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in our sample b eing due to gravitational exp ected from a random distribution present ep o ch in orderis to the have case b een the detectedthe at galaxies such must may a b e b e high much in brighter groups than at at the the redshift If this cation the sample by gravitational lensing is evidence If the galaxies aretions at but lower the cause thanless has the clear not Asso ciations b een there have unequivocal l b y een detected established in recent observa quasar redshift case of lowredshift dep ends on the redshifts of the quasars and galaxies In the compact macrolensing by the p otential or to microlensing by the Heckman andare Ellingson rep orted Green in thewith Yee literature the eg but quasar Yee in Several Greentect instances asso ciations of Smith due lowredshift to clustering galaxies lying in clusters asso ciated foreground In this pap er we lo ok at the asso ciation b etween quasars and August astro-ph/9408088 29 Aug 1994 P Quasargalaxy Mon Not R Astron So c AngloAustralian Observatory Coonabarabran NSWSchool of Australia Physics UniversityAstronomy of Centre MAPS Melbourne University Parkvil le of Victoria Sussex Brighton Australia BN QH Data obtained at lObservatoire du Mont Quebec Megantic INTRODUCTION present A Until The physical The situation for highredshift of Thomas ob jects recently the galaxies that these are biased study are intrinsically background asso ciated signicance we are z most We R nd a signicant quasars we might exp ect to de not lensing ie many of the quasars studies with the galaxy sources L of quasargalaxy interested Key words the quasars are sootherwise aected b e although to o the faintwhich allowed to we error attribute b e to in included the this in magnication fraction by our gravitational is sample lensing large Ab out of quasars one which quarter would to one third of ies quasars and faint presumably foregroundThere galaxies We is lo ok controversy at ab out theABSTRACT distribution the of measurement galax of statistical asso ciations b etween bright nd statistic faint but are magnied asso ciations linesofsight Webster around detected a z may which we interpret as signicant quasars is much based in b e excess over that an galaxies a due Alternatively quasars general gravitational lensing unbiased asso ciations statistically on The ampli and either excess the at the into separation M to sample of ? close J tribute Harding Webster discussion In of addition the dierent observational groups problems at is given by Hewett will is ing lensing ifan it observing were programme present which The woulddegrees b e choice of optimal of signicance for quasar observ in previous sample work we set out to design redshifts are obtained for the asso ciated galaxies low resp ect In quasars observed vary markedlydierent in metho dologies redshift have and b eenpublished magnitude used Comparison and of dierent thestatistical samples samples excess is of though dicult quantitative since Fletcher results have yet and to Yeeever b e Filipp enko some more recent studies eg and Crampton Hintzen McClure Romanishin Valdes How redshift shift signicant out detected MgI Iabsorption separately lines These we show analysed a theunintentional subsample similar favouring of of quasars quasars with whosewas sp random ectra show To MgI I testthors the of p ossibili ty pap ers on MgI I samples claim the quasar selection is high redshift gives a reasonable crosssection for lensing It nitude Drinkwater of neighbours of crucial describ ed of addition only b e clearly resolved Because of the hints of gravitational We quasars the Paper enhances the excess to dierent bright to chose quasar the excess imp ortance at the but Tyson z at presence to length mo derate the algorithm separations and of lo ok quasars the relevant fraction galaxies its in at that the sample of Drinkwater nearest redshift bright galaxies for Webster when a substantial of physical less near galaxy the lensed p oints m Tang claim no neighbour than that there has b een an quasars mo derately near V bright et Webster detection reasons That issue quasars al are reiterated lensing of various b e unbiased ab out quasars apparent using galaxy We number of high while Fugmann mo derate varies Thomas the asso ci a arcsec mag with new red au the b e A

2 Thomas Webster and Drinkwater

i m ation of quasars and foreground galaxies see Section

V

ii z Preliminary results from essentially the same sample were

q so

iii no bias with resp ect to nearby galaxies or absorption presented by Drinkwater et al but we now apply a

