Astronomy and Astrophysics Review Manuscript Nr
will b e inserted by hand later
Gravitational Lensing in Quasar Samples
Jean Fran cois Claeskens and Jean Surdej
Institut d Astrophysique et de G eophysique Universit e de Li ege Avenue de Cointe B
Li ege Belgium
Received April Accepted
Summary The rst cosmic mirage was discovered approximately years ago as the double
optical counterpart of a radio source This phenomenon had b een predicted some years
earlier as a consequence of General Relativity We present here a summary of what we have
learnt since The applications are so numerous that we had to concentrate on a few selected
asp ects of this new eld of research
This review is fo cused on strong gravitational lensing i e the formation of multiple images
in QSO samples It is intended to give an up to date status of the observations and to present
an overview of its most interesting p otential applications in cosmology and astrophysics as
well as numerous imp ortant results achieved so far
The rst Section follows an intuitive approach to the basics of gravitational lensing and
is develop ed in view of our interest in multiply imaged quasars The astrophysical and cosmo
logical applications of gravitational lensing are outlined in Section and the most imp ortant
results are presented in Section Sections and are devoted to the observations Finally
conclusions are summarized in the last Section
We have tried to avoid duplication with existing and excellent intro ductions to the eld
of gravitational lensing For this reason we did not concentrate on the individual prop erties
of sp eci c lens mo dels as these are already well presented in Narayan and Bartelmann
and on a more intuitive ground in Refsdal and Surdej Wambsganss prop oses a
broad view on gravitational lensing in astronomy the reviews by Fort and Mellier and
Hattori et al deal with lensing by galaxy clusters microlensing in the Galaxy and the
lo cal group is reviewed by Paczynski and a general panorama on weak lensing is given
by Bartelmann and Schneider The monograph on the theory of gravitational lensing
by Schneider Ehlers and Falco also remains a reference in the eld
Key words Gravitational Lensing Cosmology observations
Quasars general Galaxies general
Charg e de Recherches du F N R S Belgium
Directeur de Recherches du F N R S Belgium
Correspondence to surdej astro ulg ac b e
J F Claeskens J Surdej * I1 A) B) *I C) *I2
* S *S *S *
I I3
Fig Light propagation in an euclidian space A following a straight line normal situation
B following a curved tra jectory in this case the image p osition I is di erent from the source
p osition S as seen by the observer C following multiple curved tra jectories with the formation
of multiple images of the source S
Gravitational lensing
In this Section we rst prop ose a general de nition of a cosmic mirage We
then intro duce the basic formalism of the lensing equation the de ection angle
the ampli cation and the time delays Finally we explain how to nd cosmic
mirages as e ciently as p ossible
What is a cosmic mirage
People sometimes b elieve that mirages alike atmospheric mirages are synony
mous of hallucinations This is absolutely not the case Common sense of reality
is based on our every day p erception of classical spacetime whose geometry is
at and static and where light propagates along straight lines In this case we
can only see one image of a given p oint source and it is precisely lo cated in the
direction of the source p osition see Fig A The apparent source size i e its
solid angle is then inversely prop ortional to the square of the source distance
A very general de nition of a mirage would b e a distorted view of the reality
compared with what is exp ected by common sense Following that de nition
a mirage may arise in two situations if the light tra jectory is not straight
then the observer sees the image in a direction di erent from that of the source
Fig B multiple imaging o ccurs if more than one light tra jectory can reach
the observer Fig C if space is expanding as in standard cosmologies the
ob jects lo cated in the past light cone of the observer lo ok bigger or closer than
they actually are at the time of observation see app earance of sizes in Fig
This cosmological mirage is corrected for by the use of cosmological angular
distances which also take into account the e ects due to the curvature of the
Universe see Section
In this review we are mainly interested in the rst kind of mirages i e
when the light tra jectories are curved This happ ens when the light sp eed is not
isotropic along the directions p erp endicular to the light path For example since
the light sp eed in a material medium is v c n where n is the refractive index
of that medium and c is the light sp eed in the vacuum the light rays are b ent
when they travel into an inhomogeneous medium see Fig This happ ens in
Gravitational Lensing in Quasar Samples
5
4 8 S 7 3 6 5 α 4 2 3 α S 2 1 1 O O 1 2 3 4 5 6 7 8 1 2 3 4 5
A) t = tem B) t = tobs
Fig E ect due to the expansion of an euclidian space during light travel on the apparent
size of distant ob jects see text
Σ
M
Fig Left De ection of light in an inhomogeneous medium right euclidian representation
of the gravitational de ection of light refers to a p ortion of the wavefront The length of
the arrows at the edge of the s is prop ortional to the apparent velo city of light
the lower atmospheric air layers with strong temp erature or density gradients
and atmospheric mirages may then b e formed for a more detailed analysis of
atmospheric mirages see Refsdal and Surdej
As a consequence of General Relativity spacetime is curved by the gravita
tional p otential asso ciated with a massive ob ject In the weak eld approxi
mation j j c its metric is simply e g Schutz
c dt dx dy dz ds
c c
However this new spacetime can b e regarded as an euclidian one in which the
velo city of light is apparently slowed down in the vicinity of the massive ob ject
Indeed the light path b eing de ned by the null geo desic ds in Eq
it is easy to derive that formally acts on the light sp eed as a medium with an
e ective refractive index n where
n c
J F Claeskens J Surdej
* I
α α
b * S θ b θ s O s
DOD D DS
DOS
Fig Gravitational lensing fundamental scheme
The gradient of the Newtonian gravitational eld in the vicinity of a massive
ob ject is now resp onsible for the angular de ection of the light tra jectories
see Fig When such a de ected ray reaches the observer a gravitational
mirage is seen and the massive ob ject is called a gravitational lens
For historical reviews on gravitational lensing see for example Schneiders
Ehlers and Falco Refsdal and Surdej and Wambsganss
The lens equation
The lens equation connects the source p osition and the p osition s of the
s
image s seen by an observer O given the de ection angle pro duced by the
gravitational lens The lens is assumed to b e thin and con ned into the de ector
plane Fig shows the geometrical scheme of gravitational lensing Following
rays backward from the observer to the source it is very easy to derive the lens
equation as a relation b etween the very small angles and
s
D
DS
D
s OD
D
OS
By analogy with geometrical optics the observed images are in fact virtual images since
they are seen through the lens
The de ection of the light ray is mainly pro duced around its closest approach to the lens
b ecause astrophysical ob jects are much smaller than the total length of the light path
Gravitational Lensing in Quasar Samples
In order to correct for the cosmological mirage e ect pro duced by the
expansion and the curvature of the Universe D D and D must b e cos
OD OS DS
mological angular distances resp ectively b etween the observer and the de ector
the observer and the source and the de ector and the source In Friedmann
Lema tre Rob ertson Walker FLRW cosmological mo dels with present matter
density and without cosmological constant the angular distance of a
o o
source at redshift z seen from an ob ject at redshift z is given by
S D
c
D z z
D S
H z z
o D S
o
h i
p p
z z z z
o S o D o D o S
For other FLRW cosmologies numerical calculations can b e e ciently p erformed
thanks to the ANGSIZ algorithm develop ed by Kayser et al
The de ection angle
The de ection angle can b e estimated in several di erent ways A rst metho d
is based up on the weak eld metric Eq and the geo desic equation e g
Weinb erg A second metho d consists in applying the Fermat Principle
to null tra jectories in the metric to simultaneously derive the lens equation
and the expression of This physical approach has rst b een derived by
Schneider and is intuitively presented in Blandford Narayan
The de ection angle may also simply b e determined from the integration of the
variations of the direction i of the ray along the unperturbed tra jectory see Fig
st
by making use of the well known Descartes law n cos i C along the light
tra jectory and assuming small de ection angles i since b c for
astrophysical ob jects De ning b as the impact parameter in the de ector plane
p erp endicular to the unp erturb ed direction of motion x see Fig
b D
OD
we get
Z Z Z
di
dx r n dx r dx b
b b
dx n c
where the last equality of Eq comes from relation
The most basic de ector corresp onds to the p oint mass M whose gravita
tional p otential is simply
GM GM
p
r
b x
The de ection angle pro duced by a p oint mass is obtained by intro ducing
Eq into Eq
GM
b b
c b
J F Claeskens J Surdej
α
i b r
x 0
Fig De ection of light in the vicinity of a massive ob ject Descartes law implies that
c cos i is a constant along the light tra jectory The lo cal variation di is computed at
rst order i e along the unperturbed dotted tra jectory passing at impact parameter b
Under the thin lens approximation a general de ector is describ ed by its
surface mass density b pro jected in the de ector plane Relation for the
de ection angle then b ecomes
Z
0 0
db b b b db G
b
0
c jb b j
S
If the de ector is circularly symmetric relation reduces to
GM b
b b
c b
M b b eing the mass inside radius b
Given the expressions or for the lens equation often has
multiple solutions for corresp onding to the formation of multiple images of a
given source As an illustration to the case of a p oint mass de ector M b M
solving the lens equation yields
q
s
s
E
Two important properties of gravitational lenses
Let us assume a generic circularly symmetric integrated lens mass pro le
b
M b M
o
b
o
The p oint mass mo del or Schwarzschild lens is obtained for in Eq
corresp onds to the Singular Isothermal Sphere SIS yields the uniform sheet of matter
see Narayan and Bartelmann or Refsdal and Surdej for general reviews on
simple lens mo dels
Gravitational Lensing in Quasar Samples
Fig Critical surface mass density as a function of the lens redshift if the source is
crit
lo cated at a redshift z H km s Mp c
s o
In the highly symmetric situation of a p erfect alignment b etween the ob
server a circular de ector and a p oint source the former sees a ring centered
on the de ector It is called the Einstein ring of the lens Chwolson
Einstein and its angular size satis es the simpli ed lens equation
E
D
DS
From relations and one nds for any value of
E E
D
OS
such that the surface mass density is decreasing with b
1
r
2
GM D D GM
E DS DS o
E
c D D
OD OS
D c b D
o
OS
OD
where M is the mass inside the Einstein radius b D
E E OD E
Two imp ortant prop erties follow
For small misalignments b etween the source the lens and the observer equa
tion implies that at rst order the angular separation b etween the images
is constant and equal to
E
Thus from relation the angular separation b etween the lensed images
increases if the lens is more massive or closer to the observer
