The NOT GL survey for multiply imaged quasars

12 Pages·0.28 MB·English

by  A. O. Jaunsen

A&Amanuscriptno.
(willbeinsertedbyhandlater) ASTRONOMY
AND
Yourthesauruscodesare:
ASTROPHYSICS
02(12.07.1;12.12.1;12.04.1;11.17.3) 31.1.1995
The NOT GL survey for multiply imaged quasars
A.O.Jaunsen1 ,M.Jablonski2,B.R.Pettersen3,andR.Stabell1
?
1 InstituteofTheoreticalAstrophysics,UniversityofOslo,P.O.Box1029,Blindern,N-0315Oslo,Norway.
2 NordicOpticalTelescope,ObservatorioRoquedelosMuchachos,Apartado474,E-38700SantaCruzdeLaPalma,Spain.
3 StatensKartverk,N-3500Hønefoss,Norway
January31,1995
Abstract. Agravitationallens(GL)-search program,initiated and observational conditions at the site. In Section 3, we in-
in1990 at the Nordic Optical Telescope (NOT), has revealed vestigate our abilities to detect GL-systems and characterise
severalpossibleGL-candidatesamongasampleof168quasars the NOT angular selection function, defining the area (in the
(QSOs), chosen from three lists compiled by C. Hazard, D. magnitude difference-angular separation plane) within which
5ReimersandJ.Surdej,respectively.Someofthesecandidates, a pair of point-likeimages is considered to be a possibleGL
9
selected for having close companions (within 5 arcseconds), candidateand usedintheanalysis.InSection4,weintroduce

nwereimagedinseveralfiltersandtheircolourscompared.Low theSingularIsothermalSphere(SIS)galaxymodel,employed
a
dispersionspectraofthemostpromisingcandidateswerealso inour statisticalmodel. Furthermore, wealso includethe im-
J
obtained at the NOT and ESO New Technology Telescope portantmagnificationbias, whichaccounts forthe increasein
1
(NTT). None of these has proved to be strong candidates of theobservedfrequencyoflensing.ThepossibleGL-candidates
3
gravitational lensing effects. We present this new sample of foundintheNOTsamplearepresentedinSection5,wherewe

QSOs and combineit withpreviouslypublishedoptical QSO alsogiveabriefdiscussionofeachcandidate.FinallyinSection
7
0samplesinastatisticalanalysistoyieldconstraintsonflatcos- 6wepresentthetotalcombinedsampleandtheconstraintsour
1mologiesandgalaxyvelocitydispersions.Finally,bysimulat- computationsimposeongalaxyvelocitydispersionsandonthe
1inglargersamplesofquasarsandgravitationallenses, wedis- baryonic-matterdensityparameter (seeCarrolletal.1992).
0cusshowthe uncertaintiesaffectingourpresentresultswould Wealsobrieflycommentontheinfl(cid:10)uMenceofdarkmatter(DM)
5
bechanged. on velocitydispersions in gravitationallensing statistics. The
9
decrease intheuncertaintiesofourresultswhenthesampleis
/
h
Key words: Cosmology: gravitational lensing – large-scale artificiallyincreasedareinvestigatedbyapplyingthestatistical
p
structureoftheUniverse–darkmatter–Quasars:general modelonsyntheticsamples.
-
o
r
t 2.TheQSOsample
s
a
TheobservedQSOsample(listedinTable 1andillustratedin
1.Introduction Fig.1) was selected from 3 different QSO lists provided by
C. Hazard, D. Reimers and J. Surdej, respectively. The latter
One of the (several) aims of GL-surveys is to perform statis-
one consists of QSOs chosen from the Ve´ron-Cetty & Ve´ron
tical analysis of the lensing frequency and of the lensed im-
(1991)catalogue, whiletheothertworesultfromindependent
ageconfigurations(morphology),toderivevariousfundamen-
QSOsurveys.SomeoftheQSOsinthetwofirstsampleswere
tal parameters for a universe model. In Section 2, we discuss
difficulttoidentifyintheimagestaken,duetocrowdedCCD-
and present our sample of QSOs. We first discuss the correc-
fields. To securely identify the QSO in such cases, we have
tion for GL incompleteness in the QSO samples and define
obtainedfindingchartsfromthedigitisedPalomarAtlaswitha
the principles leading to our selection of GL-candidates. Our
magnitudecutoffatabout 21.Thisallowedustocompare
chances of findingGL-systems depend on how thesample of V '
theobservedfieldwiththatofthePalomarAtlasanddetermine
QSOsischosen.Furthermore,thelensingprobabilityisdepen-
thepresence(ornon-presence)ofthetargetQSO.
dent uponthe detectabilitylimitsimposed by the instruments
Most of the larger optical GL-surveys optimise the ef-
fectiveness of finding GLs in their surveys by including in-
Sendoffprintrequeststo:A.O.Jaunsen
Presentaddress:Nordic Optical Telescope,ObservatorioRoque trinsically bright QSOs ( 27). Such QSOs are often
?delosMuchachos,Apartado474,E-38700SantaCruzdeLaPalma, called highly luminous qMuaVsar(cid:20)s ((cid:0)HLQs) (Surdej et al. 1987).
Spain;e-mail:[email protected] The strong correlation between lensing probabilityand abso-
2 A.O.Jaunsenetal.:TheNOTGLsurveyformultiplyimagedquasars
itationallensing,becausecloselyseparatedGL-systemswould
appearelongatedunder(sub)-criticalseeingconditions1.
Dependingontheseeingconditions,whichdictatetheres-
olutionanddetectionofsmallseparationGLsatground-based
observatories, thislatterselectioneffect mightplay animpor-
tantroleinGL-surveys.Wewillthereforeconductteststhrough
simulationsinSection3toestimatetheeffectsoflimitedresolu-
tiononthedetectabilityofcandidatesanddetermineanangular
selectionfunctionwhichdescribesthevalidityofourobserva-
tionalconclusions.
Furthermore,acolourcriterionusedinsomeQSOsurveys
maybiastheselectionofQSOs.AQSOsuperposedona(lens-
ing)galaxyissubjecttoareddeningeffect(fromtheredcolour
ofthegalaxy)whichmay endangeralensed QSOfrombeing
recognised as a QSO, thereby affecting the completeness of
the QSO catalogue. This effect was pointedoutbyKochanek
(1991), where as much as 30% of the gravitationally lensed
QSOsarebelievedtobeexcludedfromQSOcataloguesdueto
Fig.1.Magnitude-redshiftdistributionofthe168QSONOTsample, sucheffects.Surdejetal.(1993)correctedforthiseffectintheir
eachobjectindicatedby . ThesmalldotsrepresenttheQSOsfrom
computationsofthelensingfrequenciesfromGLsurveys,thus
(cid:3)
theVe´ron-Cetty&Ve´ron(1991)andHewitt&Burbidge(1993)cat-
multiplyingtheopticaldepthbyacorrectionfactor =07.
alogues.Thesolidlinesindicatetheabsolutemagnitudes(cid:0)27&(cid:0)30 This factor is included in the present computationSsc,aats mo:st
foranEinstein-deSitteruniversemodel( =1 =0).