iv degrees more rigorous statistical analysis

The outline of the pap er is as follows The selection cri

v determined by the allo cated observing

times teria and data analysis are briey describ ed in Section for

a fuller account we refer the reader to Paper In Section

The full observed is given in Table

we describ e the statistics of quasargalaxy asso ciations We

None of the samples we used were strictly magnitude

rst discuss the use of the sparameter as a measure of

limited but all are of bright quasars The ma jority of quasar

quasargalaxy separation and then show that it is signi

magnitudes in our nal sample are in the range m

R

cantly biased to low values The number of elds which show

asso ciated galaxies is then quantied Section assesses the

validity of our results we can think of no reasonable expla

nation other than gravitational lensing and compares them

Image Catalogues

with previous work We then go on to lo ok at the prop er

The CCD images were pro cessed and calibrated using the

ties of individua l lensing galaxies and of the p opulation as a

y

whole The signicance for is discussed Finally

IRAF image analysis software The FOCAS faint ob ject

Section presents a summary of the most imp ortant features

classicatio n and analysis system package Valdes

of our results

was then used to detect and classify images in each eld

We used the DAOPHOT package to detect and measure any

images very close to the quasar which were then added into

the FOCAS catalogues The magnitudes of all the ob jects

DATA

were then measured with the ap erture photometry routines

in IRAF All these pro cedures are describ ed in more detail in

Our data consist of Rband KronCousins CCD images of

Paper apart from the following mo dications which were

bright quasars observed at the Observatoire astronomique

made to avoid in bias in our catalogues

du Mont Megantic Quebec Most of these were part of the

study of MgI I absorption systems describ ed in Paper al

i We use a more conservative magnitude limit now de

though some ob jects are excluded from the present sample

ned as the magnitude of the brightest ob ject with a

b ecause we apply stricter selection criteria We also include

photometry error m mag in each frame This re

additional ob jects not in Paper Our observing pro cedure

sults in limits a few tenths of a magnitude brighter than

and data reduction are essentially the same as describ ed in

the previous denition the magnitude of the faintest

Paper with some mo dications that we describ e in this

ob ject with a photometry error m mag In fact

Section

the results are not sensitive to the exact value of the

magnitude error chosen It can b e reduced to mag

nitudes b efore the signal from galaxies asso ciated with

Selection Criteria

quasars b egins to decrease

ii We include only those ob jects which lie more than

To measure quasargalaxy asso ciations we require a sam

pixels from the edge of the eld This is to avoid incom

ple of bright quasars that is unbiased with resp ect to the

pleteness which might otherwise o ccur for bright ob jects

presence of galaxies near the quasars This condition means

which extend over the eld b oundary

that we must exclude ob jects from the sample in Paper

iii We have checked the extra ob jects included from the

and

DAOPHOT analysis to ensure they all have signicant

which were taken from references that only listed detections

detections all were in fact clearly visible in the raw

of MgI I absorption and may therefore b e biased We also

images

excluded the quasar since it was added to the

iv A new set of control has b een dened using an

Young Sargent Boksenberg compilation b ecause

ob jective algorithm to avoid any bias These satisfy the

it was known to b e gravitationally lensed and therefore was

following criteria distance from the edge arcsec

biased towards having a close galaxy the lens in this case

distance from the quasar arcsec and magnitude

To this list we add more quasars of these are

range m If more than one p er eld

R

from the Kiso survey see Wegner Swanson b They

satised these criteria one of them was chosen at ran

were selected by colour and morphological criteria from op

dom In some cases no star satised these criteria so

tical photographic plates and have no bias to the presence

only elds have control stars

of galaxies or absorption The remaining ob jects were se

lected at random from the Hewitt Burbidge cat

Table lists all detected ob jects within arcsec of

alogue sub ject to the magnitude and redshift constraints

each quasar The eect of the DAOPHOT analysis is to

describ ed b elow to ll a gap in our observing programme

add an extra galaxy close to the quasar in elds

Two of them were excluded from our statistical analysis as

they are b elow our redshift cuto see Section the oth

ers do not show a particularly close asso ciation of quasar

y

IRAF is distributed by the National Optical Obser

and nearestneighbor galaxy

vatories NOAO which is op erated by the Asso ciation of Univer

Combining the ab ove we have a sample of quasars

sities for Research in Astronomy Inc AURA under co op erative

agreement with the National Foundation satisfying the following criteria

Quasargalaxy associations 3

Table Observing details for the quasars

QSO type RA Dec z ref date exp fwhm phot m m

q so R lim

RX p

R

R

RX

R

C

R

C

CR

CR

C

C d

R

RX

C d

C

RX

OXR

OR d

R

R p

C

R

C

C

R

O

R d

R

RX d

C d

O

C

C p

O d

C d

CXR d

CR

C p

C

C d

R

OX

C

C dp

4 Thomas Webster and Drinkwater

Table continued

QSO type RA Dec z ref date exp fwhm phot m m

q so R lim

a CX

b C

C

RX

O

R

RX

R

C

R

C d

R

R

RX p

C

RX p

R

R

C p

C

C d

C

R

CX d

RX p

RX

C

RX

RX

R

R

RX

RX

R

RX

Notes to Table

quasar name discovery technique C color O sp ectral survey R radio X Xray RA and Dec

quasar redshift from Hewitt Burbidge reference see Table date observed UT

exp osure time s FWHM seeing arcsec photometry ag blank photometric p not photometric d

no DAOPHOT tting was p ossible quasar R magnitude limiting R magnitude

References for Table

Weymann et al Young et al Foltz et al Wegner McMahan Wegner

McMahan Tytler et al Sargent et al Hewitt Burbidge Wegner Swanson a Wegner Swanson b

Quasargalaxy associations 5

really are distributed at random then the s ought to b e uni quasargalaxy separation arcsec arc

formly distributed in the interval In practice we nd a sec arcsec and arcsec In

signicant bias towards small separations addition several galaxies were added to eld and

There are several p oints worthy of note one to eld however these quasars are of low red

