A twelve-image gravitational lens system in the z ~ 0.84 cluster Cl J0152.7-1357
C. Grillo, M. Lombardi, P. Rosati, G. Bertin, R. Gobat, R. Demarco, C. Lidman, V. Motta, M. Nonino
aa r X i v : . [ a s t r o - ph ] M a y Astronomy&Astrophysicsmanuscript no. 09434 c (cid:13)
ESO 2018November 4, 2018
A twelve-image gravitational lens system in the z ≃ . clusterCl J0152.7-1357 ⋆ C. Grillo , , M. Lombardi , , P. Rosati , G. Bertin , R. Gobat , R. Demarco , C. Lidman , V. Motta , and M. Nonino European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748, Garching bei M¨unchen, Germanye-mail: [email protected] Universit`a degli Studi di Milano, Department of Physics, via Celoria 16, I-20133 Milan, Italy Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 European Southern Observatory, Alonso de Cordova 3107, Vitacura, Casilla 19011, Santiago 19, Chile Universidad de Valpara´ıso, Departamento de F´ısica y Astronomia, Avda. Gran Breta˜na 1111, Valpara´ıso, Chile INAF-Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, I-34141 Trieste, ItalyReceived X X, X; accepted Y Y, Y
ABSTRACT
Context.
Gravitational lens modeling is presented for the first discovered example of a three-component source for which each com-ponent is quadruply imaged. The lens is a massive galaxy member of the cluster Cl J0152.7-1357 at z ≃ .
84 .
Aims.
Taking advantage of this exceptional configuration and of the excellent angular resolution of the
HST Advanced Camera forSurveys ( ACS ), we measure the properties of the lens. In particular, the lensing mass estimates of the galaxy are compared to thosefrom stellar dynamics and multiwavelength photometry.
Methods.
Several parametric macroscopic models were developed for the lens galaxy, starting from pointlike to extended image mod-els. By combining lensing, stellar dynamics, photometry, and spectroscopy, we find an allowed range of values for the redshift of thesource and the required minimum amount of dark matter enclosed within the disk defined by the Einstein ring of the lens.
Results.
For a lens model in terms of a singular isothermal sphere with external shear, the Einstein radius is found to be R E = . ± .
15 kpc. The external shear points to the cluster’s northern mass peak. The unknown redshift of the source is determinedto be higher than 1.9 and lower than 2.9. Our estimate of the lensing projected total mass inside the Einstein radius, M len ( R ≤ .
54 kpc),depends on the source distance and lies between 4 . . × M ⊙ . This result turns out to be compatible with the dynamicalestimate based on an isothermal model. By considering the constraint on the stellar mass-to-light ratio that comes from the evolutionof the Fundamental Plane, we can exclude the possibility that at more than 4 σ level the total mass enclosed inside the Einstein ringis only luminous matter. Moreover, the photometric-stellar mass measurement within the Einstein radius gives a minimum value of50% (1 σ ) for the dark-to-total matter fraction. Conclusions.
The lensing analysis has allowed us to investigate the distribution of mass of the deflector, also providing some in-teresting indications on scales that are larger (cluster) and smaller (substructure) than the Einstein radius of the lens galaxy. Thecombination of di ff erent diagnostics has proved to be essential in determining quantities that otherwise would have not been directlymeasurable (with only the currently available data): the redshift of the source and the amount of dark matter in the lens. Key words. cosmology: observations – galaxies: high-redshift – galaxies: elliptical and lenticular, cD – dark matter – gravitationallensing – galaxies: kinematics and dynamics
1. Introduction
Accurate measurements of the mass present in galaxies in theforms of dark and visible matter define the empirical frameworkfor the theory of galaxy formation and evolution. The knowledgeof the galaxy mass function is essential for testing galaxy forma-tion models (e.g., Hernquist & Springel 2003; De Lucia et al.2006). Among the estimators of total mass in elliptical galaxies,stellar dynamics is particularly valuable in the local Universe(e.g., Saglia et al. 1992; Gerhard et al. 2001), while gravita-tional lensing o ff ers the best direct diagnostics at high redshift(e.g., Kochanek 1995; Impey et al. 1998). Recently, spectral en- Send o ff print requests to : C. Grillo ⋆ Based on observations carried out with
ESO VLT (programs 69.A-0683, 72.A-0759, and 78.A-0746) and
ESO NTT (program 61.A-0676). ergy distribution (SED) fitting methods have achieved a levelof precision su ffi ciently high to give reliable estimates of themass contained in the form of stars (e.g., Fontana et al. 2004;Rocca-Volmerange et al. 2004; Saracco et al. 2004; Grillo et al.2008a). By combining (e.g., Trott & Webster 2002; Treu et al.2006; Koopmans et al. 2006) or by comparing (e.g., Drory et al.2004; Ferreras et al. 2005; Rettura et al. 2006) di ff erent mass es-timators, the internal structure of galaxies can be investigated. Inparticular, the total density distribution and the fraction of massin the form of dark matter can be determined.Gravitational lensing has proved to be a unique tool tomeasure the (total) projected mass of galaxies and clusters ofgalaxies on radial scales from kiloparsecs to megaparsecs (e.g.,Kochanek 1995; Broadhurst et al. 2005), and in particular, to C. Grillo et al.: A twelve-image gravitational lens system in the z ≃ .
84 cluster Cl J0152.7-1357 study in detail the relationship between dark and luminous mat-ter for these systems.In this respect, strong lensing models of multiply imagedsources are especially important because the large number ofobservational constraints can lead to robust and detailed massmodels. The most complex system known so far is a ten-imageradio gravitational lens (Sykes et al. 1998; Nair 1998).Cl J0152.7-1357 is a rich, irregular, and X-ray luminous dis-tant ( z ≃ .