(cid:10)M ;(cid:10)(cid:3) oftheQSOsinvestigatedherearechosenundersimilarcondi-
tions.Thisfactorwillthereforebeincludedintheopticaldepth,
deducedinSection4.
lutemagnitudeisdiscussedinSurdejetal.(1993).Mostofthe 3.AngularSelectionFunction
QSOsfromoursample(markedby inFig. 1)tendtoliebe-
(cid:3) Severalimportantissuesmustbetakenintoconsiderationwhen
neaththelineindicatingabsolutemagnitude = 27.The
irregularpatternof the absolute magnitude liMneVsis d(cid:0)ue tothe we define the angular selection function (ASF) (Surdej etal.
1993).Firstwemustestimatethelimitationsonresolutionand
correctionforemissionlinesappearingintheV-filterforvarious
dynamical range(detectable magnitudedifferences), affecting
redshifts.Theemissionlinecorrection,K-correctionandcom-
ourabilitytoresolveclosecomponentsandlargemagnitudedif-
putationof absolutemagnitudesarediscussed inVe´ron-Cetty
ferences, respectively.Theselectionfunctionwillthensimply
&Ve´ron(1991).
describe our observational windowin the angular separation-
magnitudedifferenceplane.WededucetheASFforourpartic-
The selection of a flux limited sample of HLQs to max-
ularsurveyinthefollowingsubsections.
imisethechances of findingGLs isconsistentwiththe previ-
ouslypresentedsamplesbySurdejetal.(1993),Cramptonetal.
(1992),Yeeetal.(1993)andMaozet al.(1993)(hereafterthe 3.1.Smallseparations
SCYMsample).Amongthe645HLQsfromthissample,only
Fig.2illustratesthedistributionofthefullwidthathalfmax-
31wereduplicatedinthe168HLQNOTsample, leaving137
imum (FWHM) values for each of the 229 observations of
unduplicatedquasars. The median apparent magnitude of the
the 168 objects. The seeing is distributedin a range between
NOT sample is 175, the median redshift is 20
and the medianmabVsol(cid:24)ute m:agnitude is 27z7 ((cid:24)usin:g 05 20arc-second,indicatingthehighlyvariableimagequal-
: (cid:0) :
=1 =0and =50kms 1MMpcV1)(cid:24). (cid:0) : itytypicalofground-basedobservatories.Thisimpliesthateach
(cid:10)M ;(cid:10)(cid:3) H0 (cid:0) (cid:0) potentialGLcandidatehasadifferentdetectabilityrangeinthe
angular separation-magnitude difference plane. These differ-
Among the lens surveys conducted in the previous years,
ences obviously affect the possibilityof detecting small sep-
most of the objects have been selected from already existing
aration GL-candidates ( 1 0). It is therefore necessary to
00
QSO catalogues. It has been suggested that many QSO cat- (cid:18) < :
weigheachobservedimagebyitsimagequality(seeing-FWHM
alogues are biased against the inclusion of elongated or dif-
value). This is done by estimating the maximum detectable
fuseQSOs,becauseoftheselectionroutinesusedinsearchfor
magnitudedifferencebetweentwopoint-likecomponentsasa
QSOs. According to Kochanek (1991), some GL candidates
and real GL-systems are lost insurveys searching for GLs as 1 In fact bearingin mind the highlyvariable seeingandpoor res-
adirect consequence of the inherentselection effects in QSO olution of sky-plates, from which the QSOs are often chosen, the
catalogues.ElongatedQSOsareinterestingcandidatestograv- incompletenessaccusationsofQSOcataloguesseemsensible.
A.O.Jaunsenetal.:TheNOTGLsurveyformultiplyimagedquasars 3
Table1.Thecompleteobservationallistofthe168QSOsintheNOTsample.Seethenotesattheendofthistableforadescriptionofthe
columns.
Object RA1950 Dec1950 F FWHM z m Sep GLc Note
mV (cid:1)
H0000-263 000049.45 -261959.2 I 1.11 4.11 17.5 0 1
H0000+158 000325.0 155304 R 1.5 0.45 16.4 0 1
H0007+1041 000728.06 104125 R 0.71 2.2 18.0* 0 2,3
H0017+154 001750.5 152423 R 1.3 2.01 18.2 0 1
H0029+073 002943.35 072200.0 R 0.71 3.26 18.4 0 1
H0033+156 003318.2 153655 R 1.5 1.16 18.0 0 1
H0035+0725 003545.99 072532.6 R 0.58 3.0 17.8 0 3
H0037+1206 003724.43 120654.2 R 0.5 2.5 18.5* 0 3
H0055-2659 005532.5 -265925 R 1.1 3.67 17.5 2 2
H0105-2634 010548.19 -263420.2 R 1.45 3.5 17.5 2 2
H0131+154 013129.7 152744 R 0.84 1.33 17.3 0 2
H0143-0050 014339 -005038 R 0.74 3.1 17.0 0 1
H0146+0146 014644 014228 R 0.93 2.9 17.0 0 1
HS0202+1848 020241.9 184811 R 1.2 2.71 17.5 0 1
HS0211+18 021143.2 185840 R 1.2 2.48 18.0 0 1
H0211+1118 021159.13 111804.0 R 1.07 2.0 16.0 0 2,3
H0214+0820 021420.81 082007.1 R 1.16 2.0 18.0 0 2
TEX0215+165 021555.3 163223.8 V,I,R 1.13 1.9 18.0 0 1
H0216+0803 021618.1 080341 R 0.66 2.993 18.1 0 2
H0218+0931 021813.52 093153.5 R 1.13 2.0 16.0 0 2,3
HS0227+0558 022742.0 055829 R 0.71 2.06 17.5* 0 1
Q0229+1309 022902.63 130941 V,R,I 1.2 2.07 17.7 4.0 6.7 0 1
Q0308+1902 030851.8 190225 V,I,R 0.86 2.84 18.6 3.1 4.4 1 1
H0428-1342 042820 -134212 R 1.26 3.2 17.0 0 1
H0432-1246 043207.2 -124608 R 1.05 2.8 17.0 0 1
H0443-1702 044340.6 -170243.4 R 0.9 1.6 17.0 0 1
H0446-1440 044619 -144027 R 1.42 1.6 17.0 0 1