shift and are subsequently omitted from the statistics see

i This denition of s diers slightly from that in Paper

Section Similarly stars close to the quasar are added in

There we assumed a Poisson distribution of galaxies of

several elds and some merged pairs are split into two The

known surface density N A This overlooks the fact

list given here diers slightly from that given in Table of

that the measured value of will b e scattered ab out the

Paper b ecause of the dierent selection criteria used

true value We then had

We also note that the quasar is multiply im

aged by gravitational lensing The DAOPHOT analysis re

s exp r

vealed two main comp onents to the quasar image and we

It is easy to see that these two denitions agree in the

have used the mean co ordinate of the two as the quasar

limit that N b ecomes very large In practice the dier

p osition We have also checked that the quasar was not in

ence b etween the two is small

cluded in the original reference b ecause it was known to

ii There are areas in each eld in which galaxies would es

b e lensed Note that we do not in fact detect the lensing

cap e detection These include regions close to the quasar

galaxy Christian Crabtree Waddell which is hid

and other bright stars The former will b e the most im

den under the quasar image

p ortant and once again will tend to reinforce our con

clusions In principle one should divide the useful area

of the chip into two regions at separations less than and

STATISTICS OF THE QUASARGALAXY

greater than r Then s would b e

ASSOCIATIONS

N

A r

s

In this section we will rst test the hypothesis that the

A

quasars and galaxies in our elds are indep endently dis

tributed in p osition which we will nd to b e strongly re

The eect of this change is to enhance the signicance

jected Then we will consider estimates of the number of

of the asso ciations as will b e discussed in Sections

quasars with an asso ciated excess galaxy

and b elow

iii If the galaxies are clustered in the eld then s will not

b e uniform In eect we will have a lower N than oth

The sparameter

erwise b ecause if one galaxy is lo cated at a distance

of greater than r from the quasar then there will b e a

The fundamental parameter which we choose to work with

higher probability that the others will also This raises

is the separation of the quasar and its nearestneighbour

the exp ected value of s and strengthens our conclusions

galaxy nng This has the advantages that its statistical

In fact clustering of galaxies in our data app ears to b e

prop erties are easy to compute and it weights each quasar

negligibl e see Section although there is signicant

eld equallyfor example a quasar which is lo cated b ehind

eldtoeld variation in the number counts This is to

a rich cluster of galaxies will not swamp the statistics

b e exp ected as a typical cluster will ll the frame even

In all tests for asso ciations the critical unknown is the

at z

surface density of galaxies This is likely to change dep end

ing up on the observational technique exp osure time seeing

Table shows the value of the sparameter for b oth

and p osition on the sky It is therefore dicult to combine

galaxies and stars which are brighter than the magnitude

data from dierent elds or dierent surveys For this rea

limit in each eld as describ ed in Section Also shown

son we normalise the background counts to the number of

are the number of detected ob jects the magnitude of the

detected galaxies in the same eld This removes all external

nng and its separation from the quasar We have also lo oked

bias which might aect the signicance of the asso ciations

at the results using a variety of brighter magnitude limits

The p ossibili ty of a bias introduced by our observational

As the magnitude cut is lowered so the number of ob jects

technique or data reduction is discussed in Section b e

decreases and the sparameter increases until such time as

low

the nng is itself excluded from the sample This will b e dis

Consider a circle of radius r ab out the quasar The prob

cussed in detail in the following Sections

ability that any particular galaxy do es not lie within the cir

cle is r A where A is the total area in which galaxies

could b e detected If we assume that the galaxies are scat

Testing for asso ciations

tered at random across the eld then the probability that

N

We adopt as our null hypothesis that the galaxies are ran

there is no galaxy within the circle is r A where N

domly distributed in each eld Then s should b e drawn

is the total number of galaxies Hence the probabili ty that

from a uniform distribution

the quasar and the nng have separation greater than r is

n

s

N

U

r

otherwise

s

A

Quasargalaxy asso ciations will tend to lower s to small val

We use two statistics to test for devi ues typically s We use the value of s corresp onding to the quasarnng sep

ation from U The rst of these is the KolmogorovSmirnov aration as our fundamental random variable If the galaxies