As a consequence of relation the mean surface mass density within
E
is a constant de ned as the critical surface mass density
E
M c D
E OS
E crit
D GD D
OD E OD DS
Relation implies that a nite massive ob ject is a gravitational lens ca
pable to pro duce multiple images if its central mass density The
crit
denser the ob ject the wider the angular separation b etween the lensed im
ages in order to get the average surface mass density b etween the images
J F Claeskens J Surdej
Fig A glass of wine redistributes the light from a background source It may form a caustic
left photograph whose enlargment is shown in the central photograph Multiple images of
the background source are recorded if the ob jective of a standard camera is lo cated inside the
caustic right photograph
equal to On the contrary if everywhere the ob ject is not
crit crit
capable to form a cosmic mirage
Note that is only a function of the distances b etween the source the
crit
lens and the observer Fig shows the value of as a function of the lens
crit
redshift for a distant source lo cated at z A given astrophysical ob ject
s
is a more e cient lens if it is lo cated around z where is minimum
crit
and roughly amounts to the surface density of a cm thick water layer
g cm see also Section
Caustics multiple imaging and ampli cation
Caustics and multiple imaging
Let us rst recall a basic prop erty of optical lenses A p erfectly converging lens
fo cuses the light from a very distant p oint source lo cated on the optical axis into
a single bright p oint the fo cus Putting one s eye at the fo cus one exp ects to see
a deformed and much brighter image of the source Indeed the lens do es app ear
uniformly illuminated If the optical lens su ers from spherical ab errations its
fo cus is spread along a line segment An observer lo cated somewhere on this
segment then sees a ring of light whose radius dep ends on his her distance
from the lens this ring may b e compared with the Einstein ring seen through a
symmetric gravitational lens
The optical quality of most natural lenses is very p o or their fo cus is not a
p oint nor even a line but a two dimensional envelop e called the caustic envelop e
The intersection of this envelop e with a plane de nes a bright closed curve the
caustic line simply called the caustic Fig a and b illustrate the caustic created
by a glass of wine illuminated by a distant background light source cf a candle
An observer putting his her eye inside the caustic will see multiple images of the
source Fig c If the observer is not able to resolve the multiple images of the
lensed source he she will merely detect an increase in the apparent ux coming
from the source see the brighter region of the observer plane enclosed by the
caustic in Fig b
Gravitational Lensing in Quasar Samples
Fig Another example of caustics Twenty seven coins have b een placed at the b ottom of
a swimming p o ol In the absence of waves they app ear to the observer as seen on the left
photograph At right the sunlight is refracted through a wavy water surface which creates a
complex network of caustics at the b ottom of the p o ol The wavefronts of sunlight are strongly
distorted as well as the observed images of the coins Note that some of the coins cf several
ones at right are multiply imaged
In the formalism of gravitational lensing the direction observer de ec
tor is used as a reference instead of the direction source de ector the lens
equation is therefore a backward ray tracing equation Caustics in the source
plane only di er from those in the observer plane by a scaling factor dep ending
on the distance ratio D D Now for a given observer de ector direction
OD DS
a light source is multiply imaged and its apparent luminosity strongly increases
if it is lo cated inside the caustic An example of caustics in the source plane is
illustrated in the swimming p o ol exp eriment see Fig
Therefore the area inside the caustic in the source plane is a natural cross
section asso ciated with multiple imaging it scales as A transition b etween
E
single imaging and multiple imaging o ccurs when the source just lies on the
caustic a new single strongly distorted image is then created
From a mathematical p oint of view the lo cus of p oints in the de ector
plane where strongly distorted images are formed is de ned by those p oints
where the lens equation can not b e lo cally inverted i e where its jacobian J is
equal to zero
s
J dtm J
This lo cus is called the critical line and its mapping onto the source plane by
the lens equation yields the caustic
The shap e and numb er of critical lines and corresp onding caustics dep end on
the exact lens mo del but for centrally condensed mo dels some generic prop erties
can easily b e derived First if the lens is circular Eq for the critical lines
simply reduces to
d
s s
J d
J F Claeskens J Surdej
Circular Circular Non Circular Non Circular Singular Non Singular Singular Non Singular 1 1 1 1 2 3 2 3 Caustics 4 5
Critical lines
Fig Numb er or of lensed images generic shap e of caustics and critical lines
for non singular and non circular lens mo dels The caustic of circular singular mo dels is
degenerated into a single p oint In the limiting case of an isothermal mo del if the source is
just inside the cut dotted lines one secondary image is formed close to the center of the
de ector this cut b ecomes a second caustic dashed lines in non singular mo dels and two
new images are then pro duced close to the corresp onding critical line For non circular mo dels
the degeneracy is broken and the inner caustic often has the shap e of a diamond more than
images may b e pro duced
Therefore in that case there is always one caustic degenerated into the central
p oint the corresp onding critical line is the Einstein ring Then if the
s
mo del is non singular there is a second circular critical line called the radial
critical line and given by the solution of d d see Eq The caustics
s
pro duced by circular mo dels are illustrated on the left panels of Fig
For a non circular mo del the degeneracy is broken and the previous inner
p oint like caustic often takes the shap e of a diamond allowing the formation of
more than images Asymmetric and non singular mo dels may form a larger va
riety of caustics see e g Schneider Ehlers and Falco Kassiola and Kovner
but they always pro duce an o dd numb er of images Burke The
most common caustics of these mo dels are shown on the right panels of Fig
and representative observed examples are illustrated in Fig
A lens mo del is singular if b / b with must b e smaller than to get a
nite central mass It is easy to show from Eq that in the case of a circular mo del a
radial critical line is only formed if The p oint mass and the SIS lens mo dels
are singular mo dels
A non circular mo del is either a circular mo del p erturb ed by an external anisotropy like a
star in the p otential of the host galaxy Chang Refsdal or an intrinsically asymmetric
p otential e g Blandford Ko chanek or asymmetric mass distribution e g Kassiola
Kovner Kormann et al
Gravitational Lensing in Quasar Samples
Fig Illustration of representative multiply imaged quasars as seen in the H band
with HST CfA Arizona Space Telescop e LEns Survey CASTLES left column The central
column is the b est t of an elliptical singular isothermal mo del Kassiola and Kovner
Korman et al x computed p ositions squares and observed p ositions of lensed
images and lensing galaxy The right column shows the source p osition x and the caustics
Note the multiplicity and a symmetry of the images as a function of the source p osition with
resp ect to the caustics images are nearly merging when the source is close to the caustic More
information on these mirages may b e found in Table
J F Claeskens J Surdej
Caustics and ampli cation
Both the source and the observer b eing very far from the de ector gravitational
lenses do not intro duce any extra frequency shift in the sp ectral intensity of
the lensed images in addition to the cosmological redshift On the other hand
and in a rst approximation gravitational lenses are transparent Therefore the
surface brightness of the lensed images is equal to that of the source which
according to Liouville s theorem is I z where I is the surface brightness
e e
measured in the reference frame of the source and z the cosmological redshift
e g Peebles Conservation of the surface brightness can b e appreciated
by comparing the images of the coins lo cated at the b ottom of the swimming
p o ol Fig
As a consequence the ux of a lensed image is ampli ed with resp ect to that
of an in nitesimal source by a quantity A equal to the ratio of the solid angle
d of the magni ed image to that d of the real source
s
d
A
d J
s
where J is given by the rst equalities of relation Thus formally an in
nitesimal source lo cated on a caustic is in nitely ampli ed On the other hand
nite transparent and non singular lenses always pro duce at least one magni ed
image i e with A Schneider For that reason gravitational lenses
also act as natural telescop es
If the de ector has circular symmetry relation simply reduces to
d
A
d
s s
Since the gradient of is always in nite at the center for singular mo dels see
Eq one easily sees that for such mo dels the central image is always
in nitely deampli ed The lack of central images in observed gravitational lenses
tends to show that the mass distribution of the lensing galaxies is strongly p eaked
at the center Wallington and Narayan
As an application of relation the ux ampli cation of a lensed image
formed at p osition by a p oint mass is
A
E
The p ositions of the images b eing given by Eq the total ampli cation of
the source can b e found for a given value of
s
s
E
p
A
s
s
s
E
For circular lens mo dels a graphical approach of the lensing equation is useful to qualita
tively derive the numb er shap e and ampli cation of the lensed images see Refsdal Surdej
Gravitational Lensing in Quasar Samples
Time delays
The light travel time t from the source S to the observer O dep ends on the
geometrical length of the tra jectory and on the apparent light sp eed along the
path as measured by the observer It can b e derived from the expression of
the static weak eld metric Eq with c for photon tra jectories
ds or from the analogy with optical refraction Eq
Z Z
S S
dl ct dl
c
O O
p
dy dz The two terms on the right side of Eq are where dl dx
called the geometrical and the p otential contributions t and t resp ec
g eom pot
tively Co oke and Kantowski Except when a symmetric lens is p erfectly
aligned with the source and the observer the light travel time is di erent along
each light tra jectory corresp onding to each individual image since the geo
metrical length and the encountered p otential are di erent Thus if a signal
is emitted by the source i e a ash or some ux variations time delays will
separate its detection in each of the multiple images Refsdal
To b e more quantitative it is easier to compute the time delay with resp ect to
the pure geometrical case without any lens Let us rst assume a static euclidian
space and consider b oth geometrical and p otential contributions From Fig
and the lens equation and again assuming one can derive
D D
OD OS
c t
s g eom
D
DS
The p otential delay can b e explicitly computed at rst order by integrating
the second term of equation along the unde ected ray For a p oint mass
is given by Eq and we nd
GM
ln b C c t
pot
c
where b is the impact parameter and C is a constant dep ending only on the
distances b etween the observer the lens and the source Generalizing Eq
into
c t P b C
pot
where P represents a de ection p otential and using Eqs and we
