Herschel-ATLAS: Modelling the first strong gravitational lenses
S. Dye, M. Negrello, R. Hopwood, J. W. Nightingale, R. S. Bussmann, S. Amber, N. Bourne, A. Cooray, A. Dariush, L. Dunne, S. A. Eales, J. Gonzalez-Nuevo, E. Ibar, R. J. Ivison, S. Maddox, E. Valiante, M. Smith
aa r X i v : . [ a s t r o - ph . C O ] F e b Mon. Not. R. Astron. Soc. , 1–14 (2014) Printed 16 August 2018 (MN L A TEX style file v2.2)
Herschel ⋆ -ATLAS: Modelling the first strong gravitationallenses S. Dye, † M. Negrello , R. Hopwood , J. W. Nightingale , R. S. Bussmann , ,S. Amber , N. Bourne , , A. Cooray , A. Dariush , L. Dunne , S. A. Eales , J.Gonzalez-Nuevo , E. Ibar , R. J. Ivison , S. Maddox , E. Valiante , M. Smith School of Physics and Astronomy, Nottingham University, University Park, Nottingham, NG7 2RD, UK INAF, Osservatorio Astronomico di Padova, Vicolo Osservatorio 5, I-35122 Padova, Italy Astrophysics Group, Imperial College London, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK Harvard Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA Department of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK7 6AA, U.K. Institute for Astronomy, Royal Observatory Edinburgh, Blackford Hill, Edinburgh, EH9 3HJ, UK. Astronomy Department, California Institute of Technology, MC 249-17, 1200 East California Boulevard, Pasadena, CA 91125, USA. Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand School of Physics and Astronomy, Cardiff University, The Parade, Cardiff, CF24 3AA, UK. Instituto de F´ı sica de Cantabria (CSIC-UC), Av. los Castros s/n, 39005 Santander, Spain. Instituto de Astrof´ısica, Facultad de F´ısica, Pontificia Universidad Cat´olica de Chile, Casilla 306, Santiago 22, Chile. Department of Astronomy, Space Science Building, Cornell University, Ithaca, NY, 14853-6801.
ABSTRACT
We have determined the mass-density radial profiles of the first five strong gravita-tional lens systems discovered by the Herschel Astrophysical Terahertz Large AreaSurvey (H-ATLAS). We present an enhancement of the semi-linear lens inversionmethod of Warren & Dye which allows simultaneous reconstruction of several dif-ferent wavebands and apply this to dual-band imaging of the lenses acquired withthe Hubble Space Telescope. The five systems analysed here have lens redshifts whichspan a range, 0 . z .
94. Our findings are consistent with other studies byconcluding that: 1) the logarithmic slope of the total mass density profile steepenswith decreasing redshift; 2) the slope is positively correlated with the average totalprojected mass density of the lens contained within half the effective radius and neg-atively correlated with the effective radius; 3) the fraction of dark matter containedwithin half the effective radius increases with increasing effective radius and increaseswith redshift.
Key words: gravitational lensing - galaxies: structure
Early type galaxies, despite being relatively well stud-ied, continue to challenge our complete understanding oftheir formation and evolution. Current unanswered ques-tions include quantifying the role of mergers in their evo-lution (e.g., van Dokkum et al. 1999; Khochfar & Burkert2003; Bell et al. 2006; Hilz, Naab & Ostriker 2013), reli-ably determining their stellar build up and reconciling thiswith downsizing (e.g., Thomas et al. 2005; Maraston et al. ⋆ Herschel is an ESA space observatory with science instrumentsprovided by European-led Principal Investigator consortia andwith important participation from NASA. † E-mail:[email protected] c (cid:13) S. Dye et al. hole mass with central velocity dispersion and the near-isothermality of total mass density profiles.Regarding the measurement of density profiles, this hasrecently become a very active pursuit within the field, mo-tivated by the many scientific applications made possible.These applications include the provision of an observationalbenchmark for simulations of large scale structure forma-tion, constraining the initial mass function (IMF) by com-paring with stellar synthesis masses (e.g., Barnab`e et al.2013; Treu et al. 2010; Auger et al. 2010), determining theHubble constant from gravitational lens time delays (e.g.Tewes et al. 2013, see also the review by Jackson 2007)and cosmography (see Treu 2010b, and references therein).Other novel applications include using density profiles ofstrongly lensed systems embedded within a cluster or groupenvironment as a direct probe of the larger scale gravi-tational potential (e.g., Dye et al. 2007; Limousin et al.2010) and making predictions of the self-annihilation signalof dark matter to guide annihilation detection experiments(e.g., Walker et al. 2011).A debate that continues to be re-kindled is the issue ofwhether density profiles are cored, whereby the density tendsto a constant value towards small radii or whether they arecuspy, whereby the density continues to increase