6 Thomas Webster and Drinkwater

Table Images within arcsec of the quasars

RA Dec sep cls m RA Dec sep cls m

R m R m

R R

QSO z seeing arcsec magnitude limit

g s

s s

fg s

fs s

s s

fs fs

Q s

s s

QSO z seeing arcsec magnitude limit

fg Q

s fs

fs s

s fs

g fs

s fg

s s

g s

QSO z seeing arcsec magnitude limit

s Q

fg s

s s

fs fg

fs g

fg fs

QSO z seeing arcsec magnitude limit

fg g

fs g

fs g

Q s

s fg

QSO z seeing arcsec magnitude limit

Q fg

s

QSO z seeing arcsec magnitude limit

fg fs

Q

QSO z seeing arcsec magnitude limit

g fg

g g

Q s

fg fs

g

Quasargalaxy associations 7

Table continued

RA Dec sep cls m RA Dec sep cls m

R m R m

R R

QSO z seeing arcsec magnitude limit

s g

fg fg

Q

QSO z seeing arcsec magnitude limit

Q fg

fs s

fs

QSO z seeing arcsec magnitude limit

g s

s s

Q

QSO z seeing arcsec magnitude limit

Q fs

QSO z seeing arcsec magnitude limit

g Q

s s

s

QSO z seeing arcsec magnitude limit

g s

s g

Q s

s

QSO z seeing arcsec magnitude limit

s g

s s

Q s

g

QSO z seeing arcsec magnitude limit

fs g

fs Q

fs fs

fs

QSO z seeing arcsec magnitude limit

fs g

Q s

g

QSO z seeing arcsec magnitude limit

s g

Q g

QSO z seeing arcsec magnitude limit

g Q

fs fs

g g

8 Thomas Webster and Drinkwater

Table continued

RA Dec sep cls m RA Dec sep cls m

R m R m

R R

QSO z seeing arcsec magnitude limit

s s

Q s

s s

QSO z seeing arcsec magnitude limit

g s

s g

g g

Q

QSO z seeing arcsec magnitude limit

s SAT Q

fg s

fs g

fs s

QSO z seeing arcsec magnitude limit

g s

g g

g g

Q

QSO z seeing arcsec magnitude limit

Q g

fg fs

QSO z seeing arcsec magnitude limit

Q g

s

QSO z seeing arcsec magnitude limit

Q g

QSO z seeing arcsec magnitude limit

g Q

s fs

s fs

QSO z seeing arcsec magnitude limit

s Q

s g

s

QSO z seeing arcsec magnitude limit

g fg

fs s

Q fs

fs

QSO z seeing arcsec magnitude limit

s s

fs Q

Quasargalaxy associations 9

Table continued

RA Dec sep cls m RA Dec sep cls m

R m R m

R R

QSO z seeing arcsec magnitude limit

fs s

Q fs

QSO z seeing arcsec magnitude limit

g g

Q

QSO z seeing arcsec magnitude limit

s fs

g s

Q

QSO z seeing arcsec magnitude limit

s fs

g Q

QSO z seeing arcsec magnitude limit

Q s

QSO z seeing arcsec magnitude limit

fs fs

Q fs

QSO z seeing arcsec magnitude limit

fs fs

Q s

QSO z seeing arcsec magnitude limit

g g

g s

Q

QSO z seeing arcsec magnitude limit

Q s

g

QSO z seeing arcsec magnitude limit

fg s

g fg

Q s

g fs

QSO z seeing arcsec magnitude limit

fg g

Q

QSO z seeing arcsec magnitude limit

fs g

g fs

Q

10 Thomas Webster and Drinkwater

Table continued

RA Dec sep cls m RA Dec sep cls m

R m R m

R R

QSO z seeing arcsec magnitude limit

fs s

fs Q

s fg

s g

QSO z seeing arcsec magnitude limit

fg s

Q

QSO z seeing arcsec magnitude limit

s s

Q g

QSO z seeing arcsec magnitude limit

fs fs

Q fs

QSO a z seeing arcsec magnitude limit

Q

QSO b z seeing arcsec magnitude limit

fg Q

fs fs

QSO z seeing arcsec magnitude limit

s s

Q

QSO z seeing arcsec magnitude limit

Q g

fs

QSO z seeing arcsec magnitude limit

s s

fs fs

s fs

Q s

g

QSO z seeing arcsec magnitude limit

g g

fs fg

g fs

Q

QSO z seeing arcsec magnitude limit

g Q

fs s

QSO z seeing arcsec magnitude limit

g Q

fg fs

s

Quasargalaxy associations 11

Table continued

RA Dec sep cls m RA Dec sep cls m

R m R m

R R

QSO z seeing arcsec magnitude limit

g Q

QSO z seeing arcsec magnitude limit

Q s

s g

fs fs

g

QSO z seeing arcsec magnitude limit

g fs

Q

QSO z seeing arcsec magnitude limit

Q g

fs

QSO z seeing arcsec magnitude limit

fs s

s Q

g fs

QSO z seeing arcsec magnitude limit

fs fg

g Q

g g

QSO z seeing arcsec magnitude limit

Q fs

QSO z seeing arcsec magnitude limit

g fg

fs g

Q g

fs

QSO z seeing arcsec magnitude limit

s fs

s SAT s

g s

fg fg

fg fs

g s

Q

QSO z seeing arcsec magnitude limit

g s

s s

fs fs

s fs

Q s

QSO z seeing arcsec magnitude limit

Q fs

fg

12 Thomas Webster and Drinkwater

Table continued

RA Dec sep cls m RA Dec sep cls m

R m R m

R R

QSO z seeing arcsec magnitude limit

s g

Q fg

g g

QSO z seeing arcsec magnitude limit

s Q

g g

s

QSO z seeing arcsec magnitude limit

Q s

QSO z seeing arcsec magnitude limit

fs g

g s

fs fs

s s

Q s

fs fg

QSO z seeing arcsec magnitude limit

fg s

Q fg

QSO z seeing arcsec magnitude limit

fs Q

g g

fg s

QSO z seeing arcsec magnitude limit

s fs

Q fs

g fs

QSO z seeing arcsec magnitude limit

g s

g s

Q g

QSO z seeing arcsec magnitude limit

fg Q

fs fg

fs fs

g fs

s s

g s

s g

s s

QSO z seeing arcsec magnitude limit

g fg

s s

Q

Quasargalaxy associations 13

Table continued

RA Dec sep cls m RA Dec sep cls m

R m R m

R R

QSO z seeing arcsec magnitude limit

fs s

s s

s s

s s

Q

QSO z seeing arcsec magnitude limit

s s

g Q

s fs

s s

g g

g s

g s

s g

s s

s s

s s

g s

s s

s

QSO z seeing arcsec magnitude limit

s fg

s fs

s fs

s fs

Q

QSO z seeing arcsec magnitude limit

fs Q

fs

QSO z seeing arcsec magnitude limit

fs fg

s g

fg s

Q s

QSO z seeing arcsec magnitude limit

g fg

g s

Q s

Notes to Table

The columns are as follows p osition relative to quasar in arcseconds of RA and Dec resp ectively

separation from quasar in arcseconds classication gal ax y g faint galaxy fg star s faint

star fs or quasar Q Categories fg and fs are ob jects selected at a xed instrumental magnitude

whose classicatio n we consider to b e very uncertain R magnitude relative measure of SN

of detection see Paper as for additional ob jects SAT means the stellar ob ject was saturated

14 Thomas Webster and Drinkwater

Table Nearestneighbour galaxy data for each quasar eld

QSO z mlim mqso mgal area N sep s LL

q 

Quasargalaxy associations 15

Table continued

QSO z mlim mqso mgal area N sep s LL

q 

a

b

Notes to Table

quasar name quasar redshift limiting magnitude measured quasar R

magnitude measured R magnitude of nng useful area of eld arcsec

number of galaxies on eld separation of quasar and nng arcsec s of nng if at quasar redshift

16 Thomas Webster and Drinkwater

We next discuss several asp ects of the quasargalaxy

distributio n in more detail

i One obvious explanation for the observed asso ciation

would b e if the galaxies were clustered around the

quasar itself We have tried to avoid this p ossibili ty by

rejecting all quasar elds where the quasar redshift is

less than unity However there is one eld with a low

value of s in which the quasar redshift is

quite low z and the nng reasonably faint

q

m Can we really state with condence that

R

the galaxy is not physically asso ciated with the quasar

One ob jective measure is the luminosity the nng would

have if it were at the quasar redshift we call this L

q

Its calculation is outlined in the App endix of Paper

In the ab ove case L L While this is large it is

q 

p erhaps not imp ossibly so for the dominant galaxy in

a cluster say We have tried imp osing the more strin

gent conditions L L and L L with the

q  q 

results shown in Table The eect of the rst con

straint is to admit two previously rejected elds while

eliminatin g three others including the one mentioned

Figure Histograms of the values of the sparameter for the

ab ove The number of elds with s drops by one

sample z

q

and the Binomial probabili ty increases to With

the higher luminosity cut the probability rises still fur

ther to and the asso ciations b ecome statistically

insignica nt Note however that the number of close

asso ciations p er eld is exactly the same for the orig test which lo oks at the maximum deviation of the cumula

inal z constraint it is just that there are fewer tive distribution of svalues as compared with a linear dis

q

tribution This has the advantage that it is nonparametric

admissible elds and so the signicance has decreased

Finally we ought to note that the pro cedure describ ed but unfortunately it is not particularly sensitive to the kinds

here introduces a slight bias although once again it acts of uctuations we exp ect It is more useful as a general

check that our analysis of the star distributio n and of ob jects

so as to strengthen our conclusions we should really

eliminate al l galaxies fainter than the threshold not around control stars do es not show any p eculiarities which

just throw out those elds in which the nng galaxy is might indicate an error in our pro cedures In no case do es

it give a signicant result and we do not rep ort the results

this faint b ecause otherwise they will add to the back

ground counts and increase s here To test sp ecically for nearby neighbours we split the

sample into two bins with s and s Then we

ii We considered the p ossibili ty that the catalogues from

calculate the probabili ty of getting the observed number or

which we drew our quasar sample were biased towards

more ob jects in the smaller bin given as our null hypoth

the inclusion of quasars which might have a nearby

esis that the distribution is Binomial with probabiliti es

galaxy For example the quasar had to b e

and of ob jects app earing in each bin resp ectively

eliminated from our sample as discussed in Section

In general however we would exp ect the observational The results are shown in Table for b oth galaxies and

bias to b e towards isolated quasars b ecause some selec stars and for various magnitude cuts as indicated in the

tion criteria favour stellar images To check for a bias we rst two columns Column shows which of the various cri

rep eated our analysis on two subset of quasars those in teria has b een used to try and eliminate elds in which the

which there are no known MgI I absorption systems in nng may b e at the quasar redshift The simplest of these is

