Schmidt's discovery of the evolution of the quasar luminosity function immediately stimulated work on the nature of the evolution. While powerful for showing the existence of evolution, the V / Vm test by itself was not capable of delineating the nature of the evolution. Furthermore, the available quasar samples were too small to permit analyses in much detail. Schmidt explored different forms of density evolution, i.e., evolution of the number density with cosmic epoch. He found that both a power-law evolution of the form (1 + z)k and an exponential function of look-back time could fit the data up to redshift 2. Mathez (1976, 1978), building on the work of Lynds & Petrosian (1972), demonstrated that luminosity evolution, in which the characteristic luminosity of quasars increased with redshift also provided a satisfactory fit to the data. Schmidt & Green (1983) presented results from the 92 quasars in the Palomar Bright Quasar Survey that showed the increase of space density with redshift to depend on the luminosity of the objects. This indicated that a simple parameterization of either pure density or pure luminosity evolution did not fit the data well.
Subsequently, the work of Boyle, Shanks, & Peterson (1988, hereafter BSP), using the UVX technique, marked a significant advance in sample size and limiting magnitude. They compiled a sample of 420 quasars to B < 20.9 mag from UK Schmidt plates scanned with COSMOS. They found that a two-power law luminosity function and luminosity evolution adequately describe the data for objects with MB < - 23 mag and z < 2.2, a result that has been widely used and is consistent with recent 2dF results, as described below.
Thus, the situation by the late 1980s was that either the space density of quasars increased by more than a factor of 100 between redshift 0 and 2 (Schmidt & Green 1983), or their characteristic luminosity increased by a factor of 30 (BSP).
It was also understood that the density and luminosity evolution pictures led to significantly different estimates of the lifetimes of quasars, about 107 years in the density evolution picture and 109 years or more in the luminosity evolution picture. Another consequence was that most galaxies would pass through a quasar phase in the density evolution model; for luminosity evolution, only a few percent of galaxies would be active.
A different and also important question was raised early on in studies of quasar evolution: What happened at high redshift, z > 2? The redshift histograms of quasar catalogs showed a marked decline in numbers at z > 2 (e.g., Hewitt & Burbidge 1980), with the implication that the evolution also declined. However, it was also realized that the traditional UVX method was not suitable for finding high-redshift quasars, and the lack of suitably defined samples blocked progress. As mentioned above, the slitless-spectrum technique provided an efficient means of discovering high-redshift quasars, and Osmer (1982) showed from a differential study with the CTIO 4-m telescope and grism that there was strong evidence for a decline in the space density of quasars at z > 3. Nonetheless, he could only provide an upper limit on the decline because no quasars with z > 3 were found in his survey, and it was clear that more work was needed. Also, it was pointed out by Heisler & Ostriker (1988) that dust absorption by intervening galaxies along the line of sight could produce a decline in the observed space density determined from flux-limited samples.
Significant advances occurred in the 1990s, when the first large,
digital surveys for high-redshift quasars were carried out.
Warren, Hewett, & Osmer
(1991a,
b,
1994,
hereafter WHO) made use of APM scans of UK Schmidt plates in six colors,
u, bj,
, or,
r, i to cover an effective area of 43
deg2. Their sample contained 86 objects with
16 < mor < 20 mag and
2.2 < z < 4.5. They developed a numerical modeling technique
to determine the selection probabilities for their objects as a function
of redshift and magnitude, allowing for different spectral slopes and
emission-line strengths. They used the selection probabilities to make
two different estimates of the quasar luminosity
function and its evolution. They found strong evidence for a decline in
the space density beyond z = 3.3 by a factor of 6 for the
interval
3.5 
z < 4.5 for
luminous quasars with MC < - 25.6 mag
3.
Schmidt, Schneider, & Gunn
(1995,
hereafter SSG, and references therein) used the Palomar Transit Grism Survey
(Schneider, Schmidt, &
Gunn 1994)
to establish a sample of 90 objects with
Ly
emission and
redshifts 2.75 < z < 4.75 to
AB1450 < 21.7 mag in an area of 61.5 deg2.
Their digital survey used CCD
detectors, and they determined the completeness and selection effects
for their sample based on the line fluxes and signal-to-noise ratio of
the data. Their sample contained 8 objects with z > 4, and
they found a decline in the space density of a factor of 2.7 per
unit redshift for quasars with MB < - 26 mag and
z > 2.7. This result was very important because it used a
survey technique
different from WHO and had many more quasars with z > 4.
Kennefick, Djorgovski, & de Carvalho (1995) made use of three colors, J, F, N, in the second Palomar Sky Survey in a program covering 681 deg2 in the magnitude range 16.5 < r < 19.6. They had 10 quasars with z > 4 in their sample and found a decline in space density of a factor of 7 at z = 4.35 relative to z = 2.0.
Taken together, the three surveys agreed well within their respective estimated errors and provided convincing evidence for a steep decline at z > 3 in the observed space density of luminous, optically selected quasars. When the results are combined with those of BSP for lower redshifts and plotted on linear scales of space density versus look-back time (Fig. 1, left), the behavior is dramatic and indicates a remarkable spike of quasar activity when the Universe was 15%-20% of its current age.
 |
 |
Figure 1. Left: A linear plot of the space density of luminous quasars versus look-back time for the BSP and WHO samples. Right: The observed luminosity functions for the quasars with 0.35 < z < 2.3 in the 2dF sample compiled by Boyle et al. (2000). |
|
At the same time, a number of important questions remained about the
nature of the evolution of the quasar luminosity function: (1) At what
redshift does the peak of the space density occur? This is a result of
the optical SEDs of z = 3 quasars being similar to those of
stars. (2) How do lower-luminosity quasars and AGNs, which
constitute the bulk of the population, evolve? This requires deeper
surveys. (3) What is the form of the
evolution and its possible dependence on redshift?
Hewett, Chaffee, & Foltz
(1993)
showed from a study of the 1049 quasars and AGNs from the Large Bright
Quasar Survey, which cover 0.2 < z < 3
and 16.5 < mBJ < 18.85, that the data
are not fit well by a pure luminosity evolution
model with a two-power law luminosity function. They found that the
slope of the luminosity function became steeper at higher redshifts, the
rate of evolution was slower for
0.2 < z < 2 than the Boyle et al. results, and the
evolution continued, more slowly, until
z 
3. Thus,
more work needs to be done.
3 MC is the absolute
magnitude on the AB system for the continuum level at
Ly (1216 Å).
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