Gaia GraL II - Gaia DR2 Gravitational Lens Systems: The Known Multiply Imaged Quasars
C. Ducourant, O. Wertz, A. Krone-Martins, R. Teixeira, J.-F. Le Campion, L. Galluccio, J. Klüter, L. Delchambre, J. Surdej, F. Mignard, J. Wambsganss, U. Bastian, M.J. Graham, S.G. Djorgovski, E. Slezak
AAstronomy & Astrophysics manuscript no. main c (cid:13)
ESO 2018May 22, 2018
Gaia GraL II –
Gaia
DR2 Gravitational Lens Systems:The Known Multiply Imaged Quasars (cid:63)
C. Ducourant , O. Wertz , A. Krone-Martins , R. Teixeira , J.-F. Le Campion , L. Galluccio , J. Klüter , L.Delchambre , J. Surdej , F. Mignard , J. Wambsganss , U. Bastian , M.J. Graham , S.G. Djorgovski , E. Slezak Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geo ff roy Saint-Hilaire, 33615 Pessac, Francee-mail: [email protected] Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany CENTRA, Faculdade de Ciências, Universidade de Lisboa, Ed. C8, Campo Grande, 1749-016 Lisboa, Portugal Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, Rua do Matão, 1226, Cidade Universitária,05508- 900 São Paulo, SP, Brazil Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Boulevard de l’Observatoire, CS 34229,06304 Nice, France Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut, Mönchhofstr. 12-14, 69120 Heidelberg,Germany Institut d’Astrophysique et de Géophysique, Université de Liège, 19c, Allée du 6 Août, B-4000 Liège, Belgium California Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91125, USAReceived May —, 2018; accepted —, —
ABSTRACT
Context.
Thanks to its spatial resolution the ESA / Gaia space mission o ff ers a unique opportunity to discover new multiply-imagedquasars and to study the already known lensed systems at sub-milliarcsecond astrometric precisions. Aims.
In this paper, we address the detection of the known multiply-imaged quasars from the
Gaia
Data Release 2 and determine theastrometric and photometric properties of the individually detected images found in the
Gaia
DR2 catalogue.
Methods.
We have compiled an exhaustive list of quasar gravitational lenses from the literature to search for counterparts in the
Gaia
Data Release 2. We then analyze the astrometric and photometric properties of these
Gaia ’s detections. To highlight the tremendouspotential of
Gaia at the sub-milliarcsecond level we finally perform a simple Bayesian modeling of the well-known gravitational lenssystem HE0435-1223, using
Gaia
Data Release 2 and HST astrometry.
Results.
From 478 known multiply imaged quasars, 200 have at least one image found in the
Gaia
Data Release 2. Among the 41known quadruply-imaged quasars of the list, 26 have at least one image in the
Gaia
Data Release 2, 12 of which are fully detected(2MASX J01471020 + + + + + Gaia astrometry compared to HST astrometry, in particular the relative positions of the background quasarsource and the centroid of the deflector. The
Gaia sub-milliarcsecond astrometry also significantly reduces the parameter correlations.
Conclusions.
Besides providing an up-to-date list of multiply imaged quasars and their detection in the
Gaia
DR2, this paper showsthat more complex modeling scenarios will certainly benefit from
Gaia sub-milliarcsecond astrometry.
Key words.
Gravitational lensing: strong, Quasars: general, Astrometry, Methods: data analysis, Catalogues, Surveys
1. Introduction
The ESA / Gaia space mission (Gaia Collaboration et al. 2016b)constitutes an exceptional opportunity to characterize and to dis-cover multiply-imaged quasars, although this was not put forthas one of the science objectives in the mission proposal. Witha spatial resolution of ∼ Gaia is roughly comparable toHST for this particular feature (e.g. Bellini et al. 2011). How-ever
Gaia being a scanning mission is unique in providing anall-sky coverage with that angular resolution. Thus, by the final
Gaia
Data Release (DR), a whole population of such multiply-imaged quasars would be revealed, providing an all-sky, and the (cid:63)
Table of lenses (confirmed and candidates, detected or not in
Gaia
DR2) is only available in electronic form at the CDS via anony-mous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http: // cdsweb.u-strasbg.fr / cgi-bin / gcat?J / A + A / first of this kind, survey of multiply imaged quasars with wellunderstood source detection biases (e.g. de Bruijne et al. 2015;Arenou et al. 2017, 2018).Several programs dedicated to systematic searches for lensesin large astronomical surveys such as SDSS, WISE, DES,PanSTARRS, among others, have been developed in recent years(e.g. More et al. 2016; Lin et al. 2017; More et al. 2017; Ostro-vski et al. 2018), and many of them rely on supervised machinelearning algorithms trained on simulations to handle the largevolume of imaging data (e.g. Petrillo et al. 2017; Perreault Lev-asseur et al. 2017; Hartley et al. 2017; Pourrahmani et al. 2018;Lanusse et al. 2018). Naturally, even if Gaia does not provideimages of the observed sources, contrary to the previously men-tioned surveys, its high angular resolution over the entire skyis a major asset to contribute to the discovery and the study ofmultiply-imaged quasars.