cluding those quasars for which there is no absorption to limit the sample to quasars with redshifts greater than

line data and those in which there has b een an un unity others will b e discussed b elow We also reject elds in

successful search for MgI I absorptionthi s should bias which there are fewer than detected ob jects in addition to

against the presence of a nearby galaxy The results the quasar although this only o ccurs at bright magnitude

shown in Table do indeed show reduced signicance limits the third column gives the number of elds which

but once again this is largely due to the reduced size survive these constraints Next come the number of elds

of the sample The detection of nng with s for which s and the Binomial probability that this is

in the latter case corresp onds to only slightly consistent with a uniform distributio n Columns will b e

fewer than in the whole sample We conclude that there describ ed in Section b elow

is no evidence for a selection bias

Concentrating on the full sample we nd that the hy

iii The signicance of the asso ciations varies as the mag p othesis that the galaxy distribution is random is rejected

nitude limit is decreased The faintest magnitude limit at the p ercent condence level Figure shows that there

imp osed by the condition that the magnitude error b e is a signicant concentration of galaxies at low values of s

less than is As this is lowered so faint galaxies ie small separations This is an extremely robust conclusion

disapp ear from the catalogues and the values of s de and we can see no way of escaping from it

Quasargalaxy associations 17

Table Nearestneighbour statistics

sample constraints N N prob N range p notes

g

q g z

q

q g Lz L

q 

q g Lz L

q 

q g z a

q

q g z b

q

q g z c

q

q g z m

q R

q g z m

q R

q g z m

q R

q g z m

q R

q g z m

q R

q g z

q

c g z

q

q s z

q

c s z

q

q g z

q

q g z

q

q g z M

q q

q g z

q

q g z d

q

nngg z

q

nngs z

q

Notes to Table

samplegala xie s g or stars s around quasars q control starsc or nearest

neighbour galaxies nng constraints imp osed on the quasar redshift or absolute

magnitude on the redshift the nng would have if at the quasar redshift or on the

limiting magnitude number of useful elds number of nng or nns with s

Binomial probabili ty of N given N number of excess galaxies estimated from

N and N p ercentile range for N fractional lensing path over which a

g

galaxy with luminosity L could have b een detected further notes as listed



b elow a unsuccessful search for MgI I in quasar sp ectra b unsuccessful or no search

for MgI I in quasar sp ectra c radioloud quasars d area correction for hole under quasar image

18 Thomas Webster and Drinkwater

vi A further check is provided by the distributio n of stars

around b oth quasars and control stars These are also

consistent with b eing random but once again show a

small decrement in the number of nearestneighbour

stars nns with s

vii It is vital to our conclusions that the sensitivity to de

tection of faint ob jects is indep endent of p osition on

the eld For example vignetting might lower the back

ground galaxy count relative to that under the quasar

and so give articially low values of s To some extent

we have checked this by the adoption of control stars

However a further check is provided by the measure

ment of the surface density of galaxies and stars in dif

ferent parts of the eld as shown in Table

The mean number density of galaxies avoiding the re

gion within arcsec of each quasar is approximately

galaxies p er square arcsecond b oth for the

whole eld and for the central region only approxi

mately one third of the total area If we include the re

gion around the quasar the equivalent numbers are still

consistent with the original gure but go up slightly

Figure A histogram of the separations of the quasars and the

reecting the excess of nng at close separations

nngs in physical units for the sample z

q

The data for the stars is not so clearcut There do es

app ear to b e a marginally signicantly greater den

sity of stars near the centre of the frame rather than

around the edge This excess is limited to the bright

crease slightly see Table Eventually however the

stars however which have very large images whose radii

nng themselves are eliminated and the number with

are greater than the pixel margin which we exclude

s drops The signicance of the asso ciations p eaks

from the edge of each eld when compiling the image

at m then declines rapidly at lower magnitude

R

catalogues see Section The catalogues are there

cuts This suggests that many of the nng are at the faint

fore incomplete around the edge of the eld for these

end of the magnitude distribution see Section It

bright ob jects When we restrict the analysis to stars

also suggests that we may b e missing many nng which

with m then they do app ear to b e uniformly

R

are b elow the magnitude limits of our elds some of

distributed

which do not extend b elow m an attempt is

R

made to correct for this in Section b elow

viii It is obvious that we cannot detect ob jects very close to

the quasars and that this will adversely aect the statis iv The distribution of quasarnng separations for a mag

nitude limit m is shown in arcseconds in Fig

tics One estimate of the missing numbers taken from

R

ure Also plotted is the Poisson distribution exp ected

the number of detections around control stars given

ab ove was nng with s p er elds This is from the mean galaxy surface density averaged over all

elds These two distribution s agree in the KStest with

consistent with number density data if we lo ok at the

a probabili ty of The excess of nng with separa

number density of nng around control stars then this

shows a decrement at small separations see Table tion less than arcsec is signicant at the p ercent

level based on the assumption that the probability dis

In elds the number of missing galaxies is

tribution is Binomial However raising the background

and within circles of radius and arcsec

around the control star resp ectively None of these de normalisation by just p ercent increases these proba

bilities to and resp ectively This emphasises

ciencies is signicant but they also suggest that we are

the diculty of using an external normalisation of the

missing one or two foreground galaxies from our sample

of quasar elds Adding two extra ob jects to the s galaxy surfacedensity to try to detect excess galaxies

bin would increase the signicance of the asso ciation to v As a check on our results we also analysed the distri

bution of galaxies around control stars as dened in

One way to correct for the missing area around quasars Section We show one set of results in Table but

is to allow for it in the denition of s as describ ed this is representative of every case we have tried There

in Section The diculty with this is in deciding are fewer elds than for the quasars so we would not

how much area is hidden underneath the quasar One exp ect a signicant result however the number of nng

crude estimate for galaxies is that the quasargalaxy with s is now less than one would exp ect for

separation must b e r m arcsec where m is a random distribution This is an indication that our

R R

the measured quasar magnitude This relation is taken sample is incomplete and is actually biased against the

from the lo cus of p oints in the r m plane but takes detection of galaxies near quasars We will attempt to