as a radialpower-law. To the advocates of cuspy profiles, the debate isover the extent to which they are cuspy, i.e. the exponentof the radial power-law. The motivation that drives thesestudies originates from comparing observed density profileswith those predicted by N-body simulations of large scalestructure formation.Early simulations favoured cuspy profiles that are typ-ically steeper than those inferred from observations (see,for example, de Blok & Bosma 2002, and citations to thiswork). However, these early studies were largely based onpure dark matter simulations which ignored the effects ofbaryons. Accordingly, the observational data concentratedon dwarf galaxies where baryons behave more like test par-ticles in a dominating dark matter potential. Recent workby Cole et al. (2012) shows that cuspy dark matter profilesin simulated dwarf spheroidals results in stronger dynamicalfriction causing globular clusters to fall into the centres ona dynamical time scale, in contrast to what is observed inthese systems.Simulations of large scale structure are now begin-ning to incorporate baryons, but this is a highly complextask, fraught with many complicating factors such as blackhole accretion and their subsequent feedback (e.g., Croton2006; Ciotti, Ostriker & Proga 2009; Bryan et al. 2013),feedback from supernovae and cooling (see, for example,Duffy et al. 2010; Newton & Kay 2013). Understandingthe interplay of baryons and dark matter is not only essen-tial to a full comprehension of the formation and evolutionof galaxies, but can also shed light on the properties of thedark matter itself, such as constraining the self-interactioncross-section of dark matter (Spergel & Steinhardt 2000;Loeb & Weiner 2011). In this regard, Lovell et al. (2012)find that the velocity profiles of satellite galaxies around theMilky Way are considerably better matched by warm darkmatter density profiles than cold dark matter density pro-files.Improving the quality of observations of density profilesof galaxies, particularly the more poorly understood early types, therefore provides a much needed benchmark to assistin discrimination of the many different scenarios describingtheir history. Gravitational lensing offers a very powerfuland yet conceptually simple approach to achieving this, in-dependent of assumptions about the kinematical state of thedeflecting mass. Whilst weak galaxy-galaxy lensing can beused to constrain density profiles, this, by necessity, must beconducted in a statistical sense (e.g., Velander et al. 2013)and provides measurements of the density profile on largerscales where the dark matter dominates. Conversely, stronggalaxy-galaxy lensing is applicable on a per-galaxy basisand is sensitive to density profiles on small scales where thepoorly constrained baryon physics is more dominant.Early type galaxies have a higher average lensing cross-section than disk galaxies (e.g., Maoz & Rix 1993) andhence strong galaxy-galaxy lens samples tend to harboursignificantly more early than late type lenses. In this way,such samples provide a perfect opportunity to gain uniqueinsights into the formation of early types, a fact that hasinspired the culmination of several different lens samplesto date. Recent strong galaxy-galaxy lens samples includethe Sloan Lens ACS (SLACS) survey (Bolton et al. 2006)with 85 lenses out to a redshift of z ≃ . ≃ . z . ≃ .
5; Sonnenfeld et al. 2013), the Sloan WFC Edge-onLate-type Lens Survey (SWELLS; Treu et al. 2011) with20 disk galaxy lenses at z < ∼ . . z . ∼
550 deg ) conducted in five passbands in the sub-millimetre (submm) wavelength range 100 µ m < ∼ λ < ∼ µ musing the Herschel Space Observatory Pilbratt et al. (2010).Being a submm survey, the negative K-correction affordedby submm galaxies means that lensed sources are much morereadily detected out to significantly greater redshifts thansurveys conducted at optical wavelengths. Increasing the dis-tance of a source increases the probability of it being lensed c (cid:13)000
550 deg ) conducted in five passbands in the sub-millimetre (submm) wavelength range 100 µ m < ∼ λ < ∼ µ musing the Herschel Space Observatory Pilbratt et al. (2010).Being a submm survey, the negative K-correction affordedby submm galaxies means that lensed sources are much morereadily detected out to significantly greater redshifts thansurveys conducted at optical wavelengths. Increasing the dis-tance of a source increases the probability of it being lensed c (cid:13)000 , 1–14 -ATLAS: Modelling the first lenses by intervening matter. Combining this fact with the largeareal coverage of H-ATLAS results in an anticipated sampleof hundreds of strong galaxy-galaxy lenses (Negrello et al.2010; Gonz´alez-Nuevo et al. 2012).Such lenses also have the advantage that their submmemission is unaffected by any dust in the lens which meansthat a clean view of the