Article number, page 1 of 12 a r X i v : . [ a s t r o - ph . I M ] M a y & A proofs: manuscript no. main
Finet & Surdej (2016) have investigated the potential of Gaiafor gravitational lensing and compared it to the detectability withseeing-limited observations for the same limiting magnitude (G = ∼ ∼
80 would be composed by more than two images. However, theypredict that detections from space are much more encouraging,raising the number of multiply imaged quasars detectable by aGaia-like survey to ∼ ff ective angular resolution necessary to includemost of the multiply-imaged quasars. This happened due to dataprocessing issues and final astrometric quality reasons (Fabri-cius et al. 2016; Arenou et al. 2017). Yet, several multiply-imaged quasars discovered from other large surveys such as Pan-STARRS, DES, SDSS-III BOSS, HSCS or VST-ATLAS, weresubsequently identified with at least one Gaia
DR1 detection(e.g. Agnello et al. 2015; Agnello 2017; Lemon et al. 2017; Ag-nello et al. 2018).The
Gaia
Data Release 2 (DR2; Gaia Collaboration 2018)on the other hand, starts to reach e ff ective angular resolutionsthat are capable of resolving more multiply-imaged quasars (ex-pected with typical separations below 1"). The Gaia
DR2 e ff ec-tive resolution reaches ∼ . ∼ .
2" (Gaia Collaboration 2018). However this res-olution applies strictly only to astrometry and G band photome-try; color data are available for objects with separations downto ∼ ∼ .
5" (Gaia Collabo-ration 2018). Even if it is still far from the ultimate resolvingpower of the
Gaia instrument, the
Gaia
DR2 is a significant ad-vance over DR1, as beyond its much improved e ff ective angu-lar resolution, it contains five-parameters astrometric data (po-sitions, proper-motions, parallax) and also color information formost objects. This simplifies significantly the extraction of gen-uine extragalactic sources from the galactic stellar contaminants.Only the faintest or most problematic objects are characterizedby just a two-parameters solution in this data release, which isunfortunately the case for several multiply imaged quasars sincetheir magnitudes are often close to the Gaia limiting sensitivityat (G ∼ ff ort to discover and study multiply-imaged quasar candidates from the various Gaia Data Releases,our group first searched for new lensed systems around knownor candidate quasars, enabling the discovery of highly probablemultiply-imaged quasar candidates for the first time from Gaia data alone (
Gaia
GraL Paper I; Krone-Martins et al. 2018). In thepresent work, we report our findings regarding the identificationof known gravitationally lensed quasars in
Gaia
DR2. We ana-lyze the statistical astrometric properties of the detected lensedimages and provide improved relative astrometry for them. Wealso derive soft astrometric filters that will be applied, as part ofa global blind search (
Gaia
GraL paper III; Delchambre et al. inprep), to di ff erentiate foreground stars from extragalactic objectswithout rejecting the faint components of known lensed systems.To illustrate how the exquisite optical astrometry of Gaia at thesub-milliarcsecond level may help to better constrain the lenses,we perform a simple modeling of the quadruple lens HE0435-1223 in a Bayesian framework, both using
Gaia and HST as-trometry, for comparison purposes. The paper is organized as follows: In Sect. 2 we describethe construction of our list of gravitationally lensed quasars andcandidates from published data. Sect. 3 presents the matchingstatistics of this list of known systems with the
Gaia
DR2. Sect. 4presents the astrometric properties of the
Gaia
DR2 data for theknown systems. A simple modeling within the Bayesian frame-work of a known lens using
Gaia
DR2 astrometry is describedand discussed in Sect. 5. Finally, we summarize our findings inSect. 6.
2. Compiled list of gravitationally lensed quasars
We have attempted to compile an as-complete-as-possible list ofknown gravitationally lensed quasars published in the literatureprior to the
Gaia
DR2, including some recent candidates that arenot yet spectroscopically confirmed. The major source of knowngravitational lenses included in our list is the CASTLES (CfA-Arizona Space Telescope LEns Survey of gravitational lenses)site (Kochanek et al. 1999) providing information for about100 lenses, most of them observed with HST. Another importantsingle source of known multiply imaged quasars is the SDSSQuasar Lens Search site (SQLS) , aimed to discover lensedquasars from the large homogeneous data of the Sloan DigitalSky Survey (SDSS) providing data on 49 additional lensed sys-tems. We also included several quasar systems from the Mas-ter Lens Database (Moustakas 2012) , a community-supportedcompilation of all discovered strong gravitational lenses. Finallywe complemented our list with recent and more scattered discov-eries from the literature. This list is being kept up-to-date, andwill be maintained at least until the final Gaia
Data Release. Forthe sake of completeness, we also included in this list the candi-dates with indication in the literature of just one image (usuallyspectroscopic candidates) expecting from the exceptional resolv-ing power of
Gaia that it may resolve some of them into multipleimages in one of its Data Releases.Our resulting list of published lensed or lens-candidatequasars contains 478 systems (234 confirmed systems and 244lensed quasar candidates). This list is only available in electronicform at the CDS, including access through Virtual Observatoryready tools, it comprises lens identifiers, references and the Gaiaastrometry and photometry when a match was found in the DR2.The summarized statistical properties of our list in terms of num-ber of systems with 1, 2, 3 and 4 and more images and status aregiven in Table1.