H0449-1325 044924 -132532 R 1.0 3.1 17.0 0 1
H0449-1645 044959 -164509 R 1.30 2.6 17.0 0 2
H0450-1310 045054 -131039 R 1.07 2.3 16.5 0 1
HS0621+6738 062138.5 673837 R 0.78 1.57 18.0* 0 1
HS0624+6907 062435.2 690703 R 0.83 0.37 13.9 5.8 8.0 0 1
HS0626+6745 062655.3 674552 R 0.86 0.23 18.0* 2.5 10.0 0 1
Q0636+6801 063647.6 680127 R 0.94 3.18 16.5 0 1
Q0640.3+4489 064018.2 445339 V,R 0.9 1.805 18.2 -3.0 6.6 0 1
B20650+37 065035.2 370927.1 R 0.9 1.982 18.0 0 1
HS0701+6405 070130.3 640545 R 0.92 1.92 18.0 0 1
HS0710+6024 071023.4 602441 R 0.94 1.77 18.0 0 1
HS0727+6342 072746.2 634218 R,I 0.88 2.38 18.5 3.8 4.7 1 1
HS0734+5956 073403.0 595643 R 0.94 1.75 16.5 0 1
HS0734+6226 073413.0 622658 R 0.92 1.08 18.0 0 2
H0738+3119 073800.2 311902.1 R 1.14 0.63 16.1 4.4 6.5 0 1
HS0740+3222 074022.1 322219 R 1.1 1.52 18.0* 0 1
HS0742+3150 074230.7 315016 V,R 1.04 0.46 16.0 0 1
HS0742+3320 074246.2 332055 R 0.94 0.61 17.7 2.5 9.9 0 1
HS0743+6601 074358.6 660100 R 0.9 2.19 17.0 0 1
HS0748+3321 074841.0 332104.0 R 1.12 1.932 18.5 0 1
B20751+29 075151.0 294952 R 1.04 2.106 18.5 0 1
HS0751+6107 075158.9 610747 V,R,I 1.3 2.61 17.5 3.75 5.6 0 1
TEX0759+341 075933.4 340746 R 0.9 2.44 18.5 0 1
HS0804+6218 080401.7 621826 R 0.9 1.13 17.5 0 1
OJ508 080458.3 495923 R 0.9 1.433 17.5 0 1
B20808+28 080832.2 285402 R 0.9 1.91 18.0 0 1
4 A.O.Jaunsenetal.:TheNOTGLsurveyformultiplyimagedquasars
Object RA1950 Dec1950 F FWHM z m Sep GLc Note
mV (cid:1)
H0820+1209 082037 120928 R 0.85 1.7 18.0* 0 1
H0821+1022 082127 102245 R 1.02 2.185 18.5* 0 1
H0822+0849 082217 084941 R 0.85 1.8 17.5* 0 2
H0828+1229 082830.3 122955 R 0.8 2.8 18.0* 0 1
H0831+1248 083123.11 124852.5 R 0.94 2.8 17.8 0 2
H0834+1056 083405.4 105645 R 0.74 1.9 18.0* 0 1
H0834+0937 083434.4 093746 R 0.8 2.24 18.0* 0 1
H0836+1122 083649.0 112242 R 0.86 2.67 18.8 0 1
CSO199 083807.6 355542 R 1.16 1.775 16.0 0 1
HS0839+2858 083929.3 285811 R 1.27 1.34 18.0 0 1
H0841+1256 084138.9 125643 R 0.73 2.2 18.0 0 1
CSO203 084230.5 343154 R 0.96 2.126 17.0 0 1
H0843+1454 084317.17 145423.9 R 0.86 2.28 18.0 0 1
HS0843+2743 084333.1 274344 R 1.4 2.03 18.5 0 1
H0845+1523 084549.76 152310.8 R 0.72 2.4 18.0 0 1
HS0845+3013 084559.9 301344 R 0.92 0.67 17.0* 0 2
H0846+1540 084620.58 154039.5 R 0.93 2.9 18.0 0 2,3
H0846+1517 084650.95 151733.2 R 0.86 2.6 18.0 0 1
RQ0849+2845 084905.8 284516 R 0.92 1.27 20.2 0 1
RQ0849+2820 084948.7 282001 R 0.94 0.2 18.5 0 2
HS0850+2852 085022.3 285233 V,I,R 1.2 2.09 17.5 4.5 3.7 1 1
H0850+1755 085047.2 175512.2 R 0.72 3.21 18.0 0 1
H0853+1953 085335.45 195312.0 R 1.23 2.8 18.0 0 1
H0854+1632 085459.37 163236.6 R 0.88 2.54 18.0 0 1
HS0855+2549 085503.1 254928 R 0.9 1.80 18.0 4.3 3.3 1 1
H0903+1534 090305.39 153450.3 R 0.92 2.8 18.0 0 1
H0904+2003 090429.86 200316.9 R 1.0 2.54 18.5 0 1
H0905+1507 090537.49 150724.7 R 0.92 3.16 19.0 2.7 3.1 1 1
CSO233 093632.3 365348 R 1.06 2.03 17.0 0 2
HS0945+4630 094536.1 463029 R 1.0 0.99 17.5* 0 2
HS0945+4646 094555.0 464614 R 1.2 1.91 18.0* 0 1
HS0948+4631 094814.6 463154 R 1.11 1.8 18.0* 0 1
HS1003+4733 100325.0 473345 R 1.15 0.27 17.5* 0 2,3
HS1004+4515 100431.4 451531 R 1.2 1.3 17.0* 0 1
HS1004+4543 100449.4 454306 R 1.15 1.66 17.5* 0 1
CSO38 100904.6 295648 R 1.0 2.62 16.0 0 2,3
CSO261 101653.6 355654 R 1.04 2.67 17.0 0 1
Q1107+487 110748.2 484730 R 0.77 3.00 16.7 0 1
CSO340 112332.6 353636 R 0.93 1.285 17.0 0 1
B31123+395 112345.8 393515.1 V,I,R 1.06 1.47 16.4 2.5 5.4 0 1
Q1123+434 112349.4 432607.4 R 1.06 2.01 18.4 0 1
CBS42 112839.8 292054 R 1.11 1.319 17.0 0 1
US2694 113417.2 300808 V,I,R 1.14 1.858 18.3 2 2
PG1148+549 114842.6 545413 R 0.85 0.969 16.1 0 2
PC1158+4635 115802.9 463529 R 1.2 4.733 22.4 1.5 8.9 0 1
Q12076+399 120738.6 395617 R 1.3 2.4 17.5 4.0 7.3 0 2,3
Q1210+1731 121030.4 173104 R 0.87 2.537 17.4 0 3
Q1222.7+22.6 122247.2 223704 V,I,R 1.15 2.29 18.0 0.8 4.3 1 1
Q1223+1753 122335.8 175325 R 0.92 2.918 18.1 0 1
Q1230+1627 123039.4 162726 R 0.98 2.7 17.8 0 1
CSO151 123126.9 292424 R 1.2 2.011 16.0 0 2
SP1 135806.0 390854 R 0.75 3.28 17.0 0 2
UM627 135837.0 000124 R 0.98 1.87 16.0 0 2
HS1404+32 140445 320331 R 1.35 2.37 17.5* 0 2
CSO609 140635.7 491624 R 0.95 2.13 17.0 0 2,3
Q1412+0925 141225.6 092510 R,I 1.05 1.70 17.4 2.5 6.3 0 2
A.O.Jaunsenetal.:TheNOTGLsurveyformultiplyimagedquasars 5
Object RA1950 Dec1950 F FWHM z m Sep GLc Note
mV (cid:1)
GB21413+373 141322.7 372015 R 1.54 2.36 18.0 0 1
HS1420+326 142021.1 323647 R 0.94 0.69 17.5 0 2,3
HS1421+330 142117.5 330555 R 1.03 1.9 16.5 0 2,3
TEX1421+359 142144.1 355606 R 0.98 1.57 17.5 0 2
Q1429+1153 142947.2 115306 R 1.85 3.01 18.6 0 1
Q1435-0134 143513.2 -013413 R 1.7 1.31 16.0 0 1
Q1442+295 144244.4 293142 V,R,I 1.7 2.67 16.2 2.0 3.4 1 1