source is obtained. This proves par-ticularly important when reconstructing high resolution sur-face brightness maps of the high redshift lensed source formorphological studies. Furthermore, submm galaxy num-ber counts are steep so that strongly lensed galaxies can bestraightforwardly identified with simple flux selection crite-ria. This simple technique has also been applied by the HER-schel Multi-tiered Extragalactic Survey (HerMES; Oliver etal. 2012. See Wardlow et al. 2013, for an account of the lens-ing aspects of this survey) and the survey carried out at mmwavelengths by the South Pole Telescope (Carlstrom et al.2011; Vieira et al. 2013).The ultimate size of the H-ATLAS sample is an obviousadvantage in terms of improving statistical uncertainties.However, another far more compelling benefit that arisesfrom the negative K-correction in the submm is that higherredshift lensed sources are more likely to be lensed by higherredshift lenses. From an evolutionary point of view, thisbrings about an increase in the period over which transfor-mations in density profiles can be determined, back to ear-lier times in the Universe’s history when the rate of galaxyevolution was stronger (for a theoretical perspective, see,for e.g., Schaye et al. 2010). In addition to this, almost allsubmm galaxies have extended structure on the scales of typ-ical galaxy lens caustics so that their lensed images compriseextended arcs and ring-like structures. As demonstrated byDye & Warren (2005) in application of the semi-linear in-version (SLI) algorithm (Warren & Dye 2003), extendedstructure in lensed images allows stronger constraints to beplaced on the density profile of the lensing galaxy.In this paper, we apply an enhanced version of the SLImethod which allows multiple datasets observed at differ-ent wavelengths to be simultaneously reconstructed with thesame lens model. We apply this to Hubble Space Telescope(HST) images acquired in both the F110W and F160W fil-ters of each of the five lenses identified in the 14.4 deg datareleased by the H-ATLAS consortium as science demonstra-tion phase (SDP) data.The layout of this paper is as follows: Section 2 out-lines the data. In Section 3 we describe the methodologyof the lens modelling, including a description of the en-hanced SLI method. Section 4 presents the results and wesummarise the findings of this work in Section 6. Through-out this paper, we assume the following cosmological pa-rameters; H = 67 km s − Mpc − , Ω m = 0 .
32, Ω Λ = 0 . The data analysed in this work are more thoroughly de-scribed in a companion paper (Negrello et al., 2013, here-after denoted N13) but we include the pertinent details herefor completeness.The HST observations were carried out in April 2011in Cycle 18 under proposal 12194 (PI Negrello) using the Wide Field Camera 3 (WFC3). Two orbits were allocatedper target with at least three quarters of the total exposuretime per target of 5130s acquired in the F160W filter and theremainder in the F110W filter. Images were reduced usingthe IRAF
MultiDrizzle package and resampled to a pixelscale of 0.064”, half the intrinsic pixel scale of the WFC3.The lens galaxy flux and lensed background source im-age in each system were then simultaneously fitted withsmooth profiles using the
GALFIT software (Peng et al.2002) and the lens profiles subtracted to leave the lensedimage. These lens-subtracted images, along with their cor-responding noise maps and point spread functions (PSFs)modelled by
TinyTim (Krist 1993) are those used by theSLI reconstruction algorithm.The left-hand column in Figure 1 shows the resultingF110W and F160W images for each system. We applied an-nular elliptical masks (after PSF convolution), fitted by eyeto each image, to include only the lensed image features.This also masks any noisy residuals which remain after the
GALFIT subtraction.
In this paper, we apply the SLI method originally derived byWarren & Dye (2003). We use the Bayesian version of theSLI method applied by Dye et al. (2007) and Dye et al.(2008), based on the version developed by Suyu et al.(2006). In addition, the adaptive source plane grid intro-duced by Dye & Warren (2005) is used.In this section, we describe an enhancement to the SLImethod that allows multiple images to be simultaneouslyreconstructed using the same lens mass model. Includingmultiple images in the inversion gives rise to stronger con-straints on the lens model parameters. This is particularlytrue if the images are observed at different wavelengths sincecolour variations across the lensed source mean that each im-age probes a different line of sight through the gravitationalpotential of the lensing galaxy. We describe the modifica-tions necessary for the inclusion of multiple images but referthe reader to the aforementioned papers for more compre-hensive details of the underlying SLI method.