84) cluster (see Della Ceca et al. 2000; Demarcoet al. 2005). Its inner regions exhibit spectacular strong grav-itational lensing features in the form of multiple images andarcs. Strong lensing of background galaxies is also detected onsmaller scales, around some individual cluster members. A newand particularly interesting example is studied in this paper.The paper is organized as follows. In Sect. 2, the obser-vations of the galaxy cluster Cl J0152.7-1357 are described.In Sect. 3, we address the strong lensing analysis of the sys-tem presented in Fig. 1. We report the derived information onthe redshift of the multiply imaged source in Sect. 4. Then, inSect. 5, di ff erent stellar and total mass measurements of thelens galaxy are compared. Finally, in Sect. 6 we summarizethe results obtained in this paper. Throughout this work weassume the following values for the cosmological parameters: H =
70 km s − Mpc − , Ω m = .
3, and Ω Λ = .
7; in this model1 ′′ corresponds to a linear size of 7 .
57 kpc at the lens plane.
2. Observations
Cl J0152.7-1357 was discovered in the
ROSAT
Deep ClusterSurvey (RDCS; Rosati et al. 1998; Della Ceca et al. 2000) asan extended source with a double core structure. Spectroscopyof six galaxies (Ebeling et al. 2000) confirmed the cluster andgave a redshift of z ≃ .
83. The X-ray properties of Cl J0152.7-1357 have been studied in greater detail by
BeppoSAX (DellaCeca et al. 2000),
XMM-Newton , and
Chandra (Maughan et al.2003; Huo et al. 2004). The X-ray observations were used toderive the X-ray luminosity of the cluster and the temperature( kT ≈ ≈ ′ (corresponding to ≈
730 kpcat the cluster redshift.)The cluster was observed with the Wide Field Channel ofthe
ACS in November and December 2002. It was imaged in theF625W ( r ), F775W ( i ), and F850LP ( z ) bandpasses as part ofa Guaranteed Time Observation program (proposal 9290). Theobservations were done in a 2 × ≈ ′′ overlap between pointings, with integrated exposure of ≈ ACS observations, a weak lensing analysis provided a detailed massmap of the cluster (Jee et al. 2005). The mass reconstructionshowed complicated substructure in spatial agreement with thetwo peaks of the ICM traced by the X-ray emission. Moreover,the X-ray (2 . + . − . × M ⊙ ) and weak lensing [(2 . ± . × M ⊙ ] estimates of the total mass enclosed within small radii( ≈ ′′ ) turned out to be consistent.Further multi-band optical and near-IR imaging observa-tions of Cl J0152.7-1357 were performed to select targets forspectroscopy (see Demarco et al. 2005; Jørgensen et al. 2005).Optical photometry in the B -, V -, R -, and I -bands was obtainedwith the Low Resolution Imaging Spectrometer ( LRIS ) at the W.
Fig. 1.
Left : Color image of a small portion ( ∼ . ′ × ∼ . ′ )of the northern subcluster created using the riz HST / ACS filters.The green circle on the top right, at a projected distance of 488kpc and in direction 26 . ◦ NE with respect to the centroid of thenorthern mass clump, which corresponds to two central galax-ies (indicated by the red cross on the bottom left), shows theposition of the strong lensing system considered in this paper.
Right : Zoom-in view of a 4 ′′ × ′′ field around the lens galaxy at z l = . LRIS images cover a region of 4.9 ′ × ′ . The cluster was observed in the V -, R -, and I -bands withthe FOcal Reducer and low dispersion Spectrograph ( FORS1 )at the
VLT . The
FORS1 images cover a region of 6.8 ′ × ′ .Imaging was also done in the three r ′ -, i ′ -, and z ′ -bands with theGemini Multi-Object Spectrograph on Gemini North ( GMOS-N ). The
GMOS-N images cover a region of 5.5 ′ × ′ . The clus-ter was imaged in the near-infrared ( J - and K s -bands) with
SofI ,on the
NTT at the Cerro La Silla Observatory. The
SofI imagescover a region of 4.9 ′ × ′ .Cl J0152.7-1357 was at the center of an extensive spectro-scopic campaign carried out with both FORS1 and
FORS2 at the
VLT (Demarco et al. 2005). A total of 11 masks for multi-objectspectroscopy were used, covering the wavelength range 4000-10000 Å, with a total exposure time of ≈ GMOS-N , with a total exposure time of ≈ z = . ± . ≈
919 and ≈
737 km s − were estimated for the northern andsouthern subclusters, respectively.In conclusion, X-ray, weak lensing, and dynamical studiesall agree in finding in this system that light traces total mass,which is concentrated in two main peaks. The inner parts of thesesubclusters coincide with the two regions where strong gravita-tional lensing mostly occurs.Finally, the temperature and the mass [ M ( < ′′ ) = (2 . ± . × M ⊙ ] of the cluster were also measured from Sunyaev-Zel’dovich e ff ect observations, obtained with the interferometersof the Berkeley-Illinois-Maryland Association ( BIMA ; Joy et al.2001). A good agreement with the results inferred from the X-ray analyses was found.In Fig. 1 we show a color-composite image of a small re-gion in the northern subcluster obtained by combining the three
HST / ACS filters. The strong lensing system considered in thiswork is indicated by a green circle, on the left, and shown in de-tail, on the right of Fig. 1. The cluster lens galaxy is located at aprojected distance of 488 kpc from the centroid of the northern . Grillo et al.: A twelve-image gravitational lens system in the z ≃ .
84 cluster Cl J0152.7-1357 3
Table 1.
The lens galaxy.
R.A. Dec. z l e P.A. r AB R e (J2000) (J2000) ( ◦ ) (mag) ( ′′ )01:52:42.43 − Table 2.
Photometry of the four images.
