We deal here with space densities in comoving coordinates, so that the (1+z)³ due to the Hubble expansion is factored out.

Number counts: For any set of sources with the same luminosity L and constant space density r, in the approximation of flat spacetime the observed distribution of fluxes S will have the number of sources brighter than S given by N(> S) ~ S^-3/2 or log N(> S) = const - 1.5 log S which is why one reads of a log N - log S relation. Since this holds for any individual value of L, it is also true for any non-evolving luminosity function F(L). This may be applied without redshift information, so that it has been done effectively for extragalactic radio sources over a range exceeding five orders of magnitude in flux. Independent of one's redshift model, substantial changes in the luminosity function or space density of quasars and radio galaxies have occurred. This is demonstrated by the plot from Windhorst et al (1993, Fig. 3 from ApJ 405, 498, courtesy AAS), shown in the typical fashion normalized to the Euclidean expectation (slope 2.5 because these are differential rather than integral counts) to highlight departures:

The important features are (1) an initial rise from the very highest fluxes (too many faint sources), (2) a strong drop as one goes fainter (can be modelled by source evolution), and (3) another excess of very weak sources (possibly a different population, including starbursts and normal spirals; what Condon has called the dregs of the universe). Identifications of very weak radio sources at faint optical levels suggest that interaction-triggered starbursts at moderate redshift start to dominate at these levels (Windhorst et al. 1995 Nature 375, 471).

Much of the power of source counts is in telling that something has changed over cosmic time, independent of any but the most general assumptions (we don't need thousands of redshifts, for example). One must be able to assemble certifiably complete samples, which is tough for optical data. Also, just what changes may be quite model-dependent. The distinction between evolution of the source population in density and in luminosity may be quite subtle, though it has markedly different physical consequences. Also one might deal with evolution in duty cycle, if AGN are a stage that much of the galaxy population goes through for some fraction of the time; the consequences of different duty cycle might be manifested in the mass function of central black holes today.

The SchmidtV/V_m test (ApJ 151, 393, 1968) uses the fact that any selection technique has some limiting flux or magnitude, and that we would ordinarily expect to find objects anywhere within the associated volume unless they occur preferentially at larger distances (greater lookback times). If we see individual objects at distances R_obs and expect to detect them to R_limit, then for a nonevolving population we would have the quantity

uniformly distributed from 0 to 1 for whole samples. Any error in the assumed limiting magnitude can only reduce the mean value. Observed samples of QSOs give V/V_m = 0.51 - 0.66, so there must be a real local decrease in quasar number density. In practice, various corrections for color and emission-line properties are necessary (see Weedman chapter 6). Selection effects such as having the wrong limiting flux can only make the mean value of V/V_m less than 0.5, so that higher values may be taken as either a strong geometrical effect or evidence for some kind of evolution in the luminosity function. If we were sure of our world model, we could use a luminosity-distance formulation instead of simple r in calculating V/V_m. As set out by Schmidt 1968, we then use as a distance measure not just cz/H₀ but multiply this by

This and related techniques show a strong increase in the number of luminous QSOs with increasing redshift up to about z=2.5, with the comoving density varying approximately as (1+z)⁵.

Luminosity-function evolution. We would really like to know not only that something about the AGN population changes with cosmic time (redshift), but what. It might be the total number of AGN, the characteristic luminosity of each one, or the duty cycle of intermittent activity - the fraction of time a typical object spends in an ``on" state. One approach to sorting these out is to watch the luminosity function change with redshift. There exist redshift-dependent selection effects in optical surveys, so we need to sidestep these here. Most prominent are those for color and objective-prism selection. Below redshifts of 0.4 or so, QSOs almost uniformly appear much bluer than faint high-latitude stars. At z~0.4, Mg II l 2798 emission leaves the U band and makes QSO colors less distinct. Similarly, at very high redshifts Lyman a emission dominates; as soon as it passes the bluer passband of a pair QSOs become quite red. Multicolor selection reduces confusion with stars, but there remains nonuniform selection probability with redshift especially for faint objects. Similar effects occur in objective-prism surveys for emission-line objects; there are redshift ranges in which the only accessible emission lines are rather weak and only the brightest (or unusually strongest-lined) objects will be found.