obtain
b r P b
b
Comparing Eqs and for the case of a p oint mass lens yields
GM
P b ln b
c
and for a general surface mass density distribution
Z
G
0 0
P b b ln jb b jdb db
c S
J F Claeskens J Surdej
Given the relations and and including the factor z due to
D
the expansion of the Universe the time delay can b e rewritten as
D D
OD OS
c t c z t t z P b C
D g eom pot D s
D
DS
where D D and D represent angular cosmological distances
OD OS DS
In practice time delays can only b e measured b etween a pair of physically
observed images The delay b etween the ux variations in image and image
is then simply t t t The p ositions of the lensed images are related
together through the lens equation so that can b e eliminated in Eq
s
We nd
D D D c t z
OD OD OD D
P D P D
OD OD
It is interesting to note that the time delay do es not dep end explicitly on
H Indeed from Eqs and and with b eing the solid angle of the
o D
de ector we have
D D r P D
OD OD OD
Z
0 0 0
P D R P ln j j d C R
OD s s
D
where
D
OD
D
OD
M
tot
and
GM
tot
R
s
c
are the relative surface mass distribution within d and the Schwarzschild
radius R resp ectively They are indep endent of H
s o
Inserting the latter results into Eq the time delay can b e rewritten in
a very simple form
The origin of the factor z in the p otential delay is intuitive to rst order the
D
e ects of de ection and apparent slowing down of light are con ned near the de ector
plane b ecause of the expansion the time delay pro duced at z is longer by a factor z
D D
for an observer at z Concerning the geometrical delay one should note that it is much
smaller than the expansion time H of the Universe so c t R where R is
g eom o o
o
the present scaling factor and is the comoving distance in the FLRW mo dels b etween
the de ected and unde ected rays can b e computed with the relations in at spherical or
hyp erb olic triangles The factor z then arises after transforming the comoving distances
D
into angular ones
Gravitational Lensing in Quasar Samples
c t R z P P P P r r
s d
Equation shows that if we know the exact surface mass distribution the
p ositions of the multiple images with resp ect to the lens and the lens redshift
then the time delay measurement yields the total mass of the lens irresp ective of
the values of the cosmological parameters H etc or the source redshift Once
o
the de ector mass is known the Hubble constant can b e extracted within the
adopted lens mo del from the observed angular separation of the lensed images
see Section
As an illustration in the case of the p oint mass lens mo del P ln and
ln c t R z
P M s D
j j
Dep ending on the exact con guration of the lensed images the exp ected time
delay ranges b etween a few days and a few months for a M de ector and
it scales as the de ector mass i e as R
s
What is a go o d gravitational lens
An astrophysical ob ject is a good lens if it is capable to form strongly distorted
and or multiple images of a distant source Its surface mass density must lo cally
b e larger than the critical surface mass density in order to pro duce an
crit
averaged surface mass density just equal to b etween the lensed images see
crit
Eq On the other hand since the angular separation b etween lensed images
is ab out see Eq the latter will b e resolved if the lens is su ciently
E
massive or close enough to the observer see Eq and if where
E R
is the ob ject apparent size Fig and Table illustrate the quality of
R
known compact astrophysical ob jects to act as gravitational lenses given their
total mass distance and apparent size Solar planets globular clusters and lo cal
galaxies are to o extended exoplanets and extragalactic stars lead to typical
angular separations of one micro arcsecond they are refered to as microlenses
that are well b elow the current instrumental resolution Galactic stars distant
elliptical galaxies and rich galaxy clusters or central parts of clusters are go o d
gravitational lenses
How to search at best for cosmic mirages
In order to discover cosmic mirages two di erent strategies may b e followed
selecting go o d lenses or selecting go o d sources
Selecting go o d lenses
According to the last column of Table the b est gravitational lenses consist
of dense galaxy clusters since the angular region enclosed by the caustics pro
p ortional to the square of the scaling factor is the largest They are more E
J F Claeskens J Surdej
Fig Mass within the Einstein radius versus de ector angular distance for di erent values
of thick lines Distance and total mass ranges are considered for various massive astro
E
physical ob jects the sources are assumed to b e at in nity thin solid lines if and
R E
dotted lines otherwise see Table
e cient at redshifts in the range see Fig Giant arcs are pro duced
by the merging of strongly distorted images of an extended source intersecting
or lo cated inside the caustics On the other hand sources lo cated outside the
caustic are weakly distorted in arclets by the lens shear Observations must b e
designed to detect distant ob jects with a very high space density or integrated
luminosity function such as faint blue galaxies Tyson Ultra deep exp o
sures of galaxy clusters through the B lter are clearly optimal for that purp ose
Using the swimming p o ol analogy this is equivalent to count as many coins as
p ossible with the hop e that some of them lie close to a caustic Giant arcs and
arclets are used as a diagnostic of the cluster mass distribution For more details
Table Physical prop erties of p otential strong gravitational lenses is the apparent angular
R
radius The last column represents the angular cross section for lensing brackets indicate that
the resulting lensed images cannot b e seen
R E
Ob jects Mass M Radius p c D p c
OD R E
E
arcsec
Solar planets
Exoplanets
Nearby stars
Extragalactic stars
Globular clusters
Lo cal galaxies
Distant galaxies
Galaxy clusters
Gravitational Lensing in Quasar Samples
see the review pap ers on arcs and arclets by Fort and Mellier and Hattori
et al
On the other hand selecting go o d lenses like galaxy clusters enhances the
chance to resolve very distant background galaxies or AGNs lo cated nearly on
the same line of sight and which would otherwise b e angularly to o small to b e
studied at all Indeed as already mentioned in Section a gravitational lens
helps in signi cantly magnifying the regions of a background resolved source and
thus increases the e ective angular resolution of the observations This was rst
p ointed out by Zwicky in The discovery of a young galaxy at z
lo cated b ehind the cluster CL has recently b een rep orted by Franx et al
Several indep endent teams have also used cluster lenses as gravitational
telescop es either with ISOCAM onb oard the ISO satellite or using very sensitive
detectors at the fo cus of m telescop es in order to detect optical near and
mid IR sources intrinsically fainter than those directly recordable outside the
cluster Altieri et al Barvainis et al Metcalfe et al Pello et al
In addition using b oth the magni cation by foreground galaxy clusters
and the high angular resolution of HST it has b een p ossible to resolve the stellar
p opulations in a z lensed galaxy Bunker et al and to study the star
formation rate at very high redshifts B ezecourt et al Franx et al
We shall not further explore here this approach of selecting lenses as our
review mainly deals with gravitational lensing among quasars
Selecting go o d sources
If some luminous sources are a priori more likely to b e lensed than others they
should b e selected in order to discover new mirages Let us assume for simplicity
a non evolving p opulation of lenses with mass M whose comoving space density
is thus a constant n M The optical depth for lensing a source lo cated at
o
redshift z is
s
z M V z M n M
s e s o
where V is the e ective prop er volume in which the lens must b e lo cated in
e
order to pro duce an observable gravitational mirage Nemiro Observ
able means that the angular separation and the magnitude di erence b etween
the multiple images can b e resolved with the instrument used for the observa
tions V simply results from the integration of the e ective cross section
e e
along the line of sight
Z
z
s
cdt
dz z z M z p V z M
e s i e s
dz
where the p are the lens parameters
i
The line of sight element c dt dz is given in the FLRW cosmologies by the fol
lowing relation e g Kayser et al
c cdt
p p
dz
H z
z z
o
o o o o
J F Claeskens J Surdej
If the instrumental angular selection function S is equal to for the only observ
able con gurations of multiple images and zero otherwise if y and if
s E
p are the parameters of the lens mo del the e ective cross section is
i
Z Z
z M z p D z M S y z p dy dy
e s i OD E i
2
R
Since the space density n scales as h or h dep ending on whether it is derived
from lo cal counts or from a cosmological density in FLRW mo dels Eqs
2 2
2 2
or h Thus the and easily reveal that h
optical depth is independent of H either for the SIS lens mo del in the
o
rst case or for the p oint mass mo del in the second hyp othesis
On the other hand the total ux coming from multiple images is always
ampli ed by a certain factor A with resp ect to the source ux see Section
tot
Therefore the probability that a source with redshift z and magnitude b
s s
is a lensed ob ject is not simply z M but is given by
s
z N z b log A N z b
s s s s tot L s s
z B ias z b P z b
s s s s s
N z b N z b
s s s s s s
where the numb er magnitude relation N z b resp N z b represents
L s s s s s
the numb er of multiply imaged sources resp unlensed sources at redshift z
s
and blue magnitude b p er square degree and p er magnitude interval the last
s
equality de nes the so called ampli cation bias
Usually faint sources are more numerous than bright ones so that the ampli
cation bias is larger than Moreover if the logarithmic slop e increases towards
bright magnitudes we exp ect the proportion of mirages to b e larger at bright
magnitudes
Therefore relations and show that the most likely lensed sources are
i distant V is maximized and ii bright ob jects b elonging to a p opulation with
e
a steep numb er magnitude relation at the observed wavelength the ampli cation
bias is then high Turner
Highly Luminous Quasars HLQs M for H km s Mp c
V o
have b een recognized long ago as excellent targets to search for new gravita
tional lenses b ecause they are b oth distant and bright sources Turner et al
Surdej et al b Their numb er magnitude relation has a steep bright
end with a break around b Boyle et al Hartwick Schade
They have b een selected to e ciently search for gravitational lenses by sev
eral teams successful results are presented in Section However optical HLQ
More concretely the angular selection function S de nes a pseudo caustic into which
the source must b e lo cated for its resulting multiple images to b e detectable For symmetric
lens mo dels the detection criteria de ne the radius of the pseudo caustic for each value of
the lens redshift
The ampli cation A dep ends on the source p osition y so that the ampli cation bias
tot
is generally merged into a new de nition of the e ective cross section and Eq b ecomes
RR
2
D z M
OD E
z M z b p N z b log A y p S y z p dy dy
s s s s s tot
i i i
e
2
N z b
R s s s
Gravitational Lensing in Quasar Samples
samples might su er from dust extinction extinguished secondary images or ex
tremely reddened QSOs could remain undetected resulting in incompleteness
in the parent QSO sample and a ected statistics High resolution radio obser
vations of at sp ectrum radio sources escap e this issue but the lensed images
are contaminated by double compact sources or by source structure Helbig et