Object x x distance a r AB ( ′′ ) ( ′′ ) ( ′′ ) (mag)A -0.76 1.69 1.86 25.58B 1.04 -0.28 1.07 25.99C 0.79 -0.89 1.19 25.32D -0.31 -0.92 0.97 25.87 a With respect to the galaxy center.
Table 3.
Astrometry of the sub-images.
Object A A A B B B x ( ′′ ) a -0.81 -0.80 -0.58 1.04 1.04 1.04 x ( ′′ ) a C C D D D x ( ′′ ) a x ( ′′ ) a -0.93 -1.10 -0.77 -0.98 -0.93 -0.88 a With respect to the galaxy center. mass clump (which corresponds to two central galaxies), wherethe most multiple images and arcs produced by Cl J0152.7-1357were detected. This geometrical configuration will justify theneed for an external shear component in the lensing models ofthe next section. From its spectral and photometrical properties,the lens can be safely classified as a bright elliptical galaxy lo-cated at a redshift z l of 0 .
82 and with a stellar central velocitydispersion σ of 239 ±
21 km s − (see Jørgensen et al. 2005).Despite the outstanding observational e ff orts that will be de-scribed in Sect. 4.2, the redshift of the quadruply-imaged source z s was not secured. It was only possible to give an upper limit: z s ≤ .
9. The measured photometric properties of the lensingsystem are summarized in Tables 1, 2, and 3; more details on theproperties of this system will be given below.
3. Gravitational lensing models
At first, we model the source as a single point-like object, whichis lensed approximately in the four images of Table 2. Then,we employ a three-component source, trying to reproduce thetwelve images of Table 3 (each of the previous four images,hence also the source, is considered here as a triple object).Finally, we study models with extended sources, in order to com-pare the model-predicted luminosity distribution of the imagesdirectly with the observations.
For the lens we consider three di ff erent models: a singularisothermal sphere (SIS), a singular isothermal ellipsoid (SIE),and a singular isothermal sphere with external shear (SIS + ES).An SIS is characterized by three parameters: the Einstein angle θ E and the two source coordinates ( y , y ). The remaining mod-els involve two additional parameters: the ellipticity e = − b / a Table 4.
The best-fit parameters for the four-image models.
Model θ E x l x l e /γ a θ e /γ a χ dof c ( ′′ ) ( ′′ ) ( ′′ ) ( ◦ )SIE b + ES b + ES 1.23 0.06 0.05 0.185 28.6 1.00 1 a Ellipticity or external shear values, depending on the model. b The lens center is fixed to the galaxy center. c Number of degrees of freedom. and the position angle θ e for an SIE; the shear γ and its posi-tion angle θ γ for an SIS + ES (see Keeton 2001). Initially, eachmodel is analysed by fixing the lens center ( x l , x l ) to the mea-sured galaxy position; in a second stage, the lens coordinates arealso taken as free parameters. Varying these parameters and theposition of the source, we minimize the chi-square function χ = X i = k x i obs − x i k σ x , (1)where x i obs is the position vector of the i -th observed image (seeTable 2), x i is the corresponding position predicted by the model,and σ x is the position uncertainty. This last quantity is fixed toone image pixel (0.05 ′′ ) because the centroids of the extendedimages are not well defined.The best-fit parameters are shown in Table 4. These mod-els have di ff erent properties. The SIS is not able to reproducethe correct number of images, and thus the parameters of thismodel are not registered. The SIE, with the center coordinatesas free parameters, has a low χ , but the high value of the lensellipticity, compared to that measured for the galaxy (see Table1), suggests that this model is inadequate. The least χ value isachieved by an SIS + ES, setting the lens center as a free param-eter; the second best model is the SIS + ES with fixed center (thehigher χ is partially compensated for by the higher number ofdegrees of freedom, dof). In Fig. 2 we plot the source and im-age planes with caustics and critical curves for the last model ofTable 4. The positions of the four images, typical of a cusp con-figuration, are there compared with the positions predicted bythe model. We also show the Fermat potential (see Schneider etal. 1992), its stationary points, corresponding to the image loca-tions (two minima and two saddle points with, respectively, thesame and the opposite parity of the source), and the predictedlevel of distorsion of the images from a round source.We notice that the high values found for the external shearare plausible in a massive cluster, as is the case of Cl J0152.7-1357. For instance, a lens cluster with an Eistein radius of 200kpc causes an external shear of 0.2 at a distance of 500 kpc fromthe cluster center (a simplified SIS model is assumed here tomodel the lens). We will see in Sect. 5 that the values of theexternal shear determined in this section are fully consistent withthe mass estimates of the northern subcluster measured throughstudies of X-ray emission (Huo et al. 2004), weak lensing (Jee etal. 2005), and cluster member dynamics (Demarco et al. 2005).Moreover, it is interesting to remark that the position angle of theellipticity for the SIE and that of the shear for the SIS + ES di ff erby about one degree. This common direction points towards theclosest cluster mass peak, coinciding with the northern clumpcenter of the cluster shown in Fig. 1. C. Grillo et al.: A twelve-image gravitational lens system in the z ≃ .
84 cluster Cl J0152.7-1357
Source plane -1.0 -0.5 0.0 0.5 1.0 y (arcsec)-1.0-0.50.00.51.0 y ( a r c s ec ) P.A. θ γ θ NC θ SC Image plane -2 -1 0 1 2 x (arcsec)-2-1012 x ( a r c s ec ) A BCD -2 -1 0 1 2 x (arcsec)-2-1012 x ( a r c s ec ) Image plane
A BCD
Image plane -2 -1 0 1 2 x (arcsec)-2-1012 x ( a r c s ec ) Fig. 2.
Best four-image SIS + ES model.
