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\title{\bf Counts of Galaxies Around Distant Highly Luminous
QSOs\footnote{Based on data collected at the European Southern Observatory (La
Silla, Chile)} }
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\author{E.~Van Drom $^1$\thanks{This is a footnote in the author list},
R.~J.~Drofnats $^2$\\and V.~D.~Escamillo $^3$\\
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\normalsize $^1$Institut d'Astrophysique, Universit\'e de Li\`ege, Belgique\\
\normalsize $^2$University of Li\`ege, Astrophysics Institute, Belgium\\
\normalsize $^3$GNU World and gnus, California}
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``From Optical to Millimetric Interferometry~: Scientific and Technological Challenges'';
36$^{\mbox{\rm th}}$ Li\`ege\ Int.\ Astroph.\ Coll., 2001\quad\bull}%
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{\noindent\small{\bf Abstract:} 
The analysis of a new sample of 91 high redshift quasars observed with the New
Technology Telescope (NTT) (European Southern Observatory, ESO, La Silla) leads
to the detection of a 49 \% overdensity of galaxies near the quasars (3" $\leq$
$r$ $\leq$ 13.7"), with a Student confidence level (SCL) of 97 \%. Dividing
this sample into radio loud and radio quiet subsamples, we find that the galaxy
overdensity remains statistically significant only in the latter subsample of
QSOs (excess of 54 \% at a 98 \% SCL).  }
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\section{Introduction}
Several investigators have reported an overdensity of galaxies near quasars in
flux limited samples, this effect being generally interpreted as due to a
magnification of the quasars by matter associated with the foreground galaxies.
Let us first recall some key contributions on this subject.

Fugmann (1988) reports an excess of bright galaxies ($m_R$ $<$ 21.5) near 12
distant flat spectrum radio sources ($z$ $>$ 1.7) at a 95 \% confidence level
(CL). The same year, using the APM survey for gravitational lenses, Webster et
al. (1988) identify 11 QSOs ($z$ $>$ 0.5) closer than 6" from a bright galaxy
($m_R$ $\sim$ 21), instead of the 2.6 expected, the CL being here greater than
99.99 \%. Later, Magain et al. (1990) report a 30 \% (resp. 80 \%) overdensity
of galaxies near 83 (resp. 24 radio loud) quasars (within a radius between 3"
and 13.7") with a 98.5 \% (resp. 99.2 \%) CL.  Fugmann (1990) again finds that
strong ($F_{\nu}$(5 GHz) $\geq$ 1 Jy) and distant ($z$ $\geq$ 1) radio sources
are associated with Lick galaxies at a 96 \% CL. Finally, to conclude this non
exhaustive overview, we mention that Hintzen et al. (1991) derive a 75 \%
excess of galaxies within 15" from 16 radio loud quasars (0.9 $<$ $z$ $<$ 1.5),
at a CL larger than 99.5 \%.

In the present work, we investigate a new homogeneous sample of 91 high
redshift ($z$ $>$ 1.0) QSOs, observed with the New Technology Telescope, in
order to test the possible correlation between quasar and galaxy positions.
\section{Count Techniques and Statistical Tests}
Using the MIDAS package set up and developed at the European Southern
Observatory (ESO), we define  on each  CCD image two circular fields having a
radius of 23.3".  The first one, named the QSO field, is centered on the
quasar; the comparison field is tangent to the previous one, the center being
set towards the most distant CCD corner. For each field, we exclude the central
region (3" radius) in order to avoid quasar light contamination. The analysis
of this internal region was performed by Magain et al. (see these proceedings).
We divide the remaining surface of the fields in three rings of equal surface
(between 3" and 13.7" for the first ring, 13.7" and 19.1" for the second one
and between 19.1" and 23.3" for the last one).  We then consider all the
objects found in the two fields and we characterize them as point-like objects,
galaxies, defects or dubious objects.  The exact position and the shape of each
object are then computed by fitting a bidimensional gaussian surface. Their
respective signal-to-noise parameter is also evaluated. Finally, physical
characteristics (redshift, magnitude, absolute magnitude,...) of the QSO under
analysis are included in a MIDAS table.  Let us add that we compare the FWHM
(computed by the gaussian fit) of the point-like and the dubious objects in
order to include or discard these last ones in the galaxy category.  We then
construct a table with two columns : the number of galaxies in the QSO field
for each CCD image and the number of galaxies in the corresponding comparison
field. Subsequently, we use the statistical tests described hereafter.