al and their redshift dep endent numb er magnitude relation is not very
well known yet Helbig et al Falco et al The ampli cation bias
a ecting at sp ectrum radio sources seems to b e lower than for HLQs Finally
let us consider space X ray observations In that wavelength range the simple
source structure and the very rare spurious alignments with foreground galactic
sources make the lens candidate selection easy On the other hand the ampli ca
tion bias is intermediate b etween optical and radio wavelengths Unfortunately
the exp ected detection rate remains small for Chandra simulations Munoz et
al b
Astrophysical and cosmological applications
It is now time to convince the reader that gravitational lensing among distant
quasars do es not just consist of an exotic or amazing consequence of General
Relativity but that it do es also provide excellent prosp ects for interesting cos
mological and astrophysical applications Two di erent kinds of approaches are
p ossible While statistics of multiple images in a complete sample of distant
sources are needed to measure and and to b ound the cosmological density
o o
of putative compact ob jects Section high quality observations of individual
gravitational lens systems may lead to unique determinations of H or of some
o
astrophysical prop erties of the lens the source and the intergalactic medium
Section
Statistical studies
The observed number of multiply imaged QSOs in a sample of HLQs but also
for each of them the observed multiplicity of the lensed images their angu
lar separations the p ossible detection of the lens and the measurement of its
redshift provide useful information to constrain some cosmological as well as
some astrophysical parameters related to the lens mo del Indeed for example
the relative numb er of quadruply imaged QSOs increases with the ellipticity
of the pro jected p otential the velo city disp ersion of the galaxies governs the
mean angular separation b etween the lensed images and the numb er of observed
mirages is a function of the numb er of galaxies of the extinction and of the cos
mological mo del see b elow On the theoretical side statistics of gravitational
lenses have rst b een established in detail by Turner Ostriker and Gott in
Further developments were p erformed by Fukugita et al and Ko chanek
a
On the observational side ab out HLQs have b een imaged during the
last ten years at optical wavelengths and more than thousand sources have
b een investigated in radio surveys see Section
The rst comparisons b etween the exp ected and the observed numb ers of
lenses were made by Maoz et al Surdej et al a and Ko chanek
J F Claeskens J Surdej
b who was the rst to apply the maximum likeliho o d analysis They
found that as exp ected from theoretical mo dels approximately of HLQs
are multiply imaged by lensing galaxies see also Section However there are
degeneracies b etween some parameters and although gravitational lensing may
help in setting individual constraints on their values it can also b e combined
with prior knowledge of some of the parameters Ko chanek Quast and
Helbig
While the main results are discussed in Section we explain here the interest
of statistical lensing with two concrete examples
The cosmological parameters and
o o
The fate of the Universe is intimately related to the values of the cosmological
density parameter and of the cosmological constant Their determina
o o
tion constitutes one of the most imp ortant challenges in present observational
cosmology How can gravitational lensing help and intervene in the com
o o
putations of the angular distances and of the e ective volume in which a lens
pro duces multiple images of a source see Eq Thus the exp ected numb er
of multiply imaged QSOs in a large sample strongly dep ends on those param
eters as was rst p ointed out by Turner and Fukugita et al
Cosmological distances to a given redshift increase for lower values of or for
o
larger values of this results in a degeneracy b etween these two parameters
o
in most cosmological tests and gravitational lensing is not an exception Fortu
nately the in uence of on V is much stronger than that of whatever a
o e o
reasonable value of values of close to lead to the prediction of detect
o o
ing many more lenses than is actually observed in optical samples Gravitational
lensing statistical studies thus yield a natural upper limit on the value of the cos
mological constant Fukugita et al also showed that the mean redshift of
the de ectors is larger if dominates over
o o
Space density of dark compact ob jects
We saw in Section that an in nitesimal source is necessarily multiply imaged
by a foreground ob ject lo cated close to its line of sight provided the latter one
is su ciently compact The de ector do es not need to b e visible Press and
Gunn had already noted in that counting gravitational lensing events in a
sample of distant sources would help in constraining the contribution to the
L
critical density of the Universe due to a putative cosmological p opulation of dark
compact ob jects One can show from Section that the angular separation
p
M M arcsec where M is the mass of b etween lensed images is ab out
L L
the dark compact extragalactic lens Thus a given instrumentation is capable
to detect the lensing e ects of compact ob jects in a relatively narrow range of
masses see Fig For example ground based optical telescop es can reveal the
e ects of lenses with M b etween and M while a higher resolution
L
and a smaller eld make the radio observations more sensitive around M
Below M the resulting multiple images cannot b e resolved this is the so
called milli or microlensing range However the ux variations induced in the
Gravitational Lensing in Quasar Samples
Photometric Imaging monitoring Space Telescope (HST) QSO microlensing VLBI, VLBA Ground based telescopes
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 log(∆θ("))
log(t(year)) -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
log(M/M ) Sol -10 -5 0 5 10 15 Population III objects Galaxies Clusters
Dwarfs Massive black holes
Jupiter Stellar black hole Jeans' Mass
at recombination
Fig Corresp ondence b etween the mass of a Schwarzschild lens lo cated at a cosmological
distance the lifetime of the multiple images assuming relative transverse velo cities of
km s their typical angular separation the range of application of existing observational
techniques and the p ossible astrophysical nature of the lens
lensed images by the relative motion of a de ector with resp ect to the observer
source direction can b e recorded by means of a photometric monitoring the
ampli cation of the source increases when it gets closer to a caustic see Eq
Note however that for a M lens the typical time scale of the event
gets rather large years see Fig Observed constraints are presented
in Section
Photometric variations due to microlensing are also observed lo cally on stars
lo cated in the Magellanic Clouds or in the bulge of the Milk Way These observa
tions are used to constrain and to characterize the p opulation of dark compact
ob jects present in the halo and to investigate the structure of our Galaxy For
more details on this technique see the review by Paczynski and references
therein
Individual studies
Detailed studies of individual multiply imaged QSOs do also lead to interesting
prob es for cosmology and astrophysics We intro duce b elow some of the most
representative examples
Time delays and the measurement of H
o
Refsdal was the rst to p oint out that in principle the Hubble constant
H could b e determined from gravitational lensing studies of distant sources o
J F Claeskens J Surdej
without any assumption on the existence of a standard candle As the angular
p
separation of multiple images is prop ortional to M H see Eqs
E o o
and it is not p ossible to disentangle the e ect of a larger de ecting
mass combined with that of a lower value of H The measurement of a time
o
delay t b etween ux variations of two lensed images i and j breaks the
i j
degeneracy as the total mass can b e derived from Eq provided that the
mass distribution is known More generally one can see from relations
and that H is inversely prop ortional to the time delay as follows
o
t H z D z z f lens mo del
i j D D s o o i j
o
where D D D D and f is a lens mo del dep endent function of the
OD OS DS
observed image p ositions and
i j
Therefore the successful determination of H relies on
o
intensive photometric monitoring of a variable multi imaged QSO in order
to precisely determine t
i j
accurate observations of the p ositions of the lensed images with resp ect
i
to the de ector
go o d knowledge of the lens redshift z and of the cosmological parameters
D
The error due to unknown precise values of and is not imp ortant as
o o
long as the lens redshift is mo derate z
D
a very go o d estimate of the de ector mass distribution
The last item represents the most di cult issue A generic problem comes
from the fact that the observed lensed image p ositions and ux ratios are
functions of the de ection angle and of its rst derivatives resp ectively see Eqs
and while the time delay is a function of the de ection p otential P
which is the integral of the de ection angle see Eq Thus several di erent
mo dels can repro duce the observed lensed image p ositions and ux ratios but
not the time delay leading to di erent estimates of H This is known as the
o
degeneracy problem It has rst b een p ointed out by Falco et al and
Gorenstein et al b They noted that adding a dark sheet of matter with
constant normalized surface mass density and reducing the lensing
crit
mass by a factor do es not a ect the image con guration p ositions and
ux ratios but reduces the predicted value of H by a factor Assuming
o
would yield an upper limit on the value of H
o
Thus additionnal observational constraints must b e used whenever available
to b etter determine the p otential of the lens The detection of lensed extended
structures provide extra values for the derivatives of the p otential and help
in improving the mo del Such extended structures may consist of radio jets
alike those detected with VLBI in the case of Q Porcas et al
Gorenstein et al a or the quasar host galaxy observed with HST e g Falco
et al a and Bernstein et al for Q but see additional
cases in Section On the other hand mapping the velo city distribution in
the de ector breaks the mass sheet degeneracy In the case of Q the
main lens is emb edded in a galaxy cluster The detection of a weak shear on
faint background galaxies and or the measurement of the velo city disp ersion of
The ux ratio must b e free of contamination by microlensing and or dust absorption
An extreme example is given by assuming that the de ector is a p oint mass in the case of
Q A B the derived value of H would then b e km s Mp c o
Gravitational Lensing in Quasar Samples
Fig Probing the size of absorbing intergalactic clouds with gravitational lensing Small
clouds usually a ect only one line of sight left while large clouds often extend over the two
lines of sight and create coincident absorption features right
the cluster of galaxies enable one to indep endently determine the contribution
of to the lensing p otential P and also to break the degeneracy
Ultimately only indep endent lens mo delings based up on the most exhaustive
set of observational constraints will attest the reliability of Refsdal s pro
p osal to measure H and the size of the Universe This imp ortant but di cult
o
endeavor has driven much e ort during the past years to improve our knowledge
of known mirages and to discover new ones in larger samples
Size of intergalactic clouds
