Astronomy & Astrophysics manuscript no. 2929 (cid:13)c ESO 2008 February 5, 2008 COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses IV. 6 0 Models of prospective time-delay lenses 0 2 P. Saha1,2, F. Courbin3, D. Sluse3, S. Dye4, and G. Meylan3 n a J 1 Astronomy Unit, Queen Mary and Westfield College, University of London, London E1 4NS,UK. 7 2 Institu¨t fu¨r Theoretische Physik, Universit¨at Zu¨rich, Winterthurerstr190, CH-8057 Zu¨rich, Switzerland. 1 3 Laboratoire d’Astrophysique,Ecole PolytechniqueF´ed´erale deLausanne, Observatoire, CH-1290 Sauverny,Switzerland. 4 School of Physics and Astronomy,Cardiff University,5 The Parade, Cardiff, CF24 3YB, UK. 1 v 0 7 ABSTRACT 3 1 Aims.Topredicttimedelaysforasampleofgravitationallylensedquasarsandtoevaluatetheaccuracythatcanberealistically 0 achieved on thevalue of H0. 6 Methods.Weconsider14lensedquasarsthatarecandidatesfortime-delaymonitoringandmodelthemindetailusingpixelized 0 lens models. For each system, we provide a mass map, arrival-time surface and the distribution of predicted time-delays in h/ a concordance cosmology, assuming H0−1 = 14 Gyr (H0 = 70 in local units). Based on the predicted time-delays and on the p observational circumstances, we rate each lens as ‘excellent’ or ‘good’ or ‘unpromising’ for time-delay monitoring. Finally, we o- analyze simulated timedelays for the11 lens rated excellent orgood, and show that H0 can berecovered toa precision of 5%. Results. Incombination with COSMOGRAILpaperI onthetemporal sampling oflensed quasar light curves,thepresent work r t will help design monitoring campaigns of lensed quasars. s a : v Key words.Cosmology: distance scale, cosmological parameters – Gravitational lensing – quasars: individual i X r a 1. Introduction The dominantuncertaintyinmeasuringH fromlens- 0 ing is the non-uniqueness of lens mass profiles that can Gravitational lensing of distant quasars is one of many reproduce the observables. Before the non-uniqueness of possible routes to H0. It has unique advantages. First, mass-models was widely appreciated, researchers would lensing depends on well-understood physics: gravitation. usually fit a single family of mass models to data, Second,time-delayobservationsrequiremodestresources, leading to over-optimistic error bars. Experimenting hence low-demand telescopes can make a significant con- with different kinds of mass model for the same data tribution. Third, the galaxy models used to convert pointed to much larger uncertainties (Schechter et al. time-delays into H0 have made considerable progress in 1997, Saha & Williams 1997, Bernstein & Fischer 1999, the past decade. As a result, time-delay measurements Keeton et al. 2000). More recently, procedures involving have become an increasingly active research topic.1 So sampling an ensemble of models according to some prior far there are 12 secure time-delays (Table 1), of which are being preferred, in order to derive a more use- 10 yield an estimate of the Hubble constant — the ful picture of the uncertainties (Williams & Saha 2000, lens identification in PKS 1830–211remains controversial Saha & Williams 2004, Oguri et al. 2004a, Jakobsson et (Courbin et al. 2002, Winn et al. 2002), and the lensing al.2005).AfairsummaryofcurrentH resultsfromlens- 0 galaxyHE0435–122maybeanomalous(Kochanek2005). ing is that the error-bars are competitive on the young- Universe (i.e., high H ) side but the old-Universe side 0 needs improvement. 1 According to ADS, the original paper by Refsdal (1964) Clearly, to reach the 5–10% accuracy claimed pointingouttheconnectionbetweengravitationallensingtime- delays and H0 was cited on-average once every two years by some other techniques (e.g., Freedman et al. 2001, throughthe1960sand70s,whereasnowadaysitiscitedabout Spergel et al. 2003), more time-delays are needed. But to once every two weeks. run monitoring campaigns efficiently, it is important to 2 P.Saha et al.: COSMOGRAIL:theCOSmological MOnitoring of GRAvItationalLenses IV. have preliminary estimates for time-delays — witness the Table 1. The 12 time-delays