Luminosity-dependent Density Evolution Model Research Articles

Active galactic nucleus X-ray luminosity function and absorption function in the Early Universe (3 ≤ z ≤ 6)

The X-ray luminosity function (XLF) of active galactic nuclei (AGN) offers a robust tool to study the evolution and the growth of the supermassive black-hole population over cosmic time. Owing to the limited area probed by X-ray surveys, optical surveys are routinely used to probe the accretion in the high-redshift Universe z ≥ 3. However, optical surveys may be incomplete because they are strongly affected by dust redenning. In this work we derive the XLF and its evolution at high redshifts (z ≥ 3) using a large sample of AGN selected in different fields with various areas and depths covering a wide range of luminosities. Additionally, we put the tightest yet constraints on the absorption function in this redshift regime. In particular, we used more than 600 soft X-ray selected (0.5 − 2 keV) high-z sources in the Chandra deep fields, the Chandra COSMOS Legacy survey, and the XMM-XXL northern field. We derived the X-ray spectral properties for all sources via spectral fitting, using a consistent technique and model. To model the parametric form of the XLF and the absorption function, we used a Bayesian methodology, allowing us to correctly propagate the uncertainties for the observed X-ray properties of our sources and also the absorption effects. The evolution of XLF is in agreement with a pure density evolution model similar to what is witnessed at optical wavelengths, although a luminosity-dependent density evolution model cannot be securely ruled out. A large fraction (∼60%) of our sources are absorbed by column densities of NH ≥ 1023 cm−2, while ∼17% of the sources are Compton-Thick. Our results favour a scenario where both the interstellar medium of the host and the AGN torus contribute to the obscuration. The derived black hole accretion rate density is roughly in agreement with the large-scale cosmological hydrodynamical simulations, if one takes into account the results that the X-ray AGN are hosted by massive galaxies, while it differs from that derived using JWST data. The latter could be due to the differences in the AGN and host-galaxy properties.

The XXL survey

We model the evolution of active galactic nuclei (AGN) by constructing their radio LFs. We used a set of surveys of varying area and depth, namely, the deep COSMOS survey of 1916 AGN sources; the wide, shallow 3CRR, 7C, and 6CE surveys, together containing 356 AGN; and the intermediate XXL-North and South fields consisting of 899 and 1484 sources, respectively. We also used the CENSORS, BRL, Wall & Peacock, and Config surveys, respectively consisting of 150, 178, 233, and 230 sources. Together, these surveys account for 5446 AGN sources and constrained the LFs at high redshift and over a wide range of luminosities (up to z ≈ 3 and log(L/W Hz−1)∈[22, 29]). We concentrated on parametric methods within the Bayesian framework, which allowed us to perform model selection between a set of different models. By comparing the marginalised likelihoods and both the Akaike information criterion and the Bayesian information criterion, we show that the luminosity-dependent density evolution (LDDE) model fits the data best, with evidence ratios varying from “strong” (> 10) to “decisive” (> 100), according to the Jeffreys’ interpretation. The best-fitting model gives insight into the physical picture of AGN evolution, where AGN evolve differently as a function of their radio luminosity. We determined the number density, luminosity density, and kinetic luminosity density as a function of redshift, and we observed a flattening of these functions at higher redshifts, which is not present in simpler models. We explain these trends by our use of the LDDE model. Finally, we divided our sample into subsets according to the stellar mass of the host galaxies in order to investigate a possible bimodality in evolution. We found a difference in LF shape and evolution between these subsets. All together, these findings point to a physical picture where the evolution and density of AGN cannot be explained well by simple models but require more complex models either via AGN sub-populations, where the total AGN sample is divided into sub-samples according to various properties, such as optical properties and stellar mass, or via luminosity-dependent functions.

Cosmological Evolution of Flat-spectrum Radio Quasars Based on the Swift/BAT 105 Month Catalog and Their Contribution to the Cosmic MeV Gamma-Ray Background Radiation

Abstract We present a new X-ray luminosity function of flat-spectrum radio quasars (FSRQs) utilizing the latest Swift/BAT 105 month X-ray source catalog. Contrary to previous studies of FSRQs in the X-ray band, using the luminosity-dependent density evolution model we find that FSRQs show evolutionary peaks at z ∼ 1−2 depending on luminosities. Our result is rather consistent with the evolution of FSRQs seen in the radio and GeV bands, although the number density is a factor of 5–10 smaller. We further explore the contribution of FSRQs to the cosmic MeV gamma-ray background radiation. We find that FSRQs can explain only ∼3% of the observed MeV gamma-ray background fluxes around 1 MeV, indicating other populations are required. Future MeV gamma-ray observations will be keys for understanding the origin of the MeV gamma-ray background radiation.

