QUASISTELLAR OBJECTS, STATISTICS
AND DISTRIBUTION

MALCOLM G. SMITH

The discovery of very high  redshift (z>3) galaxies and quasars offers
some hope that we shall be able to make direct tests of models for the
formation and evolution of both classes of object. Complete samples of
radio galaxies have been studied  at optical and infrared wavelengths,
and it is found  that the faintest  radio sources in these samples are
so readily  detected in the infrared  that very few of  these galaxies
could lie  at redshifts z>2.5. The  idea of a  formation epoch for all
massive  galaxies (some  of which  may host  quasars) suggests itself;
furthermore, in a recent  sample of radio  galaxies, all  the galaxies
with z>0.8 were  found to show colors  consistent  with star formation
activity in excess  of that expected  from an old, passively evolving,
elliptical galaxy. It is, however, still difficult to obtain redshifts
for the bulk of the galaxy population beyond z*0.5.

  Quasars, which are    much brighter than  most galaxies,   offer the
opportunity to look  back over 80-90% of the  time since the Big Bang.
Their relevance to galaxy formation models  depends on how much can be
deduced about the  formation and space density  of galaxies in general
by observing quasars  that have a space  density  about two orders  of
magnitude lower. In this context it is  important to try to deduce the
masses of quasar host  systems at high  redshift.  There is a  growing
body  of evidence that  typical  masses of  central objects in  nearby
normal and active galaxies are less than 10** M*. If these objects are
derived from luminous  quasars, and the  luminous quasars were powered
by gravitational  accretion of matter  without  significant mass loss,
then the masses  of  the central objects  in  nearby galaxies will  be
greater than the masses of the high-redshift progenitors. This in turn
will constrain the total amount of accreted matter and radiated energy
over the lifetime of  the quasar. The  luminosity function (defined in
the  next  section), coupled with  suitable  models, also provides, in
principle,   a  constraint  on the  integrated   energy  and hence the
(possibly  episodic) active lifetime of  the quasar. The duty cycle of
activity may be  a guide  to the fraction   of all galaxies that  have
harbored quasars. Physical models such as  this can be used to compute
the evolving luminosity function. Unfortunately, it turns out that the
reverse process  of deriving an   unambiguous physical model  from the
observed  data on  fluxes  and redshifts  has  proved to  be much less
secure.

In this entry, it is assumed that redshift is a measure of distance in
a   standard Big  Bang  cosmology,  as   described elsewhere in   this
encyclopedia.  [The Astronomy and Astrophysics encyclopedia, copyright
1992.] This assumption has yet to be rigorously proven.

LUMINOSITY FUNCTIONS AND THEIR EVOLUTION AT z<2.2

Surveys of  large samples  of quasistellar  objects have,  as one aim,
provision of a statistical basis for deductions about the distribution
and time evolution   of these objects. These observational  deductions
can then be compared with a series of alternative concepts, or models,
to  gain  a better understanding  of  the underlying astrophysics. The
statistics  used   to describe the  distribution  of  quasars in space
depend on the concepts of space density and luminosity function.

  Consider first a volume of space containing a number of quasars. The
volume must be specified with respect to the redshift  or epoch of the
universe at which the volume is seen, because redshift is a measure of
the  scale factor  of  the universe   at  the time the   radiation was
emitted.   In conventional Big  Bang models, the  galaxies and quasars
are roughly stationary in space; space itself is expanding, stretching
the   wavelengths  of radiated  photons   passing through it. Comoving
volumes  scale with  this expansion of   the universe. The concepts of
comoving volume and comoving space density provide corrections for the
cosmological changes associated with the expansion of the universe. An
unchanging population of objects has a comoving  space density that is
constant with time and is therefore  independent of redshift. We find,
however,  that the number   of  quasars observed in  a  given comoving
volume begins  to increase rapidly as we  look back  to earlier times-
corresponding to greater  redshifts.   The comoving space   density of
quasars appears to reach a  maximum somewhere  between 2<z<3 and  then
may decrease again.

  The quasars  in any given  volume will,  like stars, usually  differ
from  each other in their   intrinsic luminosity. At great  distances,
many are too  faint to be detectable  in surveys that  are necessarily
flux limited.  Any  description of  the three-dimensional distribution
of astronomical  objects such as  stars and quasars must  therefore be
restricted to a finite range of intrinsic  luminosities. This range is
set by  the flux limit of the  survey  and by relations  between flux,
luminosity, and   distance.  The luminosity function  at  a particular
redshift  is the variation   of  the comoving space  density  per unit
luminosity as a function  of luminosity *=*(L,z). Luminosity functions
are  also   often quoted  per unit  magnitude,   for  which the symbol
#=*(M,z) is used. Once this  function is determined for all  redshifts
and luminosities, one has a complete  evolution function for the given
object  population. Figure   1  presents model   fits  to the  optical
luminosity functions of nearby galaxies, z-O, and for quasars at z-0.5
and z-2. High-redshift quasars are clearly much more luminous than the
population  of galaxies  as  a whole.  On the   other  hand, the space
density of galaxies today (z-0) is several orders of magnitude greater
than  the space   density of  quasars  at   any   redshift (as  little
significant increase in  quasar space density   has been found  beyond
z-2).

