A&A 372, 1-7 (2001)
DOI: 10.1051/0004-6361:20010283
V. I. Zhdanov1,2 -
J. Surdej1,
1 - Institut d'Astrophysique, Université de Liège, Avenue
de Cointe 5,
4000 Liège, Belgium
2 -
Astronomical Observatory of Kyiv University, Observatorna St. 3, UA-
04053 Kyiv, Ukraine
Received 19 October 2000 / Accepted 16 February 2001
Abstract
We use the Véron-Cetty & Véron (2000) catalog (VV) of
13 213 quasars to
investigate their possible physical grouping over angular scales
.
We first estimate the
number of quasar
pairs that would be expected in VV assuming a random distribution for
the quasar
positions and taking into account observational selection effects
affecting
heterogeneous catalogs. We find in VV a statistically significant
(>3
)
excess
of pairs of quasars with similar redshifts (
)
and
angular separations
in the
range, corresponding to projected
linear separations
or
.
There is also some excess in the
range
corresponding
to (1-5) Mpc in projected linear separations. If most of these
quasar pairs do indeed
belong to large physical entities, these separations must represent
the inner scales of
huge mass concentrations (cf. galaxy clusters or superclusters) at
high redshifts; but
it is not excluded that some of the pairs may actually consist of
multiple quasar images
produced by gravitational lensing. Of course, a fraction of
these pairs could also
arise due to random projections of quasars on the sky.
The list of 11 pairs of quasars with redshift differences
and angular separations
is presented in order to stimulate further observational studies and
to better
understand the astrophysical and cosmological significance of these
interesting objects.
Key words: quasars - clusters - gravitational lenses - observations
Close pairs of quasars with small angular separations (typically
)
and small redshift differences (
)
have attracted much attention
in recent years because of their possible relevance to a number of
challenging
astrophysical and cosmological problems (e.g. Kochanek et al. 1999).
Identification of multiply imaged quasars in optical and radio
surveys has frequently
been used to set interesting constraints on cosmological parameters,
including the
Hubble constant (cf. the recent review by Claeskens & Surdej
2001).
However, little is known about the statistics of physical pairs of
quasars or of
multiply imaged lensed quasars with angular separations
,
which would probe lensing masses over scales of galaxy clusters, or
even superclusters.
Maoz et al. (1997)
have carried out a survey with HST for very large image separation
lensed quasars, but they failed to detect any secondary image near
each
of their 76 primarily selected quasars with separations in the
7
-50
range.
On the other
hand, Shaver (1984) has pointed out an excess of quasar
pairs over
several Mpc linear scales, based upon an original statistical
analysis of the
Véron-Cetty & Véron (1984) catalog, which included at
that time
2251 quasars. This has been later confirmed by correlation function
analysis
with smaller but homogeneous datasets (Andreani & Cristiani
1992;
Mo & Fang 1993; Croom & Shanks 1996).
It is obvious that alike for the case of close pairs
of quasars, the
identification of very large separation ones (with
)
would have
very challenging astrophysical and cosmological implications. Indeed,
such physical
pairs of quasars could be associated with high redshift galaxy
clusters and provide
interesting clues on the origin and early evolution of clusters, dark
matter, etc.
Similarly, setting more stringent observational limits on the
frequency of gravitational
lensing at very large angular scales would enable us to rule out the
existence of
galaxy clusters with very large M/L ratio, to set upper
limits on the central density of clusters
and superclusters, to reject
certain proposed cosmogonic models and to set an independent upper
limit on the
cosmological constant (Kochanek 1995; Wambsganss et al.
1995).
In the present paper, we show that in the recent
version of the
Véron-Cetty & Véron catalog (2000, hereafter VV) the
number
of quasar pairs
with similar redshift (
)
deviates significantly,
within certain specific angular separation intervals,
from the number
that would be expected
assuming a random distribution of quasars over the sky.
Therefore, in these intervals, there is an excess
of pairs that may
either be caused by statistical fluctuations or
consist of very interesting genuine physical pairs of quasars, or,
possibly, doubly imaged quasars.
Because the VV catalog is heterogeneous, it is important to obtain a
reliable
estimate of
in spite of the various unphysical selection
effects (cf. different survey areas, limiting magnitudes, ...) that
may
accordingly affect the two-point correlation function. Shaver
(1984) has
proposed to take into account such selection effects by using
information from the
distribution of quasar pairs
with different, but nevertheless close redshifts, that may only arise
due to random
coincidences. In our case, thanks to the very large number of entries
available in
VV, it is possible to supplement Shaver's method with estimates of
and their
dispersions. We have applied this improved method
to VV and report here on some interesting results in the
angular
separation interval.