Gamma-ray luminosity function of BL Lac objects and contribution to the extragalactic gamma-ray background

ABSTRACT Using a significantly enlarged Fermi-LAT BL Lac objects (BL Lacs) sample, we construct the gamma-ray luminosity function (GLF) of BL Lacs, by the joint use of the space density distribution and source counts distribution. We use three well-studied forms of the GLF, i.e. the forms of pure density evolution (PDE), pure luminosity evolution (PLE), and luminosity-dependent density evolution (LDDE). The Markov Chain Monte Carlo (MCMC) technique is used to constrain model parameters. Our results suggest that LDDE model can give the best description for the BL Lac GLF. And the model shows that the BL Lacs with a harder GeV spectrum and a less luminosity evolve as strongly as flat spectrum radio quasars, and the evolution decreases as increasing luminosity. We also model the average photon spectra of BL Lacs with a double power-laws model. Using this modelled spectra, BL Lacs contribute $\sim \!20{{\ \rm per\ cent}}$ of the total extragalactic gamma-ray background (EGB) at E > 100 MeV, $\sim \!100{{\ \rm per\ cent}}$ of the EGB at E > 50 GeV, and the unresolved BL Lacs contribute $\sim\! 20 {{\ \rm per\ cent}}$ of the isotropic diffuse gamma-ray background at E > 100 MeV. A prediction of the TeV EGB spectra are given, which may be tested by the future detectors.

The hard X-ray luminosity function of high-redshift (3 < z ≲ 5) active galactic nuclei

We present the hard-band ($2-10\,\mathrm{keV}$) X-ray luminosity function (HXLF) of $0.5-2\,\mathrm{keV}$ band selected AGN at high redshift. We have assembled a sample of 141 AGN at $3<z\lesssim5$ from X-ray surveys of different size and depth, in order to sample different regions in the $ L_X - z$ plane. The HXLF is fitted in the range $\mathrm{logL_X\sim43-45}$ with standard analytical evolutionary models through a maximum likelihood procedure. The evolution of the HXLF is well described by a pure density evolution, with the AGN space density declining by a factor of $\sim10$ from $z=3$ to 5. A luminosity-dependent density evolution model which, normally, best represents the HXLF evolution at lower redshift, is also consistent with the data, but a larger sample of low-luminosity ($\mathrm{logL_X}<44$), high-redshift AGN is necessary to constrain this model. We also estimated the intrinsic fraction of AGN obscured by a column density $\mathrm{logN_H}\geq23$ to be $0.54\pm0.05$, with no strong dependence on luminosity. This fraction is higher than the value in the Local Universe, suggesting an evolution of the luminous ($\mathrm{L_X>10^{44}\mathrm{erg\,s^{-1}}}$) obscured AGN fraction from $z=0$ to $z>3$.

The largest X-ray-selected sample of $\boldsymbol {z&gt;3}$ AGNs: C-COSMOS and ChaMP

We present results from an analysis of the largest high-redshift (z > 3) X-ray-selected active galactic nucleus (AGN) sample to date, combining the Chandra C-COSMOS and ChaMP surveys and doubling the previous samples. The sample comprises 209 X-ray-detected AGN, over a wide range of rest frame 2-10 keV luminosities logL_{X}=43.3 - 46.0 erg s^{-1}. X-ray hardness rates show that ~39% of the sources are highly obscured, N_{H}>10^{22} cm^{-2}, in agreement with the ~37% of type-2 AGN found in our sample based on their optical classification. For ~26% of objects have mismatched optical and X-ray classifications. Using the 1/V_{max} method, we confirm that the comoving space density of all luminosity ranges of AGNs decreases with redshift above z > 3 and up to z ~ 7. With a significant sample of AGN (N=27) at z > 4, it is found that both source number counts in the 0.5 -2 keV band and comoving space density are consistent with the expectation of a luminosity dependent density evolution (LDDE) model at all redshifts, while they exclude the luminosity and density evolution (LADE) model. The measured comoving space density of type-1 and type-2 AGN shows a constant ratio between the two types at z > 3. Our results for both AGN types at these redshifts are consistent with the expectations of LDDE model.