3. Gravitationally lensed quasars in Gaia DR2
We extracted sources from the
Gaia
Data Release 2 within aradius of 10" around each source of our compiled list of knowngravitationally lensed quasars using ADQL and the
Gaia archivefacility at ESAC (Salgado et al. 2017). We obtained the posi-tions ( α, δ ), parallaxes ( (cid:36) ), proper-motion components ( µ α , µ δ )and fluxes in the G , G BP and G RP pass-bands (Evans et al. 2018)along with their respective uncertainties.For each individual image of each system, we performed apositional cross-match within a maximum angular separation of0.5" between the astrometry found in the literature and the Gaia
DR2. We visually inspected all systems one by one, by com-paring the
Gaia
DR2 detections to the system discovery papers https: // / castles / http: // / sdss / sqls / lens.html http: // admin.masterlens.org / index.php?Article number, page 2 of 12. Ducourant et al.: Gaia GraL II – The Known Lensed Quasars in Gaia
DR2 and / or archival images from Aladin (Bonnarel et al. 2000; Boch& Fernique 2014).Of the 478 gravitational lens systems (including candidates),200 have at least one image matched with a Gaia
DR2 source.The overall detection statistics of known systems that result fromour examination is given in Table 1. An all-sky chart in galacticcoordinates of the known lenses is shown in Fig. 1 along with aspecification of the
Gaia detection.In Table 4 we present an extract of our list containing thelenses with three and more images for which at least one matchwas found in the
Gaia
DR2. The complete list of lenses and de-tection is available in electronic form only at the CDS.Of the 41 known systems with four images (or more), 26have at least one image detected in
Gaia
DR2. Within this group,one system has just one image detected, 7 have two images,6 have three images and 12 are fully detected with four imageseen in the
Gaia data around the target direction. In Fig. A.1, weprovide charts for the 12 systems with four detections with theGaia DR2 positions referred to the A image (the brightest im-age in the system discovery passband) together with flux ratios.Of those which are fully detected, only five are characterizedby sub-milliarcsec astrometry, and are reported in Table 2. Thefainter image (in G band) of the others is detected but poorlyconstrained. Table 1.
Statistics of the known multiply imaged quasars present inour reference list (col. 2) and of the corresponding detected systemsin the
Gaia
Data Release 2 (col. 3). A lensed system is considered tobe detected in the
Gaia
DR2 if at least one of its images is detected.Numbers in parentheses correspond to the gravitationally lensed quasarcandidates not spectroscopically confirmed yet.
Lensed Number of Number detectedimages known lenses in
Gaia
DR21 55 + (213) =
268 11 + (17) =
282 133 + (28) =
161 112 + (28) = + (2) = + (2) = + + (1) =
41 25 + (1) = + (244) =
478 152 + (48) =
4. Astrometric properties of the Gaia DR2gravitationally lensed quasars
The images of a quasar produced by strong gravitational lensingare peculiar since they are not independent astronomical sourcesbut multiple images of the same source, possibly with part ofthe host galaxy visible as small segments of an arc. Accord-ingly, they can produce some particular astrometric signatures inthe
Gaia
DR2 solution, that could be helpful to discover furtherlensed quasar systems in the
Gaia data.Of the 382 individual images found in the
Gaia
DR2 com-ing from the 152 confirmed gravitationally lensed quasars withtwo or more images, 65 have a
Gaia
Gaia
DR2 astrometric solu-tion selection). The other 317 images have complete 5-parametersolutions ( α, δ, µ α cos ( δ ) , µ δ , (cid:36) ). We investigated the statisticalproperties of the Gaia
DR2 parameters of the multiple imagesof the known gravitationally lensed quasars, with results shownin Fig.2. This figure shows that parallaxes and proper motions ofthe images resulting from lensing occasionally reach large valuesfor sources expected to have neither parallax nor motion. How-ever, this results from the fact that these images are rather faint,
Table 2.
Relative astrometry for five known quadruply imaged quasarsfully detected in the
Gaia
DR2. The image references have been chosento match those reported either in https: // / castles / orin their reference papers. They are not necessarily the brightest imagesin the Gaia
G-band.
Identifier ∆ α cos( δ ) (mas) ∆ δ (mas)HE0435-1223A 0 . ± .
16 0 . ± . − . ± .
19 552 . ± . − . ± . − . ± . − . ± . − . ± . + . ± .
35 0 . ± .
52B 1315 . ± .
36 3531 . ± . − . ± . − . ± . − . ± .
21 9701 . ± . . ± .
36 1118 . ± .
23B 617 . ± .
39 2305 . ± .
25C 0 . ± .
47 0 . ± . − . ± .
60 1993 . ± . . ± .
11 0 . ± .
07B 729 . ± .
11 1755 . ± . − . ± . − . ± . − . ± .
28 1366 . ± . − . ± .
33 1261 . ± . − . ± .
26 1375 . ± .
30B 0 . ± .
27 0 . ± . − . ± . − . ± . Gaia
DR2 sensitivity where the uncertaintiesfrom random noise are also large. In addition it may be also thecase that some sources / images are embedded in extended anddi ff use structures.In a search for multiply imaged quasars in the Gaia
DR2, ap-plying a straight astrometric filter aiming at excluding stars fromthe deviation from zero parallaxes and proper motions weightedby the expected uncertainties, would likely also exclude a largenumber of images of lenses. So, based on the distribution ofthese parameters for the known lenses, we established the fol-lowing softer astrometric cuts, that at the expense of a certainlevel of stellar contamination, avoid the rejection of genuine lenssystems or of one or several images within a system.
Gaia DR2 sources that should be accepted to such a searchwould likely comply with (cid:36) -3 σ (cid:36) < | µ | − σ µ < / yr). We note here that µ stands for µ α cos ( δ ) and µ δ .Indeed, we also adopted these soft filters in Gaia
GraL PaperI (Krone-Martins et al. 2018), where we presented the first everdiscoveries of quadruply imaged quasar candidates from data ofan astrometric space mission. These statistical astrometric prop-erties derived from
Gaia measurements are also being used in alarge, machine learning based, systematic blind-search for lensesin
Gaia
DR2 (
Gaia
GraL Paper III; Delchambre et al., in prep).