The SLI method assumes a pixelised image and a pixelisedsource plane. For a given lens model, the method computesthe linear superposition of lensed images of each source planepixel that best fits the observed lensed image. In the originalformulation, the rectangular matrix f ij held the fluxes oflensed image pixels j for each source plane pixel i of unitsurface brightness. In this way, a model lensed image wascreated with flux values equal to P i s i f ij for each imagepixel j given source pixel surface brightnesses s i . Subtractingthis model image from the observed image which has pixelflux values d j and 1 σ uncertainties σ j allows the χ statisticto be computed.To cope with multiple images, we need to introduce anew index to each of these quantities to denote separateimage numbers. The χ statistic in this case becomes c (cid:13) , 1–14 S. Dye et al. χ = K X k =1 " J k X j =1 P I k i =1 s ki f kij − d kj σ kj ! (1)where there is now an additional sum over images k . Notethat each image k has its own source image with surfacebrightnesses s ki in pixels i . The image of each of these pixelsstored in f kij must be convolved with the PSF of the observedimage k . Also note that each of the k sources and k imagescan have different numbers of pixels, I k and J k respectively.As in the single image version of the SLI method, theminimum χ solution is given by s = F − d (2)but now the matrix F is a block-diagonal matrixdiag( F , F , ..., F K ) comprising the sub-matrices F k and d is a column vector which itself has column vector elements d k . The elements of F k and d k are respectively F kij = J n X n =1 f kin f kjn / ( σ kn ) , d ki = J n X n =1 f kin d kn / ( σ kn ) . (3)Finally, the column vector s contains the source pixel surfacebrightnesses arranged in order s , s , ...s I , s , ...s KI K − , s KI K .To regularise the solution, equation (2) must bemodified by the regularisation matrix H as describedin Warren & Dye (2003). However, in the case of mul-tiple images, H becomes the block diagonal matrixdiag( λ H , λ H , ..., λ K H K ) where each sub-matrix H k corresponds to the chosen regularisation matrix for source k . Note that in this formalism, each source k is assignedits own independent regularisation weight λ k . We regulariseeach source plane using the scheme described in Dye et al.(2008) appropriate for adaptive source grids. In principle,instead of regularising each source plane independently, dif-ferent source planes could be allowed to regularise one an-other in which case H would not be block-diagonal. Thiscould be beneficial if the source is expected to be similarbetween the different input images but would bias the lensmodel if not.The procedure for finding the most probable lens modelparameters then turns to Bayesian inference as describedby Dye et al. (2008). Adapting equation (7) in Dye et al.(2008) to the multi-image case here results in the followingexpression for the Bayesian evidence, ǫ , − ǫ = χ + ln [det( F + H )] − ln [det( H )]+ s T H s + K X k =1 J k X j =1 ln (cid:2) π ( σ kj ) (cid:3) (4)with χ given by equation (1) and where F , H and s arethe multi-image quantities defined above. The negative log-arithm of the evidence as given above is then minimisedby applying the Marcov Chain Monte Carlo (MCMC) tech-nique to the lens model parameters (see next section), theregularisation weights and a parameter called the ‘splittingfactor’ which controls the distribution of source plane pixelsizes on the adaptive grid (see Dye et al. 2008, for more de- In practice, we have opted to set the same regularisation weightacross all images to simplify the MCMC minimisation. tails). After the MCMC chain has burnt in, we allow a fur-ther 100,000 iterations to estimate parameter confidences.We note a further practicality. When computing the χ term in equation (4), we carry out the sum over imagepixels contained within an annular mask surrounding thering. The mask is tailored for each image to include theimage of the entire source plane, with minimal extraneoussky. This increases the fraction of significant image pixelswith the effect that the evidence is more sensitive to themodel parameters.Finally, we point out that the multi-image SLI methodas presented assumes that all images are statistically inde-pendent of each other. In the case of images that are not sta-tistically independent, for example, as could be the case withimage slices in an integral field unit data cube or spectral-line interferometric data cube, equation (1) must be modi-fied to include the relevant covariance terms. We model each of the five lenses considered in this workwith a single smooth density profile to describe the distri-bution of the total (baryonic and dark) lens mass. In orderto directly compare with the work of Bolton et al. (2012)and Sonnenfeld et al. (2013), we use the power-law densityprofile assumed in these studies. The volume mass densityof this profile, ρ , scales with radius, r , as ρ ∝ r − α . The im-plicit assumption made with this profile is that the power-law slope, α , is scale invariant. This assumption appears tobe reasonable, at least on the scales probed by strong lens-ing, since there is no apparent trend in slope with the ratio ofEinstein radius to effective radius (Koopmans et al. 2006;Ruff et al. 2011).The corresponding projected mass density profile wetherefore use in the lens modelling is the elliptical power-law profile introduced by Kassiola & Kovner (1993) whichhas a surface mass density, κ , given by κ = κ (˜ r/ − α . (5)where κ is the normalisation surface mass density (the spe-cial case of α = 2 corresponds to the singular isothermalellipsoid). The radius ˜ r is the elliptical radius defined by˜ r = x ′ + y ′ /ǫ where ǫ is the lens elongation defined as theratio of the semi-major to semi-minor axes. There are threefurther parameters that describe this profile: the orienta-tion of the semi-major axis measured in a counter-clockwisesense from north, θ , and the co-ordinates of the centre of thelens in the image plane, ( x c , y c ). We also include two furtherparameters to allow for an external shear field, namely, theshear strength, γ , and shear direction angle, again measuredcounter-clockwise from north, θ γ . The shear direction angleis defined to be perpendicular to the direction of resultingimage stretch. This brings the total number of lens modelparameters to eight. We assume a uniform prior for all eightparameters. In the MCMC contour plots presented in theappendix, we marginalise over ( x c , y c ) since we did not de-tect any significant offsets between the lens mass centre andthe centroid of the lens galaxy light. c (cid:13) , 1–14 -ATLAS: Modelling the first lenses The reconstruction of each of the five lenses is shown inFigure 1. Table 1 gives the lens model parameters, includingthe geometric average Einstein radius, θ E , computed as (cid:18) θ E (cid:19) = (cid:18) − α √ ǫ κ o Σ CR (cid:19) α − (6)where Σ CR is the critical surface mass density (see, for ex-ample Schneider, Ehlers & Falco 1992). In this section we detail the characteristics of each lenssystem. In particular, we compare with the results ofBussmann et al. (2013, B13 hereafter) who have mod-elled imaging data acquired with the Sub-Millimeter Array(SMA) for ∼
30 candidate lenses discovered by H-ATLASand HerMES. All five of the H-ATLAS SDP lenses are mod-elled by B13, although we point out that external shear isnot included in their lens model.
