## 5. Evolution of luminous QSOs
In this section, we consider QSOs with high soft X-ray luminosities
(), where the behavior of the SXLF
can be traced up to high redshifts. Also in the high-luminosity
regime, at least in the local universe, we observe very few absorbed
AGNs, which could cause problems with the K-correction, in the local
universe (e.g. Miyaji et al. 1999b). If this tendency extends to the
high redshift universe, our
In both cases, the number density increases up to and flattens beyond this redshift. In both cosmologies, the number density for is consistent with no evolution. The Maximum-Likelihood fits in the , region gave density evolution indices () of and for =(1.0,0.0) and (0.3,0.0) respectively. Subtle differences of the density curves seen in Fig. 11 between the two cosmologies come from two effects. Because different cosmologies give different luminosity distances, some objects which do not fall in the region for (1.0,0.0) come into the sample in lower density cosmologies. Also the comoving volume per solid angle in a certain redshift range becomes larger in lower density cosmologies, thus the number density lowers accordingly. These two effects work in the opposite sense and tend to compensate with each other, but the former effect is somewhat stronger. It is interesting to compare this curve with similar ones from
surveys in other wavelengths. In Fig. 11, we overplot number densities
of optically- (Schmidt et al. 1995, hereafter SSG95) and
radio-selected (Shaver et al. 1999) QSOs for
(1.0,0.0). The densities of these
QSOs have been normalized to match the where We have also checked statistical significance of the difference
using the density evolution-weighted
statistics, (Avni & Bahcall
1980), which is a variant of the
statistics (Schmidt 1968) for the cases where surveys in different
depths are combined. The and
are primed to represent that they
are density evolution-weighted (comoving) volumes. If we take
in Eq. (13) with
as the weighting function,
will give a value of 0.5 if the
sample's redshift distribution follows the density evolution law of
SSG95. An advantage of this method over the likelihood fitting is that
one can check the consistency to an evolution law in a
model-independent way, i.e., without assuming the shape of the
luminosity function. Applying this statistics to 17 AGNs in
,
, we have obtained
, where the
1 error has been estimated by
( © European Southern Observatory (ESO) 2000 Online publication: December 8, 1999 |