5. Gravitational lens modeling with sub-masastrometry
Gravitational lensing provides an e ffi cient tool to explore vari-ous aspects of our universe and several of its components. In thestrong regime, the inference of physically meaningful quantities Article number, page 3 of 12 & A proofs: manuscript no. main ll l lllll ll lllllll l l llllll lllllll lll llllll llll llll lll llll lllllll llllllll lllllllll ll lllll llll llllll ll lllll llllll lllll llllll lll lllllllll llll l l l l llllllllllll lllll lllll l llll llllll llllll l ll lllll lll lll lllll lll llll llll llllllllll lllllllll l ll llll llllllll l l llll lllllllll llll lllllllll l llllll lll ll ll llllll lllllllllllll lllll llllllllllll llll lllll llllllllll l llll llllll llllll ll l ll llll lllll lll l ll lllll l llll l llllllll llllllllllll l llllll lll llllllllllllll lllllllll ll lllllll llll llllllllllll l l llllll ll lllll l ll lll ll llll l llllllllll ll llll ll ll lllllll llll l llllllll ll lll lllll lllll llllllll l ll lll llll llllllllllllllll lllll lll lllllllll llllllllllllll lllllllll l llll lllllllllllll llll llllllllll l lllllllll llllll llll llll l ll llll llllll llllllllll l lllllllll lllllll lll lllll llllll llll lllll ll lll lll llllllll l llllllllllll ll llllll llllllll llllllllllllllll l llllll llll lllll lll llll lll llllllll ll lllll lllll lllllll l lll llll lll l lllll llll lll l llll l llllll llll l lllllllll lllllllllll lllll llll llllll ll ll ll lllllll llllllllllllllllll ll ll lllllllllllll llll llllllllll ll l lll l llll − − − − − ll l lllll ll lllllllll llllll llllllllll llllll llll llll lll llll lllllll llllllll lllllllll ll lllll llll llllll ll lllll llllll lllll lllllllll lllllllllllll l l l lllllllllllll lllll lllll l llll llllll llllll l ll lllll lll lll lllll lll llll llll llllllllll llllllllll ll llll lllllllll l llll lllllllll llll lllllllll l llllll lll ll ll llllll lllllllllllll lllll llllllllllll llll lllll llllllllll l llll llllll llllllll l ll llll lllll lll l ll lllll l llll l llllllll llllllllllll l llllll lll llllllllllllll lllllllll ll lllllll llll llllllllllll l l llllll ll llllll ll lll ll llll l llllllllll ll llll ll ll lllllll llll l llllllll ll lll lllll lllll lllllllll ll lllllll llllllllllllllll lllll llllllllllll llllllllllllll lllllllll l llll lllllllllllll llll llllllllll l lllllllll llllll llll llll l ll llll llllll llllllllll l lllllllll lllllll lll lllll llllll llll lllll ll lll lll llllllll l llllllllllll ll llllll llllllll llllllllllllllll l llllll llll lllll lllllll lll llllllll ll llllllllll lllllll l lll llll llll lllll llll lllllllllllllll llll l lllllllll lllllllllll lllll llll llllllllll ll lllllll llllllllllllllllll ll ll lllllllllllll llll llllllllll ll llll l llll llllll llll llll lllllll llllll lllll lllll llllllllllllll llllll lllll lllllllll lllll llll lll llllllllll llllll lllll llllllllllllll ll lllllllll llllll llll lllllllllllllllll lllll lllllll llll llllllll llllll lllll llllllll lll llll lllllllllllllll llllllllll lllllllllll llllllllllll llllll lllllll lll llll lllll lllllll llll llllllllll lllll lllll llllll llllll lllllll llllllllll llllllllllllllll lllllll lllllllll llllll ll llll llllll lll llllllllllll lllll llllll llll llll ll lll lll llllllllllllllllll l lllllllllll lllllllllllll llll llllllllllll ll lllllllllll lllllllll lllll llll llllllllll ll lllllll llllllllll lllllllllll llll lllllll ll ll l llll lllllllllllll lllll llllllll llll lllllllll lllllllllll llllllllllllll llllll llllllll llllll lllll llllllllllll llll llll Known lensN
DR2 = 1, 2N
DR2 = DR2 ‡ Fig. 1.
All-sky chart in galactic coordinates with the galactic anti-center in the middle. The known multiply-imaged quasars are indicated in gray.The systems presenting one or two counterparts in
Gaia
DR2 are surrounded by a green open circle. The systems with three
Gaia
DR2 detectionsare indicated with purple filled circles, while the systems with four or more detections are indicated with orange filled circles. m a cos d [mas/yr] D en s i t y m d [mas/yr] D en s i t y v [mas] D en s i t y s m a cos d [mas/yr] D en s i t y s m d [mas/yr] D en s i t y s v [mas] D en s i t y Fig. 2.
Distributions of the astrometric parameters and their uncertainties for all the
Gaia
DR2 counterparts of the individual images of knownmultiply-imaged quasars with five parameter astrometric solutions.Article number, page 4 of 12. Ducourant et al.: Gaia GraL II – The Known Lensed Quasars in
Gaia
DR2 .
192 1 .
196 1 .
200 1 .
204 1 . . . . . q .
88 0 .
92 0 .
96 1 . − − − − θ q ( ◦ ) − − − − . . . . γ .
072 0 .
080 0 .
088 0 . .
192 1 .
196 1 .
200 1 .
204 1 . θ E ( ) . . . . θ γ ( ◦ ) .
88 0 .
92 0 .
96 1 . q − − − − θ q ( ◦ ) .
072 0 .
080 0 .
088 0 . γ . . . . θ γ ( ◦ ) Fig. 3.
Results of the MCMC simulations for HE0435-1223, displayed as a corner plot for the five model parameters. The diagonal panels illustratethe posterior PDFs while the o ff -axis panels illustrate the correlation between the parameters. We show the results obtained from Gaia ’s data withshaded red contours and red histograms and with HST data with shaded black contours and black histograms. The three inner contours representthe 68 . . .