In order to study the physical pairing of quasars, Shaver (1984) has
considered, for given angular separation intervals, the ratio of the
number of quasar
pairs having nearly the same redshifts (e.g.
,
which may include
physical pairs) to that with different, but nevertheless close
redshifts (e.g.
)
that may only arise due to random coincidences.
Because several tens of multiply imaged quasars have been reported
with angular
separations
(Claeskens & Surdej
2001) and since our
search in the VV catalog has not revealed any single pair with
and
,
we restrict hereafter
our study of
physical pairs of quasars to those with angular separations
.
Given that any apparent excess of quasar pairs could possibly result
from large
statistical fluctuations in the random projections of quasars,
combined with the
inherent observational selection effects in VV, a correct
investigation of this problem
requires to justify the validity of extrapolating the relations for
the expected number
from large angular separations to smaller ones. Similarly,
a realistic estimate
of the dispersion
is necessary to check for
possible deviations from
Poisson statistics, which could arise from hidden selection effects.
Estimates of
and
are made possible thanks to the very
large number of
entries available in VV. We do this by considering the pairs of
quasars with small but
definite redshift differences from 10 selected comparison bins (i.e.
)
and the pairs of quasars with
and
angular separations
(our investigation
for
yields similar results). For both
these
sets of quasar pairs, no physical grouping is expected between the
quasars
(cf. Andreani & Cristiani 1992; Mo & Fang 1993;
Croom & Shanks 1996) and we may
then use this information to estimate
and
for
and
.
The results are presented in terms of the pair numbers
having an angular
separation
,
representing the width of
the ring with angular radius
,
and a redshift difference
.
In the remainder, we use the normalized pair numbers
defined per unit
interval of
and per unit area of the ring
Our choice to discretize the redshifts in bins having a width
prevents us to deal with the problem of redshift measurement errors,
roundoffs in VV or
peculiar velocities which are always smaller than 0.01.
We define the normalized number of quasar pairs from VV with
approximately similar redshifts as
,
adopting
.
We assume that PP may
contribute to
up
to
,
at maximum, but that they do not contribute to
,
neither to
for
.
Accordingly,
we denote
the expected value of
that would be
in VV, provided PP
were absent. Following Shaver (1984), we also assume that
for small values of
,
the distribution of
must bear the same imprint of non
physical effects as
.
It should be noted that the values of
,
and
their dispersions need
not necessarily be the same (though they appear to be rather close)
because of the very
irregular dependence of the number counts of quasars with redshift,
but their dependence
upon angular separations must be similar. Thus, if there were no
physical pairs or
lensed quasar images in VV, we should have for small values of
(typically
)
a behaviour for
as a function of
that is
similar to that of
.
But, as we shall see below, this is just not the case.
The artificial catalogs have been created from VV as follows.
We have taken the list of quasars from the original VV with their
positions unchanged,
but their
redshifts have been randomly rearranged without changing their
values. Thus, we obtain
new "permutated'' catalogs having the same positional inhomogeneities
and the same global
redshift distribution. However, all possible correlations existing
between position and
redshift due to observational selection effects in VV should have
been washed out.
We have generated 2500 such rearranged catalogs to derive average
data for comparison
with VV and calculated the functions
,
and
,
marked with an
asterisk,
by averaging the corresponding functions
,
and
over
the artificial
catalogs. Obviously, these averaged dependences are smoother than
the original
,
and
from VV (see, e.g., Fig. 1 for
and
),
thus increasing the quality of the extrapolations.
![]() |
Figure 1:
The functions
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Open with DEXTER |
We present in Figs. 2, 3 the values of
and
as a function
of
for
.
![]() |
Figure 2:
Ratios
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Open with DEXTER |
![]() |
Figure 3:
The same as in Fig. 2 over the
![]() ![]() ![]() |
Open with DEXTER |
The main result apparent from these figures is that the values of
vary slowly up to
angular separations; the deviations
from a linear
(even nearly constant) behavior can be neglected in comparison with
the considerable
scatter of
and the large excess of
present within certain
angular separation bins. We conclude on the basis of the
dependence that the
selection effects do not produce any significant changes of
when we pass from large angular separations (up to
)
to
smaller ones (
).
The weak variation of
,
and therefore, of the expected
value
,
makes
extrapolations from large
very simple to estimate
at small angular separations.
This allows us to use the
data from the
range to estimate the expected number of
quasar pairs
and its dispersion at smaller angular separations.
The similar behaviour of
and
may be interpreted as
reflecting the
absence of any significant angle-redshift correlations in VV due to
unphysical selection
effects over several degrees; at least they are not important for
our particular problem.