We have to consider the problem of testing whether the mean numbers of galaxies
in the QSO fields (or in a ring) and in the comparison fields (or in the
corresponding ring) are equal or not. We take into account the fact that the
sample is paired and we do not make any assumption about the variances of the
two samples.

The Student distribution is
\begin{equation}
\Phi(x) = {1\over\sqrt{n\pi}}{\Gamma\left({n+1\over2}\right)
\over\Gamma(n/2)}\int_{-\infty}^x\left(1+{t^2\over n}\right)^{-(n+1)/2} \,dt.
\end{equation}
In order to apply the well known Student test on the computed means we have
verified the normality of the sample's distributions using a Kolmogorov-Smirnov
test. In all cases, we obtained a positive answer, with a confidence level
larger than 95 \%.

We also applied the Wilcoxon one-sample or signed rank test.  In contrast to
the previous method which is restricted to normal distributions, this test is a
nonparametric method.  The confidence level determined with this method agrees
in all cases with the Student's results. Let us now describe the samples under
study.
\subsection{The 2.2m and 3.6m Telescope Samples (S1)}
The observations of the sample S1 were carried out at La Silla between April
1987 and November 1988.  From the 82 QSO frames, 43 R filter frames were taken
with the 2.2m telescope (Direct Camera) using a 512 x 320 RCA CCD (scale of
0.351 arcsec/pixel). The other 39 R filter frames were taken with the 3.6m
telescope (EFOSC) with a 1024 x 640 RCA CCD (scale of 0.3375 arcsec/pixel). The
global sample, containing 25 radio loud and 57 radio quiet QSOs, is
characterized by an average redshift of 2.4 and an average absolute magnitude
of $-$29.2. The seeing was in general around 1.2" and the exposure times ranged
between 300 s and 900 s.
 
Statistics were already applied to this sample S1 and described by Magain et
al. (1990): we nevertheless wished to check their results and the consistency
with our results. These are summarized in Table 1.  The results are roughly the
same as those reported by Magain and his collaborators.
\begin{table}
\begin{center}
\begin{tabular}{|c|c|c|c|}    \hline\hline
                &  Sample of  & Excess of & Student confi-  \\
                &    QSOs     &  galaxies &  dence level      \\
\cline{2-4}
                &    All      & S1: 40 \% & S1: 90 \%           \\
Overdensities   &    QSOs     & S2: 49 \% & S2: 97 \%          \\
\cline{2-4}
(In first ring  & Radio quiet & S1: 20 \% & S1: 60 \%         \\
 around QSOs)   &    QSOs     & S2: 54 \% & S2: 98 \%     \\
\cline{2-4}
                & Radio loud  & S1: 80 \% & S1: 95 \%      \\
                &    QSOs     & S2: 41 \% & S2: 60 \%        \\
\hline
Completeness    & \multicolumn{3}{c|}{For S1 and S2:}         \\
   limit        & \multicolumn{3}{c|}{R magnitudes between 22.5 and 23.}\\
\hline
R magnitude     & \multicolumn{3}{c|}{S1: 21.5 $\pm$ 0.5}                 \\
of the galaxies & \multicolumn{3}{c|}{}                                   \\
  in excess     & \multicolumn{3}{c|}{S2: 22.5 $\pm$ 0.5}                 \\
\hline\hline
\end{tabular}
\end{center}
\caption{Results of the galaxy counts in the S1 and S2 samples}
\end{table}
We consider hereafter a new sample of quasars obtained under particularly good
seeing conditions, and in a more homogeneous way (same telescope, same exposure
time) than S1.
\subsection{The New Technology Telescope Sample (S2)}
A total of 132 R filter frames was obtained at the 3.5m NTT (La Silla) during
the August-September 1989 commissioning period. Using the EFOSC instrumentation
and a 512 x 320 RCA CCD (scale of 0.27 arcsec/pixel), two subsamples were
defined : a 41 low redshift sample ($z$ $\leq$ 0.5) and a 91 high redshift QSO
sample ($z$ $\geq$ 1.0). We consider hereafter essentially the high redshift
sample which contains 33 radio loud QSOs and 58 radio quiet ones. The average
seeing was around 0.9 arcsecond and the typical exposure time was $\sim$ 120 s.
In this case, the average value of the redshift and the absolute magnitude are
2.0 and $-$28.8, respectively.
 
We have plotted in Figs. 1, 2 and 3 our results normalized to the ones of S1.
The numerical values are found in Table 1.