CSO722 150445.0 542324 V,I,R 0.84 1.9 17.0 2.4 6.4 0 1
LB9612 151708.2 235652 R 0.96 1.9 17.3 0 1
SP43 152030.0 412212 R 0.84 3.1 17.5 0 1
LB9707 152308.8 212436 R 1.1 1.924 18.0 0 1
TEX1558+187 155802.9 184654 R 0.9 2.4 18.0 0 1
PKS1559+17317 155904.6 172236 R 1.05 1.944 18.0 0 1
B31621+392 162123.4 391627 V,I,R 0.6 1.97 17.5 2.3 3.8 1 1
Q1623+268 162345.4 265354 R 1.15 2.52 16.0 0 1
HS1626+64 162620.4 643332 R 0.92 2.32 16.5* 3.2 9.0 0 1
Q1628+3808 162828.0 380447 R 0.73 1.461 16.8 0 1
Q1630+3749 163032.2 373925 R 0.73 2.037 18.2 0 1
Q1633.5+26.7 163334.8 264417 R,I 1.16 1.84 17.0 0 1
PG1634+706 163451.7 703737 R 2.24 1.33 14.9 0 2
HS1638+61 163846.8 612153 R 0.88 0.46 18.0* 0 1
Q1643+401 164326.7 400443 R 0.84 1.877 18.0 0 1
HS1700+6416 170040.5 641625 R 0.8 2.74 16.1 2 2
HS1704+6048 170403.5 604831 R 1.1 0.37 15.3 0 1
1E1704+710 170500.6 710134.0 R 1.0 2.00 17.5 0 1
HS1709+6027 170951.4 602723 R 1.1 1.54 17.0* 0 1
PG1715+535 171530.7 533124 V,I,R,Z,B 0.72 1.93 16.5 0.116 3.7 1 1
HS1716+6839 171627.9 683948 R 1.7 0.78 18.5 0 1
PG1718+481 171817.7 480711 R 1.45 1.08 14.7 0 1
Q1720+3470 172002.3 344149 V,I,R 1.5 2.4 18.4 1.3 7.7 0 1
Q1722+34 172259.8 344437 R 1.2 2.2 18.5 1.9 6.1 0 1
HS1723+6550 172307.2 655026 R 1.15 1.45 17.0* 0 1
TEX1726+344 172601.3 342504 I 1.6 2.425 18.5 0 1
HS1732+6535 173246.2 653523.0 R 0.97 0.86 17.6 0 1
HS1742+6147 174221.6 614711.0 R 1.22 0.52 18.6 0 1
HS1749+7006 174903.4 700639 R 0.94 0.77 17.4 0 1
HS1803+6737 180337.4 673754 R 1.9 0.14 15.8 0 1
HS1807+6948 180718.5 694857.1 R 1.8 0.051 14.4 0 1
PKS1821+10 182141.6 104244 R 1.03 1.36 17.3 3.4 8.0 0 1
HS1824+6507 182435.9 650737 V,B,R,I 1.75 0.3 16.5* 1.5 5.2 0 1
4C56.28 185730.1 564146 V,Z,R,I 1.2 1.595 17.3 2.7 3.2 1 1
HS1946+7658 194641.0 765826 V,I,R 1.2 3.02 15.9 0 1
PC2047+0123 204750.7 012356 R 1.10 3.799 19.7 0 1
TEX2048+196 204856.7 193849 R 0.85 2.36 18.5 0 1
TEX2116+203 211617.2 202122 V,R,I 0.98 1.68 17.0 2.75 3.7 1 1
TEX2127+176 212717.7 174136 V,R,Z,I 0.9 2.01 18.0 1.3 2.1 1 1
TEX2127+348 212746.2 345324.0 R,I 1.6 2.4 18.5 2.7 8.1 0 1
PKS2150+050 215054.1 052209 R 0.9 1.979 17.8 0 1
H2230+114 223007.81 112822.5 R 0.75 1.04 16.5 0 1
Q2231+0125 223142.1 012541 R 0.9 1.9 18.2 0 1
H2251+158 225129.4 155254.0 R,I 0.7 0.86 15.3 0 1
H2251+113 225140.7 112036.8 R 1.51 0.32 15.8 0 1
TEX2300+345 230059.7 343038 R 0.7 2.490 18.0 0 1
B22310+383 231036.3 383123.0 R 1.6 2.17 17.5 0 1
H2310+0018 231050.8 001826.4 R 0.83 2.2 17.0* 0 2,3
6 A.O.Jaunsenetal.:TheNOTGLsurveyformultiplyimagedquasars
Object RA1950 Dec1950 F FWHM z m Sep GLc Note
mV (cid:1)
H2314+160 231409.7 160143.5 R 1.5 0.66 18.0 0 2
H2355+0845 235521.6 084521.6 R 0.7 2.8 18.0* 2 2
Q2359+0653 235906.77 065313.3 R 0.45 3.24 18.8 0 2,3
H2359+1305 235957.4 130532 R 0.77 2.8 18.0* 0 3
:
Notes
:QSOidentification,wheretheidindicateslistoforigin;H-fromHazard,HS-fromReimers(HamburgSternwarte)andothersfrom
Col. 1
theVéroncatalogue
:QSORA(hhmmss)inequatorial1950coord.
Col. 2
:QSODec(ddmmss)inequatorial1950coord.
Col. 3
:Filtertypes
Col. 4
:Seeing(FWHM)inarcsec
Col. 5
:RedshiftzoftheQSO
Col. 6
:V-bandmagnitudeoftheQSOasestimatedfromourdataortabulatedinotherQSOcatalogues.TheQSOswithnopreviouslymeasured
Col.7
magnitudewereestimatedbycomparingthemtoQSOsonotherCCDframes(forasimilarexposuretime).Theseestimatedmagnitudesare
markedbyanasterix( )andhaveerrorsupto 05mag
(cid:3) (cid:6) :
:Magnitudedifferencebetweenclosestcompanionwithweakerapparentbrightnessandwithin5 ofQSO
00
Col. 8
:Separation(inarcsecond)ofclosestcompanionwithweakerapparentbrightnessandwithin5 ofQSO
00
Col. 9
:A“1”indicatesthattheQSOistreatedasapossibleGLcandidate,whilea“2”indicatesthattheobjectiselongated,diffuseorotherwise
Col.10
especiallyinteresting.ThelatterobjectsarenottreatedasGLcandidatesinthepresentanalysis,butshouldbefurtheranalysedinfuturework
: A “3”indicatesthat there are noPSFsother thanthe QSO in theimage, a “2”indicatesthat the QSO appearselongated(this is
Col. 11
sometimesduetobadtracking)anda“1”indicatesthatthereareoneormorePSFsandtheQSOisnotelongated
3.2.Largeseparations
In the identification of possible GL-candidates we chose all
QSOswithacompanionweakerthantheQSOwithinthearea
2. If more than one close companion exists, we chose the
b(cid:25)rricghterone, because ithas thehighestprobabilityof beinga
gravitationallylensed image of the QSO. We have adopted a
cutoffradius =5arc-secondtosecuretheinclusionofmost
GL-systems prrcoducedbyasingleisolatedgalaxyandexclude
those produced by clusters of galaxies. Using a larger cutoff
radius would also include many star or galaxy companions
and, hence, increase the number of false positives(Kochanek
1993b).