7% confidence intervals. from observational data usually requires the accurate modelingof the gravitational potential of the deflector. For example, theability of modern time delay cosmography to infer the Hubbleconstant H with a competitive precision relies significantly onits capacity in dealing with families of degeneracies existing be-tween di ff erent plausible lens mass profiles (Saha 2000; Wuck-nitz 2002; Liesenborgs & De Rijcke 2012; Schneider & Sluse2013). To probe the deflector mass distribution in the regionwhere multiple images are formed, simple parametrized massmodels are commonly used whose parameters are fixed by theobservational constraints (e.g. Keeton 2001, 2010; Lefor & Fu- tamase 2013; Lefor 2014), typically the lensed quasar image po-sitions, the morphology of extended components, microlensing-free flux ratios, and time delays between image pairs. Nat-urally, a better accuracy in the observed parameters leads toa more reliable model. For the five known lenses RXJ1131-1231, SDSS1004 + Gaia
DR2 provides quasar image po-sition measurements with an unprecedented precision of a fewtenths of a milliarcsecond. With an order of magnitude improve-ment over typical HST astrometric accuracy, these new astromet-ric data should help to better constrain the lens models. Consid-
Article number, page 5 of 12 & A proofs: manuscript no. main − . − . − . − . − . − . − . − . β y ( ) − . − . − . − . − . − . − . − . x G ( ) − . − . − . − . − . − . − . − . β x ( ) − . − . − . − . y G ( ) − . − . − . − . β y ( ) − . − . − . − . x G ( ) − . − . − . − . y G ( ) Fig. 4.
Results of the MCMC simulations for HE0435-1223, displayed as a corner plot for the source and deflector positions. The diagonal panelsillustrate the posterior PDFs while the o ff -axis panels illustrate the correlation between the parameters. We show the results obtained from Gaia ’sdata with shaded red contours and red histograms and with HST data with shaded black contours and black histograms. The three inner contoursrepresent the 68 . . .
7% confidence intervals. ering four of the five known quadruply imaged quasars reportedin Table 2 for which Gaia and HST astrometric data are avail-able, the average of the Gaia astrometric uncertainties a ff ectingthe equatorial coordinates of the four lensed quasar images isfound to be 0.43 mas compared to 3.29 mas using the corre-sponding HST data. This represents a huge gain (by more than afactor 7) in astrometric precision.In this section, we illustrate how the improved astrometricaccuracy obtained with Gaia may impact the lens modeling. Tothis end, we propose to optimize a smooth model to the ob- served image positions only, within the Bayesian framework.The idea consists in simultaneously sampling the posterior Prob-ability Density Functions (PDFs) for all model parameters usinga Markov Chain Monte Carlo (MCMC) method, and then com-paring the PDFs obtained from Gaia’s astrometry with the onesderived from the astrometry found in the literature. We want topoint out that our objective here is not to construct a set of re-alistic lens models in the sense that they could be used to per-form time delay cosmography. Instead, we focus on how
Gaia astrometric uncertainties may positively a ff ect the goodness of Article number, page 6 of 12. Ducourant et al.: Gaia GraL II – The Known Lensed Quasars in
Gaia
DR2 a more complex fit, which would include microlensing-free fluxratios, time delays, non-lensing data related to the main deflector,or even simultaneous reconstruction of the source and deflectorsurface brightnesses.We model the main deflector as a singular isothermal el-lipsoid (SIE, see e.g. Kormann et al. 1994) which e ff ectivelydescribes the mass distribution of a massive early-type galaxyin the region where multiple images are formed (Gilman et al.2017). An SIE is characterized by five free parameters; the Ein-stein radius θ E , the elliptical axes ratio q and position angle θ q ,and the lens centroid ( x G , y G ) with respect to image A. Since thelensed quasar image positions are generally most sensitive to thelocal mass distribution, we model the large-scale contributionsand possible close line-of-sight galaxy perturbing e ff ects withan external shear term characterized by its absolute value γ andposition angle θ γ . The model is thus kept simple, which lim-its the number of free parameters and avoids the use of the fullmulti-plane lensing formalism (Schneider 2014; McCully et al.2014, 2016). In addition, we consider the position of the point-like source ( β x , β y ) with respect to image A that is also free tovary during the optimization process, bringing the number offree parameters n k to nine.To draw samples from the posterior PDFs, we used emcee (Foreman-Mackey et al. 2013), a python package which imple-ments the a ffi ne invariant ensemble sampler for MCMC pro-posed by Goodman & Weare (2010). Since we only use thelensed image positions θ obs as observational data to fit, the log-likelihood function simply readsln p ( θ obs | k ) = − N (cid:88) j = (cid:16) θ obs , j − θ model , j ( k ) (cid:17) σ , j − ln (cid:16) σ , j (cid:17) , (1)where k is the vector of free parameters, N the number of lensedimages (hence 2 N constraints), σ obs the astrometric uncertain-ties, and θ model ( k ) the lensed image positions obtained fromthe free parameters k and generated with the python package pySPT (Wertz & Orthen 2018). To control the sampling, onlytwo hyperparameters need to be tuned: an adjustable scale pa-rameter a and the number N w of walkers. The scale parameter a has a direct impact on the acceptance rate of each walker,namely the ratio of accepted to proposed candidates, and wasset to a =
2, following Goodman & Weare (2010). A walker canbe seen as a Metropolis-Hastings chain (see, e.g., MacKay 2003)whose associated proposal distribution depends on the positionsof all the other walkers (Foreman-Mackey et al. 2013). Prior torun the MCMC, we initialized N w =
350 walkers in a small n k -dimensional ball of the parameter space around a highly prob-able solution, formerly obtained using the public lens modelingcode lensmodel (v1.99, Keeton 2001). Obviously this initialmodel may not be the most appropriate one and is more likely alocal solution in the parameter space. Nevertheless, it constitutesa valid starting point to illustrate our intention.The analysis has been performed for the five lenses from Ta-ble 2 for which HST image position measurements are avail-able, namely HE0435-1223, SDSS1004 + https: // github.com / dfm / emcee https: // github.com / owertz / pySPT http: // physics.rutgers.edu / keeton / gravlens / / Table 3.