As a CCD image gradient could be responsible for the observed excess of
galaxies near the quasars, the previous procedure has also been applied to star
counts. We do not detect any excess of stars neither in the QSO fields nor in
the comparison fields.  Furthermore, we divided all the comparison fields in
two parts, one oriented towards the QSO and the other one oriented towards the
most remote CCD corner. Statistical tests do not show the presence of any
gradient between these two regions.  We therefore conclude that the observed
overdensities of galaxies are not caused by effects inherent to the CCD.

One should note that an overdensity (25 \%) of galaxies is also found around
low redshift QSOs, but with a Student confidence level (SCL) of only 46 \%.
\begin{figure}
\vspace{5 cm}
\caption{Counts of galaxies : in five rings in the S1 sample (circles) and in
three rings in the S2 sample (asterisks). The S2 results are normalized to
those of S1.  {\bf N} is the total number of galaxies in the corresponding
ring.  The dashed line represents counts of galaxies in the S1 comparison
fields.  The ring distances ({\bf d}) from the QSO are expressed in arcseconds.
The global samples are considered here: 82 QSOs and 91 QSOs for the S1 and S2
samples, respectively. }
\end{figure}
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  \begin{figure}
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  \caption{Same as Fig. 1. Only radio quiet QSOs are considered: 57 QSOs in S1
            and 58 QSOs in S2.}
  \end{minipage}
  \hfill
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  \caption{Same as Fig. 1. Only radio loud QSOs are considered: 25 QSOs in S1
           and 33 QSOs in S2.}
  \end{minipage}
  \end{figure}
\vfill  
\section{Conclusions}
During this International Conference we learned more about other statistical
studies applied to new samples. For instance, Webster et al. (see these
proceedings) showed that a 100 \% overdensity of galaxies seems to appear
within 10" in their 71 object subsample (1.2 $<$ $z$ $<$ 2.2). On the other
hand, Yee \& Crampton (see these proceedings) do not detect any significant
excess of galaxies in their respective samples (94 QSOs and 101 QSOs).

In the present work, however, we have shown on the basis of the new sample (S2)
that there does exist a statistically significant overdensity of galaxies
around distant HLQs  (first ring): 49 \% at a 97 \% SCL, the excess being
mostly significant (98 \%) in the radio quiet QSO subsample (overdensity of 54
\%).

An understanding of these differences is of course essential. Two main points
may be of concern : the way the comparison fields are drawn is generally
different for each sample and, above all, counts could be quite sensitive to
the selection criteria of the samples.

In order to try to derive a final answer concerning a statistical association
between QSOs and galaxies, the ESO Key Program ``Gravitational Lensing'' team
defined a double magnification bias sample (Borgeest et al. 1991, see also
von Linde et al., these proceedings). Using such a flux limited sample, we know
well what are the selection criteria. Furthermore, from the observational point
of view, we plan to observe objects with the same exposure time as the
comparison fields chosen 1 degree apart in galactic longitude from the QSO. In
this way, the influence of galaxy clusters will be avoided as much as possible.
This is the cleanest way to define the comparison fields, although of course a
time consuming one.
  
Up to now, we have only obtained 13 CCD frames with the NTT (March 1991, EMMI,
scale of 0.44 arcsec/pixel, three times each with offsets and exposure times
$\sim$ 600s, average seeing $\geq$ 1.2"). Using the method described in this
work (Section 2), we do not detect any evidence in favour of an excess of
galaxies around the QSOs. The poor atmospheric conditions, the small size of
the sample and the fact that we have still defined the comparison field in the
QSO frame could explain this result.

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\section*{Acknowledgements}
This research was supported in part by contract ARC 90/94-140 ``Action de
Recherche Concert\'ee de la Communaut\'e Fran\c{c}aise'' (Belgium).
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\beginrefer
\refer Borgeest U., von Linde J., Refsdal S., 1991, submitted to A\&A Letters

\refer Fugmann W., 1988, A\&A 204, 73

\refer Fugmann W., 1990, A\&A 240, 11

\refer Hintzen P., Romanishin W., Valdes F., 1991, ApJ 366, 7

\refer Magain P., Remy M., Surdej J., Swings J.-P., Smette A., 1990.
In: Kayser R., Schramm, T., Nieser L. (eds.)
Lecture Notes in Physics 360, Gravitational Lensing.
Heidelberg, Springer Verlag, p.~57

\refer Webster R.L., Hewett P.C., Harding M.E., Wegner G.A., 1988, Nat 336, 358

\endrefer           
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