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CHAPTER 1: INTRODUCTION
1.6.2 Space density of AGN
As we have seen before, AGN can be detected at cosmological distances thanks
to their large luminosity and hence they are of great interest to study the Universe
at earlier epochs. However, all observations have a limiting flux for detection,
such that an object with a flux below this limit cannot be distinguished
from the background. The limiting luminosity for detection varies with distance
so that we end up seeing different populations of AGN at different redshifts.
The luminosity function enables us to represent what is observed in
terms of different distances and luminosities, and is thus defined as the number
of objects detected per unit comoving volume per unit luminosity. In general,
the luminosity function will be a function of both luminosity and redshift. The
comoving volume is the volume that a region of space would have if it were
observed at the present epoch. Hence, the comoving volume is independent
of the expansion of the Universe and therefore there is no density evolution of
objects caused by this cosmological expansion.
Evolution in the comoving space density or luminsity of AGN is seen as a
change in the luminosity function. This can be described in different forms:
• Pure Luminosity Evolution (PLE): In PLE, the number of AGN per unit
comoving volume remains constant while the luminosity of each AGN
evolves, at a rate that is the same for AGN of all luminosities. In the
framework of a PLE model, the luminosity function retains its shape at all
redshifts and depends only on the evolution law and the luminosity function
at zero redshift. It has been a fairly succesful model for the evolution
of AGN at radio ([56], [169], [198]), optical ([27], [26], [106], [107], [108],
[205]) and X-ray ([51], [25], [118], [171]) wavelengths, although deviations
from this model have been seen at high redshifts and overproductions of
the X-ray background have been reported ([157], [224]).
• Pure Density Evolution (PDE): In PDE, the number of AGN per unit comoving
volume is assumed to evolve while the distribution of luminosities remains
constant. This model has failed to fit the current observations well
since it clearly overpredicts the measured cosmic X-ray background (e.g.
[99], [157], [224]) and therefore has been ruled out as a possible description
of the evolution of AGN.
• Luminosity-dependent Density Evolution (LDDE): In LDDE, both the num-
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