Top left : Source planewith caustics. The predicted source position is indicated by thecross. The arrows display the directions of the northern clusterclump ( θ NC ), of the external shear predicted by the model ( θ γ ),of the galaxy ellipticity position angle (P.A.), and of the southerncluster clump ( θ SC ). Top right : Image plane with critical curves.The observed (squares) and predicted (crosses) image positionsare shown.
Bottom left : Contour levels of the Fermat potential.The images are two minima (A, C) and two saddle points (B, D).
Bottom right : Predicted deformation of the four images obtainedby locating a small round source in the position illustrated on thetop left panel.
We start here from a triple source (labelled by an index runningfrom one to three) lensed into twelve images angularly close tothe measured positions of Table 3. Considering the results of theprevious subsection, a three-component source, for which eachcomponent is imaged four times, is the most natural assumptionon the source structure. Three of the observed images, B i , areso close to each other that they cannot be deblended; hence, wejust measure their bright center. The position uncertainty of eachsub-image is chosen to be one image pixel, as before, exceptfor B i which is taken five times larger, by analyzing the peculiarluminosity distribution of the pixels. We model the lens as anSIE and an SIS + ES.The χ minimization results are summarized in Table 5. Thebest χ , 23.3, is achieved by an SIS + ES, a model consisting onlyof three parameters. If the lens center is also taken as a free pa-rameter, this reduces the χ by 1.7, but lowers by two the numberof dof. The source and image planes with caustics and criticalcurves for the third model of Table 5 are plotted in Fig. 3.We note that the value of the Einstein angle of the SIS isvery similar to that of the best four-image model and that thevalues of magnitude and orientation of the external shear givegood evidence about the northern subcluster mass peak, as al-ready mentioned in the last subsection. Table 5.
The best-fit parameters for the twelve-image models.
Model θ E x l x l e /γ a θ e /γ a χ dof c ( ′′ ) ( ′′ ) ( ′′ ) ( ◦ )SIE b + ES b + ES 1.27 0.03 0.04 0.169 26.7 21.6 13 a Ellipticity or external shear values, depending on the model. b The lens center is fixed to the galaxy center. c Number of degrees of freedom.
Source plane -1.0 -0.5 0.0 0.5 1.0 y (arcsec)-1.0-0.50.00.51.0 y ( a r c s ec ) Image plane -2 -1 0 1 2 x (arcsec)-2-1012 x ( a r c s ec ) Fig. 3.
Best twelve-image SIS + ES model.
Left : Source planewith caustics. The predicted components of the source areshown.
Right : Image plane with critical curves. The observed(squares) and predicted (triangles, crosses, and diamonds) im-ages are shown.Then, we determine the statistical uncertainties on theEinstein angle and on the external shear, starting from two hun-dred χ minimizations on simulated data sets. In particular, weextract image positions from Gaussian distributions centered onthe measured values and with standard deviations equal to theposition uncertainties reported previously, and for each set wesearch for the best-fit parameters.The parameter distributions are shown in Fig. 4 and the re-sults are presented in Table 6. The marginal density functions areapproximately Gaussian and the joint density functions revealcorrelations (for definitions see Cowan 1998): the correlationcoe ffi cients are r θ E ,γ = − . r θ E ,θ γ = − .
03, and r γ,θ γ = . z l = .
82, an Einsteinangle of (1 . ± . ′′ corresponds to an Einstein radius ( R E )of (9 . ± .
15) kpc. Moreover, we remark that the low uncer-tainty values on the parameters suggest that the measurementsare accurate and robust.The model just presented is valuable in describing the lensproperties with only three parameters, although it cannot repro-duce the complex image configuration very accurately. In orderto improve the agreement between the observed and the recon-structed image geometry we have tried more refined models,without gaining any real improvement. For instance, some el-lipticity is inserted in the SIS + ES model, but, as expected fromthe known degeneracy between external shear and ellipticity (seeWitt et al. 1997), we cannot find a lower value of the χ .We interpret the external shear as due to the mass distribu-tion on the cluster scale. So, instead of employing an externalshear component, we decide to model both the northern subclus-ter (the most relevant mass clump for this study) and the galaxy . Grillo et al.: A twelve-image gravitational lens system in the z ≃ .
84 cluster Cl J0152.7-1357 5 θ E marginal distribution θ E (arcsec)010203040 N γ marginal distribution γ N θ γ marginal distribution
23 24 25 26 27 28 29 θ γ (deg)01020304050 N θ E vs γ values θ E (arcsec)0.150.160.170.180.190.200.21 γ θ E vs θ γ values θ E (arcsec)23242526272829 θ γ ( d e g ) γ vs θ γ values γ θ γ ( d e g ) Fig. 4.
Results of the χ minimizations of 200 Monte-Carlo gen-erated data sets. Top : Marginal distributions of the model param-eters with their approximate normal distributions.
Bottom : Thejoint density distributions show the parameter correlations.
Table 6.
The best-fit parameters with the relative marginalizederrors for the twelve-image SIS + ES model. θ E ( ′′ ) γ θ γ ( ◦ )1 . ± .
02 0 . ± .