TOWARD THE STANDARD POPULATION SYNTHESIS MODEL OF THE X-RAY BACKGROUND: EVOLUTION OF X-RAY LUMINOSITY AND ABSORPTION FUNCTIONS OF ACTIVE GALACTIC NUCLEI INCLUDING COMPTON-THICK POPULATIONS

We present the most up-to-date X-ray luminosity function (XLF) and absorption function of Active Galactic Nuclei (AGNs) over the redshift range from 0 to 5, utilizing the largest, highly complete sample ever available obtained from surveys performed with Swift/BAT, MAXI, ASCA, XMM-Newton, Chandra, and ROSAT. The combined sample, including that of the Subaru/XMM-Newton Deep Survey, consists of 4039 detections in the soft (0.5--2 keV) and/or hard ($>2$ keV) band. We utilize a maximum likelihood method to reproduce the count-rate versus redshift distribution for each survey, by taking into account the evolution of the absorbed fraction, the contribution from Compton-thick (CTK) AGNs, and broad band spectra of AGNs including reflection components from tori based on the luminosity and redshift dependent unified scheme. We find that the shape of the XLF at $z \sim 1-3$ is significantly different from that in the local universe, for which the luminosity dependent density evolution model gives much better description than the luminosity and density evolution model. These results establish the standard population synthesis model of the X-Ray Background (XRB), which well reproduces the source counts, the observed fractions of CTK AGNs, and the spectrum of the hard XRB. The number ratio of CTK AGNs to the absorbed Compton-thin (CTN) AGNs is constrained to be $\approx$0.5--1.6 to produce the 20--50 keV XRB intensity within present uncertainties, by assuming that they follow the same evolution as CTN AGNs. The growth history of supermassive black holes is discussed based on the new AGN bolometric luminosity function.

Models of the contribution of blazars to the anisotropy of the extragalactic diffuse gamma-ray background

We study the relation between the measured anisotropies in the extragalactic diffuse gamma-ray background (DGRB) and the DGRB spectral intensity, and their potential origin from the unresolved blazar population. Using a physical-evolution model for blazars with a luminosity dependent density evolution (LDDE) and an observationally-determined luminosity-dependent blazar spectral energy distribution (SED), we find that blazars can account for the observed anisotropy of the DGRB consistent with their observed source-count distribution, but are in turn constrained in contributing significantly to the observed DGRB intensity. For the best-fit LDDE model accounting for the DGRB anisotropy and source-count distribution, blazars only contribute 5.9+2.1−1.0% (68% CL) of the DGRB intensity above 1 GeV. Requiring a higher fraction of the DGRB intensity contribution by blazars overproduces the DGRB anisotropy, and therefore blazars in the LDDE+SED-sequence model cannot simultaneously account for the DGRB intensity as well as anisotropy.We discuss the limitations of LDDE models. However, these models do not require the many unjustified and observationally-inconsistent simplifying assumptions — including a single power law for all blazar spectra and a simple broken power-law model for their source-count distribution — that are present in much previous work.

Angular correlation functions of X-ray point-like sources in the full exposure XMM-LSS field

Our aim is to study the large-scale structure of different types of AGN using the medium-deep XMM-LSS survey. We measure the two-point angular correlation function of ~ 5700 and 2500 X-ray point-like sources over the ~ 11 sq. deg. XMM-LSS field in the soft (0.5-2 keV) and hard (2-10 keV) bands. For the conversion from the angular to the spatial correlation function we used the Limber integral equation and the luminosity-dependent density evolution model of the AGN X-ray luminosity function. We have found significant angular correlations with the power-law parameters gamma = 1.81 +/- 0.02, theta_0 = 1.3" +/- 0.2" for the soft, and gamma = 2.00 +/- 0.04, theta_0 = 7.3" +/- 1.0" for the hard bands. The amplitude of the correlation function w(theta) is higher in the hard than in the soft band for f_x < 10^-14 erg s^-1 cm^-2 and lower above this flux limit. We confirm that the clustering strength theta_0 grows with the flux limit of the sample, a trend which is also present in the amplitude of the spatial correlation function, but only for the soft band. In the hard band, it remains almost constant with r_0 = 10h^-1$ Mpc, irrespective of the flux limit. Our analysis of AGN subsamples with different hardness ratios shows that the sources with a hard-spectrum are more clustered than soft-spectrum ones. This result may be a hint that the two main types of AGN populate different environments. Finally, we find that our clustering results correspond to an X-ray selected AGN bias factor of ~ 2.5 for the soft-band sources (at a median z = 1.1) and ~ 3.3 for the hard-band sources (at a median z = 1), which translates into a host dark matter halo mass of ~ 10^13 h^-1 M_o and ~ 10^13.7 h^-1 M_o for the soft and hard bands, respectively.