Astrophysical ob jects can b e detected not only by their emitted radiation but
also by their absorption signature in the sp ectra of luminous background sources
Cold intergalactic clouds are revealed by their Ly and or metallic absorption
lines C iv Mg i i seen in the sp ectra of distant quasars If such a QSO is mul
tiply imaged by gravitational lensing the di erent lines of sight prob e the clouds
at various impact parameters A determination of the numb ers of coincident or
anti coincident absorption lines in high resolution sp ectra of the lensed comp o
nents allows to constrain the size of the clouds see Fig this is particularly
interesting as some of these clouds might b e connected with galaxy formation
e g Wolfe
Extinction in lensing galaxies
Lensing galaxies have long b een thought to b e transparent This simplifying hy
p othesis was justi ed by the fact that de ected light rays avoid the most central
parts of the de ector and have a typical impact parameter of kp c Moreover
the most e cient lensing galaxies are the elliptical ones However extinction by
dust lo cated in the lens has b een susp ected from the di erential reddening ob
served in some multiply imaged quasars like Q Yee Nadeau
et al MG Hewitt et al Lawrence et al McLeo d
et al MG Larkin et al or RXJ Burud
et al On the other hand some lenses are edge on spiral galaxies e g
B Jaunsen Hjorth The latter can pro duce strong lensing ef
fects just by pro jection of the disk M oller Blain but they are more
dusty and the resulting mirages could mostly remain undetected Bartelmann
Lo eb
Quantifying the e ects of dust constitutes an imp ortant issue in statistical
studies of gravitational lensing when dealing with optical samples of QSOs The
J F Claeskens J Surdej
determination of for example will b e strongly a ected if many multiply imaged
o
QSOs are hidden by dust see Section this favours the use of radio samples
for statistical purp oses b ecause dust has no e ect at radio wavelengths but we
are then faced with the p o or knowledge of the redshift dep endent luminosity
function of radio sources Falco et al Helbig et al
On the p ositive side the observed di erential reddening in multiply imaged
QSOs may b e used to determine the dust extinction law in very remote galaxies
and compare it to what we know ab out the dust prop erties in the Milky Way
the Magellanic Clouds and some very nearby galaxies This was rst p ointed out
by Nadeau et al for the case of Q and was further develop ed
by Jean Surdej in order to retrieve the redshift of the lens even if the
latter is not directly detected To achieve this accurate sp ectrophotometry or
photometric measurements through many passbands ranging from UV to near
IR are needed for each lensed comp onent
Microlensing and structure of the QSOs
We saw in Section that a given star lo cated at a cosmological distance is not a
very go o d lens b ecause it has nearly no chance to b e coaligned with a background
source However when a QSO is lensed by a galaxy into multiple images the
probability that one of the stars b elonging to the lens transits just in front of one
of the macrolensed QSO images is much higher The angular separation b etween
the sub images cannot b e resolved but the variations of the integrated
ux of the a ected macro image can b e recorded The stellar microlens only
quantitatively mo di es the ux for very small sources typically those with a
size smal ler than that of the caustic in the source plane it acts as a magnifying
glass whose space motion allows to scan very compact sources Quasars are
not angularly resolved with conventional telescop es But since microlensing is
achromatic it can b e used to analyse the chromatic structure of quasars Indeed
microlensing preferentially ampli es the continuum emission region coming from
the central part of the QSO p c corresp onding to angular separations
while the broad emission line ux emitting region p c remains
unchanged Microlensing induces uncorrelated variations of macrolensed images
of a QSO during a photometric monitoring The b est cases o ccur with nearby
lenses such as Q b ecause of their larger angular size of the larger
value of the stellar Einstein radius of the faster apparent motion of stars and
b ecause the time delay is only ab out day Lewis et al Several other
astrophysical uses of microlensed sources have b een suggested for instance Agol
and Krolik have investigated the p ossibility to image a quasar accretion
disk using induced microlensing variability of a lensed QSO image
Surveys for multiply imaged quasars
As stated in Section the dep endence of the probability P z b for a distant
s s
source to b e lensed as a function of b oth its redshift z Eq and its apparent
s
magnitude b via the ampli cation bias in Eq has prompted several groups
s
to search for gravitational lens candidates in large samples of bright and distant
quasars whose luminosity function is known to b e very steep Turner et al
Gravitational Lensing in Quasar Samples
Surdej et al b Highly Luminous Quasars typically M
V
for H km s Mp c hereafter HLQs were the rst such bright sources to
o
b e systematically imaged at high angular resolution with the aim of p erforming
statistical studies
In this section we review most of the surveys for multiply imaged quasars
that have b een carried out using b oth optical and radio telescop es
Optical surveys
Most of the HLQs selected in the di erent optical samples describ ed hereafter
were drawn from the catalogue of V eron Cetty V eron
available at the time of the observations As stated by V eron Cetty V eron
their catalogue do es not represent by any means a complete sample of quasars
it merely consists of a non exhaustive compilation of quasars that have b een
published up to a certain date in the scienti c literature and which are a ected
by multiple and complex observational biases One of these biases relates to the
publication e ect which is known to privilege the insertion of interesting or
p eculiar ob jects in a quasar catalogue On the contrary Ko chanek has
estimated that some of multiply imaged quasars could have b een missed
in quasar samples b ecause of the initial search criteria used to select QSO
candidates as p oint like and blue ob jects For instance multiply imaged quasars
reddened by the lens or displaying a complex image morphology have most
likely b een rejected as quasar candidates in the original samples Futhermore
the apparent magnitudes listed in quasar catalogues also raise serious problems
Indeed in order to prop erly estimate the ampli cation bias cf Eq one
should make use of an accurate estimate of the quasar apparent magnitude at
the time of discovery Unfortunately most of the published quasar magnitudes
only consist of rough estimates very often based up on photographic plates that
were used some time ago to search for the quasars More recent and accurate
photometric measurements are usually available but due to the photometric
variability of quasars it is quite unsafe to use the latter magnitudes in order to
calculate the ampli cation bias
Nevertheless the V eron Cetty V eron compilation of quasars has still the
merit of providing a reliable and trustworthy set of observational data on quasars
in general It is now foreseen that on going and future automated searches for
quasars such as the Hamburg ESO survey Wisotzki et al b Reimers and
Wisotzki the Sloan Digital Sky Survey Loveday the dF QSO
redshift survey Smith et al the International m Liquid Mirror Tele
scop e ILMT pro ject Surdej and Claeskens or the prop osed GAIA space
exp eriment will pro duce large sets of complete well controled and calibrated
data which are absolutely necessary in order to accomplish further progress based
up on gravitational lensing statistics
We list b elow all individual quasar samples that we have used and merged
hereafter to form a nal optical catalogue of some distinct bright quasars
for which gravitational lensing statistics has b een applied in Section All details
ab out the quasars included in these individual samples may also b e found in a
Information on GAIA space mission may b e found at ESA s URL
http astro estec esa nl GAIA
J F Claeskens J Surdej
long table published by Claeskens the table is also available through
Internet
The ESO sample
This sample of bright and distant quasars has b een observed at ESO La Silla
b etween and with the m m and m telescop es Surdej et al
A total of HLQs essentially selected from the V eron Cetty V eron
catalogue of quasars have b een imaged at high angular resolution and under
go o d seeing conditions The average observational characteristics of this and all
subsequent quasar samples are summarized in Table During the course of
these observations three new gravitational lens systems have b een identi ed
Q A B Magain et al Q A B Surdej et al b
and J A B Claeskens et al a Surdej et al and four known
gravitational lens systems have b een re discovered H A D Magain et
al PG A C Weymann et al UM A B Surdej et
al a and HE A B Wisotzki et al
The Crampton et al CFHT sample
A sample of HLQs also drawn from the V eron Cetty V eron cat
alogue has b een observed with an active CCD camera at the prime fo cus of
the CFH telescop e in order to detect close separation gravitational lens systems
Crampton et al In spite of the excellent image seeing conditions prevail
ing during the observations average FWHM no new gravitational lens
was identi ed
The Yee et al CFHT sample
Another set of HLQs selected from the Hewitt Burbidge catalogue
of quasars has also b een imaged with the CFHT at high angular resolution by
Yee et al Among several identi ed lens candidates H was
rediscovered but all other mutiple image systems turned out to b e stars
The NOT sample
The initial numb er of quasars imaged with the NOT at La Palma amounts to
Jaunsen et al These quasars mainly lo cated in the northern hemi
sphere have b een selected on the basis of their bright absolute magnitude listed
in the V eron Cetty V eron catalogue but also from an unpublished list
of quasars by C Hazard and from a preliminary list of bright quasars discovered
by the Hamburg team Jaunsen private communication The numb er of dis
tinct quasars that have b een observed with the NOT is now approximately
Several of these have shown an interesting and or complex image morphology
but no new lens has b een identi ed among these
The URL address is
http vela astro ulg ac b e themes extragal gravlens bib dat eng l table html
Gravitational Lensing in Quasar Samples
Fig Probability P z b for each QSO in the merged optical sample see Tab and
s s
Section to b e multiply imaged as a function of its V absolute magnitude The seven
known lensed quasars in that sample are encircled
The HST sample
This sample consists of HLQs from the V eron Cetty V eron cata
logue They were observed in the snapshot mo de with the Hubble Space Tele
scop e Maoz et al Due to the observing p olicy with HST known lenses
were excluded from the sample Only one new case of multiply imaged quasar
has b een found among the HLQs Q has b een indep endently re
discovered with HST Bahcall et al
Table Average observational characteristics of the di erent optical samples
QSO sample z b M FWHM N N
s s q
V
q best
arcsec
ESO
Claeskens
CFHT
Crampton et al
CFHT
Yee et al
NOT
Jaunsen et al
HST
Maoz et al
MERGED
J F Claeskens J Surdej
The merged sample
As exp ected quite a few quasars have b een indep endently observed by the dif
ferent teams If we merge all previous optical samples the resulting one do es
actually have observations for a total of distinct quasars In case of
duplication we kept the most outstanding observation i e the observation for
