Studies of the quasar population require, as a minimum, determination of redshift and luminosity for a sample of objects. Improvements in wavelength coverage and overall efficiency of modern spectrographs and detectors have made the determination of redshifts routine, if still time consuming at faint magnitudes. A luminosity may be calculated from a flux measurement, an adopted cosmology, and knowledge of the quasar spectral energy distribution (see e.g., Schmidt and Green 1983). Deriving the intrinsic properties of a quasar from high quality observations should not present difficulties in principle. The complexities of compiling a sample capable of discriminating between competing theoretical predictions become evident only when the ranges in luminosity, redshift and spectral energy distributions within the quasar population are taken into account. The situation is compounded by unavoidable correlations between fundamental quantities such as redshift and luminosity in samples of objects obtained from flux-limited surveys.
2.1 Absolute Magnitudes and Luminosities
The division in absolute blue magnitude between quasars and the lower
luminosity population of active galactic nuclei (AGN) is usually taken
by astronomers working at ultraviolet and optical wavelengths to be
MB = -23, for H0 = 50 km
s-1 Mpc-1, q0 = 0.0, and 
= 0.0 (e.g.,
Schmidt and Green 1983). The physical basis for this convention is
somewhat arbitrary, and the choice of the B band is historical, but
even with this somewhat artificial truncation at low luminosities, the
quasar luminosity function extends over a factor > 1000 in
luminosity. Away from the optical regime the situation is similarly
daunting. For example, at fixed optical luminosity, the ratio of
radio-to-optical luminosity in the quasar population spans four
orders of magnitude. Therefore, observations in any wavelength regime
that constrain the form of the luminosity function must cover a large
dynamic range in flux. A number of workers draw a distinction between
objects based on their radio power, with ``radio-loud'' objects termed
quasars, and ``radio-quiet'' objects termed QSOs. While there is some
evidence to support the interpretation that two distinct populations
exist (Kellerman
et al. 1989,
Miller, Peacock and
Mead 1990,
Visnovsky et
al. 1992), objects with intermediate properties are found, and the
existence of a clear-cut boundary has yet to be established.
Furthermore, the physical significance of the spread in radio power is
not understood, although an explanation related to the nature of the
host galaxy is favored by many (e.g.,
Miller et al.
1990). Energetically,
the radio-frequency regime is insignificant even for the most extreme
radio-loud quasars, and without a physical basis for making a
distinction, the rationale for defining two classes of object is not
clear. For these reasons we employ the term ``quasars'' throughout to
refer to all objects irrespective of their radio-power.
At bright flux levels the quasar source counts show a rapid increase
with decreasing flux. In the optical for example, the differential
number-magnitude counts have the form, log (N) 
0.8
mB, for mB 
19
(Goldschmidt et
al. 1992). Given such a steep
dependence, a flux-limited survey probing this regime is necessarily
dominated by quasars detected close to the flux limit. To achieve a
useful dynamic range, surveys to bright flux limits over large areas of
sky must be combined with small-area investigations extending to
fainter fluxes, a technique employed very successfully by
Dunlop and Peacock
(1990) to constrain the evolution of the radio source
population. In a flux-limited sample there is a strong coupling
between the redshift of an object and its luminosity, such that objects
detected at even moderately different redshifts 
z 
1,
occur in disjoint luminosity ranges, with increasingly bright portions
of the luminosity function probed at higher redshifts. To date, it has
proved impossible to ascribe a number of observed trends in the
properties of quasars unambiguously to either redshift or luminosity.
At radio wavelengths, quasar spectra are well represented by
power laws as a function of frequency, F(
) 
,
where F is the flux,
the frequency, and values of are
typically ~ -0.7. With such a simple spectral form a well-defined
bolometric correction can be applied to a flux estimate at a specified
rest-frame frequency to give a bolometric luminosity. However, while
quasars with nearly pure power-law spectral energy distributions (SEDs)
do exist, the majority of
quasar SEDs are poorly represented by such a parametrization.
Multi-wavelength investigations have demonstrated large
departures from a power-law, the most significant of which is a broad
feature at rest-frame ultraviolet wavelengths, the so-called Big Blue
Bump (Malkan
1983). The dispersion in the form of SEDs over both
large and small frequency intervals (Section 2.3)
means that knowledge of the
form of a quasar's SED is required before a monochromatic flux can be
accurately translated into a bolometric luminosity.