measured so far, with 1σ tenfold range in the known values in Table 1 — as well error bars. Lens redshifts in parenthesis are either photo- as to identify the most promising systems to monitor. metric or based on absorption lines in the quasar images. This paper supplies such information. For a sample of 14 lensesweprovidepredictedtimedelayswithuncertainties, a rating of prospects as ‘excellent’, ‘good’, or ‘unpromis- Object Type zlens ∆tastrom ∆tobs ing’basedonbothmodelsandtheobservationalsituation, B0218+357 AD 0.68 10 10±1a,b and finally an estimate of the precision on H0 obtainable J0951+263 ID (0.24) 11 16±2c from these lenses. A companion paper by Eigenbrod et B1115+080 IQ 0.31 24 25±4d,e al.(2005;COSMOGRAIL I) is devotedto the determina- B1600+434 AD 0.41 35 51±4f tion of the optimal strategy to use in order to measure B0435–122 CQ 0.46 41 14±1g time-delays(temporalsamplingofthe lightcurves,object B1830–211 AD (0.89) 42 26+−54h visibility and variability, contamination by microlensing, B2149–274 AD 0.50 59 103±12i etc). Together, these papers help design an observational B1608+656 IQ 0.63 60 77±3j campaign. B1520+530 ID 0.72 92 130±3k J0911+055 SQ 0.77 119 146±8l An ideal time-delay lensing system has the following B1104–181 AD 0.73 345 161±7m features: 1- bright optical images, 2- large angular image separations (>1′′), 3- light path unperturbed by nearby B0957+561 ID 0.36 536 423±1n structure,4-knownoreasy-to-measurelensredshiftzlens. aCohen et al. (2000) bBiggs et al. (1999) Our sample of 14 has been selected using these criteria cJakobsson et al. (2005) dSchechteret al. (1997) as a guideline, though not a strict requirement. We have eBarkana (1997) fBurud et al. (2000) considered only objects for which the time-delay can be gKochanek et al. (2005) hLovell et al. (1998) measured in the optical. iBurud et al. (2002a) jFassnacht et al. (2002) kBurud et al. (2002b) lHjorth et al. (2002) The main results of this paper are in Sect. 3 and 4, mOfek & Maoz, D. (2003) nOscoz et al. (2001) which present ensembles of models for the 14 individual systemsandthenestimatetheprecisiontowhichH could 0 be recovered from them. But before going into details of themodels,itisusefultopreviewtheresultsandcompare them with measured systems. We do this in Sect. 2. 2. Comparing observed and predicted delays It is possible to make a preliminary prediction of time delays from image positions before any modelling, by re- calling the scales involved. In lensing theory, the geometric part of the time de- lay is of the order of the image-separation squared times DH−1, where D is the usual dimensionless distance fac- 0 tordependingoncosmology.2 Thetotaltimedelaywillbe smallerbutofthesameorder.Saha (2004)showsthatthe longest time delay can be expressed as ∆t=ϕD(cid:2)116(θ1+θ2)2H0−1(cid:3) (1) Fig.1.Plotof∆t against∆t fortheknowntime- where where θ ,θ are the lens-centric distances (in ra- obs astrom 1 2 dians) of the first and last images to arrive3 and ϕ is delay systems, showing that known and prospective sys- tems can be easily compared. Squares denote quadruple a dimensionless factor that ranges within about 0–2 for systems, triangles are for doubles. quadruples and 2–6 for doubles. The expressionin square brackets in Eq. (1) has the elegant interpretation of the fraction of the sky covered by the lens, times H−1. 0 We now define an ‘astrometric time delay’ ∆tastrom for all quadruples and 4 for all doubles. This is a useful by taking Eq. (1) and setting ϕ to a fiducial value of 1.5 preliminarypredictoroftime delays,aswe willseebelow. Table1givestheastrometricandactualobservedtime 2 Wereferalltime-delaypredictionsinthispapertothecon- cordance cosmology (Ωm = 0.3,ΩΛ = 0.7) and H0−1 = 14Gyr delays for the 11 known time-delay systems (disregarding (or H0=70 in local units). here the middle two images in quadruples, i.e., images 2 3 In this section, in order to summarize the time-delays of and 3 in the figures). The ‘type’ refers to the morpholog- manylenses, wewill makethebrutalsimplification ofneglect- ical classification