3.3.TheASF
TodeterminetheASFoftheNOTsampleforawiderangeof
seeing values we performed detection tests on synthetic data.
Fig.2.Theseeing(FWHMinarc-sec.)distributionof229observations ThesedatawereproducedfromnumericalPSFsobtainedfrom
of168QSOs oneor several stars in an image of acertain quality(weused
PSFswithFWHMof0 6 0 75 1 0and1 2).Thesyntheticim-
00 00 00 00
: ; : ; : :
agesconsistedofacloselyseparatedimage-pairofPSFs,which
wereproducedusingrandomangular-separationandmagnitude
difference.Photon(Poisson)noiseandread-outnoisewerein-
functionoftheirangularseparation,whichweevaluatebyper- cludedinthesesimulations.Inspectionbyeyewas performed
formingasimulation-test.Usingatypicalpointspreadfunction for aseries ofsyntheticimages ineach FWHM category. For
(PSF)fordifferentseeingvalues,wehaveproducedsimulated each ofthesecategories,asetofconstants( , , and )
1 2
C C A B
imagesofvariouscloselyseparated pair-scenarios,adoptinga weredetermined,describingtheparticularASFforthatpartic-
random flux ratio. The results of these tests are illustrated in ularseeing(FWHM)value.Cubicinterpolationwasappliedto
Fig.3,whichalsoshowtheselectionfunctionforsomeofthe determine these constants for the intermediate seeing values,
othersurveysbeingaddedinSection6.Wediscussthesetests therebyestimatingtheASFforany givenseeing valuewithin
inmoredetailinSection3.3. reasonable range of the actual measured values. The ASF is
A.O.Jaunsenetal.:TheNOTGLsurveyformultiplyimagedquasars 7
valid for seeing values from these tests in the range 0 5
00
: (cid:20)
FWHM 1 5.Wealsofoundfromtheseteststhatthedetec-
00
(cid:20) :
tionprobabilitiesare slightlydependenton the positionangle
(PA)oftheimagepairforsmallseparations.Specifically,align-
ments alongtherows orcolumns ofthe detectordecrease the
probabilityofseparatingthepaironthebasisofinspectionby
eye.
The complete ASF, which we apply in our work, is now
representedby
8nosolution for0
00 1
< <(cid:18) (cid:20)C
( )= + for (1)
1 2
(cid:1)m (cid:18) B A(cid:2)(cid:18) C <(cid:18) (cid:20)C
:5.0mag for 2
C <(cid:18) (cid:20)rc
where and are determined for each FWHM value and
1 2
C C
constitutethestartingvalueand“break”pointoftheASF, re-
spectively. Some of the constants that determine the ASF for
various values of seeing (FWHM) are listed in Table 2. The
ASFisalsoshowninFig.3.
Fig.3.TheASFforNOTobservationsat0 7and1 0seeing(FWHM)
00 00
: :
(solid lines). Also included,for comparison,are the ESO-KP ASFs
for ground-basedobservationswith inspectionbyEYE (dotted) and
Table2. Constantsdescribingthe ASFfor variousseeing(FWHM) PSF-subtraction (dashed) for 1.0” seeing and the ASF for Hubble
values. SpaceTelescope(HST)snapshotsurvey(dash-dot)(seeSurdejetal.
1993).
FWHM A B
1 2
C C
0005 22.318 -4.305 0.192 0.416 ,istheonlyfreeparameterinthismodel,thestatisticalanaly-
00:06 17.700 -3.520 0.198 0.482 s(cid:27)isisverysensitiveto .Recently,Kochanek(1993c)proposed
:
0 7 14.193 -3.185 0.224 0.576 (cid:27)
00 thatthecorrectionfactorofp3 2tothe value,whichiscom-
:
00:08 12.845 -3.536 0.276 0.664 monlyappliedinlens statistics=toaccou(cid:27)nt forthe presence of
0 9 13.390 -4.508 0.336 0.710
0:0 DMinlate-typegalaxies(TOG,F&T),shouldnotbeused.We
1 0 14.176 -5.712 0.402 0.756
00
: willdiscussthisinSection6andpresentresultsforbothcases
1 1 13.809 -6.854 0.496 0.858
00
1:2 12.599 -8.000 0.636 1.032 (withandwithouttheDMcorrection).
00
1:3 11.526 -9.385 0.814 1.248 Asusual,weestimatethepopulationofSISgalaxiesfrom
00
: theSchechtergalaxyluminosityfunction
(cid:18) (cid:19)(cid:11)
= L exp( L ) (2)
(cid:30)gdL n(cid:3) (cid:0) dL=L(cid:3);
L(cid:3) L(cid:3)
4.Statisticalmodel
wherethegalaxynumberdensity = 156( 04) 10 2 3
(cid:0)
Following previous GL statistical studies such as Turner Mpc 3and = 11 01,followni(cid:3)ngEf:stath(cid:6)iou:et(cid:2)al.(1988h).
(cid:0)
etal.(1984),hereafterTOG;Fukugita&Turner(1991),hereafter TheHubble(cid:11)cons(cid:0)tan:ti(cid:6)s :0 =100hkms(cid:0)1Mpc(cid:0)1.Thegalaxy
H
F&T;Surdejet al.(1993);Kochanek(1993c)andMaoz&Rix luminosity, ,isestimatedbyusingtheFaber-Jacksonrelation
L
(1993),wehaveusedthewellknownsingularisothermalsphere
1
(SIS)modelinthestatisticalanalysisofthecombinedSCYM (cid:18) (cid:19)(cid:13) (cid:18) (cid:19) =(cid:13)
= (cid:27) = L (3)
andNOTsamples.InthissectionweoutlinetheSISmodelas L L(cid:3) )(cid:27) (cid:27)(cid:3) ;
(cid:27)(cid:3) L(cid:3)
wellasthemagnificationbias.