011 26 . ± . as SISs. The description of the subcluster in terms of an SIS isonly a first-order approximation, but it is adequate to representthe mass distribution at distances from the center large comparedto the Einstein radius of the clump (below we will prove that thisstatement is valid in our system). The two Einstein angles are theonly needed parameters (hence, the number of dof is here 16).In fact, the first center is set equal to the average position of thetwo brightest galaxies of the northern subcluster (see Fig. 1), thesecond one to the center of the lens galaxy. We measure a χ of 25.5, and Einstein angles for the subcluster ( θ E C ) and for thegalaxy ( θ E G ) of 19.6 ′′ ( R E C =
148 kpc) and 1.07 ′′ ( R E G = . ′′ , equivalent to approximately 0.7 kpc at a hypothetical red-shifts of 2.5. In addition, the total absolute magnification of thesub-images ( µ = | µ A | + | µ B | + | µ C | + | µ D | , where µ i is the mag-nification of the i -th image, with a positive or negative sign ifthe image is, respectively, a minimum or a saddle point of theFermat potential) is 27.9, a reasonable value in the vicinity ofcritical lines.Taking into consideration the irregular and compact shapeand the blue color of the source, it is very likely that this objectis a high-redshift star-forming region. As a final step, we employ an extended parametric approach.For this purpose, we have developed an ad hoc algorithm, whichreconstructs the properties of both a lens and a source by com-paring the observed and the predicted luminous intensity of anarray of pixels on the image plane. Before presenting the results,we describe this technique shortly, since it is not as well-knownas the point-like parametric (Keeton 2001) or the non-parametric(Saha & Williams 1997; Koopmans 2005) approaches.
Table 7.
The best-fit parameters for the extended-image model.
Model θ E γ θ γ e χ ( ′′ ) ( ◦ )SIS + ES a a The lens center is fixed to the galaxy center.
In principle, the method is straightforward, because it ex-ploits only the ray-tracing equation, y ( x ) = x − α ( x ), and thesurface brightness conservation in lensing, I ( x ) = I s (cid:16) y ( x ) (cid:17) (formore details see Schneider et al. 1992). First, the image andthe source planes are divided into sub-pixels. In particular, eachCCD pixel of the image plane is splitted into 16 sub-pixels.Furthermore, in order to deal with large magnified images, thepixel size on the source plane is fixed to 1 /
256 the pixel size ofthe CCD. Then, starting values for the parameters of the mod-els that describe the lens ( p l ) and the luminosity distributionof the source ( p s ) are assigned. According to the tentative lensmodel, each point of the image grid is ray-traced into the sourceplane and is associated with the closest point of the source grid.Finally, the images of the lensed source are obtained by giv-ing to the image sub-pixels the values of the source sub-pixelsmatched in the previous step. The e ff ect of the point spread func-tion (PSF), I ( x ) = (cid:16) PSF ∗ I s (cid:17)(cid:16) y ( x ) (cid:17) , and the e ff ect of the sub-pixels (anti-aliasing) are taken into account. The best parametersfor the adopted lens and source models are found by minimizingthe following chi-square function e χ ( p l , p s ) = P N pix (cid:16) I obs ( x ) − I ( x ) (cid:17) σ I N pix , (2)where N pix is the total number of pixels of the observation con-sidered in the modeling, I obs ( x ) and I ( x ) are, respectively, theintensity observed and predicted by the model in the CCD pixellocated at x , and σ I is the standard deviation of the intensity eval-uated on a blank field of the CCD (i.e., the noise). The methodhas been tested on artificial but plausible lens systems and hasprovided good results for the values of the reconstructed param-eters.Following the best models discussed above, we represent thelens as an SIS + ES and, on first approximation, we model thesource as the sum of three gaussian functions with independentparameters.The best-fit parameters and model resulting from the applica-tion of our algorithm are shown in Table 7 and Fig. 5. The prop-erties of the lens are essentially the same as those obtained pre-viously; on the other hand, we note slight variations in the valuesof the source parameters. In fact, the values of the Einstein an-gle and of the external shear are consistent with those of the bestpoint-like model (see Table 6). The largest separation among thecenters of the three gaussians now gives a predicted linear extentfor the source of about 0 . ′′ , which corresponds to approxi-mately 1.4 kpc at a redshift of 2.5. The total absolute magnifi-cation, i.e. the integrated intensity of the images divided by thatof the source, is on the order of 14.9. Table 8 summarizes thesigned (positive or negative if the nature of the two Fermat sta-tionary points of each pair is, respectively, the same or not) fluxratios of the images A ( f A / f C ), B ( f B / f C ), and D ( f D / f C ), withrespect to the most magnified image C, and the cusp ratio ( R cusp ) C. Grillo et al.: A twelve-image gravitational lens system in the z ≃ .
84 cluster Cl J0152.7-1357
Fig. 5.
Best extended-image SIS + ES model.
Top left:
The ob-served
HST / ACS r field (5 ′′ across). Top right:
The same imageafter the subtraction of an elliptical model fitted on the luminos-ity profile of the lens galaxy. Some residuals of the galaxy lumi-nosity are still visible in the inner region.
Bottom left:
The bestreconstruction of the lensed system.
Bottom right:
The residualsafter the subtraction of the model predicted (third panel) fromthe observed (second panel) images. The central residuals due tothe lens galaxy subtraction have been masked here.
Table 8.
Signed flux and cusp ratios. f A / f C f B / f C f D / f C ( R cusp ) BCD
Obs. 0 . ± . − . ± . − . ± .
08 0 . ± . − . − .
56 0.07 for the closest triplet of images B, C, and D. This last quantity,which is introduced by Keeton et al. 2003, can be written as( R cusp ) BCD = (cid:12)(cid:12)(cid:12)(cid:12) + f B f C + f D f C (cid:12)(cid:12)(cid:12)(cid:12) + (cid:12)(cid:12)(cid:12)(cid:12) f B f C (cid:12)(cid:12)(cid:12)(cid:12) + (cid:12)(cid:12)(cid:12)(cid:12) f D f C (cid:12)(cid:12)(cid:12)(cid:12) . (3)In Table 8 we report the observed values and their uncertainties,assuming a 10% error on each flux, and the model-predicted val-ues of the previously defined quantities. For the three images B,C, and D, we measure an opening angle θ of 93 . ◦ and a dimen-sionless separation d /θ E of 1 .