Contribution of blazars to the extragalactic diffuse gamma-ray background and their future spatial resolution

We examine the constraints on the luminosity-dependent density evolution model for the evolution of blazars given the observed spectrum of the diffuse gamma-ray background (DGRB), blazar source-count distribution, and the blazar spectral energy distribution sequence model, which relates the observed the blazar spectrum to its luminosity. We show that the DGRB observed by the Large Area Telescope (LAT) aboard the Fermi Gamma Ray Space Telescope can be produced entirely by gamma-ray emission from blazars and nonblazar active galactic nuclei, and that our blazar evolution model is consistent with and constrained by the spectrum of the DGRB and flux source-count distribution function of blazars observed by Fermi-LAT. Our results are consistent with previous work that used EGRET spectral data to forecast the Fermi-LAT DGRB. The model includes only three free parameters, and forecasts that >~ 95% of the flux from blazars will be resolved into point sources by Fermi-LAT with 5 years of observation, with a corresponding reduction of the flux in the DGRB by a factor of ~2 to 3 (95% confidence level), which has implications for the Fermi-LAT's sensitivity to dark matter annihilation photons.

The [O iii] emission line luminosity function of optically selected type-2 AGN from zCOSMOS$^{\rm,}$

We present a catalog of 213 type-2 AGN selected from the zCOSMOS survey. The selected sample covers a wide redshift range (0.15<z<0.92) and is deeper than any other previous study, encompassing the luminosity range 10^{5.5} < Lsun< L[OIII] < 10^{9.1} Lsun. We explore the intrinsic properties of these AGN and the relation to their X-ray emission (derived from the XMM-COSMOS observations). We study their evolution by computing the [OIII]5007A line luminosity function (LF) and we constrain the fraction of obscured AGN as a function of luminosity and redshift. The sample was selected on the basis of the optical emission line ratios, after applying a cut to the signal-to-noise ratio (S/N) of the relevant lines. We used the standard diagnostic diagrams [OIII]/Hbeta versus [NII]/Halpha and ([OIII]/Hbeta versus [SII]/Halpha) to isolate AGN in the redshift range 0.15<z<0.45 and the diagnostic diagram [OIII]/Hbeta versus [OII]/Hbeta to extend the selection to higher redshift (0.5<z<0.92). Combining our sample with one drawn from SDSS, we found that the best description of the evolution of type-2 AGN is a luminosity-dependent density evolution model. Moreover, using the type-1 AGN LF we were able to constrain the fraction of type-2 AGN to the total (type-1 + type-2) AGN population. We found that the type-2 fraction decreases with luminosity, in agreement with the most recent results, and shows signs of a slight increase with redshift. However, the trend with luminosity is visible only after combining the SDSS+zCOSMOS samples. From the COSMOS data points alone, the type-2 fraction seems to be quite constant with luminosity.

Gamma-ray luminosity function of blazars and the cosmic gamma-ray background: evidence for the luminosity-dependent density evolution

We present a comprehensive study of the gamma-ray luminosity function (GLF) of blazars and their contribution to the extragalactic diffuse gamma-ray background (EGRB). Radio and gamma-ray luminosity correlation is introduced with a modest dispersion, consistent with observations, to take into account the radio detectability, which is important for blazar identification. Previous studies considered only pure luminosity evolution (PLE) or pure density evolution, but here we introduce the luminosity-dependent density evolution (LDDE) model, which is favored on the basis of the evolution of the X-ray luminosity function (XLF) of AGNs. The model parameters are constrained by likelihood analyses of the observed redshift and gamma-ray flux distributions of the EGRET blazars. Interestingly, we find that the LDDE model gives a better fit to the observed distributions than the PLE model, indicating that the LDDE model is also appropriate for gamma-ray blazars and that the jet activity is universally correlated with the accretion history of AGNs. We then find that only 25–50% of the EGRB can be explained by unresolved blazars with the best-fit LDDE parameters. Unresolved blazars can account for all the EGRB only with a steeper index of the faint-end slope of the GLF, which is marginally consistent with the EGRET data but inconsistent with XLF data. Therefore, unresolved AGNs cannot be the dominant source of the EGRB, unless there is a new population of gamma-ray emitting AGNs that evolves differently from the XLF of AGNs. Predictions for the GLAST mission are made, and we find that the best-fit LDDE model predicts about 3000 blazars in the entire sky, which is considerably fewer (by a factor of more than 3) than a previous estimate.