Thus, the permutated catalogs appear to provide a very useful tool
for studying the
selection effects in the VV catalog, because they retain all of them
except those due to position-redshift correlations.
In particular, the positional effects reveal themselves in the
and
dependences showing a similar behavior (Fig. 1).
The latter would have
been constant if positional inhomogeneities were absent.
It should be noted that an excess of
(i.e. in the
range), and therefore
,
is
clearly seen
from the figures; however it must be complemented with dispersion
estimates.
Some additional excess of quasar pairs is possibly present in the
range. If there were only RP in the VV catalog, the behaviour of
should be much
the same as that of
.
Now it is easy to calculate
in the
angular separation
interval. Extrapolating from the
range, we
obtain the
expected values of
in case of RP, and using the known
dependence (see
Fig. 1), we derive
in the desired interval. The
results are shown in
Fig. 4 with the dispersion estimates calculated here under
the assumption of
Poisson statistics that will be justified in the next subsection.
From the observed
data in Fig. 4, we directly see that a
significant excess of
pairs of quasars is detected in the
ring
and this appears to be well beyond the
limit.
![]() |
Figure 4:
Normalized numbers ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Open with DEXTER |
In the
interval for
,
the
expected data
correspond to
pairs. In reality, there are 9
quasar pairs in
this interval present in the VV catalog.
Additional excess of quasar pairs with separations in the
100
range also seems to be present but it is
just very near
the
limit (see Fig. 4). Nevertheless, it
is evident that the data for
in this range are systematically
higher than
.
The cumulative number of quasar pairs with
in
the whole
interval is 133 against 86 expected; that
is
.
This excess of pairs of quasars in VV is thus
found to be highly statistically significant by more than
.
The results for the expected number of quasar pairs are robust:
appears to be
approximately the same for the extrapolation versions with
or
,
and for a comparison bin size
and
in the [0.03,0.23]
interval. Similar estimates are obtained using extrapolations from
the
interval.
An analogous procedure has been applied to the
data from the
comparison bins.
The value of
estimated for
is
.
These estimates change insignificantly if we take into account the
small trend
in the
and
data.
All these estimates are compatible with Poisson statistics.
It is now important to
check the dispersions over those angular separation intervals where
we
have an excess of .
For this, we use the dispersions from the
comparison bins that
are in fact even somewhat overestimated: they have been computed
using deviations
from the average
,
but there are some additional systematic variations with
between
different bins that are not due to variations with
.
The results are shown in Fig. 5; we see that the data from
the comparison bins
agree very well with those obtained according to Eq. (2)
from the
extrapolated data. This convinces us that, at least for our particular
problem, there is no
violation of the Poisson statistics due to the selection effects.
![]() |
Figure 5:
Dispersions of the normalized pair numbers ![]() ![]() ![]() |
Open with DEXTER |
The results obtained in this section may be used to study the
correlation functions of the quasar distribution. In particular, the
ratio
is directly related to the two-point angular
correlation function
(Peebles 1980).
![]() |
Figure 6:
Normalized numbers ![]() ![]() ![]() ![]() ![]() |
Open with DEXTER |
![]() |
Figure 7:
The same as in Fig. 6 for
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Open with DEXTER |
![]() |
S |
![]() |
![]() |
![]() |
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||||
0 | 0.2-0.5 | 7.15 | 1.4 | 79% |
1.0-5.0 | 69 | 13 | 28% | |
0.7 | 0.4-0.7 | 7.5 | 1.4 | 84% |
1.0-5.0 | 57 | 10 | 38% |
We have estimated the number of quasar pairs expected in VV
for the case of
random quasar positions and have compared this
to the actual number of pairs in this catalog. The results of the
comparison are presented
in Fig. 4 in terms of the angular separation
and
in Figs. 6, 7
as a function of the projected linear separation for two popular
cosmological models.
These figures along with Table 1 show that there is a
considerable excess
of quasar pairs in VV over the expected value within certain
separation intervals.
In particular, there are 9 pairs of quasars in VV against two
expected ones with redshift differences
and angular separations
in the
range (see Table 2, 9
first pairs).
Therefore, this excess of pairs of quasars - probably consisting of
genuine physical pairs or doubly imaged quasars - is highly statistically
significant by more than 3
.
If we extend
to 0.02, two additional
pairs of quasars must be included in the above list (Table 2, two last pairs).
We also find that there is a highly statistically significant excess of
close redshift pairs (
)
in the
range
by more than 5
.
In terms of projected linear separations, we have an analogous excess
near
0.5 Mpc. There does also appear to be a significant excess of pairs of
quasars in the
projected linear separation range. If PP consist of genuine physical pairs
of quasars, these ranges correspond to
some inner scales of huge mass concentrations at high redshifts.