20 (for definitions see Keeton et al.2003).The image positions taken into consideration in the pointlikemodels are supposed to coincide approximately with the centersof the images of the extended models. Nonetheless, the formeranalyses consider essentially only the regions where the imagesare maximally amplified by lensing, whereas the latter studiesprobe also the smaller amplification regime. Therefore, we donot have any obvious explanation for the di ff erent predicted sizesof the source; while, the di ff erence between the values of thetotal magnification found here and in the previous paragraph canbe easily understood. For an ideal cusp catastrophe, the cusp ratio should exactlyvanish (Schneider et al. 1992), but, since real lenses are notideal cusps, this general property is expected to hold only ap-proximately, depending on the opening angle and the dimension-less separation of the triplet considered (for a detailed study seeKeeton et al. 2003). Surprisingly, most of the observed lens sys-tems show a significant violation of the cusp relation (knownalso as flux ratio “anomaly”; e.g., see Kent & Falco 1988; Sluseet al. 2003). This fact can be explained by assuming the presenceof small-scale structure in the lens galaxy, on a scale comparableto the separation between the images (Mao & Schneider 1998).Although we measure a cusp ratio which is consistent with zero(and thus, given the measured values of the opening angle andof the dimensionless separation, the cusp relation is here satis-fied), a possible clue on the existence of small perturbations inthe lens potential might be the significant inconsistency betweenthe observed and the predicted flux ratio for image A (see Table8 and the last panel of Fig. 5).
4. The source redshift
A precise value for the redshift of the lensed source is not avail-able yet. Its measurement is very di ffi cult because of the faint-ness of the object and its proximity to the bright lens galaxy (seeTable 2). However, some information about this redshift can beextracted from di ff erent diagnostics, as explained below. The Einstein angle for an SIS is explicitly given by θ E = π σ SIS c ! D ls D os , (4)where σ SIS is the lens “velocity dispersion”, c is the speed oflight, D ls and D os are the lens-source and the observer-sourceangular diameter distances, respectively. It follows from Eq. (4)that θ E may be interpreted as a function of both the lens mass M ( M ∝ σ r t ) and the source redshift z s ( D ls , D os ). A lowerlimit for this redshift can be obtained by combining gravitationallensing and stellar dynamics.In fact, several tests (Kochanek 1993, 1994; Treu et al. 2006;Grillo et al. 2008b) have proved that in elliptical galaxies thestellar central velocity dispersion ( σ ) is a good estimate of thevelocity dispersion of a one-component isothermal model ( σ SIS ).A spectroscopic measurement of σ for the lens galaxy is pre-sented by Jørgensen et al. 2005 ( σ = ±
21 km s − ). Startingfrom this result and from the value of the galaxy Einstein angleof the previous section, in Fig. 6, the velocity dispersions fromgravitational lensing and from stellar dynamics are found to becompatible at a confidence level of 95% if z s ≥ . z s ≥ . The spectra of objects A, B, and C were obtained with
VLT / FORS2 , as part of an extensive observational campaign car-ried out on the galaxy cluster (see Demarco et al. 2005 formore details on the spectroscopic analysis of other objects in ClJ0152.7-1357). An unambiguous estimate of the source redshiftwas not possible from the spectra of images B and C, due to thecontamination from the overwhelming lens galaxy light in 0 . ′′ seeing conditions. The spectrum of image A was taken in threedi ff erent exposures, with a total integration time of 5230 s, with . Grillo et al.: A twelve-image gravitational lens system in the z ≃ .
84 cluster Cl J0152.7-1357 7
Lensing and spectroscopy z s ) L e n s v e l o c it y d i s p e r s i on ( k m s − ) LensingSpectroscopy
Fig. 6.
The source redshift obtained from gravitational lensingand stellar dynamics. The Einstein angle, from lensing analy-sis, and the velocity dispersion of the galaxy, from spectroscopicmeasurements, combine to give a lower limit for the redshift ofthe source. The dashed and dotted lines represent 1 and 2 σ errorbars, respectively. The vertical long-dashed line shows the spec-troscopic upper limit of the source redshift discussed in Sect. 4.2 Fig. 7.
Spectroscopic measurements of object A.
Top : Position ofthe 1 ′′ slit. Bottom : Composite 2D sky-subtracted spectrum ob-tained with
VLT / FORS2 in 5230 s. The arrow shows the Lymanalpha drop at 4730 Å.the 300V grism, using the same mask geometry and the same slitcharacteristics. The position of the slit and the combined 2D sky-subtracted spectrum are shown in Fig. 7. Although the signal islow, no significant emission feature is observed, the continuumis visible down to 4730 Å, however the cross-correlation withtemplate spectra does not yield satisfactory results. If we inter-pret this limit as the Lyman alpha drop, blueward to the Lymanalpha emission line, then we can infer that the redshift of thesource ( z s ) is lower than 2.9.
5. Mass measurements
In this section we first determine the lens galaxy total (lumi-nous + dark) mass, based on the previously discussed lensingmodels and on the published (Jørgensen et al. 2005) stellarvelocity dispersion measurement. Next, we measure the lensgalaxy stellar mass, based on multiwavelength photometry spec-tral template fitting. This allows us to infer a lower limit for thedark matter fraction enclosed inside the Einstein radius of thedeflector. Table 9.
Luminous and dark mass measurements of the lensgalaxy, without the cluster contribution. The ranges represent theintervals at 68% confidence level. M len M dyn M phot f DM (10 M ⊙ ) (10 M ⊙ ) (10 M ⊙ ) R ≤ .
10 kpc 3 . − . . − . . − . . − . R ≤ .
54 kpc 4 . − . . − . . − . . − . Galaxy mass estimate inside R E z s ) M a ss ( M S un ) M len ( R ≤ M dyn ( R ≤ SIS+SIS mass estimates z s ) M a ss ( M S un ) M Cluster ( R ’ ≤
488 kpc) M Galaxy + Cluster ( R ≤ M Galaxy ( R ≤ M Cluster ( R ≤ Fig. 8.