  We see that Fig.  1 is apparently consistent with  a model  in which
the  population  of quasars gradually dims   with time. The luminosity
function for  quasars with z=2 can be  fitted over the one for Seyfert
galaxies near z=0 (assuming the centers of nearby Seyfert galaxies are
intrinsically faint quasars)  by sliding  the  function over  from the
right toward the  left of the  diagram. The comoving  space density of
the entire population does not appear to change appreciably with time,
whereas   the  population as  a  whole  has  dimmed  by two  orders of
magnitude (5   magnitudes in   M*,  the  absolute magnitude  in   blue
light). Such   horizontal  evolution  of the  luminosity   function is
referred to as luminosity  evolution. An alternative scenario in which
the  luminosity of a  feature  in the  luminosity function (e.g.,  the
break between  the flat and steep  sections) remains constant, but the
entire function shifts     vertically  in the diagram    as   redshift
increases, is referred to as density evolution. A diagonal movement of
the  function across the  M-z  diagram can  be caused by  a mixture of
luminosity and density evolution.  The data for quasars with z<2.2 are
consistent with pure luminosity evolution.

  The   evolution of the luminosity   function  is almost important in
determining  the contribution of  QSOs to the  x-ray background and to
the ultraviolet ionizing field at high redshift.

FINDING QUASARS: RECENT SURVEY WORK

It is unfortunately necessary  to have a  very clear understanding  of
the nature of the observational samples before one can attempt to work
out what can be  concluded from them.  Traps abound. In the early days
of work on statistics of  quasars, for example,  it was widely assumed
that  all quasars are strong  radio  sources. Most quasars known today
have  not been  detected  at all  at radio wave-lenghts.  Some optical
selection  methods  work    well  only over  a   restricted   range of
wavelengths. Surveys at  x-ray and infrared  wavelengths are still too
restricted in sensitivity  to provide much  information on the  global
properties of quasars  beyond z-0.5. One therefore  does one's best to
work on well-defined subsets of the total population of quasars.

  Our  knowledge the evolution of  the  majority of  quasars at  z<2.2
(summarized in Fig.1)  is drawn from surveys  based on sets of  direct
photographic   plate pairs taken in  ultraviolet   and blue light. The
quasars on these plates were separated from most of the stars and very
distant normal galaxies   on  account of their   stronger  ultraviolet
emission. They were separated from nearby galaxies on account of their
star-like appearance. These ultraviolet-excess (UVX) surveys appear to
be  nearly complete for objects  with  redshifts z<2.2; surveys  using
other techniques find very few additional quasars up to this redshift.


  At redshifts z>2.2,  quasars normally lose their  ultraviolet excess
with  respect to many galactic stars,  which makes them much harder to
separate out for further study. At z=2.2., the strong Lyman-* emission
line of hydrogen  (rest wavelength  121.6  nm) has  been redshifted to
389.1 nm, and moves out of the passband of the ultraviolet filter used
in most photographic surveys.   A variety of techniques therefore  has
had to be used to locate  objects at higher redshifts. Until recently,
different techniques  used  in the  same area  of  sky often  produced
rather different   lists of objects, which led   to concerns that each
list was unlikely to be representative of the total population.

The  largest sample  of  quasars  with z>3  selected in  a homogeneous
manner  consists of  about  50  objects.   The technique of   original
candidate selection  is  based  on automated  classification   of some
200,000 objects, with apparent  red magnitudes 16<**<20, measured with
a  high-speed  automated plate measuring machine   (APM) on UK Schmidt
telescope  plates; sets  of  plates were taken  through five different
colored filters with  the telescope  centered in  turn on  two  fields
giving an   effective survey area  of 50    square degrees. Again  the
technique of measuring ratios of fluxes through filters has proved the
most effective, but  it is necessary to  use more than  two filters to
separate out the high-redshift quasars  from the bulk of normal  stars
and high-redshift galaxies;  the method is based  on a measure  of the
degree  of isolation of  each  image in a four-dimensional  flux-ratio
diagram.  Only quasars whose flux ratios (colors) are similar to those
of galactic stars  escape  detection by this technique.  The selection
function  of the survey-a  measure   of the probability of   detecting
different  known classes  of  objects having  distinct spectral energy
distributions-can   be  determined   because the candidate   selection
procedure is automated.