It should be noted that any amplification bias due to enhanced
convergence, induced by some hypothetical foreground smooth
structures, is easily
ruled out from our treatment. It would actually change the brightness
of all
the quasars with different z, and this would equivalently affect both
the numbers
and
of quasar pairs.
Name | ![]() |
![]() |
S | S' | R |
![]() |
(Mpc) | (Mpc) | |||
Q 0053-3342A | 2.00 | 83.7 | 0.46 | 0.65 | 1 |
Q 0053-3342B | 2.00 | ||||
Q 0107-0235 | 0.958 | 77.5 | 0.44 | 0.57 | 2 |
PB 6291 | 0.956 | ||||
CTS H26.12 | 2.33 | 58.9 | 0.31 | 0.45 | 3 |
CTS H26.13 | 2.33 | ||||
Q 1310+4254A | 2.561 | 91.4 | 0.47 | 0.69 | 4 |
Q 1310+4254B | 2.561 | ||||
1WGA | 1.89 | 82.2 | 0.46 | 0.65 | 5 |
J1334.7+3757 | |||||
1WGA | 1.89 | ||||
J1334.8+3757 | |||||
1333.2+2604 | 1.182 | 68.3 | 0.39 | 0.53 | 6 |
1333.2+2603 | 1.179 | ||||
Q 2121-4642 | 1.347 | 82.8 | 0.46 | 0.65 | 7 |
Q 2121-4641 | 1.352 | ||||
Q 2139-4433 | 3.22 | 62.6 | 0.29 | 0.44 | 8 |
Q 2139-4434 | 3.230 | ||||
QSM1:35 | 1.123 | 70.1 | 0.40 | 0.54 | 9 |
QSM1:25 | 1.128 | ||||
1336.5+2804 | 1.31 | 94.7 | 0.54 | 0.74 | 10 |
1336.6+2803 | 1.325 | ||||
Q 23540+1839 | 1.666 | 96.2 | 0.54 | 0.76 | 11 |
Q 23541+1840 | 1.680 |
Unfortunately, the present data concerning most pairs from Table
2 do
not enable us to distinguish between genuine physical pairs and
doubly
imaged quasars (cf. Kochanek et al. 1999; Mortlock et al. 1999).
However, the lensing scenario would require a rather large lens
mass.
Adopting for instance a spherically symmetric mass distribution that
is sufficiently
compact located on the sky between the putative lensed
quasar images, we do find a lens redshift
in the range
[0.1-0.3]for the 11 listed pairs of quasars, assuming a deflector mass
and making use of the magnitude
difference from the VV data.
For any reasonable value of the
M/L ratio, a
lens should have been detected at
such low
redshifts. For smaller masses, the redshift
scales almost
linearly with
and an analogous situation naturally arises. It is therefore more
likely that,
if they exist at all, the putative lenses have a mass
and are located at higher redshifts.
A search for weak lensing effects (see, e.g., Bartelmann & Schneider 1999) around the 11 pairs of quasars would be extremely helpful in order to test the lensing hypothesis. One could also look for some possible stretching of the quasar host images, which in case of the lensing scenario should reveal preferential tangential elongations due to the lens shear. Furthermore, each of the 11 pairs of quasars should be further investigated in the various regions of the electromagnetic spectrum. In particular, one could investigate the distribution of narrow absorption lines in the spectra of quasar pairs, which correspond to a region with characteristic timescales >>100 yrs, in order to exclude any possible effect due to time delays in case of the lens scenario. These same observations could be used to improve the values of the emission redshift of the individual quasars forming a pair.
On the other hand, the pairs of quasars in question may represent some of the most high redshift clusters ever identified which are expected to contain a population of early-type galaxies detectable, e.g. in the near-infrared, or hot intergalactic gas emitting in the X-rays. Such proposed observations are being planned.
But, no matter to which group they belong, these objects consist of very interesting targets for further studies. We expect that forthcoming homogeneous surveys such as 2dF and SDSS will independently confirm the physical grouping of QSOs with arcminute angular separations.
Acknowledgements
We thank the anonymous referee for her/his helpful comments and remarks on the manuscript. Our research was supported in part by the Belgian Office for Scientific, Technical and Cultural Affairs (OSTC), by PRODEX (Gravitational Lens Studies with HST), by contract P4/05 "Pôle d'Attraction Interuniversitaire" (OSTC, Belgium), by contract 1994-99 of "Action de Recherches Concertées" (Communauté Française, Belgium) and by the "Fonds National de la Recherche Scientifique" (Belgium).