J090311.6 + (ID81): This is a classic cusp-causticconfiguration lens. The near-IR emission in the lensed imageclosely matches that of the SMA data and unsurprisingly re-sults in a consistent magnification. The reconstructed sourcein both HST filters shows little structure other than a slightelongation along the NE-SW direction. The centroid of thesource is well aligned with that found by B13. The lensmodel is an excellent fit to the observed data and leavesno significant residuals. The model requires a small amountof external shear with strength γ ≃ .
05 and direction θ γ ≃ ◦ , consistent with perturbations expected from anearby group of galaxies to the east. The elongation andorientation of the required model is entirely consistent withthat of the observed light profile. J090740.0 − (ID9): This lens system is domi-nated by a single doubly-imaged source with a simple mor-phology lying to the north of the lens galaxy centroid. Thedouble imaging is consistent with the SMA data but theemission appears to originate from a different location inthe source compared to what is observed in the near-IR HSTdata. The reconstructed source F110W-F160W colour mapshows a reddening gradient which points from the near-IRsource towards the SMA source centroid. Some of the fainteremission from the source in the near-IR crosses the caus-tic and gives rise to the observed complete Einstein ring.There is also some fainter structure in the ring which is fitin the model by a fainter source to the east of the lens cen-troid. Negligible external shear is required in the best fitlens model. The modest elongation of ǫ = 1 .
14 indicates amore radially symmetric mass profile compared to the light.The alignment of the mass and light elongation in this lensis significantly different (see section 4.4).
J091043.1 − (ID11): Like ID9, this system hasa complete Einstein ring. The ring’s significant ellipticityis the result of a relatively strong external shear field ofstrength γ = 0 .
23. The direction of this shear points almostexactly to the centre of a nearby edge-on spiral galaxy tothe NW located at a redshift of z = 0 . ± .
09 (see N13).The implication is therefore that this spiral is almost en-tirely responsible for the shear perturbation. We attempted a model where external shear was replaced by a second sin-gular isothermal lens to represent the spiral’s total massbut found no significant improvement in the fit. The recon-structed source exhibits clear small scale structure in bothfilters, required to fit the observed structure in the ring. Themajority of the emission observed in the ring comes from adoubly imaged source lying just outside the caustic and thesmaller-scale structure comes from smaller knots of emissionin the source, some of which are quadruply imaged. As theresidual plot in Figure 1 indicates, the model image does notperfectly account for the observed features in the ring andthis is also reflected in the fact that the model fit is onlymarginally acceptable. It is therefore possible that some ofthe ring structure is actually structure in the lens galaxynot fully removed by
GALFIT . The SMA data imply a dou-bly imaged source which, like J090740.0 − J091305.0 − (ID130): The lens galaxy is rela-tively poorly constrained in this system. The best fit modelis consistent with zero external shear (as might be expectedfrom the lack of observed nearby perturbers) and the lenshas one of the higher elongations found in the sample of ǫ = 1 .
34. The best fit reconstructed source is very extendedand as such, the magnification is low. The residual mapshown in Figure 1 shows some significant features towardsthe lens centre which is not surprising given the difficultyreported by N13 in removing the lens light. However, theresiduals contribute an insignificant amount of light to theoverall source and as such will have a negligible effect on thelens model parameters. The SMA data are in close agree-ment with the near-IR data which increases confidence inthe
GALFIT subtraction (see N13), although the near-IR dataimply a slightly larger magnification than the SMA data. Wemake the caveat that this lens, as pointed out by N13, is alikely Sa galaxy. In order to compare our results with those ofthe aforementioned lensing studies which include only earlytype lenses, we have omitted this system from our fits to thetrends reported later in this paper.
