marconi & Hunt (2003)), assuming all quasars have constantL/LEdd = 1.0, 0.3, 0.1 (dot-dashed, long-dashed, dotted lines, respectively), or assumingL/LEdd = L/L∗ (short dashed line;L∗ is the QLF break luminosity). Host galaxy contributions should be negligible at most luminosities and redshifts for the observed bands weconsider, but will be important for future optical, near- and mid-IR surveys which probe fainter luminositiesL . 1012L⊙ (MB & −23).

FIG. 9.— Total number density of quasars in various luminosity in ervals (in log (Lband/[ergs−1]) as labeled) as a function of redshift, from the best-fit evolving double-power law model (lines) and the compiled observations n Table 1 (points of corresponding colors, symbols for each sample listed therein) in bolometric luminosity,B-band, soft X-rays (0.5−2 keV), and hard X-rays (2−10 keV). The trend that the density of lower-luminosity AGN peaks at lower redshift is manifest in all bands.

FIG. 2.— The bolometric QLF from the observations in Table 1 at various wavebands (optical: green, soft X-ray: blue, hard X-ray: red, IR: cyan; see Table 1 for the plotting symbols). For ease of comparison, the points in the different bands are rescaled as described in the text to indicate the bolometric QLF implied by each set of measurements. Left panels show thebolometric QLF adopting our full (luminosity-dependent) bolometric corrections and column density distributions (see also Ueda et al. 2003; Marconi etal. 2004; La Franca et al. 2005), at several redshifts (as labeled). Center-left shows the result with the full column distribution, but adopting the constant bolometric corrections of Elvis et al. (1994). Center-right uses the full bolometric corrections, but a luminosity-independent column density distribution (obscured fraction). Right uses the full bolometric corrections and a strongly redshift-dependent column density distribution from La Franca et al. (2005). Each panel shows the reducedχ2 for the assumption that the data yield a consistent bolometric QLF at each redshift. The latter three assumptions do not yield a consistent bolometric QLF at each redshift, unlike for the observationally derived luminosity-dependent bolometric corrections and column density distributions.

TABLE 1 MEASUREMENTS OF THEQLF

FIG. 4.— The best-fit bolometric QLF atz∼ 1 (black lines), with the resulting observed QLF in each of several bands: optical (green), soft X-ray (blue), hard X-ray (red), and IR (cyan). Each corresponding panel plots the compiled observations in Table 1 for the appropriate redshift and frequency (points). Symbols denote the parent sample as given in Table 1. The observations at each band are consistently produced from a single bolometric QLF, and together provide strong constraints on the QLF shape. Different wavebands accur tely represent different aspects of the bolometric QLFshape. With only a weaklyL-dependent bolometric correction but significant effects of obscuration, the optical QLF faithfully traces the bolometric brightend shape, but is flatter at faintL. Hard X-rays, conversely, are weakly affected by obscuration but can havea strongly luminosity-dependent bolometric correction, reproducing the faint end shape but being steeper at brightL. The IR QLF better follows the bolometric shape, but is currently least well-constrained.

FIG. 8.— The best-fit QLF double-power law parameters as a functio of redshift. Points show the best-fit values to data at eachredshift, dotted lines the best-fit PLE model, and solid lines the best-fit full model (with cyan shaded range showing the 1σ uncertainty). Open diamonds inγ2(z) show the bright-end slope fits from Richards et al. (2006b). Although PLE is appropriate for a lowest-order fit, both the bright and faint-end slopes evolve with redshift to high significance (> 6σ). Lower right shows the predicted number density of bright optical (MB < −27) quasars from the full fit (solid), compared to that observed in Croom et al. (2004) (square), Richards et al. (2006b) (diamonds and dashe line), and Fan et al. (2004) (circle).