To work around these problems, one might (a) look at only a set of redshift ranges for which selection is very efficient (Weedman ch. 6, Gaston 1983 ApJ 272, 411), or (b) use complete magnitude-limited samples and fit a model incorporating known selection functions (Schmidt and Green 1983 ApJ 269, 352). Further integral limits on the unseen part of the LF are provided by the diffuse X-ray and extreme UV backgrounds (Olbers' paradox revisited - we don't see quasars covering the sky either). Results indicate that the shape of the LF doesn't change much except at low luminosities, but that there are far fewer QSOs now than there were at z=2.5.

There have been many attempts to extend our knowledge of QSO evolution to higher redshifts. If galaxies are needed to host QSOs, the highest-redshift QSOs would be telling us when galaxies have to have already formed, and maybe what the rate of galaxy formation was. It is interesting (if not slightly suspicious) that some QSOs at z~3 are not very faint (visual magnitudes 16-18). The current redshift record is 5.80 (as of November 2000 with the first round of SDSS objects, Fan et al. 2000 AJ 120, 1167). Objects at redshifts above 4 have been found via multicolor searches, slitless spectroscopy, and incredibly in one case by sheer accident while observing an unrelated radio galaxy. There are still far too few high-redshift AGN to continue the trend seen up to z~2.5, something happened to the QSO population. This might have been

Up to redshift 2.5, the main effects are of increasing number and flattening toward higher luminosities, shown in fig. 4 of Schmidt and Green (courtesy of the AAS):

This schematic behavior has held up in later studies, while at higher redshift the observed numbers are increasingly deficient compared to extrapolations of this behavior. This has been reviewed by, for example, Shaver et al. 1996 Nature 384, 449) from which the following plot was adapted:

The implications of quasars at redshifts z> 4 have been discussed by Turner 1991 (AJ 101, 5), and are only getting stronger as a few objects turn up at higher and higher redshift. Generally, galaxies must have formed by z=5 or even better z=10 to expect enough dense cores to make high-redshift quasars. He cautions that beaming or gravitational amplification, if either operates differently on this population than for other QSOs, would complicate the analysis tremendously. There has been an explosion in the number of high-redshift quasars known, with 104 listed above z=4.0 in the 9th edition of the Veron-Cetty and Veron catalog. And this, of course, was before the SDSS color-selected samples became available.

There is a serious worry about whether we can see many objects at these pathlengths free of degradation by intervening material (via dust extinction, Lyman-limit absorbers, or the accumulation of narrow Lyman-a lines) or gravitational distortion, and thus about whether what we see is what we get. Heisler and Ostriker (1988 ApJ 332, 543) looked at the effects of dust in intervening galaxies. Virtually all high-redshift objects are seen through the disks of several foreground galaxies (a.k.a. metal-absorption-line systems) which might contain significant dust. This would have the effect of hiding very distant objects (optical depth t ~ (1+z)^2.5). In flux-limited samples, we would have missing rather than reddened objects. A key test here is whether there are enough faint radio sources to be the obscured QSOs, and whether there are many optically unidentified X-ray sources of appropriate flux. Also, at longer path lengths the probability of gravitational amplification goes up, since there is more spacetime volume for lens galaxies to be effective (they work best about midway in proper distance between the QSO and us). It seems clear that such effects contaminate QSO samples to some extent, but probably not in a statistically significant way at least to z~ 2; typical spiral-disk opacities today seem to be rather less than they assumed (modesty forbids, but see ApJ 542, 761, 2000), and would have been even smaller at the more relevant early epochs, with fewer generations of massive stars to enrich the ISM.

In all these issues, there is a nontrivial transformation between what we can trace - statistical changes in the source population - and where this actually happens - physical properties of individual objects. For example, on might consider that the luminosity function of QSOs might change either by the objects as a class varying their energy output (pure luminosity evolution) or by the actual comoving density of objects above some threshold changing (pure density evolution). This might in turn reflect a different typical duty cycle or phase of accretion in the earlier Universe.