introduced in Saha & Williams (2003): ing thesecond and third images in quadruples. AD = axial double, ID = inclined double, CQ = P.Saha et al.: COSMOGRAIL:theCOSmological MOnitoring of GRAvItationalLenses IV. 3 Table 2.Predictedtime-delays(and1σerrorbars)sorted by increasing astrometric delay, for objects with no mea- sured time-delay. Lens redshifts in parenthesis are either photometric or based on absorption lines in the quasar images. Object Type zlens ∆tastrom ∆tpred B1422+231 LQ 0.34 8 18+5 −5 J2026–453 IQ (0.5) 14 15+2 −6 J1155+634 AD 0.18 19 35+8 −10 J0924+021 IQ 0.39 19 12+6 −4 J1650+425 ID (0.5) 46 54+8 −13 J1335+011 AD 0.44 47 49+13 −16 J1355–225 AD (0.70) 68 89+28 −39 J1131–123 LQ 0.30 69 1376−139 J2033–472 IQ 0.66 70 72+33 −20 B1030+074 AD 0.60 75 153+29 −57 B0909+532 ID (0.83) 90 72+−1107 Fig.3. Plot of ∆tpred against ∆tobs for the current time- B1009–025 AD 0.87 98 161+−3549 delay systems. Again, squares are for quadruple systems, B0818+122 ID 0.39 111 110+16 −26 triangles for doubles. J0903+502 ID 0.39 122 110+13 −23 Howreliablearethetime-delaypredictions?Pixellated models generically involve a choice of prior (also called secondary constraints); if the prior is too different from whatlensesarereallylikethentheresultswillbeincorrect. Our prior is basically the PixeLens default; in detail, we assumed the following: 1. In most cases we required the mass profile to be inversion-symmetric about the lens centre. But if the lensing galaxy appeared very asymmetric, or the im- age morphology was unusual, we let the mass profile be asymmetric. 2. If there was evidence of external shear from the lens environmentand/ortheimagemorphology,weallowed the code to fit for constant external shear. That is to say,weallowedacontributionoftheformγ (θ2−θ2)+ 1 x y 2γ θ θ to the arrival time, with adjustable constants 2 x y γ ,γ . 1 2 ◦ 3. Thedensitygradientmustpointwithin45 ofthelens Fig.2. Plot of ∆t against ∆t for the prospec- pred astrom center(thus ensuringthatthelens iscentrallyconcen- tive time-delay systems. Error bars are 68% confidence. trated). Squares denote quadruple systems, triangles are for dou- 4. The radial mass profile must be steeper than θ−0.5. bles. That implies a 3D profile steeper than r−1.5, which is consistent with available estimates from stellar or gas dynamics; for example, Binney et al. (1991)report an core quad, LQ = long-axis quad, SQ = short-axis quad, r−1.75 profile near the Galactic centre. IQ=inclined quad. 5. The density on any pixel must be ≤ twice the average Fig.1plotsthedatasummarizedinTable1.Itisstrik- of its neighbours, except for the central pixel, which ing that while ∆tobs ranges over a factor of 40, it tracks can be arbitrarily dense. ∆t to a factor of 2. astrom Fig. 2 and Table 2 summarize our time-delay predic- Asatestwe‘postdicted’the time-delaysinthe known tions. To make these predictions we used the PixeLens systems. The results are summarized in Fig. 3. We find code (Saha & Williams 2004) to generate an ensemble of that our prior tends to overestimate the time-delays for 200modelsfor eachlens,leadingto anensemble ofmodel the systems with the largestangularseparations,perhaps time-delays, which we interpret as the probability distri- because these lenses have a significant cluster contribu- bution for the predicted time-delays. tionandtheprofilesaremuchshallowerthaninourprior. 4 P.Saha et al.: COSMOGRAIL:theCOSmological MOnitoring of GRAvItationalLenses IV. One of the discrepant lenses is PKS 1830-211, which has a double lens galaxy. The two others are B0957+561and J0911+055, which both have significant contribution by a group or cluster of galaxies along the line of sight. But 2 1 predictedtimedelaysoflessthan200daysappearreliable. The candidate lenses are all in the reliable regime. 