J090302.9 − (ID17): This is a relatively poorlyconstrained lens although the fit is acceptable. There aresome minor features in the residual image which occur at3 o’clock and 11 o’clock around the inner radius of the an-nulus as shown in Figure 1. N13 have modelled the flux inthe lensed image by fitting individual GALFIT profiles to thedifferent components. Two of these profiles lie on the innerradius of the annulus and these coincide with the locationsof the residuals found in the lens modelling here. One inter-pretation is therefore that spatially dependent extinction inthe lensing galaxy affects the lensed image. This is consistentwith the colour of the feature at 11 o’clock which N13 deter- c (cid:13) , 1–14 S. Dye et al.
J090311.6+003906 F160WJ090311.6+003906 F110W model residuals sourceimage model residuals sourceimage
J090740.0−004200 F160W model residuals sourceimage model residuals sourceimage
J090740.0−004200 F110WJ091043.1−000321 F160W model residuals sourceimage model residuals sourceimage
J091043.1−000321 F110WID81ID81ID9ID9ID11ID11 1kpc1kpc1kpc1kpc1kpc1kpc
Figure 1.
Lens reconstructions. Reading from left to right, columns show the observed image (masked and lens subtracted), the modelimage, the residuals (observed image minus model; grey-scale same as corresponding images) and reconstructed source surface brightnessmap (the solid black or white line shows the caustic and the dashed white line and small circle respectively show the source half-lightarea and source centre obtained by B13 at 880 µ m). For each system, the F110W and F160W data are shown. In all panels, north pointsalong the positive y-axis and west points along the positive x-axis. c (cid:13) , 1–14 -ATLAS: Modelling the first lenses ID z d z s α κ ǫ θ ( ◦ ) γ θ E ( ′′ )J090311.6+003906 (ID81) 0.2999 3.042 1 . +0 . − . . +0 . − . . +0 . − . +8 − . +0 . − . . ± . − . +0 . − . . +0 . − . . +0 . − . +3 − . +0 . − . . ± . − . +0 . − . . +0 . − . . +0 . − . +3 − . +0 . − . . ± . − . +0 . − . . +0 . − . . +0 . − . +14 − . +0 . − . . ± . − . +0 . − . . +0 . − . . +0 . − . +19 − . +0 . − . . ± . Table 1.
Lens model parameters. Reading from left to right, columns are the H-ATLAS identifier (including the Negrello et al. 2010 iden-tifier), the lens redshift, z d , the source redshift, z s , the density profile slope, α , the lens mass normalisation, κ (in units of 10 M ⊙ kpc − ),the elongation of the lens mass profile, ǫ , the orientation of the semi-major axis of the lens, θ , measured counter-clockwise from north,the strength of the external shear component, γ , and the Einstein radius, θ E , in arcsec computed from equation (6). J091305.0−005343 F160W model residuals sourceimage model residuals sourceimage model residuals sourceimage model residuals sourceimage
J091305.0−005343 F110WJ090302.9−014127 F160WJ090302.9−014127 F110WID130ID17ID17ID130 1kpc1kpc1kpc1kpc
Figure 1 – continued mine as having a significantly redder colour than the averagecolour of the other GALFIT profiles, but not with the featureat 3 o’clock which is consistent in colour. An alternative ex-planation might therefore be that the lensed image containsresidual flux from the lensing galaxy itself which is highlypossible given the complexity in removing the lens from thissystem. Nevertheless, the reconstructed source plane showstwo very prominent elongated objects in both bands which converge at a point interior to the caustic. The majorityof this source plane emission is doubly imaged but someof the flux in the merged region is quadruply imaged. Thefact that the lensed image is well fit by a relatively simplesource surface brightness map adds reassurance that the re-construction is plausible; an over-complicated source oftenindicates that there are non-lensed features in the lensedimage. Although the SMA data for this lens are unable to c (cid:13) , 1–14 S. Dye et al. z d α This workSL2S (Sonnenfeld et al. 2013)SL2S+SLACS+LSD (Sonnenfeld et al. 2013)SLACS+BOSS (Bolton et al. 2012)
Figure 2.