which the probability of detecting a gravitational lens is the highest usually
corresp onding to the b est seeing conditions or characterized by the b est angular
selection function Indeed the non detection of multiple images for most of the
HLQs also helps in constraining the lensing mo dels and the strength of these
constraints directly relates to the image quality of the observations Table
summarizes the average observing conditions p ertaining to the individual opti
cal samples of quasars It gives the mean redshift z the mean blue magnitude b
s s
and the resulting average absolute magnitude M H km s Mp c
V o o
of the N observed quasars under an average seeing FWHM in each
o q
individual sample The N column lists the nal numb er or p ercentage
q best
of HLQs retained after elimination of the duplicated observations Thanks to
the higher angular resolution of the Hubble Space Telescop e this sample turns
out to include the higher prop ortion of retained observations followed in
numb ers by the NOT and the ESO samples Table in Section summarizes
the observed prop erties of the seven multiply imaged quasars identi ed in the
nal optical sample of HLQs Fig illustrates the a priori probability of
detecting a gravitational lens for each of these quasars see Eq as a func
tion of their V absolute magnitude In accordance with theoretical exp ectations
see Section the seven known lenses are indeed identi ed among the most
luminous HLQs
Additional optical samples
For the sake of completeness we should like to mention the existence of several
additional optical surveys for multiply imaged quasars among HLQs
Since the Hamburg ESO survey HE quasars has sampled the bright
quasar p opulation B and z over a substantial area of the southern
sky Wisotzki et al b Reimers et al Engels et al Similarly
gravitational lenses have recently b een detected among bright quasars identi ed
in the Second Byurakan Sp ectral survey SBS quasars for bright B
emission line ob jects Chavushyan et al Direct imaging of bright quasars
has also b een rep orted in the FKS survey Ko chanek et al Some inter
esting gravitational lens systems discovered in these bright QSO samples have
b een de nitely con rmed and are also listed in Table
Ratnatunga et al have searched for multiply imaged sources
double images quads arcs around foreground galaxies at sub arcsec angu
lar scales on parallel recorded WFPC CCD frames obtained in the context of
the HST Medium Deep Survey MDS Although the nature of most of the very
faint sources remains to b e determined on the basis of deep sp ectroscopic obser
vations they have set up a list of the top go o d gravitational lens candidates
see Table The rst of these HST has b een con rmed to consist
of multiple images of a faint quasar at z lensed by a foreground galaxy
Gravitational Lensing in Quasar Samples
at z Crampton et al It is probable that more faint quasars will
b e identi ed among the remaining MDS gravitational lens candidates
Finally Scarpa et al have rep orted evidence for macro lensing e ects
for at least targets in their HST WFPC Snapshot Survey of BL Lac ob jects
ES ES ES and H If some of these
candidates prove to b e real lenses they may constitute go o d prob es to deter
mine H Indeed BL Lac ob jects are known to b e highly photometric variable
o
Furthermore they are likely to b e sup erluminal sources o ering a unique p os
sibility to map the image source magni cation cf Eq radially across the
source plane in just a few years providing strong additional constraints on the
lens mo del See also Lewis and Ibata for the case of PKS no
evidence for lensing
Radio surveys
In addition to the very rst MG VLA radio survey that has led to the discovery
of several famous lenses Lawrence et al see also Table for a complete
list the largest systematic radio search is the on going CLASS Cosmic Lens
All Sky Survey Myers et al This very ambitious survey is the successor
of the pioneering JVAS Jo drell Bank VLA Astrometric Survey Patnaik et al
King et al which was aimed at the identi cation in the northern
sky of new lenses among at sp ectrum radio sources i e with
for the radio ux f b etween GHz and MHz Radio sources
with a ux density greater than mJy at GHz were selected for JVAS
against mJy for CLASS Criteria to select the gravitational lens candidates
are multiple images with angular separations in the range and ux
ratios King et al
JVAS and CLASS consist of well de ned surveys for which VLA radio images
at GHz with resolution have already b een obtained for approximately
at sp ectrum radio sources i e approximately for JVAS
for CLASS Myers et al
Flat sp ectrum radio sources are particularly well suited as a p opulation from
which one can obtain in principle unbiased samples of interesting gravitational
lenses Helbig et al Indeed the ma jority of at sp ectrum radio sources
are likely to b e single compact ob jects It is thereby easy to identi y lens candi
dates from those VLA maps which display multiple nearby at sp ectrum radio
comp onents In addition at sp ectrum radio sources often turn out to b e vari
able and thus constitute prime candidates for a determination of H from the
o
measurement of time delays
From an insp ection of the JVAS CLASS VLA images some gravi
tational lens candidates seem to have b een identi ed Fassnacht et al b
These were then imaged at higher angular resolution with the MERLIN inter
ferometric array and sometimes with the VLBA There remained of the order
of likely candidates for which additional observations were taken at optical
and IR wavelengths using either the William Herschel Telescop e on La Palma
the Hubble Space Telescop e or the Keck Telescop e on Mauna Kea More than
a dozen of these candidates have already proven to b e real gravitational lenses
Myers et al the HST direct images often revealing the faint de ecting
galaxy
J F Claeskens J Surdej
Among the most famous gravitational lens systems detected in the JVAS
CLASS survey see Table for an exhaustive list we may note B
a go o d candidate to estimate H from the measurement of the time delay
o
and B the reddening of the faint quasar image is outstanding b oth
with as lens a spiral galaxy almost seen edge on in the latter case The CLASS
lens system B corresp onds to a quadruply imaged p ost starburst radio
galaxy HST observations have enabled to resolve b oth the galaxy source and the
lens This system has b een monitored with the VLA Three indep endent time
delays have b een derived and an estimate of H has b een prop osed Fassnacht et
o
al b see Section B shows at sub arcsecond angular scales a
total of up to lensed radio images originating from di erent parts of an active
radio galaxy b oth the compact at sp ectrum radio core and one of the steep
sp ectrum radio lob es are quadruply imaged whereas the second steep sp ectrum
radio lob e is only doubly imaged King et al
The real advantages of gravitational lens radio surveys over optical ones is
that the radio emitting regions of the quasar sources ought to b e substantially
larger than the optical ones such that microlensing by stars in the de ector
should not a ect the observed ux ratios These radio ux ratios may then
b e used to b etter constrain the lens mo del Furthermore extinction e ects are
totally negligible
In spite of this the observed ux ratios observed in the radio for sev
eral JVAS CLASS systems such as the very bright quadruply imaged quasar
B B Fassnacht et al a or B Fassnacht et
al b turn out to b e very di cult to mo del For all these systems either the
lens mo del is wrong or it could b e that the structure of the radio source is more
complex than originally assumed such that the estimated ux ratios cannot b e
compared with the observed ones For the latter the lens might consist of sev
eral sub systems Ko opmans and de Bruyn also observed ux variations
in the doubly imaged radio source B at and GHz which might
b e due to microlensing of very compact sup erluminal jets
Up to now the JVAS CLASS survey constitutes the largest survey that has
b een carried out to identify gravitational lenses However it is not yet complete
in a statistical sense since the most interesting gravitational lens candidates have
probably b een lo oked at rst It is probable that other candidates consisting of
double sources or unusual con gurations for the multiple images will either not
show up in the optical or that the sometimes very distant or p ossibly dark
etc lens will remain undetected It is therefore not clear to which degree this
radio survey will b e complete In addition the parent p opulation of the radio
sources ought to b e well de ned as a function of redshift and here also it is
easy to foresee ma jor di culties in detecting their optical counterpart and thus
measuring their redshift in a complete way Finally the source redshifts of the
CLASS lensed sources turn out to b e smaller than those found in optical surveys
rendering the JVAS CLASS sample less sensitive to the cosmological parameters
Helbig et al
A harvest of multiply imaged QSOs
Past and ongoing surveys discussed in Section have led altogether to the dis
covery of more than multiply imaged sources Their general prop erties as
Gravitational Lensing in Quasar Samples
well as some more sp eci c characteristics are summarized in Table This Table
contains the most up dated observational status of multiply imaged QSOs at the
time of writing this review A version of this Table is also available through In
lens and will b e regularly ternet via the URL http vela astro ulg ac b e grav
up dated Many lens detections and magnitude measurements are due to the
CfA Arizona Space Telescop e LEns Survey CASTLES which consists of an
ongoing HST direct imaging program in the H I and V bands of all the known
gravitational lenses as well as published candidates see the URL http cfa
www harvard edu castles and Munoz et al a
Table Individual observational prop erties of the multiply imaged QSOs status in March
More details on the astrometry and photometry of the individual lensed images can b e
lens found at the CASTLES Web site as well as at URL http vela astro ulg ac b e grav
Table contains the following information
Column the standard source name or any other frequently used designation
Column the survey s in which the gravitational lens system has b een identi
ed see text
Column the numb er N of lensed images and or other image characteristic s
Column typical angular separation s in arcsec b etween the multiple
lensed images or diameter of the ring etc
Column sp ectral range s O ptical R adio or X ray in which the lensed
images have b een detected
Column sp ectroscopic redshift z of the source
s
Column sp ectroscopic redshift z of the lens
l
Column physical source typ e cf quasar jet
Column physical lens typ e cf elliptical or spiral galaxy
Column integrated magnitude s of all lensed source images If the source and
lens images cannot b e resolved we list the total magnitude of the
lensed and lens images cf R
tot
Column magnitude s of the lens If the lens and source images cannot b e
resolved we list the total magnitude of the lens and lensed images
cf R
tot
Column if known an estimate of the lens mass times the Hubble constant
expressed in unit of km sec Mp c The mass is given in solar
mass unit
Column if known an estimate of the lens mass to light ratio divided by the
Hubble constant expressed in unit of km sec Mp c The sp ectral
band used for the observed light is indicated b etween parentheses
J F Claeskens J Surdej
Column additional observed characteristics of the gravitational lens system
cf time delay s detection of microlensing or di erential reddening
b etween the lensed images