2.2 Redshifts
Any study of the quasar population as a function of look-back time involves the observation of objects covering a substantial redshift range. The small size of CCD and image-tube detectors and the limited free spectral range of most low-order grating spectrometers has restricted spectroscopic observations to a window typically 2000-3000 Å wide in the observed frame. The accessible wavelength range in the quasar rest-frame is further reduced by a factor (1 + z). For even a modest span in redshift, observations over a fixed wavelength range in the observed frame produce rest-frame spectra probing disjoint wavelength regions. The consequent restrictions are evident from noting that spectra of a redshift z = 3 quasar covering the entire observed-frame optical region (3300-9000 Å) access only ~ 1400 Å in the rest-frame, i.e., 875-2250 Å. Observations in the ultraviolet (employing satellites) or the infrared are possible but have been restricted to the brightest quasars, and the signal-to-noise ratios and spectral resolution are low (Kinney et al. 1991, Lanzetta, Turnshek and Sandoval 1993). As a consequence, information on SEDs is confined to narrow wavelength ranges that vary systematically with redshift, making attempts to study the evolution of the SEDs of the quasar population as a function of look-back time difficult at best. Recent Hubble Space Telescope observations in the vacuum ultraviolet are providing the first high-quality spectra of the rest-frame ultraviolet spectra of apparently-bright, low-redshift quasars, but the number of objects remains small.
2.3 Quasar Spectral Energy Distributions
Quasar SEDs plotted as
F() versus , show the frequencies
at which the bulk of the energy is emitted. The importance of the Big
Blue Bump is evident for the majority of quasars; see Sanders et
al. (1989:
Figure 1). In
their important paper, Sanders et al. used IRAS
observations of quasars
from the Palomar-Green survey to show that, in addition to the
presence of the Big Blue Bump, a second broad feature, which we will
term the Far-infrared Bump, exists at wavelengths of ~ 60 µ. An
underlying power-law component is almost certainly present in most if
not all objects, but only for a small percentage does the
power-law component dominate the energy output at wavelengths longward of
the hard X-ray regime. Recently, observations have
been undertaken at gamma-ray wavelengths with remarkable results at
the highest energies (Dermer and Schlickeiser 1992) which suggest that
some quasars, at least, emit significant amounts of their energy in
the 100 MeV regime.
At least four principal components, each almost certainly due to a very different emission mechanism, are believed to make a significant contribution to quasar SEDs: underlying power-law, Big Blue Bump, Far-infrared Bump and hard X-ray component. The spread of radio properties of objects selected at optical-ultraviolet wavelengths has been known for many years, and McDowell et al. (1989) have emphasized the large range in Big Blue Bump strength among quasars selected at X-ray wavelengths. The existence of the Far-infrared Bump, believed by many workers to arise through the absorption and subsequent re-emission of short wavelength radiation by dust, possibly in the form of a torus in the core of the galaxy hosting the quasar (Krolik and Begelman 1988), has led to the suggestion that a large population of quasars remain ``dust-enshrouded'' with the bulk of their energy emerging in the far infrared. In the most extreme version of this hypothesis, ultraluminous galaxies harboring enshrouded quasars and emitting predominantly at infrared wavelengths are not included in optical quasar surveys because of absorption at optical and ultraviolet wavelengths (Sanders et al. 1988). The relative proportions of quasars with very different SEDs as measured over large frequency ranges is not yet known but objects which radiate primarily at infrared, ultraviolet and X-ray wavelengths do exist. To gain a full picture of the quasar population, surveys must either be conducted over a broad range in frequency or, a very sensitive survey at a single frequency must be combined with a quantitative knowledge of the SEDs of the objects detected, measured over many decades of frequency.
Improvements in sensitivity and sky coverage at infrared and X-ray
wavelengths have been substantial, with the IRAS and ROSAT
satellites
providing recent surveys with all-sky coverage, but sensitivity
relative to that achievable in the optical remains limited. In the
radio regime, high sensitivity and extensive sky coverage have been
available for many years, but the fraction of the quasar population to
which radio surveys are sensitive is small - ~ 10%. In
practice, observations in the optical regime probe to the faintest
limits both in
terms of intrinsically faint objects and for objects at the highest
redshifts. In the quasar rest-frame, optical observations correspond
to part of the wavelength
range 700
7000
Å. As with quasar SEDs over
large frequency ranges, the rest-frame ultraviolet and optical SEDs of
quasars show a large dispersion from object to object. The most
obvious manifestation is broad emission line strength
which ranges from objects with equivalent widths of hundreds of
angstroms to objects that are
essentially lineless, and beyond, to the broad absorption line (BAL) quasars.
In the latter case, for the strongest ultraviolet lines,
emission may be entirely absent and absorption can be present with
equivalent width comparable to that of emission lines in a more typical
quasar. Also important is the dispersion in the shape of the effective
continuum, which, where a power-law representation is
adequate, corresponds to a range in the slope parameter . The Fe
II emission in the optical and ultraviolet, which contributes over
extended wavelength intervals, merging with the true ``continuum'',
also varies significantly from object to object. Factors external to the
quasars and associated host galaxies are also important. At redshifts
z > 1.7
the presence of intervening absorption, most notably the high column
density, N(HI) 1017 cm-2, Lyman limit systems
which
remove most or all of the flux shortward of 912 Å in the
rest-frame of the absorber, introduces an additional dispersion in
observed quasar SEDs.
Published data are inadequate to determine the intrinsic dispersion of SEDs, although new data of the quality required are being obtained, with some programs (e.g., Pei, Fall and Bechtold 1991) stimulated by the predictions of a dispersion in the rest-frame ultraviolet and optical SEDs arising from the presence of intervening absorbers.