R

no account of seeing or limiting magnitude Using this estimate the number of missing nng b elow but from this

relation to correct the area no further nng are added to test alone it app ears to b e ab out one p er thirty elds

the s bin and so the signicance do es not change with a large uncertainty

Quasargalaxy associations 19

with the manner in which the sample is chosen but is ab out

Table Number density of ob jects to a magnitude limit of

one tenth for the constraint z After correcting for

q

m on various parts of the elds as describ ed in the text

R

incompleteness around the quasar this fraction may rise to

as much as one sixth Given that the excess is due to gravita

sample region number density

tional lensing it is then p ossible to estimate the probability

galaxies all

that the lensing galaxy would have b een detected by our

elds central

survey and hence correct for the unseen comp onent un

allqso

der this hypothesis our b est estimate is that one quarter to

centralqso

one third of the quasars in our sample are magnied into it

The allowable range is much wider than this stars all

To estimate the number of excess galaxies we mo del

elds central

the galaxies as two separate p opulations a group of asso ci allqso

ated galaxies which are clustered close to the quasar and a centralqso

background p opulation which are distributed randomly over

stars all

the eld The cumulative distribution s for the probabili ty of

elds central

nding the nng of either p opulation within separation r we

m allqso

R

take to b e g r and f r resp ectively Then the joint cu

centralqso

mulative distribution is g f f g Next

galaxies arcsec

supp ose that out of a total of N elds there are N which

tot g

near control arcsec

have asso ciated galaxies which could have b een detected

stars arcsec

The cumulative distribution of nng separations is then

elds arcsec

N r N N f N f g

tot g g

galaxies arcsec

The distribution g of asso ciated galaxies is unknown

near quasars arcsec

however we may assume it to b e centrally concentrated ie

with z arcsec

q

arcsec see Section Then g for r

elds arcsec

N r N N f N for r r

tot g g nng

Finally if we use s as the radial coordinate instead of r

Density units are arcsec

then f is uniform and we have an expression in terms of one

free parameter N By comparing this distribution with the

g

ix Finally we note that our original intention was to se

observed separations we can determine a condence range

lect a quasar sample which would b e optimal for the de

for N

g

tection of gravitational lensing if it were present The

For a given value of s the most likely value for N is

g

need for a large sample weakened this aim somewhat

simply

We also analysed the data for two subsets closer to the

N sN

tot

original ideal and the results of these are also shown in

N

g

s

Table Restricting our attention to quasars with red

shifts greater than we nd a more signicant result

If s coincides with the value for one of the nng then this

and a greater number of excess galaxies p er quasar

should b e mo died to read

whereas the more promising cut on absolute quasar

N sN

tot

N

magnitude M gives a lo oser constraint but

g

R

s

ab out the same number of excess galaxies p er quasar

Note that these expressions can b e negative It is p otentially

We note that there is at least one eld where

more useful to to construct a condence range for N which

g

the quasar is multiplyimaged and the lensing galaxy is

we do by the following pro cedure First we pick a value of

known but is not detected by our analysis

s s and hence N N s Then we run through a

o o o

In conclusion we nd a signicant asso ciation of quasars

range of p ossible values for N For each N the distribution

g g

and nearestneighbour galaxies which dep ends solely on

of measured values of N is

counting ob jects on our frames Variations in the galaxy

Prob fN N g IN N N N s

o g tot o

surfacedensity seeing magnitude limit etc make no dif

ference to our conclusions We have checked for a large va

where I is the Incomplete Beta function We reject all values

riety of p ossible adverse biases none of which app ear to

of N which make this probability less than p ercent or

g

b e present in our data The inabili ty to detect galaxies very

greater than p ercent

close to the quasars leads to an underestimate of the number

Figure shows the results of these calculations for the

of close asso ciations and strengthens our conclusions

sample dened by z The solid line shows the ex

q

p ected value of N as a function of s while the dotted lines

g

show the p ercent condence range the lower dotted line

The number of excess galaxies

is zero Note that the predicted N go es to zero at small

g

Having established that there is a p opulation of galaxies as separations b ecause our assumption that g breaks down

so ciated with quasars we next estimate how many quasars there N should tend to a constant at larger values of s but

g

have such an observed excess galaxy This number varies the condence interval is large and b ecomes unconstraining

20 Thomas Webster and Drinkwater

suggest that the raw gure of excess galaxies should b e

revised upwards to at least to allow for missing fore

ground plus plus missing asso ciated galaxies

The redshift range in which we might detect a nng do es

not extend all the way out to the quasar indeed we have

delib erately forced this to b e the case Given the lensing

hypothesis we can predict the exp ected redshift distribution

of lensing galaxies and hence correct for the unseen com

p onent The lensing probability p er unit redshift interval is

prop ortional to

2 2 2

z z z

q

q

2 2

z z

25 25 25

z z z

q

q

25 35

z z

where the comoving number density of galaxies is assumed

to evolve as z and we assume a deceleration parameter

q Taking and q gives a minimum

observed fraction although it turns out that there is little

dierence b etween the predictions for dierent values of q

We have taken a nng luminosity of L to evaluate the



fractional lens path p which is accessible by our observa

tions in each eld as this is the typical luminosity of those

Figure The number of excess galaxies versus s for the sample

nng with known redshifts see Section The results are

z The dotted lines show the p ercent condence range

q

shown in Column of Table If we use the p to correct our

assuming a distribution of the form discussed in the text The

lower limit is zero

estimate of the number of excess galaxies for the basic sam

ple z then it rises once more from to This

q

is the basis for our statement that as much as one third of

as s tends to unity The exp ected value of N at s is

g

our quasar sample may b e lensed Using L as a more con



shown in column of Table It is dicult to know how to

servative estimate of the nng luminosity gives lensed

combine the constraints provided by dierent values of s as

quasars or just under one quarter of the whole sample

they are clearly not all indep endent Column of Table

We can carry out a similar sort of analysis for other

shows the allowable range for N at the largest value of s

g

samples The subset of quasars with M gave

R

which is less than

excess galaxies in elds This gets revised upwards to

The numbers in the Table need to b e corrected b efore

to correct for incompleteness and then to allow for the

we can get an accurate estimate of the number of elds with

p searched This is ab out the same fraction as for the full

an excess galaxy Firstly we have to correct for incomplete

sample Those quasars with z on the other hand

q

ness We have already estimated in Section that ab out

give a larger signal The numbers in this case are excess

one eld in thirty is missing a foreground galaxy hidden un

galaxies in elds rising to and after correcting

der the quasar image In addition there will b e asso ciated

for incompleteness and the p The fraction of highredshift

galaxies which have also b een missed It is hard to ascertain

quasars in our sample which are lensed could b e as large as

their number as we do not know the intrinsic distribution of

impact parameters The measured number density of galax

ies around quasars to a magnitude limit of m shown

R

in Table increases down to approximately arcsec then

declines at smaller separations Let us split the data up into

DISCUSSION

bins arcsec arcsec arcsec and

Validity of the results

arcsec As a rough estimate consistent with our earlier anal

ysis let us assume one missing galaxy in the inner bin and

We pause here to reconsider the p ossibil ity that there may

one half in the next smallest This corresp onds to zero proba

b e a aw in our arguments

bility of detecting a foreground galaxy at radii less than

i The most obvious and serious ob jection would b e that arcsec increasing to complete detection at radii exceeding