wheretheexponentistakentobe =4(Tully&Fisher1977;
ASISgalaxymodelischaracterisedbyitsconstantdeflec- (cid:13)
Faber&Jackson1976).Thevalueoftheexponent ischosen
tion angle (independent of the impact parameter) giving the (cid:13)
(rather than using the tabulated values of 3.7, 3.7 and 2.6 for
critical (Einstein) radius = 4 2 2( ), where
and are the proper dbisctrances(cid:25)2(cid:27)le=ncs-sDoulsr=cDe sand observDelrs- E, S0 and S galaxies, respectively) forcomputationalreasons
sourcDe,srespectively.A“stronglensing”eventoccurswhenthe anddonotaffectsignificantlythestatisticalresults(Kochanek
1993c). Furthermore, we assume that the number of lenses
QSOisprojectedwithintheareadefinedbythecriticalradius,
is constant in a co-moving(i.e. non-evolving)volume, hence
2 . This area denotesthe cross sectionfor lensingby aSIS
(cid:25)lebncsr.Becausetheonedimensionalcentralvelocitydispersion, tthhee d(1en+sity)3nlfaocftolernasreisseiss fgriovmentbhye nfalct=thna0t(1th+ezclo)3-,mwovhienrge
2 Thecriticalradius canbeexpressedequallyusingeitherangular volumedzeclreaseswithincreasing ,duetotheexpansionofthe
orproperdistances(Kboccrhanek1993a). universe.Thepresentdensityofiszolatedgalaxies, ,isfound
0
n
8 A.O.Jaunsenetal.:TheNOTGLsurveyformultiplyimagedquasars
Table3.Therelativeabundance,centralvelocitydispersionsandcomputedFvaluesoflate-typeE/S0galaxiesandearly-typeSspiralgalaxies,
using = 11and =4(Kochanek1993c).Thevaluesofanduncertaintiesintheabundance, and aretakenfromF&T(andreferences
therein(cid:11)).N(cid:0)ote:thatth(cid:13)eFvaluesarecomputedusing =156( 04) 10 2h3Mpc 3andwithn/(cid:3)withou(cid:27)t(cid:3)theDMcorrectionfactorofp3 2.
(cid:0) (cid:0)
n(cid:3) : (cid:6) : (cid:2) =
type abund. [ 1] F [ 1] F
(cid:0) (cid:0)
(cid:27)(cid:3) kms (cid:27)(cid:3) kms
E 12% 225+12 00085 00044 225+12 p3 2 00191 00099
S0 19% 206(cid:0)+1220 0:0094(cid:6)0:0058 206(cid:0)+1220(cid:2)p3=2 0:0212(cid:6)0:0115
S 69% 143(cid:0)+820 0:0080(cid:6)0:0042 143(cid:0)+820(cid:2) = 0:0080(cid:6)0:0042
E/S0/S 100% (cid:0)13 0:0259(cid:6)0:0084 (cid:0)13 0:0483(cid:6)0:0157
: (cid:6) : : (cid:6) :
E/S0 31% 00179 00073 00403 00151
: (cid:6) : : (cid:6) :
fromintegratingtheSchecterluminosityfunctionEq.(2)over candidates within the boundaries of the NOT ASF are listed
alllTumheinoopsittiiceasl(di.eep.tnh0, =,Rf01or(cid:30)legndsLin).g of a distant QSO with ainddTiatibolnea4l.cEolaocuhrcaannddisdpaetcetriasladlastoa,dwishcuicshsemdiignhdtiveindauballelyusantdo
(cid:28)
magnitude ,andredshift ,isgivenby reject or approve a candidate, are also presented here. Some
mV zs objects have been observed by other surveys, in which case
1
= 3( ) (4) wepresenttheirconclusions.Sinceonlyafewcandidateshave
(cid:28) 30FDs zs been observed spectroscopically at NOT using the low dis-
persionspectrograph(LDS), notmany of thecandidates have
where = 16 3 4 = 16 3 [1+ +4 ] 4 and isthe
gammaF-funcctHi(cid:25)o03nhn(T0(cid:27)OGi,F&cHT(cid:25)03)(cid:0). (cid:11) =(cid:13) n(cid:3)(cid:27)(cid:3) (cid:0) ebxepenosruejreecstewde.rFeutratkheenrmfoorret,hbeeNcaOusTesnaompphloet,owmeetarriec-ncoaltibabraletioton
In Table 3 we list all relevant abundances, velocity dis- supplycolourestimates.Wehave,however,comparedthemag-
persions and respective F parameter values with/withoutDM nitudedifferencebetweentheQSOandnearbycompanionsfor
corrections for both E/S0 and E/S0/S populations. Note that thevariousfiltersandusesimilarmagnitudedifferences asan
theDMcorrectionsareonlyappliedtolate-typegalaxies(i.e. indicationofcolourresemblance.
E/S0).
Inourstatisticalmodelwemustalsotakeintoconsideration
theimportantmagnificationbias,whichincreasestheexpected – PG 1715+535’s companion is confirmed by Yee etal.
numberoflenses.Thisisduetothemagnificationof(strongly) (1993)andCramptonetal.(1992)tobeastar,havingalso
lensed images, which effectively alters the magnitudelimited been investigated spectroscopically by these surveys. Its
sample(Narayan&Wallington1993).Weestimatethemagni- measured colourdifferences ( = 012, = 012
ficationbiasdirectlyfromtheQSOluminosityfunction,which and = 005) could no(cid:1)t rmejVect eit:her i(cid:1)ntmerpRretati:on,
wedefine as inF&T (basedondata fromHartwick& Schade whic(cid:1)hmisIwhy(cid:0)itc:ouldonlybedeterminedspectroscopically.
(1990)) Thesmallmagnitudedifference(i.e.highmagnification)is
themaincontributiontothehighlensingprobability.
(cid:26)10086( 1915) for 1915
nq(mB)= 100::28(mmBB(cid:0)(cid:0)19::15) formmBB <(cid:21)19::15 : (5) – iTdsiEftfXheer2er1en2fco7er+e((cid:1)1n7mo6tVaand=sti1rtso:3nc,og(cid:1)mcmpanaRndiio=dna0the:a5.vSaenpadecs(cid:1)tirgomnsicIfioc=pain0ct:c3oo)blsaoenurdr-
Here ( )representsthecountsofQSOsatapparentmag-
nitudenq m.BThe differential magnification bias, simply being vationswereunfortunatelynotproperlyachieved.Because
mthaegonvifiemrc-arBteipornesoefntoatriiogninoafllyQSdOimsmatermQagSnOitsudweimthBmdaugenittoudthees wcoofamsthpneaontsimosanatlil(smfaanVcgtol(cid:24)erilsy1e9pa:la5irg)a,ntiwendegostnuhsetphQeecStslOtiht.a(WtmtehVew(cid:24)ceorem1ap8ba)lneainotdno
+25 ,isgivenby
mB : logM identify the rather strong CIV emission line in the spectra
( +25log ) of the QSO, whilenothingwas detectable at that location
( )= dPM nq mB : M (6) inthefainterspectrum.Furtherspectroscopicobservations
B mB;M ( )
dM nq mB areplannedin1995andwillhopefullyconfirmorrejectthe
where =8 3isthemagnification(M)probability lensinghypothesis.
distribudtPioMn=fdoMr our p=aMrticular SIS lens model, assuming the – Q 1442+295and itscompanion show asignificantcolour
QSOisapointsource. difference ( = 20, = 16 and = 11),
indicatingth(cid:1)atmthVecomp:ani(cid:1)onmisRquite:reddert(cid:1)hamnItheQS:O.