A Spectroscopic Survey of Faint Quasars in the SDSS Deep Stripe. I. Preliminary Results from the Co-added Catalog

In this paper we present the first results of a deep spectroscopic survey of faint quasars in the Sloan Digital Sky Survey (SDSS) Southern Survey, a deep survey carried out by repeatedly imaging a 270 deg^2 area. Quasar candidates were selected from the deep data with good completeness over 0 2.0) at the faint end, indicating a break in the QLF slope. Using a luminosity-dependent density evolution model, we find that the quasar density at M_{g}<-22.5 peaks at z~2, which is later in cosmic time than the peak of z~2.5 found from surveys of more luminous objects. The SFQS QLF is consistent with the results of the 2dF QSO Redshift Survey, the SDSS, and the 2dF-SDSS LRG and QSO Survey, but probes fainter quasars. We plan to obtain more quasars from future observations and establish a complete faint quasar sample with more than 1000 objects over 10 deg^2.

Gamma‐Ray Luminosity Function of Blazars and the Cosmic Gamma‐Ray Background: Evidence for the Luminosity‐Dependent Density Evolution

We present a comprehensive study for the gamma-ray luminosity function (GLF) of blazars and their contribution to the extragalactic diffuse gamma-ray background (EGRB). Radio and gamma-ray luminosity correlation is introduced to take into account the radio detectability which is important for the blazar identification. Previous studies considered only pure luminosity evolution (PLE) or pure density evolution, but we introduce the luminosity dependent density evolution (LDDE) model, which is favored from the evolution of X-ray luminosity function (XLF) of AGNs. The model parameters are constrained by likelihood analyses about the observed redshift and gamma-ray flux distributions of the EGRET blazars. We find that the LDDE model gives a better fit to the observed distributions than the PLE model, indicating that the LDDE model is also appropriate for gamma-ray blazars, and that the jet activity is universally correlated with the accretion history of AGNs. The normalization between the GLF and XLF is consistent with the unified picture of AGNs, when the beaming and a reasonable duty cycle of jet activity are taken into account. We then find that only 25--50% of the EGRB can be explained by unresolved blazars with the best-fit LDDE parameters. Unresolved blazars can account for all the EGRB only with a steeper index of the faint-end slope of the GLF, which is marginally consistent with the EGRET data but inconsistent with that of the XLF. Therefore unresolved AGNs cannot be the dominant source of the EGRB, unless there is a new population of gamma-ray emitting AGNs that evolves differently from the XLF of AGNs. Predictions for the GLAST mission are made, and we find that the best-fit LDDE model predicts about 3000 blazars in the entire sky, which is considerably fewer than a previous estimate.

The space density of moderate-luminosity active galaxies at z = 3

Abstract We present an estimate of the space density of active galactic nuclei (AGN) at z = 3. Combining deep X-ray data with Lyman break galaxy (LBG) colour selection in the rest-frame ultraviolet makes for highly efficient identification of AGN in a narrow redshift range (z ∼ 2.5–3.5). Using Chandra data from the Groth–Westphal Strip (GWS) and the Hubble Deep Field North (HDF-N), we find a total of 15 X-ray-detected LBGs at z ∼ 3, the majority of which are unlikely to have been identified in blanket follow-up surveys of X-ray-detected objects. We find the comoving space density of moderate-luminosity AGN (MLAGN; LX = 1043–44.5 erg s−1) at z = 3 to be a factor of ∼10 higher than that of the most powerful objects. The available data are consistent with a roughly constant space density of MLAGN from z = 0.5 to 3, and they are also consistent with a mild decline in the space density above z = 1 as predicted by the luminosity-dependent density evolution models of Ueda et al. This strong AGN activity at z = 3 argues against previous suggestions that the majority of black hole accretion occurs at low redshift. A further implication of our investigation is that, as far as can be determined from current data, the majority of the AGN population at z ∼ 3 is selected by the LBG dropout technique. Although this is sensitive to AGN with an ultraviolet excess arising from an accretion disc, it predominantly identifies star-forming galaxies. A significant fraction of X-ray sources seem likely to be hosted by these more typical LBGs, further strengthening the starburst–AGN connection at high redshift.