3. Individual systems images 1-2 20 WsimeFinlaoorrwemapocrhropclheeoneldso,gtwyo.edsihscouwssthinredeivkiidnudaslolefnpsleost,.gFriorsutp,etdhebrye mber of models 10 is a mass map of the ensemble-average model. The con- nu toursinthemassmapsareinlogarithmicsteps,witheach step corresponding to a factor of 100.4 (like a magnitude 20 40 scale). The critical density contour is always the third Predicted time delay (days) from outermost. Second, we have plots showing saddle- Fig.4. Models of J1155+634 (axial double). See text in point contours. These plots also show the source position section 3 for the format. Prospects: unpromising. intheensemble-averagemodel.Thedetailedplacementof the saddle-point contours and the inferred source varies across the ensemble, but the qualitative features are ro- bust. In particular, the saddle-point contours make the time-ordering of images obvious. We will refer to individ- 1 2 ual images by their time order: 1,2 for doubles or 1,2,3,4 for quadruples, meaning that the image labelled 1 varies first, then 2, etc. Third, we have histograms for the pre- dicted time delays between different pairs of images in each lens. images 1-2 After modelling each lens, we rate its prospects as a 30 time-delay system as ‘excellent’, ‘good’, or ‘unpromising’, models bthaesecdomonpahroawtivweelela-csoenosftrmaionneidtotrhinegtiamned-dpehlaoytosmareetrayn.don mber of 20 nu 10 We remarkthat the modelling processreallyproduces a predicted distribution for H ∆t. In the present work 0 we insert a fiducial value of H to obtain a distribution 20 40 60 80 100 120 140 0 Predicted time delay (days) for ∆t, but one can equally insert a measured value of ∆t (if available) and obtain a distribution for H . But if Fig.5. Models of J1355–225 (axial double). Prospects: 0 twoormoretimedelaysbecomeavailableforaquadruple, good. their ratio provides a new constraint on the lens, and the modelling code must be run again. 1 3.1. Axial doubles J1155+634 [Fig. 4] discovery: Pindor et al. (2004). The 2 separation ∆θ = 1.83′′ is relatively large, but the lens galaxy is only ∼ 0.2′′ from the fainter image. Also, the measurementzlens =0.1756issomewhatinsecurebecause 80 images 1-2 the inferred galaxy absorption features are amongst the Lyα forest lines. As a time-delay prospect, this system models 60 aJp1p3e5a5r–s2u2n5pr[Fomigi.s5in]gd.iscovery:Morgan et al. (2003a);also mber of 40 known as CTQ 327. The quasar images are bright and nu 20 the angular separation is moderate: ∆θ = 1.22′′. Models include external shear corresponding to further mass to 20 40 60 80 the NW or SE. We rate this system as a good time-delay Predicted time delay (days) prospect. Fig.6. Models of J1335+011 (axial double). Prospects: J1335+011 [Fig. 6] discovery: Oguri et al. (2004b). We excellent. rate this system as an excellent time-delay prospect. P.Saha et al.: COSMOGRAIL:theCOSmological MOnitoring of GRAvItationalLenses IV. 5 1 1 2 2 images 1-2 images 1-2 60 models models 40 mber of 40 mber of 20 nu 20 nu 100 200 20 40 60 80 Predicted time delay (days) Predicted time delay (days) Fig.7. Models of B1030+074 (axial double). Prospects: Fig.9.ModelsofJ1650+425(inclineddouble).Prospects: unpromising. excellent. 1 2 2 1 60 images 1-2 images 1-2 40 number of models 2400 number of models 20 20 40 60 80 100 100 200 Predicted time delay (days) Predicted time delay (days) Fig.10. Models of B0909+532 (inclined double). Fig.8. Models of B1009–025 (axial double). Prospects: Prospects: excellent good. 3.2. Inclined doubles B1030+074 [Fig. 7] discovery: Xanthopoulos et al. J1650+425 [Fig. 9] discovery: Morgan et al. (2003b). It (1998). Like J1155+634 it has a relatively wide separa- has significant external shear, probably from a group tion but a second image is faint and very close to the galaxytotheE.Thehighdeclinationoftheobjectsmakes galaxy. There is evidence for variability. The peak in the it possible to observe it almost continuously from the predictedtimedelaysnear180daysisinteresting,butitis northern hemisphere. This system is an excellent time- probably not wise to over-interpret, given the resolution delay prospect. of the models used in this paper.Because of the difficulty B0909+532 [Fig. 10] discovery as multiply imaged: of accurate photometry on the secondimage, we rate this Kochanek et al. (1997). The lensing galaxy is very