  Dispersive  elements  such as  prisms and transmission-grating/prism
(grism) or grating/lens (grens)  combinations when placed ahead of the
focal plane  of a telescope  can produce spectra  of a large number of
objects at  once.   Automated detection of    emission  lines in  such
spectra,  recorded with  charged-coupled  device (CCD)  detectors,  is
producing   well-defined,   gradually     increasing   subsamples   of
large-redshift  quasars-including a   recently discovered object  with
z=4.37.

LUMINOSITY FUNCTIONS AND THEIR EVOLUTION AT REDSHIFTS z>2.2

The highest measured   galaxy redshift is  3.8.  The highest redshifts
known  for quasars  are approaching 5.   Most of  the highest-redshift
quasars are bright-rather  few faint quasars have  been found at  high
redshifts, even though  the techniques used  appear to be sufficiently
sensitive   to detect  them  if  they  exist.  The luminosity function
therefore appears to   steepen  rapidly at  fainter flux   levels. The
result is that  the decline  in  comoving space density  appears to be
sharper for the fainter objects. It may also set in at lower redshifts
than for brighter objects. Only few very bright  objects can be found,
even over a search  area of 50 square  degrees, so that one cannot yet
be certain whether, for the very brightest classes of quasar, there is
any turn-down in the comoving  space density. The situation at present
is that only the simplest  models for the  evolution of the luminosity
function can be  tested. Constraints on  the detailed shape parameters
for the luminosity function are still very weak. Extensive survey work
currently  underway using CCD   detectors on large telescopes is  very
costly in large telescope time but currently seems the most likely way
to improve the situation.

CLUSTERING OF QUASARS

We are  still a long way  from  an astrophysical  understanding of the
observed   evolution of the quasar   luminosity function. If the black
hole mass is increasing, why  is the characteristic luminosity of  the
quasar  population  decreasing? One of  the  many uncertainties is the
effect on  the quasar of its  environment. Assuming that gravitational
interaction of the quasar with close companion galaxies is responsible
for triggering  quasar  activity, evolution  of the quasar  luminosity
function would be interpreted in terms of a  change in the interaction
rate with cosmic time. Observational tests of this idea are difficult;
for  example, low-power sources may not  be seen in dense environments
because they cannot supply enough ram pressure  to overcome the static
pressure of the intergalactic  medium;  the more luminous  quasars and
galaxies would have no such  difficulties. Therefore, one has to check
each  sample   of  quasars  carefully  to   ensure   that any apparent
correlation   with redshift is  not   in fact produced  by a  stronger
correlation with intrinsic luminosity.

  The extent to which quasars cluster among themselves is important if
only because the standard cosmological models assume a homogeneous and
isotropic  universe, whereas the   distribution  of galaxies and  even
clusters of galaxies is  patently not homogeneous. Current  studies of
quasar association provide no evidence for quasar-quasar clustering on
the large  scale;  however, evidence for  quasar-quasar  clustering on
scales of order 10 Mpc or less has recently been reported.

                              Additional Reading

Begelman, M.C., Blandford, R.D., and Rees, M.J.(1984). Theory
   of extragalactic radio sources. Rev. Mod. Phys. 56 255.

Boyle, B.J., Shanks, T., and Peterson, B.A.(1988). The evolution
   of optically selected QSOs-II. Monthly Notices Roy. Astron.
   Soc. 235 935.

Osmer, P.S.(1982). Quasars as probes of the distant and early
   universe. Scientific American, 246 (No. 2) 96.

Peacock, J.A. and Miller, L.(1988). Radio quasars and radio
   galaxies-A comparison of their evolution, environments and
   clustering properties. In Proc. Workshop on Optical Surveys for
   Quasars, P.S. Osmer et al., eds.
   Astron. Soc. Pacific Conf. Ser. 2 194.

Schmidt, M., Schneider, D,P., and Gunn, J.E.(1988). Spectroscopic
   CCD surveys for quasars at large redshift. In Proc. Workshop
   on Optical Surveys for Quasars, P.S. Osmer et al., eds.
   Astron. Soc. Pacific Conf. Ser. 2 287. (See also the many other
   relevant articles in this volume.)

Warren, S.J. and Hewett, P.C.(1990). The detection of high-redshift
   quasars. Reports on Progress in Physics.

Weedman, D.W.(1986). Quasar Astronomy. Cambridge University Press,
   Cambridge, U.K.