The SIEg lens model parameters derived for HE0435-1223.The reported values are medians within 1 σ error bars. Parameters HST
Gaia θ E (") 1 . ± .
003 1 . ± . q . ± .
03 0 . ± . θ q ( ◦ ) − . ± . − . ± . γ . ± .
005 0 . ± . θ γ ( ◦ ) 15 . ± . . ± . β x (mas) − . ± . − . ± . β y (mas) − . ± . − . ± . x G (mas) − . ± . − . ± . y G (mas) − . ± . − . ± . / F160W, Robberto et al. 2002) mounted onthe HST come from Kochanek et al. (2006), showing astrometricuncertainties between 3 and 5 mas. As expected, all the poste-rior PDFs obtained from
Gaia ’s data show narrower widths thanthose obtained from HST data, while some of them are slightlyshifted. Thus the use of
Gaia ’s astrometry significantly reducesthe ranges of valid model parameters around a highly probablesolution, as shown in Table 3. The least sensitive parameter isthe Einstein radius, even if it is improved three-folded with re-spect to HST observations. In particular, the source position isconstrained within a σ -error ellipse of ( σ β x , σ β y ) = (0 . , . Gaia clearly helps to better constrainthe position of the point-like source as well as the source surfacebrightness reconstruction as part of a more realistic modelingscenario.We also note that the
Gaia
DR2 astrometry reduces signif-icantly the resulting correlation structure between the modeledparameters, in comparison with the correlations obtained fromthe modeling using HST data: the absolute value of the correla-tion coe ffi cients between θ q and θ γ , and θ q and q , in Fig. 3 andbetween β y and y G , and β x and x G in Fig. 4, are clearly reducedthanks to the improved astrometry.A more advanced version of the lens modeling within theBayesian framework described in this section will be consis-tently applied to all the known lenses and to the highly probablelens candidates discovered from the systematic blind-search forlenses in the entire Gaia
DR2 (
Gaia
GraL Paper III, Delchambreet al., in prep), and this will be presented in a forthcoming work(
Gaia
GraL Paper IV, Wertz et al., in prep).
6. Conclusions
The availability of high-precision and high-accuracy astrometricdata as provided by the ESA / Gaia space mission opens a newwindow to detect and model gravitationally lensed quasar sys-tems with an unprecedented refinement. This is bound to impacton fundamental applications in astronomy that are derived fromthis phenomena, such as the study of the lensing galaxy popu-lations, distant quasars, dark matter and dark energy propertiesand consequently the determination of cosmological parameters.To exploit this new field with
Gaia data we have set up a collab-oration group, the
Gaia
GraL team, to systematically analyze thegravitationally lensed quasar content throughout the
Gaia
DataReleases. The topics covered include searches for new multiplyimaged quasar candidates, identifications of known lenses in the
Gaia data, modeling of the lenses using the outstanding
Gaia astrometry and multi-colour photometry, and fostering ground-based follow-up for final confirmation.
Article number, page 7 of 12 & A proofs: manuscript no. main
In this paper we explain how we first generated an up-to-datelist of known gravitationally lensed quasars, including lensedquasars too faint to be observed by
Gaia . The
Gaia
GraL listof known gravitationally lensed quasars will be kept up-to-datewith respect to the astronomical literature at least until the final
Gaia
Data Release. Each
Gaia
Data Release will be analyzed toverify the detection of known gravitational lenses.Then we provide here the first ever sub-milliarcsecond as-trometric data for hundreds of known gravitationally lensedquasars. The search is based on the aforementioned list matchedto the
Gaia
DR2 astrometric catalogue, the largest and mostprecise astrometric reference available to date. Our lens resultsbring almost one order of magnitude improvement in astromet-ric precision compared to a typical HST observation. More-over, even if
Gaia
DR2 is still an early Data Release lackingmany lensed images, it brings high-precision astrometry com-plemented with photometric data for most known lensed sys-tems. Thus, it provides a glimpse of the content that will becomeavailable in the forthcoming Gaia Data Releases.Of the 478 presently known – or candidate – gravitation-ally lensed quasars, we have found in the
Gaia
DR2 at least onecounterpart for 200 of them. From these objects, the quadruply-imaged quasars occupy a specially relevant place, as they pro-vide the more stringent physical parameter inferences. There are41 presently known quads. From these, 25 have been found withat least one entry in
Gaia
DR2 and 12 of them are fully detectedwith all four images. As the images of many of these objectshave smaller angular separations than the
Gaia
DR2 best angu-lar resolution, we expect however the forthcoming Data Releasesto provide information for most of them when the releases grad-ually reach the expected
Gaia best spatial resolution. We providealso
Gaia
DR2 astrometric and photometric data for all knownlenses to date.Finally, we show that the adoption of high-precision as-trometry from
Gaia
DR2 to model the well-known lens systemHE0435-1223 results in a significant improvement in constrain-ing the lens parameters of a NSIEg model around a highly prob-able solution, and that it also significantly reduces the parametercorrelations, in comparison to standard HST astrometry. Suchconstraints will certainly be further improved with the increasedprecision of
Gaia ’s forthcoming nominal mission Data Releases,expected for 2020 (DR3) and 2022 (DR4), and the still to be an-nounced Data Release(s) of the
Gaia mission extension.As a final conclusion this work vividly demonstrates the sig-nificant impact of high-precision astrometry from
Gaia and fu-ture mission concepts as the JASMINE series (Gouda 2011), Ga-iaNIR (Hobbs et al. 2016), and Theia (The Theia Collaborationet al. 2017), to the study of strong gravitational lensing. This pa-per also exemplifies the ever wider impact of the
Gaia satellite,pushing its limits from its original goal of studying the MilkyWay galaxy towards more distant extragalactic sources and as-sociated phenomena.