faint, system as unpromising. which caused some early controversy until the issue was B1009–025 [Fig. 8] discovery: Surdej et al. (1993). Its settled by Oscoz et al. (1997) and Lubin et al. (2000). clean morphology, evidence of variability and a nearby The morphology and models indicate significant external foregroundQSOusableasastandardPSFallmakethisan shearfrommasstotheNEorSW,butthegalaxiesrespon- attractivetarget.However,thecombinationofanapproxi- sible havenotyetbeenidentified.Bothquasarimagesare matelyhalf-yeartime-delayandanear-equatoriallocation very bright, and their separation is ∆θ = 1.17′′. Its z lens is awkward (see Eigenbrod et al. 2005 for more details). is still insecure, but assuming that problem is solved,this We rate time-delay prospects as good. system is an excellent prospect. 6 P.Saha et al.: COSMOGRAIL:theCOSmological MOnitoring of GRAvItationalLenses IV. 2 3 2 4 1 1 images 1-2 images 1-3 30 models 40 models mber of 20 mber of 20 nu nu 10 20 40 60 80 100 120 140 160 1.0 2.0 3.0 4.0 Predicted time delay (days) Predicted time delay (days) Fig.11. Models of B0818+122 (inclined double). 40 images 3-4 Prospects: good models 30 mber of 20 nu 1 10 2 10 20 30 Predicted time delay (days) Fig.13. Models of B1422+231 (long-axis quadruple). 60 images 1-2 Prospects: good. models 40 mber of sbheetwareecnomthesefcrloomseatrgipalleatxyofgrimouapgetsomthaeySbEe.tToiomseh-doertlaytos nu 20 measure in the optical, but the delay to the fourth image canbeexpectedtobeuseful.Thelensinggalaxyiscompa- 20 40 60 80 100 120 140 160 180 rable in brightness to the faint fourth image, which com- Predicted time delay (days) plicates the photometry. Overall, prospects appear good. Fig.12. Models of J0903+502 (inclined double). J1131–123 [Fig. 14] discovery: Sluse et al. (2003). It is Prospects: good. a quadruple with large separation: 3.69′′. It is very like a largersiblingofB1422+231.Morphologyandmodelsindi- cate significant external shear from mass to the WNW or B0818+122[Fig.11]discovery:Hagen&Reimers(2000). ESE.Thereisevidenceforintrinsicvariability.Structures A chain of galaxies to the NE contribute a large external in the Einstein ring are likely to offer additional model shear. The fainter image is very close to the main lensing constraints, though they also contaminate the flux from galaxy,andaboutthe samebrightness.Overall,prospects the faint fourth image. Overall, prospects appear excel- appear good. lent. J0903+502 [Fig. 12] discovery: Johnston et al. (2003). There are several group galaxies in addition to the main 3.4. Inclined quadruples lensing galaxy, with one galaxy to the SW probably the major contributor of external shear. Both quasar images J2026–453 [Fig. 15] and J2033–472[Fig. 16] discovery: arefaint,R∼19−20,somonitoringisdifficultwitha1m- Morgan et al. (2004).InJ2026-453,morphologyandmod- class telescope. The distribution of predicted time-delays els indicate externalshearfrom mass to the E or W. This is narrow. Overall, we rate prospects as good. system so far lacksa z ; we assumed0.5,which is plau- lens sible given the colours of the galaxy. The morphology of J2033–472 suggests an asymmetric lens, and accordingly 3.3. Long-axis quadruples we have considered asymmetric models. We rate time- B1422+231 [Fig. 13] discovery:Patnaik et al. (1992). It delaysprospectsasgoodforJ2026andexcellentforJ2033. is a radio emitter with extremely accurate image posi- J0924+021 [Fig. 17] discovery:Inada et al. (2003). This tions. There is evidence of variability. Strong external is a complex and evidently asymmetric lens, but can be P.Saha et al.: COSMOGRAIL:theCOSmological MOnitoring of GRAvItationalLenses IV. 7 3 2 2 4 3 1 4 1 images 1-3 40 images 1-2 40 models models 30 mber of 20 mber of 20 nu nu 10 2 4 6 8 20 40 60 80 100 Predicted time delay (days) Predicted time delay (days) 40 images 3-4 images 2-3 40 models 30 models mber of 20 mber of 20 nu nu 10 100 200 300 2 4 6 8 10 Predicted time delay (days) Predicted time delay (days) Fig.14. Models of J1131–123 (long-axis quadruple). 