TheBeppoSAXHigh‐Energy Large‐Area Survey. V. The Nature of the Hard X‐Ray Source Population and Its Evolution

We present optical spectroscopic identifications of hard X-ray (5-10 keV) selected sources belonging to the High-Energy Large-Area Survey sample obtained with BeppoSAX down to a 5-10 keV flux limit of f5-10 keV ~ 3 × 10-14 ergs cm-2 s-1. The sample consists of 118 sources. There are 25 sources that have been identified through correlations with catalogs of known sources. A spectroscopic identification for 49 more has been searched for with the telescope. The results of 13 fields were empty down to R = 21. There were 37 sources identified as type 1 active galactic nuclei (AGNs) and nine as type 2 AGNs. The remaining sources are five narrow emission-line galaxies, six clusters, two BL Lac objects, one radio galaxy, and one star. Combining these objects with other hard X-ray selected AGNs from ASCA and HEAO 1, we find that the local luminosity function of type 1 AGNs (AGN 1s) in the 2-10 keV band is fairly well represented by a double power law function. There is evidence for significant cosmological evolution according to a pure luminosity evolution (PLE) model [LX(z) (1 + z)k], with k = 2.12 and 2.22 (σk 0.14) in a (Ωm, Ωλ) = (1.0, 0.0) and a (Ωm, Ωλ) = (0.3, 0.7) cosmology, respectively. The data show an excess of faint high-redshift type AGN 1s, which is well modeled by a luminosity-dependent density evolution (LDDE), similar to what is observed in soft X-rays. However, in both cosmologies, the statistics are not significant enough to distinguish between the PLE and LDDE models. The fitted models imply a contribution of AGN 1s to the 2-10 keV X-ray background from 35% up to 60%.

The space distribution of faint quasars from the CFHT survey

Basic data are presented for 163 QSOs brighter than B = 20.5 selected from 1000 A/mm CFHT blue grens observations. The data are used to investigate the form of the evolution of QSOs in order to obtain their luminosity functions, and to predict their magnitude and density distributions to allow comparison with the results of other surveys. Less than 5 percent of the QSOs have z greater than 2.5 despite the ease of detecting them up to z = 3.4, so high-redshift QSOs are rare. The surface density of QSOs brighter than m = 20.5 is 30/sq deg. While the luminosity-dependent density evolution models of Schmidt and Green (1983) are found to fit the data well, a smooth cutoff to the evolution at high redshifts is proposed which implies a density maximum at z of roughly 1.7. The clustering properties of the sample QSOs are discussed and it is shown, in agreement with previous studies, that while clustering is not a general phenomenon among QSOs, significant density enhancements apparently do exist. 26 references.

The Space Distribution of Faint CFHT Quasars

The space distribution of quasars discovered in our CFHT blue grens survey is discussed in detail. Redshifts for about 200 of the quasar candidates show that the sample is relatively complete for 0.2 &lt; z &lt; 3.4 and m &lt; 20.5. Two-thirds of the quasars have z &lt; 1.8 and only 5% have z &gt; 2.5, indicating that high redshift quasars are rare. The surface density of quasars brighter than m = 20.5 is 30 deg−2. Seven quasars with z = 1.165 ± 0.007 discovered in one of the fields have typical separations of ≈20 Mpc and may belong to a very large structure. Statistical tests on our data indicate that clustering among quasars is not common, however. The luminosity dependent density evolution models proposed by Schmidt and Green (1983) combined with a redshift cutoff at high redshift are consistent with our data and that of Schmidt and Green (1983), Marshall et al. (1984), Koo, Kron and Cudworth (1986), and Schmidt, Schneider and Gunn (1986). The model indicates that there was a broad maximum in the comoving density of quasars near z = 1.7. The results will be reported in detail in the March 1987 issue of The Astrophysical Journal.