Acknowledgements.
AKM acknowledges the support from the Por-tuguese Fundação para a Ciência e a Tecnologia (FCT) through grantsSFRH / BPD / / / FIS / / / / / NL / HB and from the Caltech Division of Physics, Mathematicsand Astronomy for hosting a research leave during 2017-2018, when thispaper was prepared. LD and JS acknowledge support from the ESA PRODEXProgramme ‘Gaia-DPAC QSOs’ and from the Belgian Federal SciencePolicy O ffi ce. OW acknowledges support from a fellowship for PostdoctoralResearchers by the Alexander von Humboldt Foundation. SGD and MJGacknowledge a partial support from the NSF grants AST-1413600 and AST-1518308, and the NASA grant 16-ADAP16-0232. We acknowledge partialsupport from ‘Actions sur projet INSU-PNGRAM’, and from the Brazil-Franceexchange programmes Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior(CAPES) – Comité Français d’Évaluation de la Coopération Universitaire etScientifique avec le Brésil (COFECUB). The authors wish to thank C. SpindolaDuarte for her help with the source referencing. This work has made use ofthe computing facilities of the Laboratory of Astroinformatics (IAG / USP,NAT / Unicsul), whose purchase was made possible by the Brazilian agencyFAPESP (grant 2009 / Gaia , the data from which were processedby the
Gaia
Data Processing and Analysis Consortium (DPAC). Funding for theDPAC has been provided by national institutions, in particular the institutionsparticipating in the
Gaia
Multilateral Agreement. The
Gaia mission website is:http: // / gaia. Some of the authors are members of the Gaia
Data Processing and Analysis Consortium (DPAC).
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P G + B . ± . . ± . . ± . P G + A . ± . . ± . . ± . . ± . . ± . P G + C . ± . . ± . . ± . . ± . . ± . P G + A . ± . . ± . . ± . . ± . . ± . R X J - D . ± . - . ± . . ± . R X J - C . ± . - . ± . . ± . R X J - A . ± . - . ± . . ± . . ± . . ± . R X J - B . ± . - . ± . . ± . M A SS J - C . ± . - . ± . . ± . . ± . . ± . M A SS J - D . ± . - . ± . . ± . M A SS J - A . ± . - . ± . . ± . . ± . . ± . M A SS J - B . ± . - . ± . . ± . . ± . . ± . S D SS + A . ± . . ± . . ± . . ± . . ± . S D SS J . + . A . ± . . ± . . ± . . ± . . ± . S D SS J . + . B . ± . . ± . . ± . S D SS J . + . A . ± . . ± . . ± . . ± . . ± . S D SS J . + . B . ± . . ± . . ± . M A SS J - D . ± . - . ± . . ± . . ± . . ± . M A SS J - C . ± . - . ± . . ± . M A SS J - B . ± . - . ± . . ± . . ± . . ± . M A SS J - A . ± . - . ± . . ± . . ± . . ± . Article number, page 10 of 12. Ducourant et al.: Gaia GraL II – The Known Lensed Quasars in
Gaia
DR2 T a b l e . c on ti nu e d . N a m e r e f N i m G a i a S ou r ce I d R i gh t a s ce n s i on D ec li n a ti on GG B P G R P [ ◦ ] ± [ m a s ][ ◦ ] ± [ m a s ][ m a g ][ m a g ][ m a g ] S D SS J + C . ± . . ± . . ± . S D SS J + A B . ± . . ± . . ± . . ± . . ± . J + B . ± . . ± . . ± . J + A . ± . . ± . . ± . . ± . . ± . H + C . ± . . ± . . ± . H + A . ± . . ± . . ± . . ± . . ± . H + B . ± . . ± . . ± . . ± . . ± . B + C . ± . . ± . . ± . B + B . ± . . ± . . ± . B + A . ± . . ± . . ± . . ± . . ± . B + D . ± . . ± . . ± . S D SS J + C . ± . . ± . . ± . S D SS J + A . ± . . ± . . ± . . ± . . ± . S D SS J + B . ± . . ± . . ± . . ± . . ± . J - C . ± . - . ± . . ± . ± J - D . ± . - . ± . . ± . ± J - A . ± . - . ± . . ± . . ± . . ± . J - B . ± . - . ± . . ± . . ± . . ± . J + C . ± . . ± . . ± . ± J + B . ± . . ± . . ± . ± J + D . ± . . ± . . ± . ± J + A . ± . . ± . . ± . . ± . . ± . J + ? *3241729026461820390400260 . ± . . ± . . ± . . ± . . ± . W F I - B . ± . - . ± . . ± . W F I - A . ± . - . ± . . ± . . ± . . ± . W F I - A . ± . - . ± . . ± . . ± . . ± . W F I - C . ± . - . ± . . ± . ± W F I - A . ± . - . ± . . ± . ± W F I - B . ± . - . ± . . ± . . ± . . ± . W GD - C *3546681326549578891648309 . ± . - . ± . . ± . W GD - A *3546681326549580116864309 . ± . - . ± . . ± . . ± . . ± . W GD - D *3546681326549578891392309 . ± . - . ± . . ± . W GD - B *3546681326549578891520309 . ± . - . ± . . ± . PS J - A . ± . - . ± . . ± . . ± . . ± . PS J - B . ± . - . ± . . ± . . ± . . ± . PS J - C . ± . - . ± . . ± . W GD - B . ± . - . ± . . ± . W GD - A . ± . - . ± . . ± . . ± . . ± . W GD - C . ± . - . ± . . ± . . ± . . ± . Q + B . ± . . ± . . ± . Q + A . ± . . ± . . ± . . ± . . ± . N o t e s . . W GD - :t h e i m a g e s ( A , B , C , D ) h a v e b ee n a tt r i bu t e d f o ll o w i ng i n c r ea s i ng G m a g , a ndno t f o ll o w i ng A gn e ll o e t a l . ( ) s i n cee v e n c on s i d e r i ng t h e pho t o m e t r i c d a t a fr o m t h ea f o r e m e n ti on e dp a p e r t h i s w ou l db e t h e d ec r ea s i ng fl uxo r d e r . N o t e s . . J - :t h e i m a g e s ( A , B , C ) h a v e b ee n a tt r i bu t e d f o ll o w i ng i n c r ea s i ng G m a g , a ndno t f o ll o w i ng L i n e t a l . ( ) . R e f ere n ce s . ( ) B l ac kbu r n ee t a l . ( ) , ( ) J ac k s on e t a l . ( ) , ( ) G ho s h & N a r a s i m h a ( ) , ( )I n a d ae t a l . ( ) , ( )I n a d ae t a l . ( ) , ( ) J ac k s on e t a l . ( ) , ( )I n a d ae t a l . ( ) , ( ) A gn e ll o e t a l . ( ) , ( ) L i m ou s i n e t a l . ( ) , ( ) M o r ee t a l . ( ) , ( )I nou ee t a l . ( ) , ( ) A r a v e n ae t a l . ( ) , ( ) R u s u e t a l . ( ) , ( ) G o i c o ec h ea & S h a l y a p i n ( ) , ( ) L ee t ho c h a w a lit e t a l . ( ) , ( ) N a yy e r i e t a l . ( ) , ( ) P a rr y e t a l . ( ) , ( ) S e r g e y e v e t a l . ( ) , ( ) S hu e t a l . ( ) , ( ) M o r ee t a l . ( ) , ( ) A gn e ll o e t a l . ( ) , ( ) A gn e ll o ( ) , ( ) L i n e t a l . ( ) , ( ) O s t r ov s k i e t a l . ( ) , ( ) K o s t r ze w a - R u t ko w s k ae t a l . ( ) , ( ) L e m on e t a l . ( ) , ( ) L u ce y e t a l . ( ) , ( ) W illi a m s e t a l . ( ) , ( ) K o s t r ze w a - R u t ko w s k ae t a l . ( ) , ( ) B o r do l o i e t a l . ( ) , ( ) W i s o t z k i e t a l . ( ) , ( ) L e m on e t a l . ( ) , ( ) B e r gh eae t a l . ( ) , ( ) M o r ee t a l . ( ) , ( ) A gn e ll o e t a l . ( ) , ( ) D a h l ee t a l . ( ) , ( ) S c h ec h t e r e t a l . ( ) , ( ) A gn e ll o ( ) , ( ) A gn e ll o e t a l . ( ) , ( ) R u s u e t a l . ( ) , ( ) M e y e r e t a l . ( ) , ( ) S c h ec h t e r e t a l . ( ) , ( ) K o c h a n e k e t a l . ( ) , ( ) A ngu it ae t a l . ( ) Article number, page 11 of 12 & A proofs: manuscript no. main
Appendix A: Gaia DR2 finding charts of known and confirmed quadruply-imaged quasars l l l l D a cos( d ) [arcsec] Dd [ a r cs e c ] l l l l D a cos( d ) [arcsec] Dd [ a r cs e c ] HE0435−1223(4h 38m 14.953s; −12° 17' 14.331'') l l l l D a cos( d ) [arcsec] Dd [ a r cs e c ] SDSS1004+4112(10h 4m 34.808s; 41° 12' 39.233'') l l l l D a cos( d ) [arcsec] Dd [ a r cs e c ] PG1115+080(11h 18m 16.951s; 7° 45' 58.050'') l l l l D a cos( d ) [arcsec] Dd [ a r cs e c ] RXJ1131−1231(11h 31m 51.582s; −12° 31' 58.884'') l l l l D a cos( d ) [arcsec] Dd [ a r cs e c ] l l l l D a cos( d ) [arcsec] Dd [ a r cs e c ] l l l l D a cos( d ) [arcsec] Dd [ a r cs e c ] B1422+231(14h 24m 38.118s; 22° 56' 0.872'') l l l l D a cos( d ) [arcsec] Dd [ a r cs e c ] J1606−2333(16h 6m 0.295s; −23° 33' 21.453'') l l l l l D a cos( d ) [arcsec] Dd [ a r cs e c ] J1721+8842(17h 21m 49.006s; 88° 42' 22.373'') l l l l D a cos( d ) [arcsec] Dd [ a r cs e c ] WFI2033−4723(20h 33m 42.084s; −47° 23' 43.350'') l l l l D a cos( d ) [arcsec] Dd [ a r cs e c ] WGD2038−4008(20h 38m 2.657s; −40° 8' 14.646'')
Fig. A.1.
Finding charts for the 12 previously known multiply-imaged quasars with four counterparts in the
Gaia
Data Release 2.
Gaia