60 images 3-4 Prospects: excellent. models 40 1 mber of nu 20 4 3 20 40 60 80 100 2 Predicted time delay (days) Fig.16. Models of J2033–472 (inclined quadruple). 60 images 1-2 Prospects: excellent. mber of models 40 wtweoll-omfotdheelletdimaenddelelaaydss.tHoorweleavteivr,eliymtaiggeht3prisedviecrtyionfasinfotr, nu 20 whichKeeton et al. (2005)argueistheresultofmicrolens- ing. This greatly complicates the measurements of time delays, so we current rate this lens as an unpromising 2 4 6 8 10 12 14 16 Predicted time delay (days) time-delay prospect. 40 images 3-4 4. Predicted precision for the Hubble time models 30 In the previous section, after considering detailed mod- number of 20 elelsnseass, wweelclonacsluodbedsertvhaattio5naslyscteirmcusmasrteaenxcceeslleonftaclalnd1i5- 10 dates for time-delay monitoring (J1650+425, J2033–472, B0909+532,J1335+011,J1131–123),and6 aregoodcan- 2 4 6 8 10 didates (J1355–225, J0903+502,B0818+122, B1009–025, Predicted time delay (days) B1422+231,J2026–453).WenowaskhowaccuratelyH−1 0 Fig.15. Models of J2026–453 (inclined quadruple). can be inferred if the 5 excellent candidates, or if the 11 Prospects: good. excellent or good candidates, have their time delays mea- sured accurate to 1d. We do not expect that either sce- 8 P.Saha et al.: COSMOGRAIL:theCOSmological MOnitoring of GRAvItationalLenses IV. Hubble constant (local units) 2 80 70 60 50 40 3 4 1 probability density00..24 60 images 1-2 models 40 Hubble time (2G0yr) mber of Fig.18. Hubble constant/time recovered from simulated nu 20 time delays of the 5 excellent candidates. The confidence intervals (read off by sorting the unbinned values) are 14.0+1.2Gyr at 68% and 14.0+2.9Gyr at 90%. 10 20 −0.7 −1.3 Predicted time delay (days) Hubble constant (local units) images 3-4 80 70 60 50 40 60 0.4 number of models 2400 probability density0.2 2 4 6 8 10 12 14 16 Predicted time delay (days) 20 Fig.17. Models of J0924+021 (inclined quadruple). Hubble time (Gyr) Prospects: currently unpromising. Fig.19. Hubble constant/time from simulated time de- lays of the 6 good candidates. The confidence intervals are 15.0+1.3 Gyr at 68% and 15.0+3.7 Gyr at 90%. −1.0 −1.5 nariowillbewhattranspiresinthefuture.Weexpectthat Hubble constant (local units) someofthese11lenseswillyieldaccuratetimedelaysover 80 70 60 the next 2–3 years, while some existing time-delay mea- surementsarerefined.Butthe5-lensand11-lenscasesare 0.6 drmeeealnasFoytisnsg.a.ob1fl8etsshuherorw5osgeatxtheceselrfloeecrnotavfecuratenuddriHedsa0−et1tesof.rfoaFmvoarsiliamebauclelhamtleeednasstuimrweee- probability density00..24 took a random model (from the ensemble of 200), read off its time delays rounded to the nearest day, and then 12 14 16 18 took them as simulated time delays. Any model delays Hubble time (Gyr) of ≤ 1d we treated as unmeasured. Using PixeLens, we Fig.20. Hubble constant/time from simulated time de- then modelled the 5 lenses simultaneously from the ac- lays of the 11 excellent or good lenses. This histogram tualimagepositionsandthesesimulatedtimedelays.The is simply the product of the two previous ones. From model-ensemble had 200 members, each member consist- a narrower binning, we read off the confidence intervals ing of models for all 5 lenses sharing a common H0−1 14.2+0.7Gyr at 68% and 14.4+1.9Gyr at 90%. (Saha & Williams 2004). Fig. 18 shows the resulting 200 −0.7 −0.8 values of H−1 after binning. We see that the original in- 0 put value 14 Gyr is recovered with <10% uncertainty at The 5-lens and 6-lens ensembles just described are 68% confidence, and no discernable bias. Also, the uncer- independent. Hence we can simply multiply their his- tainties are asymmetric. tograms. Fig. 20 shows the result. We recover H−1 with 0 Fig. 19 shows the result of a similar exercise using the an uncertainty of about 5%, at 68% confidence. 