Column astrophysical or cosmological application that has b een made for the
gravitational lens system cf estimate of H of the size of intervening
gas clouds lo cated along the line of sight of the de ector extinction
law
Column condensed reference s of the main pap ers rep orting the discovery
of the gravitational lens system rst reference as well as additional
information listed in the present table A question mark app earing
in the di erent columns indicates an approximate or doubtful value
See the precise references at the end of this pap er from Pospieszalska
Surdej et al
Contributions of gravitational lensing to cosmology and
astrophysics
In this Section we summarize the most imp ortant and most recent results
achieved by the numerous studies of gravitational lensing in the quasar p op
ulation It is intended as a quantitative answer to the qualitative motivations
exp osed in Section
The cosmological parameters and
o o
As explained in Section gravitational lensing yields a natural upper limit on
the value of the cosmological constant
o
The rst constraints on have b een obtained for at cosmologies with sim
o
ple lens mo dels and relatively small optical samples at con dence
o
level CL in a sample of HLQs Ko chanek b at CL with
o
HLQs Maoz Rix The constraint was then progressively reinforced
as the size of the observed sample was growing at CL with
o
HLQs Ko chanek at the CL with HLQs Claeskens
o
et al b Claeskens Including in the likeliho o d analysis of HLQs
the lens redshift or the lens non detection Claeskens obtains
o
at the CL the redshift and magnitude distributions of the lenses are also
compatible with a low value of In all cases the Einstein de Sitter Universe
o
is acceptable and even favoured by GL statistics see Fig
o o
However a p ositive value of has b een suggested from the analysis
o
of high z sup ernovae Perlmutter et al Riess et al If it is con
rmed this could mean that the observed numb er of lenses in HLQ samples
is to o low either b ecause the galaxy luminosity function is not correct Chiba
Yoshii or b ecause of extinction by dust in the lens Malhotra
Although Ko chanek and Claeskens show that extinction in the
lens is probably not su cient to reconcile the results with a cosmological mo del
dominated by extinction by dust remains a critical issue as it also a ects the
o
completeness of the optical QSO samples Let us note here that the presence of
dust could also mimic the e ect of a p ositive on the sup ernova magnitudes
o
in a Universe Aguirre Aguirre Haiman o
Gravitational Lensing in Quasar Samples
Fig Likeliho o d contours in the plane as derived from the observations of
o o
HLQs in the merged optical sample see Table The successive concentric contours enclose
the true values of the parameters with a probability of and resp ectively
The most likely value corresp onds to the symb ol while the X symb ol marks the corre
sp onding result obtained from the analysis of the Sup ernova distances Riess et al The
dashed line represents the lo cus of at Universes Note the lack of constraint
o o
on
o
Searches for multiple images in uniform radio surveys are not a ected by the
issue of extinction e ects Although the source p opulation entering the computa
tion of the ampli cation bias is p o orly known the statistics have b een p erformed
for the radio JVAS survey of at radio sp ectrum sources see Section
by Falco et al at CL and by Helbig et al
o o
at CL The b etter agreement b etween those results and the sup ernovae
results allow a joint analysis which yields i e at CL
o o o
in a at cosmology Helbig Additional results from the CLASS survey
see Section and a b etter knowledge of the parent radio source p opulation
are mandatory see Co oray
Cosmological density of dark compact objects
A wide panorama on existing constraints or theoretical predictions on puta
tive cosmological p opulations of compact ob jects may b e found with asso ciated
references in Dalcanton et al Hereafter we give more details from the
contributions of lensing studies
In Canizares got the rst constraint on the cosmological density
L
of dark compact ob jects from the small observed variations in the equivalent
width of broad emission lines in the sp ectrum of quasars for dark L
J F Claeskens J Surdej
Fig Current constraints from gravitational lensing on the cosmolgical density of dark
compact ob jects in unit of the critical density as a function of their mass Thick full line
c
Claeskens CL straight full line Kassiola et al CL short dashed
line Canizares dotted line Schneider CL long dashed line Dalcanton et
al X Marani et al CL
compact ob jects with M M Further constraints were provided
by counting multiply imaged sources in the VLA lens survey resp in the rst
HLQ surveys by Hewitt resp Nemiro They were improved
resp ectively by Kassiola et al who to ok advantage of the higher angular
resolution of the VLBI and by Surdej et al a who made use of a larger
HLQ sample and included the ampli cation bias
Fig summarizes the current b est constraints on in the mass range
L
M
In the M mass range i e in the microlensing domain see Fig
Canizares results have partially b een improved by Dalcanton et al
and Schneider The former also uses the equivalent width variations of
emission lines while the latter studies the statistical variability of the quasar
ux in a sample Note that this variability can only b e prob ed for a limited
mass range The lower limit M is due to the nite size of the QSO
continuum emission region the upp er limit dep ends on our ability to record long
microlensing events ab out years for a M cosmological ob ject Those
results already preclude the existence of a cosmological p opulation of stellar
black holes or dwarf stars able to stop the expansion of the Universe
A mass of M corresp onds to the Jeans mass at recombination in Cold
Dark Matter CDM mo dels and is within the mass range of pregalactic ob jects
predicted by several mo dels Carr Rees Gnedin Ostriker The
cosmological density of such dark compact ob jects is smaller than at
CL Marani et al b ecause no echo es due to gravitational time delays were
observed in Gamma Ray bursts Stronger constraints in this interesting mass
Gravitational Lensing in Quasar Samples
range could b e obtained with VLBA observations of radio sources but this is
not p ossible until the luminosity function of the source p opulation is known
Finally the strongest constraint is for M M at
L L
CL Claeskens It results from the search for multiply imaged HLQs with
no apparent lens in a sample of ob jects This means that massive ob jects
with M are nearly always in the form of visible galaxies and not in the
form of dark halo es as predicted in the CDM mo del by Navarro et al
The Hubble constant H
o
Much progress has taken place during the past years on the long way from
theory to practice in determining H with lensing studies
o
First of all the numb er of known lenses has continuously b een increasing
see Table
Secondly much e ort has b een made in order to reduce the uncertainties in
the di erent factors entering Eq which relates H to observed quantities So
o
image p ositions are well de ned by radio or HST observations e g CASTLES
the lens mo dels are b etter constrained owing to velo city disp ersion measurements
of the main lens e g Falco et al a Tonry and Franx for Q
and to the detection of extended images of some QSO host galaxies e g for
MG Falco et al b Angonin et al Q Falco
et al a Bernstein et al BRI and HE Leh ar et
al PG Imp ey et al H Alloin et al
CTQ Morgan et al and Q Mediavilla et al
Thirdly the imp ortance of sustained photometric monitoring has b een recog
nized in order to precisely determine time delays In the case of Q the
long standing debate b etween the long Press et al a b and the short
Vanderriest et al Schild Schild and Thomson Pelt et
al observed time delays has nally b een closed with t days
Kundi c at al a con rmed by Haarsma et al de nitively in favor of
the short time delay To day other lens systems have measured time delays see
Table B Biggs et al HE Wisotzki et al
PG Schechter et al Barkana B Ko opmans et
al B Fassnacht et al b and PKS Lovell et al
Although some complementary information has b een obtained on the de
ector from observations such as the velo city disp ersion of the lens or the
convergence term from weak lensing studies the lens mo del cannot b e fully
constrained from the observations and it b ecomes now the dominant source of
uncertainty on the derived value of H esp ecially through its radial logarith
o
mic slop e Despite the fact that the lens of Q is complex presence of
a cluster it is probably still the b est constrained system Using their mo del
Falco et al a nd H km s Mp c at and Kundi c et al
o
a derive H km s Mp c at on the basis of the Grogin and
o
Narayan lens mo del However allowing for more general mo dels includ
ing ellipticity of the lens Bernstein and Fischer nd larger uncertainties
H km s Mp c at A non exhaustive list of values for H derived
o o
hitherto from Q and other multiply imaged QSOs is presented in Table
J F Claeskens J Surdej
Table Determinations of H from gravitational lensing Unless stated otherwise error bars
o
are uncertainties
Lens H km s Mp c References
o
Biggs et al B
Q Falco et al a
Kundi c et al a
Tonry and Franx
Chae
Bernstein and Fischer
PG Courbin et al
Kundi c et al b
Imp ey et al
Fassnacht et al b B
Lidman et al PKS
The lensing galaxies
Lensing galaxies are di cult to observe since they are exp ected to b e faint and
extended high redshift ob jects lo cated b etween bright and angularly very close
multiple images of the background quasars However mainly thanks
to the high angular resolution of the HST and to the use of p owerful image
analysis techniques such as Point Spread Function subtraction pro le tting
and deconvolution the lens has b een detected for ab out of the multi
ply imaged QSOs see Table Even the morphological typ e could b e ob
tained for of them It is apparent that the most common lenses are iso
lated elliptical galaxies but spiral galaxies are also observed e g B
B B The main lens can also b e immersed in a galaxy
cluster e g Q B or b e comp osed of more than one galaxy
e g B MG The lens sp ectro copic redshifts are still more
di cult to measure they are presently known for only lenses i e The
median value is z as exp ected from Fig In some cases the lens red
D
shift may p ossibly b e derived from an asso ciation with that of a sp ectroscopic
absorption line system seen in the sp ectra of the lensed images or by studies of
their di erential reddening see Section
Multiply imaged QSOs provide unique information on the mass distribution
of these high redshift lensing galaxies
First the predominance of ellipticals as gravitational lenses over spirals was
exp ected from their larger mass pro ducing a larger cross section for lensing and
a wider mean angular separation b etween the lensed images which are thus easier
to detect see Eqs and Fukugita and Turner This is con rmed
by statistical studies of the angular separations of the multiple images present
in QSO samples Ko chanek b Ko chanek Falco et al Claeskens
However the prop ortion of spirals is higher in the CLASS survey see
Table and Jackson et al a M oller and Blain claim that the latter
have an increased lensing cross section with a higher related ampli cation bias
due to the inclination of the disk and that spiral lenses would only show up
when the survey is not sensitive to dust as in the radio but this is contradicted
Gravitational Lensing in Quasar Samples
by the results of Keeton and Ko chanek Gravitational lensing by spiral
galaxies should allow us to b etter study the relative contributions of their disk