Spectroscopicdata show no signofa distinctalikeness in
5.ResultsfromtheNOTsample
emission line or continuum. We conclude that this object
Weherepresenttheobjectivelydiscovered,possiblecandidates isnotastrongGLcandidate, mostprobablyastar.Recent
of gravitationallensingfrom the 168 QSO NOT sample. The spectroscopic observations of this pair, carried out at the
A.O.Jaunsenetal.:TheNOTGLsurveyformultiplyimagedquasars 9
– Q0308+19anditscompanionshowfairlysimilarcolours
Table4.ListofpossibleGL-candidatesintheNOT-sample,withred-
( 31, 30 and 30), but the
shift,Vbandmagnitude,angularseparationandmagnitudedifference. c(cid:1)ommpVani(cid:25)onh:asb(cid:1)eemnRrep(cid:25)orte:dbyCr(cid:1)ammpIton(cid:25)eta:l.(1992)to
Objectsaresortedindecreasingrelativecalculatedprobabilityofthe
beagalaxy.
companionbeingalensedimageoftheQSO.
– HS 0855+25 lacks photometricdata and demands further
investigationifitscompanion’snatureistoberevealed.
Object: m comment
zs mV (cid:18) (cid:1) – HS0850+28anditscompanionshowfairlysimilarcolours
PG1715+535 1.93 16.50 3 7 0.12 star
0:0 ( 45, 45and 45),buthas not
TEX2127+176 2.01 18.00 20:01 1.30 redcolor y(cid:1)etmbeVen(cid:25)obs:erv(cid:1)edmsRpe(cid:25)ctros:copica(cid:1)llym. I (cid:25) :
Q1442+295 2.67 16.20 3 4 2.00 redcolor
00
: – HS0727+63anditscompanionshowfairlysimilarcolours
TEX2116+203 1.68 17.00 3 7 2.75 redcolor
00
Q1222.7+22.6 2.29 18.00 4:3 0.80 spectraneeded ( 38 and 35), but has not yet been ob-
4C56.28 1.59 17.30 30:02 2.70 redcolor s(cid:1)ervmeRds(cid:25)pect:roscopi(cid:1)camllyI.(cid:25) :
00
:
H0905+1507 3.16 19.00 3 1 2.70 spectraneeded
00
:
B31621+392 1.97 17.50 3 8 2.30 star
0:0 6.Cosmologicalimplications
Q0308+1902 2.84 18.60 4 4 3.10 galaxy
00
:
HS0855+2549 1.80 18.00 3003 4.30 Tomakethebestpossiblestatisticalanalysis(i.e.usingaslarge
:
HS0850+2852 2.09 17.50 3 7 4.50
00 a sample as possible) we combine the NOT sample with the
:
HS0727+634 2.38 18.50 4 7 3.80 spectraneeded
0:0 fullopticalSCYM-samplepresentedpartially3bySurdejetal.
:
(1993).Usinglikelihoodfunctions,weestimatemaximumlike-
Notes
:HLQidentification
Col. 1 lihoodvelocitydispersions, , and lenseffectiveness param-
Col. 2:RedshiftzoftheQSO eters, ,fromthe combined(cid:27)s(cid:3)ampleof784HLQs forvarious
:V-magnitudeoftheQSOastabulatedinotherQSO F
Col. 3 flat cosmologies. In these computations we employ complete
catalogues
integralprobabilities.This is the probabilityfor agiven QSO
:Angularseparation betweentheQSOanditscompanion(if
mCoolr.e4thanone,chosenasde(cid:18)scribedinSection2) (withapparentmagnitude, ,andredshift, )tobelensedby
:MagnitudedifferenceintheV-bandbetweentheQSOand aninterveningisolatedgalamxyi. zi
Col. 5
companion Wenowwishtoexpresstheprobabilityoffindingalensed
:Commentoncomponentsnatureorcharacteristics image of a QSO under the constraints imposed by the obser-
Col. 6
vational conditions. The observational conditions are charac-
terisedbytheseeing(FWHM)ofpointsourcesintheimages.
The detectable magnitude difference is dependent on the im-
NTT, La Silla, Chile by J. Surdej also show littleresem- ageangularseparation,andiscloselyrelatedtotheseeing.We
blancebetweentheQSOandcompanion(Surdej1994). applytheASFintroducedinSection3,whichdescribesthere-
– TEX2116+203anditscompanionshowasignificantcolour lationsofdetectablemagnitudedifferences,angularseparation
difference ( = 275, = 22 and = 15). and seeing for our particular survey. Following Surdej etal.
Spectroscop(cid:1)icmobVservat:ions(cid:1)gimveRnoind:ication(cid:1)thmatItheco:m- (1993)andKochanek(1993c),wecanexpresstheprobability,
panionisalensedimageoftheQSO. , of finding a gravitationallylensed image in the vicinity
SF
– Q1222.7+22.6hasonlybeenimagedintheRandVfilters. p(wiithin )ofaQSOwithintheobservationalwindow(defined
The magnitude differences in these colours are, however, bytheserlcectionfunction)by
quitesimilar( 08and 065)and within
wanhianttwereeesxtipnegcct(cid:1)atonmdbViedpa(cid:25)ltaeuos:fiblleen.sTinh(cid:1)ge.mQSRO(cid:25)rem:ains,therefore, pSiF(mi;zi) = Sc3a0tFDs3(zi)
2
– 4C56.28 and itscompanion havebeen observed by other Z rc= ( ) ( (2 ) ) (7)
surveys, but have not yet been investigated spectroscopi- 0 pc bcr Bias mi;M bcr ;M2 dbcr:
cally.Ourphotometricdataindicatethatthecompanionis
somewhat redder thanthe QSO (in agreement withprevi- Here the critical radius probability is given by ( ) =
ous surveys), but not more than can be expected from a d(cid:28) = 2d(cid:28) (refer Eq. (4.10) in Kochanek (p1c99b3ccr))4.
reddeningeffectduetoalensinggalaxy( 27and (cid:28)dbcr( (cid:28)d(cid:18) 2) is the integral of ( ), given by
265). We therefore treat this pa(cid:1)irmaVs i(cid:25)nter:esting BEqi.as(6m),i;Mand;Mthe bias integral, usinBg mani;Minfinite upper
(cid:1)anmdpRla(cid:25)nto:performspectroscopicobservationsin1995. limit, is numerically computed by substitutionof variables 5.
– H0905+1507’scompanionwasobservedspectroscopically
3 We have also included, as did Kochanek(1993c), the extended
byJ.Surdej at the NTT and seems to be quitered, though
HSTsnapshotsamplepresentedinMaozetal.(1993).
nospectroscopicdataisyetavailable(Surdej1994).
4 Wehaveexpressedthelensingprobabilityintermsofthecritical
– B31621+392anditscompanionshowfairlysimilarcolours
radius, ,insteadoftheangularseparation .