Variation of the density profile slope, α , as a functionof the lens redshift, z d . The solid and dashed lines show the red-shift dependency of α using the SL2S lenses by Sonnenfeld et al.(2013) and the SLACS + BELLS lenses by Bolton et al. (2012)respectively. The extent of each line indicates the extent of thelens redshifts in the respective surveys. The grey data point corre-sponds to the Sa lens J091305.0 − σ error en-velope. resolve individual ring features, B13 obtain a magnificationconsistent with that measured from the near-IR data here. Figure 2 shows the fitted lens density profile slopesplotted against redshift. Discounting the likely Sa lensJ091305.0 − χ fit throughthe four data points is α = 2 . ± . − (0 . ± . z .(If we include this fifth lens, the fit becomes α = 2 . ± . − (0 . ± . z .) The dotted line and grey shaded en-velope in Figure 2 shows the fit and the 1 σ error region re-spectively. In the same figure we plot the variation in slopewith redshift from three other lens sample combinations; 1)the SL2S lens sample of α = 2 . ± . − (0 . ± . z from Sonnenfeld et al. (2013), 2) the combination of theLensing Structure and Dynamics (LSD) sample of Treu& Koopmans (2004, ApJ, 611, 739), SL2S and SLACS of α = 2 . ± . − (0 . ± . z also from Sonnenfeld et al.(2013) and 3) the combination of SLACS and BOSS of α = 2 . ± . − (0 . ± . z from Bolton et al. (2012).As is apparent from Figure 2, our inferred rate of changein slope with redshift is not inconsistent with that measuredby any of the other studies plotted in the figure, althoughneither is it inconsistent with a null rate of change. This isperhaps not surprising given the small sample size presentlyat our disposal. This limitation will be considerably reducedby our forthcoming rapidly growing lens sample. Table 2 lists the source flux magnifications. For each lens,we have computed the magnification at every point in the MCMC chain as presented in Figure A1 to form a magnifi-cation distribution. Table 2 then quotes the median magni-fication and its ±
34% bounds.We computed magnifications using the higher signal-to-noise F160W data to give more precise magnifications.We find that the magnifications computed using the F110Wdata generally have a larger spread but the distribution isalways consistent with those computed using the F160Wdata.We determined three different magnifications to give anindication of the strength of near-IR differential amplifica-tion. The first is a ‘total magnification’, µ tot , computed asthe ratio of the total flux in the masked region of the imageas shown in Figure 1 to the total flux in the source plane.The second and third, µ . and µ . , correspond to the mag-nification of the brightest region(s) of the source that con-tributes 50% and 10% respectively of the total reconstructedsource flux. Note that µ tot is almost always lower than µ . and µ . since incorporating the total source plane typicallyincludes additional regions that are less magnified.Table 2 also lists the magnifications, µ , determinedby B13 at 880 µ m. These magnifications are calculated in anelliptical disk centred on the best fit 880 µ m source bright-ness profile with a radius twice that containing half of the to-tal source flux. µ is the ratio of the integrated flux withinthe image plane region mapped by this disk to the integratedflux within the disk in the source plane itself. For the S´ersicprofiles fit to the SDP sources by B13, this corresponds toapproximately 75% of the source light in all cases. Therefore, µ corresponds to a magnification somewhere between µ tot and µ . .As Table 2 shows, for all lenses apart fromJ091305.0 − µ is consistent with a value spannedby µ tot and µ . . The consistency is generally better whenthe 880 µ m source morphology more closely resembles thereconstructed near-IR source. This is a reflection of the factthat the lens models determined at both wavelengths aregeometrically similar . The exception is J091305.0 − µ mand the near-IR, but in this case, the magnification discrep-ancy is brought about by a significantly different lens elon-gation, with the near-IR lens model favouring an elongationof ∼ . ∼ . µ m. A question which brings insight to models of galaxy forma-tion and evolution is how closely the visible mass traces thedark matter halo. One way to address this is to comparethe visible morphology of the lens galaxies to the total massprofiles determined through lensing.We used the
GALFIT models of N13 to determine theelongation and orientation of the lens galaxy surface bright-ness profiles. Table 3 lists these along with the effective radii.In the case of J091305.0 − We note that the lens elongations derived by B13 are consis-tently higher than those derived in our study and we attributethis, at least partly, to the lack of external shear in the B13 lensmodel. c (cid:13) , 1–14 -ATLAS: Modelling the first lenses ID µ tot µ . µ . µ J090311.6+003906 (ID81) 10 . +0 . − . . +1 . − . . +1 . − . . ± . − . +0 . − . . +0 . − . . +0 . − . . ± . − . +0 . − . . +0 . − . . +2 . − . . ± . − . +0 . − . . +0 . − . . +0 . − . . ± . − . +0 . − . . +0 . − . . +0 . − . . ± . Table 2.