The galaxy and cluster masses.
Left:
The lensing[ M len ( R ≤ .
54 kpc)] and dynamical [ M dyn ( R ≤ .
54 kpc)] mea-surements of the galaxy projected total mass inside a 9.54 kpcradius as a function of the source redshift. The dashed and dot-ted lines represent 1 and 2 σ error bars, respectively. Right:
The galaxy (dashed), the cluster (dotted), and the total (dashed-dotted) projected mass inside a 9.54 kpc radius centered on thegalaxy. The long-dashed line shows the projected mass of thecluster inside a circle with a radius of 488 kpc, that is the dis-tance between the cluster and the galaxy centers.
A measurement of the value of the Einstein radius of a lensingsystem can be directly translated into a mass estimate for the de-flector. In particular, the Einstein radius is defined as that radiusinside which the mean surface density of a lens is equal to thecritical surface density ( Σ cr ) of the system (for more details seeSchneider et al. 1992). So, it follows that the projected lensingmass ( M len ) enclosed within R E equals M len ( ≤ R E ) = Σ cr π R . (5)In our specific case, Σ cr can assume a range of values dependingon the source redshift. This is the main source of uncertainty inour lensing mass estimates, more relevant than that associatedto detailed modeling of the cluster. From the results of Sect. 3.2and 4, we have that the projected total mass of the lens galaxywithout the cluster contribution M len ( R ≤ .
54 kpc) is well mea-sured and its value is included between 4.6 and 6.2 × M ⊙ ,at a 68% CL. This information is shown in Table 9 and on theleft of Fig. 8.The lower value of R E G , found in Sect. 3.2 when consideringthe cluster mass contribution, suggests that the galaxy must beless massive than expected from the SIS + ES model. It is inter-esting to measure the projected total mass inside R E = .
54 kpc,predicted by the SIS + ES and SIS + SIS models. In the formercase, we use exactly Eq. (5); in the latter case, the mass is thesum of the cluster and of the galaxy masses inside the same cir-cle (see Fig. 8, on the right). The di ff erence between the values ofthe total mass from the two models is less than 0 . C. Grillo et al.: A twelve-image gravitational lens system in the z ≃ .
84 cluster Cl J0152.7-1357 cluster masses inside the galaxy Einstein radius may have di ff er-ent weights, but their sum is nearly constant. This explains theanti-correlation noted above between the Einstein radius and theexternal shear, which is interpreted as the cluster contribution.Moreover, the projected mass of the cluster inside the circle ofradius R =
488 kpc, the projected distance between the centersof the northern subcluster and the lens galaxy, agrees well withthe value of about 3 × M ⊙ from analyses in X-rays (Huoet al. 2004), weak lensing (Jee et al. 2005), and dynamics of thecluster galaxies (Demarco et al. 2005). Several studies (e.g., Rusin et al. 2003; Koopmans et al. 2006)have shown that the total (luminous + dark) density distributionof elliptical galaxies is homologous and well described by a 1 / r (isothermal) profile. A similar conclusion was also reached bystellar dynamical studies (out to R e ) of nearby galaxies, based onthe application of self-consistent equilibrium dynamical modelsthat incorporate the picture of galaxy formation by collisionlesscollapse (Bertin & Stiavelli 1993).We consider here mass measurements projected along theline of sight. The projected mass ( M ) enclosed inside a certainradius ( R ) for an SIS is M ( ≤ R ) = πσ RG , (6)where σ SIS has been introduced in Eq. (4), and G is the universalgravitational constant. As mentioned in Sect. 4.1, a good estima-tor of σ SIS is found to be σ , and this latter quantity has beenmeasured for the galaxy studied in this paper. Starting from Eq.(6) and the value of σ , we evaluate the dynamical projected totalmass, M dyn ( ≤ R ), within the two radii considered in the lensinganalysis of the previous section. The results are presented in thethird column of Table 9 and on the left of Fig. 8.The lensing and dynamical mass estimates are consistent andthe lensing measurements do not turn out to be more accuratethan the dynamical ones only because a rough estimate of thesource redshift is available. An estimate of the photometric-stellar mass ( M phot ) of a galaxycan be derived by comparing the observed SED of the galaxywith a set of composite stellar population (CSP) templates, com-puted with stellar population models. In addition to the stel-lar mass, this method also allows the age and the star forma-tion history (SFH) of the galaxy to be investigated. It is well-known that the derived stellar mass depends on the adopted ini-tial mass function (IMF) and only weakly on the assumed modelof dust extinction and metallicity evolution. Moreover, it hasbeen shown (Rettura et al. 2006) that the photometric-stellarmass does not exhibit statistically significant discrepancies whenevaluated with di ff erent stellar population models (e.g., Bruzual& Charlot 2003 vs. Maraston 2005). Finally, it must be notedthat accurate stellar mass measurements require unbiased galaxySEDs, which translates into accurate PSF-matched photometry.We derive the photometric-stellar mass of the lens galaxythrough this multi-wavelength matched aperture photometrymethod. We use Bruzual & Charlot’s (2003) templates at solarmetallicity, assuming a Salpeter (1955) time-independent IMFand a delayed exponential SFH. First, we smooth all images ( r , i , z from HST / ACS and J , Ks from NTT / SofI ) to the worst PSF
Table 10.
Multi-band photometry of the lens galaxy. θ ≤ . ′′ θ ≤ . ′′ HST / ACS r AB . ± .
014 23 . ± . HST / ACS i AB . ± .
005 22 . ± . HST / ACS z AB . ± .
004 21 . ± . NTT / SofI J AB . ± .