( 23, 225 and 24), but the 5 Thebrcerwas little or no difference in our(cid:18)results using either this
c(cid:1)ommpVani(cid:25)onh:asb(cid:1)eemnRrep(cid:25)orte:dbyBah(cid:1)camllIet(cid:25)al.(:1992)tobe methodorthatofsettingtheupperlimittoalargenumber,i.e. =
2
aG-typestar. 10000 M
10 A.O.Jaunsenetal.:TheNOTGLsurveyformultiplyimagedquasars
Table5.Estimatedvaluesof andFfromthefrequencyoflensingandtheconfigurationlikelihoodsoftheobservations.Theresultsareshown
(cid:27)(cid:3)
ineachrowfordifferentcombinationsofgalaxypopulationwithandwithoutDMcorrection.The90%confidencelevelresultsareshownin
theupperpartofthetablefortheEinstein-deSitter universemodel( = 1). Inthelowerpart, wegivethe90%confidencelevelresults
(cid:10)M
forthemaximumlikelihoodvalueofthedensityparameter(i.e. =095forE/S0/Sand =025forE/S0populations).Themaximum
(cid:10)M : (cid:10)M :
likelihoodvalueisindicatedby and ,respectively.
max max
F (cid:27)(cid:3)
galaxytypes low max high low max up
(cid:10)1M00 E/S0/S F002021 F003735 F006589 (cid:27)16(cid:3)45 1(cid:27)9(cid:3)18 2(cid:27)2(cid:3)11
: : : : : : :
100 E/S0/S(withoutDM) 000898 001660 002928 1343 1566 1805
: : : : : : :
100 E/S0 001490 002477 004031 2043 2320 2620
: : : : : : :
100 E/S0(withoutDM) 000662 001101 001792 1668 1894 2139
: : : : : : :
095 E/S0/S 001964 003615 006360 1633 1903 2191
: : : : : : :
095 E/S0/S(withoutDM) 000873 001607 002826 1334 1553 1789
: : : : : : :
025 E/S0 000609 001111 001944 1633 1899 2183
: : : : : : :
025 E/S0(withoutDM) 000271 000494 000864 1334 1550 1783
: : : : : : :
Note also that ( (2 ) ) is normalised so that lensmodelisnotabletoreproducetheimageconfigurationof
2
RM2 Bias mi=;M1. Thbcerm;Minimum detectable magni- twoofthem,thefrequencyoflensingisstillpreserved.
fimcaitni(oMn)(di.Pe.Mm=adxMimduMm magnitude difference) is given by the Kochanek(1993c)estimated forEandS0galaxypopu-
expressionforthemagnification (2 ) = 2 (2 )+1, where lationswithouttheDMcorrection(cid:27)(cid:3)factor,whileTOGandF&T
(2 )= ( )isthefluxratiocoMrrespbocnrdingtffo(2tbhbccerr)(cid:0)de1tectable computedthelenseffectivenessparameter,FwiththeDMcor-
mfagbncritudefdi(cid:18)fference ( )(givenbyEq. (1)).Inourcalcu- rection factor. Surdej et al. (1993) estimated the F parameter
lations,wehavetaken(cid:1)admva(cid:18)ntageofthe“NumericalRecipesin without á priori corrections for DM. Since we do not know
Fortran” implementation of the Romberg method for integra- theimportanceofSspiralgalaxiesnorthatofdarkmatter,we
tion(Presset al.1992).Notealsothatinabsenceofanyselec- estimate forbothpopulationsandwith/withouttheDMcor-
tionfunctiontheminimumdetectablemagnificationwouldbe rectionfa(cid:27)c(cid:3)torofp3 2.Furthermore,wewishtoinvestigateifit
=
25log2(TOG,Surdejetal.1993). ispossibletoobtainreasonableconstraintsonthecosmological
: densityparameter, .
Theprobabilityforfindingalensedpairwithacertainred- Inthesecomput(cid:10)atMionsweapplytheconfigurationprobabil-
shiftandmagnitudedifferencewithintheASF,isthustheproba-
itylikelihoodfunctionintroducedinKochanek(1993c)
bilityforlensingweightedbytheASF(Eq.(1))foreachcritical
radius . The configuration probability ( ) (the relative
probabbilcirtyofaseparation) multipliedbypthcebrcartioofthe bias =YNU(1 )YNL YNL (8)
SF SF
includingtheASFtothatwithnoASF,isthusintegratedover Ptot (cid:0)pi pj pck
=1 =1 =1
thesurveyarea( )andmultipliedbythegeneralprobabil- i j k
ityoflensing,leard(cid:20)ingrctoEq.(7).Thesumoftheprobabilitiesof which,convertedintologarithmiclikelihoods,becomes
findingaGL-systemwithinthedetectablerangesoftheselec-
tionfunctionforeachobservedobject,X SF,willthengive = XNU +XNL +XNL (9)
pi lnPtot (cid:0) pSiF lnpSjF lnpck
ustheexpectednumberoflensedQSOsiinthesample. =1 =1 =1
i j k
The combined NOT+SCYM sample, consisting of 784 under the assumption that 1. It is here assumed that
SF
QSOs, has been applied in the computations below. Among , and aretheprobapbiliti(cid:28)esofaQSObeingnotlensed,
theseQSOs, fourhavebeenidentifiedasbeinggravitationally lpeinsepdj or hpacvking a separation if lensed, respectively. The
lensed:thetwodoubleimagedlensedsystems“Q1208+1011” configurationprobabilityofacebrtainseparation isgivenby
(Magainet al.1988;Maozet al.1992)and“UM673”(Surdej b
etal.1987),theclover-leaf“H1413+117”(Magainetal.1988) ( ) 3( )
and the triple image “PG 1115+080” (Weymann etal. 1980), pck =pc(bcr)(cid:28)(cid:3) (cid:27)(cid:3)SDFs zs Bias(mk;M(bcr);M2); (10)
whichwereallfoundintheSCYM-sample.Wethereforehave pk
=4.Thewellknown“QSO0957+561”(Walshetal.1979) while and aregivenbyEq.(7).Thelogarithmiclikeli-
SF SF
iNsLnotwithinour cutoffradius and isthereforenotamong the hoodfpuinctionapdjdstogetherallprobabilitiesandcountslensed
GL-candidatesforthesurvey.Itisalsoawellknownfactthat HLQsaspositiveandunlensedHLQsasnegativecontributions.
thegravitationalpotentialofthisGL-system isnotsolelydue We, hence, compute likelihoodsfor various values of the
tothemassive centralgalaxy, butalso duetothesurrounding velocitydispersion, ,andflatcosmologicalmodels(i.e. dif-
cluster(contributingtothelargeseparationof6.1arc-second). ferent = 1 (cid:27)(cid:3) values). The value of affects the
Thefourlensedsystemsareincluded,becauseeventhoughour proper(cid:10)dMistance,(cid:0)wh(cid:10)ic(cid:3)h is part of the optical d(cid:10)eMpth (Eq. (4)),