It has long been seductive to try probing the world model of cosmology by trying to use AGN as standard candles or standard measuring rods. Radio galaxies seen at 2.2 microns have a very well-behaved Hubble diagram, and for a while it appeared that radio QSOs with flat-spectrum core sources showed a neat relation between luminosity and equivalent width of C IV l 1549 emission (the Baldwin effect, as in Nature 273, 431, 1978, which seems to have been the result of sheer bad luck in object selection and has just about gone away with recent data collections).

We can also use AGNs to probe the properties of galaxies along our line of sight to them, galaxies that are in many cases individually impossible to detect directly, by studying their influence on the propagation of light from the distant AGN. This may be in the form of gravitational lensing (which we've already treated) or absorption-line systems. Aside from the Lyman a forest, these include metal-line systems, damped Lyman a systems, and Lyman-limit systems. All three of these are telling us about some kind of gas-rich galaxy. Much of the controversy is how we are to associate them with the sorts of galaxies seen in our neighborhood to derive evolutionary changes.

Metal-line systems have been reviewed in several chapters of QSO Absorption Lines: Probing the Universe, and are considered important enough to have driven one of the few initial Key Projects for HST. Various species are seen in absorption depending on the absorber redshift z_abs < z_em: Lyman a, Mg I, Mg II, Fe II, C I, C IV, various species of Si, N, O. Complex velocity structure may be present; sometimes associated H I absorption at (1+z) × 21 cm may be found. The column densities involved are hard to assess because of uncertainties in ionization structure. Some similarity is found with the hot ISM in our galactic halo, but we sample different regions for these kinds of observations and the ionization match is still poor. There is some evidence that the absorbers are starburst galaxies because (1) there is a problem with spatial extent for normal galaxies, and starbursts are known to blow gas away in winds, and (2) the ambient QSO UV radiation field is not strong enough to ionize the gas as strongly as the absorption-line ionization levels suggest. In fact, the nearby galaxies identified with QSO absorption lines of Ca II and Na I are systematically high in SFR for their morphological types (Caulet and Keel, should have been published years ago). Also, objects at intermediate redshift z~ 0.5 for which Mg II can be seen from the ground and optical identification is possible look like some sort of starbursts. It is still not clear whether we are dealing with dwarf or luminous galaxies as the dominant absorbers. The evolution in comoving density with redshift is at most mild, unlike the Lyman a forest (essentially metal-free) systems.

Damped Lyman a systems} have much higher column densities in absorption, so that the H I resonance line is in a different part of the curve of growth. These are taken to be genuine disk galaxies, and extensive surveys (for example Wolfe et al 1986 ApJSupp 61, 249) have been carried out in hopes of watching spiral disks evolve. Straightforward assumptions indicate that these contain most of the neutral gas in teh Universe for a wide range of redshift. Metal lines are associated with these systems as well. A sample is shown by Turnshek et al 1989 ApJ 344, 567, by permission of the AAS):

Note the broad Lyman a absorption trough. A fascinating recent finding is that the metal abundances in these systems increase systematically with cosmic time, although they do not reach the levels seen in galactic stars of similar age (Lu et al. 1996 ApJSuppl 107, 475).

Many of these are also Lyman-limit systems, in which the optical depth at the Lyman edge is unity or greater. These are recognized by a step down in flux at the Lyman edge at the absorber (not QSO) redshift, frequently to zero detectable flux. The Milky Way is a Lyman limit absorber from our vantage point in every dirction at z=0. Various treatments are given by Tytler (1982 Nature 298, 427), Bechtold et al 1984 (ApJ 281, 76) and Lanzetta (1988 ApJ 332, 96). An example is shown by Sargent, Steidel, and Boksenberg (1989, ApJSuppl 69, 703, courtesy of the AAS):

Lanzetta found that these systems seem to have constant comoving space density, and that the Mg II metal-line systems seem to be disappearing relative to Lyman-limit systems.

These systems may also be sought in BL Lac objects, avoiding confusion with emission-line or BAL structure but introducing the problem that we may not know the AGN redshift except as the redshift at which the Lyman a forest disappears.

Last changes: 11/2000	  © 2000