we started with a biased quasar sample The quasars arcsec The number density of galaxies in each of the four

were selected from catalogues which have b een used to bins is then and

study the statistics of absorptionli ne systems We did galaxies p er square arcsecond resp ectively Now at the very

not select the quasars from within this list as we ob least we would exp ect the observed number density is the

served all of our p otential targets sub ject to constraints inner bin to b e equal to that in the next one out which

on telescop e time and p osition However the traditional would imply at least missing galaxies In fact this num

colour and morphological criteria used to select quasar b er is very much a lower estimate b ecause we exp ect to miss

candidates may have introduced bias For example if some asso ciated galaxies at radii larger than arcsec and

only stellar images are selected as quasar candidates b ecause there is every reason to supp ose that the number

a bias will b e introduced against quasar images with density of such ob jects should continue to rise steeply to

a nearby galaxy which is within ab out a magnitude of small separations As a conservative estimate therefore we

Quasargalaxy associations 21

tion of the distribution agrees with observations Colless the quasar magnitude Or if the quasar colour is red

private communication and with our theoretical prediction dened when seen b ehind a foreground galaxy then the

based on an unevolving galaxy p opulation and changes only quasar will not b e selected as part of a sample of UV

slightly as the galaxy type and slop e of the luminosity excess images Both these eects will mean that we have

function are varied The distribution of galaxy magnitudes underestimated the number of quasars with asso ciated

is consistent with the theoretical one except at faint magni galaxies

tudes m where incompleteness and p ossible mis ii Is it p ossible that our selection criterion for faint images

R

identication of galaxies as stars is clearly apparent or the discrimination b etween stars and galaxies is al

Also shown in Figure are the number countss of all tered in the presence of a nearby bright p oint source

nng and of those with s These show a slight bias to To check for this p ossibili ty we rep eated our analysis for

the sample of control stars dened in Section The

faint magnitudes but the numbers are so small that they are

statisticall y indistingui sha bl e from the whole p opulation results are presented in Table for a single magnitude

It is p ossible to determine neither for the cut but similar results are obtained in every case we

have tried the distribution of stars and galaxies around

nng nor impact parameters b etween the nng and the line

control stars is consistent with a Poisson distribution

ofsight to the quasar without knowing the distance to the

nng We can get such information for a partial subset of all over the whole eld

iii One p otential source of error would b e the inclusio n of

the nng if we assume that they are asso ciated with MgI I

galaxies which are at the quasar redshift We circum

absorption lines in quasar sp ectra where detected This hy

vent this p ossibility by including only those elds in

p othesis has b een discussed in Paper There are just

which the quasar redshift is greater than unity As an

nng which we are condent can b e linked with the MgI I

alternative we also considered eliminatin g those elds

absorption line systems Their luminosities are consistent

for which the nng would have a luminosity of less than

with b eing drawn from a Schechter luminosity function with

L or L if at the quasar redshift This calcula

L although the signicance of this is weak and L

 



tion describ ed in the App endix of Paper applies a

the impact parameters extend to at least h kp c Note

standard kcorrection but do es not allow for evolution

that six of these quasars were biased with resp ect to the

of the stellar p opulation The overdensities in each case

presence of MgI I absorption in their sp ectra and are there

are similar

fore omitted from the current sample However we do not

iv We have checked the sensitivity to detection of faint ob

exp ect that this bias will aect the prop erties of the nng

jects as a function of p osition on the eld For example

No new quasars with known absorption redshifts have b een

vignetting might lower the background galaxy count rel

added to the sample and so we cannot improve on these

ative to that under the quasar and so give articially low

results

values of s The results of our tests however eliminate

If we assume that each of the nng with s has a

this p ossibil ity When averaged over the whole sample

luminosity of L typical of the values found in Paper



the mean surface density of galaxies down to m

then the set of impact parameters for a at is

R

for the whole frame but excluding the region within

and

arcsec of the quasar is arcsec whereas the

h kp c Of these we exp ect ab out to b e random

density within the central third of the eld once again

asso ciations These numbers are consistent with our conclu

avoiding the quasar is arcsec These two

sions from Paper that the impact parameters extend out

values agree within the counting statistics A similar

to ab out h kp c

calculation for the region within arcsec of the quasar

We have checked for clustering of galaxies around the

pro duces a higher value arcsec and rep

nng by doing a nearest neighbour analysis centred on the

resents an excess of ab out galaxies in the elds

nng itself see nal entries in Table The distribution of

with z

svalues is uniform even for nng with s Note how

q

The equivalent numbers for faint stars m are

ever that even at a redshift of the width of our eld

R

consistent with a uniform distribution over the whole

corresp onds to just Mp c and so a mo deratelysized group

eld

would ll the whole frame

Prop erties of nearestneighbour galaxies

Cosmological implications

The measured number counts of galaxies and stars down to

The fraction of quasars in our sample which p ossess an

m avoiding the region within arcsec of the quasar

R

excess galaxy is of order one third although the allow

in each eld is shown in Figure Also shown is a theo

able range is large As we have taken every precaution to

retical distribution based on a constant comoving Schechter

eliminate galaxies which are physically asso ciated with the

luminosity function

n o

quasars we interpret this result as b eing due to lensing of

L L L L

dN d exp

the quasars which would otherwise b e to o faint to b e in

L L L L

   

cluded in our sample

A number of authors eg Schneider and references where we have taken L h L and



therein have made theoretical predictions of the exp ected L h L Mp c the Hubble constant H

number of quasargalaxy asso ciations This dep ends up on h km s Mp c and we have included the colour and

two main factors the rst of which is the total asso kcorrections appropriate for an Sb c galaxy see the Ap

ciated with galaxies the mo dels assume all the mass of the p endix of Paper for details The form and normalisa