6goodcandidates.Theuncertaintiesaresomewhatlarger TheseresultsshowthattheHubbletimecanberecov- than in Fig. 18 and similarly asymmetric. Also, there is a ered to 5% precision even if we allow for a large diversity bias,inthesensethatthemedianvalueis15.0Gyrrather in possible mass distributions (or prior). But there is a than14.0Gyr;butthebiasisinthe68%confidencerange caveat, which needs to be addressed before a claim of 5% and hence not significant. accuracy (rather than precision) can be made. Currently, P.Saha et al.: COSMOGRAIL:theCOSmological MOnitoring of GRAvItationalLenses IV. 9 amassdistributionthatsatisfiesthelensingconstraintsis The image morphologyof a lens is correlatedwith the either allowed by the prior as a plausible galaxy lens, or uncertainty in the time delays, especially in quadruples. rejected; there is no weighting in the prior. Properly, the Corequadruplesgenericallyhaveshorttimedelaysandare priorshould weightmass models accordingto their abun- unlikely to be useful for time delays; the case of B0435- dance in the real worldof galaxies.Lack of weighting will 122 is illustrative. Long- and short-axis quadruples, hav- introduceabias.(Thisprior-inducedbiasisdifferentfrom ing three images close together, are likely to have only the small statistical bias seen in Fig. 19.) The blind tests one measurable time delay. Inclined quadruples are the in Williams & Saha (2000) would have detected biases if most promising, since they usually have two time delays they were around 20% or more. But prior-induced biases in the measurable range, and sometimes three. Among at the 5% level remain untested for. Finding them and doubles, inclined systems tend to be somewhat better then eliminating them through a weighted prior could be constrained than axial systems. Significant asymmetry in doneby calibratingagainstgalaxy-formationmodels,and the lens is a disadvantage, but in compensation, asym- is an essential theoretical programneeded to complement metry increases the chance of having three measurable the observations. time delays. Thus B1608+656 is an asymmetric inclined quadruple with three measured time delays; J2033–472 may proveto be another,andis among ourexcellent can- 5. Discussion didates. Surprisingly, a large external shear appears to reduceuncertaintiesinthetimedelay.Thisisparticularly In this paper we do three things: first, we introduce a noticeableintheinclineddoublesJ1650+425,B0909+532, simple rough predictor for time delays ∆tastrom, second, andJ0903+502,andtheshort-axisquadsB1422+231and we make model predictions for 23 time delays covering14 J1131–123. The reason is not clear; it may be that since lenses,andfinallyweestimatetheprecisionintheHubble externalshearreducesamountofmassneededinthemain time inferred from simulated data on the 11 best lenses. lens to produce multiple images, it reduces the available The main conclusion is that no single lens can usefully model-space. constrain H , but time delays accurate to ≃ 1d on > 10 0 Finally, the results from combining several lenses are lenses can yield H accurate to 5%. 0 veryencouraging.Assumingtimedelaysaccurateto1dwe In the histograms in Figs. 4–17, typically 90% of the findthatthemodel-dependentuncertaintyinH−1reduces 0 area ranges over a factor of two in time delays. Hence, a tolessthan10%oncombiningthe5bestlenses,andabout monitoring program can have 90% confidence in succeed- 5%oncombiningthebest11lenses.Theuncertaintiesare ing—providedthe quasarissufficientlyvariable—ifthe asymmetric,withthelowerlimitontheHubbletimebeing samplingallowsfortheappropriate90%-rangeofpossible tighter than the upper limit. More workneeds to be done timedelays.Thereisnosinglecharacteristicshapeforthe onthemodelpriorbeforewecantrulyattain5%accuracy, histograms, but the pattern of a low-end tail and a high- but meanwhile our results help provide both motivation endcliffiscommon.Thelargeuncertaintyinthepredicted andobservingstrategiesfor accuratetime-delaymeasure- time delaysreflectsthe largevarietyofmassmodels mod- ments. elsthatcanreproducetheobservedimagepositionsinany givenlens.Thepriorwehavefordecidingwhatisanallow- Acknowledgements. The authors thank Dr. Steve Warren for able mass model for a galaxy is very conservative, so our very helpful discussions. 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