010 20 . ± . NTT / SofI Ks AB . ± .
011 20 . ± . Fig. 9.
SED of the lens galaxy at z l = .
82. The circles with theerror bars represent, from left to right, the observed flux densitiesmeasured inside the 1.07 ′′ aperture in the HST / ACS ( r , i , z ) and NTT / SofI ( J , Ks ) passbands. The illustrated best-fit has been builtwith Bruzual & Charlot 2003 models. On the bottom, the best-fitvalues of the age (t), the characteristic time of the SFH ( τ ), andthe mass (M phot ) of the galaxy are given.and then we measure the galaxy magnitudes inside the aperturessuggested by the lensing analysis (see Sect. 3.2). The results aresummarized in Table 10. In Fig. 9 we plot the observed SED ofthe galaxy and the best-fit Bruzual & Charlot 2003 model forthe first aperture. The best-fit intervals, at the 68% confidencelevel, of the stellar mass inside the two apertures are shown inthe fourth column of Table 9.Starting from the lensing and dynamical measurements ofthe total mass and from the photometric measurement of the stel-lar mass, we have determined the minimum amount of dark mat-ter ( f DM ). The radii relative to which f DM is computed are aboutfour times larger than the e ff ective radius ( R e ) of the galaxy (seeTable 1). In order to obtain the dark matter fraction, we assumethe “maximum light” hypothesis: inside each aperture the stellarmass is divided by the lower total mass estimate (in this particu-lar case, the latter value comes from the dynamical study). Thisgives an upper limit to the stellar mass fraction, from which alower limit to the dark mass fraction can be inferred. In the lastcolumn of Table 9 the measured values of f DM are presented.The total luminosity of the system inside the 9.54 kpcEinstein radius is (3 . ± . × L ⊙ , B , implying an averagemass-to-light ratio M / L B = (13 . ± . M ⊙ L − ⊙ , B (consideringthe lower dynamical estimate of the total mass). Under appro-priate assumptions (e.g., see Treu et al. 2001, 2005) the evolu-tion of the intercept of the Fundamental Plane with redshift canbe related to the evolution of the average e ff ective mass-to-lightratio. The SLACS and LSD Surveys (Treu et al. 2006) have es-tablished that, in the redshift range from 0 to 1, the e ff ective stel-lar mass-to-light ratio evolves as d log( M / L B ) / d z = − .
76, with . Grillo et al.: A twelve-image gravitational lens system in the z ≃ .
84 cluster Cl J0152.7-1357 9 an rms scatter of 0.11. If the evolution of the e ff ective mass-to-light ratio is equal to the evolution of the stellar mass-to-lightratio, we can use this result to infer M ∗ / L B of our lens galaxy,assuming that log( M ∗ / L B ) z = log( M ∗ / L B ) + ∆ log( M / L B ). Thefirst term on the right-hand side of the previous equation canbe measured for local E / S0 galaxies; e.g., using the data fromGerhard et al. 2001 ( M ∗ / L B ) = (7 . ± . M ⊙ L − ⊙ , B . Hence,we find that M ∗ / L B ( z = . = (1 . ± . M ⊙ L − ⊙ , B . We notethat the value M ∗ / L B = . M ⊙ L − ⊙ , B required to explain theprojected mass enclosed inside the Einstein radius solely by lu-minous matter is inconsistent with the above independently de-rived value at more than 4 σ level. This is further evidence of thepresence of a significant dark matter component inside the lensEinstein circle. Moreover, from the estimate of the photometric-stellar mass we obtain for M ∗ / L B a value between 2.3 and 3.5,which is consistent with the value derived from the evolution ofthe Fundamental Plane.We mention that our findings on the fraction of the dark mat-ter component are compatible with the results from other di ff er-ent studies on the amount of dark matter in elliptical galaxies(e.g., Saglia et al. 1992; Treu & Koopmans 2004; Ferreras et al.2005; Treu et al. 2006). We also note that our relatively high val-ues of f DM support the picture that the most massive ellipticalsbe dark matter dominated in their outer regions.
6. Conclusions
In this paper we have presented a strong lensing analysis ofan elliptical galaxy, member of the cluster Cl J0152.7-1357( z ≃ . HST / ACS deep observations, a three-component source highly magnified into twelve images was dis-covered. For this system we have discussed several paramet-ric macroscopic models: first point-like, then extended imagemodels have been developed. The Einstein radius of a singularisothermal sphere was found to be R E = . ± .
15 kpc, andthe value of the projected mass inside this radius was shown tobe a function of the unknown source redshift z s . By combininglensing with galaxy dynamics and by studying the source spec-trum, we have obtained for this redshift lower and upper boundsof 1.9 and 2.9, respectively. These limits have allowed us toget accurate and robust total mass measurements of the galaxy: M len ( R ≤ .
54 kpc) = (4 . − . × M ⊙ . Furthermore an ex-ternal shear component was proved to be indicative of the north-ern mass distribution of the cluster and the predicted value of thecluster mass has been shown to be in agreement with the X-ray,weak lensing, and cluster member dynamical analyses. Then, wehave measured the lens total and luminous mass from stellar dy-namics, and from optical and near-IR photometry. From theseresults we have estimated a lower limit of 50% (1 σ ) for thedark matter fraction enclosed inside the Einstein radius of thegalaxy. The presence of a significant dark matter component isalso confirmed by comparing the value of the mass-to-light ra-tio measured in our lens with the stellar one predicted from theevolution of the Fundamental Plane.Using non-parametric methods (see Bradaˇc et al. 2005), thecomplex image configuration of the lensing system might be bet-ter reproduced, but possibly with only a small gain of insight intothe lens properties. Acknowledgements.
Part of this work was supported by the
European SouthernObservatory Director General Discretionary Fund . References
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