bulge and surrounding halo
Second the relative numb er of quadruply imaged and doubly imaged QSOs
in optical samples also seems to b e explained by a reasonable ellipticity of the
lensing p otential Claeskens although the comparison with the ellipticity
of the light distribution is dangerous Keeton Ko chanek and Falco The
absence of observed cosmic mirages with images has so on b een recognized as a
signature of nearly singular p otentials Wallington and Narayan Ko chanek
This is in agreement with HST observations of lo cal elliptical galaxies
by Gebhardt et al It remains unclear however why the prop ortion of
quadruply doubly imaged radio sources is so high in the CLASS survey Jackson
et al a b but this could b e due to a pure observational selection bias
Third the statistical studies also suggest that the observations are b etter
repro duced by lensing isothermal dark matter halos rather than by constant
M L lens mo dels Maoz and Rix Ko chanek However for individual
lenses simple mo dels are not always able to adequately t the image p ositions
and ux ratios The intro duction of an additional shear term may help but its
origin cannot always b e explained by the p erturbation of galaxies close to the
main lens Keeton et al
Finally it is interesting to combine the mass of the lens estimated from
mo del tting with the photometric data The resulting M L ratio is found
to b e in the range in the B band Keeton Ko chanek and Falco see
also Jackson et al b Ko chanek et al show that most gravitational
lenses are compatible with elliptical galaxies lying on the same passively evolving
fundamental plane as the elliptical galaxies residing in clusters
Dust extinction in the lens galaxies
In order to reconcile the observed numb er of multiply imaged QSOs in the optical
samples presented ab ove with the exp ected one in a Universe with the
o
mean extinction in the lens galaxies ought to b e A mag Ko chanek
V
Claeskens A smaller value corresp onding to ab out mag in the B band
seems to b e needed to improve the t of the merged optical radio samples
and to retrieve the constraints on derived from radio samples Falco et al
o
This is at the level of the observed extinction in lo cal external galaxies
see e g Peletier Van Dokkum Franx Malhotra et al made
the rst attempt to estimate the extinction at higher redshift from the analysis
of the colours of a sample of lensed radio sources and lensed optically selected
ones But one cannot exclude intrinsic disp ersion in the colours Only di erential
reddening can directly b e measured From a sample of lens galaxies Falco et
al nd a mean value of E They tentatively come to the
B V
conclusion that the derived total extinction in the lens accounts for the di erent
The mass b etween the images is a robust mo del indep endent estimate see Eqs and
This weak di erential extinction con rms that no multiply imaged QSO is missing in the
existing HLQ optical samples see Claeskens and Surdej
J F Claeskens J Surdej
values of obtained from statistical studies of optically selected samples and
o
of radio source samples
Using existing heterogeneous photometric observations Jean and Surdej
applied their metho d to simultaneously t the R extinction param
V
eter and the redshift z of the lensing galaxies resp onsible for the quadruply
l
imaged QSOs H and MG They found in b oth cases a value
of z The redshift of the latter galaxy has b een sp ectroscopically con
l
rmed to b e z Tonry and Ko chanek Dust redshift estimates
l
for other gravitational lenses have b een p erformed by Falco et al Better
photometry and high quality sp ectroscopic data of selected lenses should very
so on provide clues on their extinction curves
Size of QSOs
Analysis of the gravitational microlensing high ampli cation event rep orted for
Q A by Irwin et al has led Wyithe et al to the conclu
sion that upp er and lower limits at CL on the intrinsic size of the R band
continuum emitting region are and cm resp ectively see also Racine
and Lewis et al for previous estimates A value of cm
for the size of the quasar Q has similarly b een prop osed by Pelt et al
see also Schmidt and Wambsganss
Let us mention here that the resulting ampli cation due to lensing galaxy
has help ed Alloin et al and Yun et al to resolve CO
extended emission at high redshift from the lensed quasar H Barvainis
et al similarly detected CO emission from MG
Size of intergalactic clouds
The large numb er of coincident absorption lines found in the sp ectra of the
multiply imaged QSOs UM A B Smette et al and HE
Smette et al implies that most of the intervening clouds extend over
b oth lines of sight A lower limit on the size of the clouds was derived to b e
h kp c and h kp c resp ectively h H in agreement with even
o
larger estimates of ab out h kp c recently found from sp ectroscopic studies
of QSO pairs D Odorico et al
The distorted apparent Universe
Gravitational lensing also distorts our view of the distant Universe although
not as strongly as rst suggested by Barnothy and Barnothy Indeed the
ampli cation bias which helps in discovering new mirages see Section
can also a ect the astrophysical prop erties inferred from ux limited samples
Here we brie y discuss three examples related to ux limited QSO samples
First the apparent QSO luminosity function could b e mo di ed and a part
of its apparent evolution with redshift could b e due to gravitational lensing
as rst p ointed out by Turner Schneider showed that the e ect
could indeed b e imp ortant provided the sources are as small as derived from their
Gravitational Lensing in Quasar Samples
variability a small fraction of the Universe is in the form of compact ob jects and
the intrinsic luminosity function is su ciently steep The e ect should thus b e
more imp ortant at the bright end Directly evaluating the ampli cation bias
from the observed luminosity functions of lensed and unlensed quasars has not
b een p ossible yet b ecause of the lack of large homogeneous surveys This should
b ecome feasible when surveys like the SDSS are completed in the near future
However the analysis of the bright end of the QSO luminosity function in the
Hamburg ESO survey already shows that it is steep er at higher redshift This is
the opp osite of what is exp ected since gravitational lensing b eing more frequent
at higher redshift the ampli cation bias should atten the bright end of the
apparent luminosity function Wisotzki
Second the ampli cation bias should create an arti cial correlation at very
small angular separations few arcsec b etween high redshift background QSOs
and foreground visible galaxies in ux limited samples even if the former are
not multiply imaged weak lensing However the numb er density of the sources
is also diluted by gravitational lensing and Narayan Kayser and Tribble
Claeskens and Surdej and others showed that the resulting ex
p ected overdensity of galaxies in the angular vicinity of QSOs is very low and
cannot repro duce the highest rep orted ones The latter authors also claim that
the comparison is hamp ered by small numb er statistics and p ossible selection
biases and that ab out HLQs should b e observed down to a limiting mag
itude of R b efore a de nite conclusion can b e drawn Positive angular
lim
correlations b etween high redshift QSOs and foreground galaxies are also ob
served on larger scales up to one degree and may b e used to constrain large
scale structures see e g Williams and Irwin and references therein
Finally as a last example let us mention that gravitational lensing might
a ect the determination of the cosmological density of neutral hydrogen
HI
based on Damp ed Ly Absorptions DLAs surveys in quasar sp ectra Bartel
mann and Lo eb Smette Claeskens and Surdej Indeed lensing by
the halo of the asso ciated spiral galaxies could cause the light rays from the
background QSOs to avoid the densest central parts of the disk while the am
pli cation bias increases the chance that a QSO with a DLA b e included in a
ux limited sample The comp etition b etween these two e ects results in a slight
overestimation of in existing high redshift surveys but the latter could b e
HI
more signi cant at lower redshift in bright QSO samples Smette et al
although the in uence of dust extinction could balance that of the ampli cation
bias Bartelmann and Lo eb
Conclusions
The rst cosmic mirage was found by chance This happ ened in with
the discovery of the doubly imaged radio loud quasar Q Walsh et
al Hunting the cosmic illusions in the distant Universe then b ecame
a sort of favorite sp ort for some adventurous observational cosmologists and
the known numb er of multiply imaged QSOs slowly increased during the s
reaching in Surdej and Soucail Later on the scienti c interest in
this phenomenon b eing widely recognized nding gravitational lenses b ecame a
p opular sp ort several indep endent teams initiated surveys among known HLQs
or radio sources At the IAU meeting of Melb ourne in mid systems were
J F Claeskens J Surdej
known among which were classi ed as certain Keeton and Ko chanek
In early more than multiply imaged QSOs or radio sources are known
and of the lenses are detected see Table A further exp onential increase
must b e exp ected since the p erio d of artisanal astronomical observations is
b eing progressively replaced by the industrial era of automated surveys At
the same time the observations are going to b e deep er and deep er They will
reach a huge p opulation of faint and extremely distant sources and the more
distant the source the larger the chance to get a gravitational lens along the
same line of sight As a consequence Barkana et al estimate that the
Next Generation Space Telescop e NGST should detect several lensed ob jects
in each eld of view What was gold for the astronomers of the s could
transform into lead for the next generation of astronomers who will rst need
to remove lensing artefacts b efore discovering the astrophysical prop erties of the
primeval ob jects
In this review we tried to illustrate the numerous p otential applications
of strong lensing and to summarize some interesting results already achieved
Automated QSO surveys SDSS dF and imp ortant radio surveys like CLASS
will provide large complete and homogeneous samples of distant sources free of
uncontrolled selection bias They will undoubtedly improve the statistical studies
based on gravitational lensing the studies of the optical QSO luminosity function
and of the prop erties of the lensing galaxy p opulation extinction M L will
also necessarily b ene t from this Newly discovered lenses will also increase our
opp ortunity to determine H Finally imp ortant discoveries will surely concern
o
the large scale structures at mo derate redshifts thanks to the study of weak
lensing on the myriads of very high redshift background sources which are going
to b e resolved with the next generation of large telescop es But this is another
story
Acknow ledgement We are very grateful to Prof L Woltjer for having invited us to write the
present review on Gravitational Lensing in Quasar Samples and for his valuable suggestions on
the rst manuscript Our research was supp orted in part by contract P P ole d Attraction
Interuniversitaire OSTC Belgium by PRODEX Gravitational lens studies with HST by
the Fonds National de la Recherche Scienti que Belgium and by contract ARC
Action de Recherche Concert ee de la Communaut e Fran caise de Belgique Our thanks also
go to Jean Pierre Swings and to Valery Zhdanov for reading the manuscript and to Anna
Pospieszalska for her help with the tables and with the Gravitational Lens Bibliography
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