22 Thomas Webster and Drinkwater ucinfrtesm oa ube fo jects ob of numb er total same the for function o h ai apeadfrwhich for and sample basic the for Figure h esrdlmnst ucindw oamgiuelmto for of limit magnitude a to down function luminosity measured The s Telfms i nec aecnan h oa ube fo et with jects ob of numb er total the contains case each in bin leftmost The a l aais b galaxies all l trc stars all m ersegborglxe o the for galaxies nearestneighb our R Tedte iesostetertclglx luminosity galaxy theoretical the shows line dotted The ai sample basic z q d

nng Figure

Quasargalaxy associations 23

tion eects as discussed by Canizares might come galaxy is in the form of compact ob jects The calculation s

into play Thus for example the sp ectra of the microlensed usually mo del galaxies as singular isothermal spheres which

quasars might show an enhanced blue continuum or weaker have a single free parameter the velocity disp ersion The

emission line equivalent widths We have tried analysing the galaxies are assumed to b e distributed uniformly in space

radioloud quasars separately ie all those agged with an with luminosities drawn from a Schechter function as de

R in Column of Table The result shown in Table scrib ed in Section These luminosities are related to the

is more signicant than for the sample as a whole This is velocity disp ersion using the FaberJackson relation Faber

esp ecially surprising given the smaller number of elds It Jackson

is p erplexing that the asso ciations seem more signicant for The second input into the theoretical calculation is the

the radioloud quasars since it is generally thought that the intrinsic quasar luminosity function A broken p owerlaw

radio emission region is substantially larger than the optical Boyle et al is the usual description however there has

region and is therefore unlikely to b e microlensed In princi b een a recent suggestion by Hawkins Veron that

ple amplication or the lack of it can b e used to constrain the quasar luminosity function may remain steep rather

the mass of putative microlenses than turning over at m This would mean that the

oretical predictions of the eects of lensing have b een to o

low Note that if a signicant number of bright quasars are

lensed then the intrinsic luminosity function may well b e

steep er than the observed one Webster

CONCLUSIONS

Schneider calculates several quantities including q the

In this pap er we search for galaxies lying close to the lineof fraction of quasars which have a galaxy within a given radius

sight to a sample of quasars The quasarnearest neigh

under the assumed lensing mo del and f the ratio of this

b our galaxy separation is describ ed by the sparameter number to that exp ected in the absence of lensing We can

which is designed so as to give a uniform distribution for a use the ratio f q f to estimate the fraction of quasars

random galaxy p ositions on the eldwe nd a signicant

which show an excess galaxy It is dicult to translate these

bias to low values of s ie small separations We have lo oked theoretical estimates into numbers which can b e compared

at many p ossible biases which might cause this result but with the observations as for example the predictions take

can nd no plausibl e explanation other than gravitational

no account of kcorrections However for parameters which

lensing which may magnify faint quasars into our sample seem representative of our sample we nd a fraction

The fraction of quasars which p ossess a nearby excess this is to b e compared with our measured value of but

galaxy is ab out one sixth but rises to one third once we cor with very large error bars With more precise theoretical

rect for the fraction of lensing galaxies which would b e to o mo deling one might hop e to turn the calculations around

faint to b e detected This result has implications b oth for the and use the observations to constrain the mass fraction of

intrinsic quasar luminosity function and for the mass density compact ob jects in galaxies

of lo ckedup in compact ob jects capable of pro duc If the mass asso ciated with luminous galaxies is mostly

ing the observed microlensing We note however that the in the form of CDM or some other elementary particle then

allowable error range for the fraction of lensed quasars is only macrolensing will b e imp ortant and high amplication

large events will only o ccur when the source is near a critical line

in the source plane However if the asso ciated mass is in the

Future work must involve obtaining as many sp ectra as

p ossible for the galaxies near to the quasars in our sample form of compact ob jects then high amplication events can

o ccur at much larger angular radii than the critical radius

Redshifts are essential b oth to test the lensing hypothesis

alb eit with lower probabiliti es Integrated over a wide area

and to determine the prop erties of the excess galaxies We

would also b e able to investigate more accurately the link these probabiliti es can b ecome signicant There have b een

several observational results which suggest that microlensin g

b etween galaxies and MgI I absorption lines discussed in Pa

of quasars might b e imp ortant Francis Koratkar

p er

nd that the dierences in UV sp ectra b etween low and

highredshift quasars are explained if p ercent of the high

redshift sample are microlensed and Hawkins has

suggested that the longterm variability seen in the ma jor

Acknowledgments

ity of quasars may b e the result of microlensing by brown

PAT and RLW would like to thank CITA and MJD would dwarfs The p ossible detection of MACHOs in the halo of our

like to thank the Physics Dept Laval Universitefor supp ort galaxy Alco ck et al Aub ourg et al strength

during the early stages of this pro ject MJD thanks MESS ens the p ossibili ty that microlensing might contribute sig

Quebec Government for travel supp ort and the SERC for nicantly to quasargalaxy asso ciations If many of the as

supp ort while a visitor at the Astronomy Centre Sussex so ciations are due to microlensin g by compact ob jects in

The data were obtained at lObservatoire du Mont Megantic extended regions with optical depths to lensing of

Queb ec which is supp orted by grants from NSERC Cana then this would explain in a natural way why they are much

dian Government and FCAR Quebec Government We more common than multiple images We note in passing that

are grateful to Bernard Malenfaut and Ghislain Turcotte the large number of wideseparation binary quasars which

for their assistance at the telescop e and to Mme Brault for are unveried as lenses might b e a link in this sequence

her excellent cuisine which kept us fortied Part of the data This idea has b een explored by Bartelmann and Schneider

analysis was carried out on the STARLINK minor no de at

Sussex using the IRAF software supp orted by the NOAO If microlensing is imp ortant then dierential amplica

24 Thomas Webster and Drinkwater

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