Source flux magnifications. The quantities listed are: the total source flux magnification, µ tot ; the magnifications, µ . and µ . which give the magnification of the brightest region(s) of the source respectively contributing 50% and 10% of the total reconstructedsource flux; the magnification at 880 µ m, µ , computed by B13 for an area of the source which is four times the source’s half-light area. ε light -80-60-40-2002040 θ − θ li gh t [ d e g r ee s ] ε light ε Figure 3.
Comparison of light with mass.
Top panel : Elongationof lens mass profile versus elongation of observed light.
Bottompanel : Difference in position angle of lens profile and observedlight versus elongation of observed light. In both panels, the greydata point corresponds to the Sa lens J091305.0 − light profiles which make up the bulge, since the bulge com-prises nearly all of the light and, unlike the faint disk, has acoherent set of profiles which give a well-defined orientationand elongation.Figure 3 plots the comparison of mass and light profileparameters. The top panel shows the comparison of elonga-tions. For all five of the lenses, the total lens mass modelhas or is consistent with a lower elongation than that of thelight. This implies that the dark matter halo is comparablein elongation or rounder in each case.The bottom panel of Figure 3 compares the offset in ori-entation of the lens mass and light profiles. Here, there aresome significant discrepancies. The offsets are substantiallyhigher on average than those found by SLACS, who mea-sured an rms scatter of 10 ◦ (Koopmans et al. 2006), butconsistent with the findings of SL2S (Gavazzi et al. 2012)who measure an rms scatter of 25 ◦ with offsets of up to 50 ◦ .As Gavazzi et al. (2012) point out, the SL2S lenses havea higher average ratio of Einstein radius to effective radius than the SLACS lenses and hence the SLACS lenses aremore dominated by the stellar component. The average ofthis ratio for our lenses is even higher than that of the SL2Ssample and so we would expect even less alignment betweenthe dark and visible components. We will be able to explorethis trend more properly with our forthcoming larger lenssample, although there are already indications from simu-lations that such large (and even larger) morphological dif-ferences between baryons and dark matter are commonplace(for example, see Bett et al. 2010; Skibba & Macci`o 2011). An important observational benchmark for models of galaxyand structure formation is the fraction of dark matter con-tained within a fixed fraction of the effective radius. Usingthe SLACS lens sample, Auger et al. (2010b) measure anaverage projected fraction of dark matter within half the ef-fective radius of 0.21 with a scatter of 0.20, for a Salpeter(1955) IMF, or 0.55 with a scatter of 0.11 for a Chabrier(2003) IMF. Ruff et al. (2011) measure the average of thisfraction to be 0.42 with a scatter of 0.20 for a Salpeter IMFfor the SL2S lenses.Table 3 lists the stellar masses and the total lensing pro-jected mass contained within half the effective radius for ourlenses. To obtain these stellar masses, we used the total stel-lar masses and the
GALFIT profiles determined for the lensgalaxies by N13. Excluding the Sa lens J091305.0 − f DM = 0 .
46 with a scatter of 0.10,for a Salpeter IMF, ( f DM = 0 .
69 with a scatter of 0.07, for aChabrier IMF). Although this is statistically consistent withthe SLACS and SL2S lenses, the higher value measured inboth our lenses and the SL2S lenses compared to the SLACSsample most likely reflects the lower average ratio of Einsteinradius to effective radius in SLACS.One of the trends detected by the SLACS survey is that f DM for early types increases with galaxy mass and galaxysize. Auger et al. (2010b) measure the linear fit f DM = − . ± .
09 + (0 . ± .
10) log(R e / f DM and R e witha measured gradient of d f DM / d R e = 0 . +0 . − . kpc − . Ourlens sample, excluding the Sa lens J091305.0 − f DM = − . ± . . ± .
46) log(R e / c (cid:13) , 1–14 S. Dye et al. ID ǫ light θ light ( ◦ ) R e (“) R e (kpc) M ∗ , SalpR e / M ∗ , ChabR e / M TotR e / J090311.6+003906 (ID81) 1 . ± .
01 10 ± . ± .
30 2 . ± .
73 6 . ± . − . ± .
01 59 ± . ± .
07 2 . ± .
60 6 . ± . − . ± .
01 21 ± . ± .
92 2 . ± .
64 8 . ± . − . ± .
02 43 ± . ± .
62 1 . ± .
35 1 . ± . − . ± .
01 16 ± . ± .
59 0 . ± .
33 3 . ± . Table 3.
Morphology of the lens light profile and lens masses. Columns are: elongation, ǫ light , position angle (measured counter-clockwisefrom north), θ light , effective radius, R e , the stellar mass contained within a radius of R e /2 for a Salpeter and Chabrier IMF, M ∗ , SalpR e / and M ∗ , ChabR e / respectively (derived from the stellar masses computed in N13) and the total mass within a radius of R e /2 inferred fromthe lens model, M TotR e / . All masses are in units of 10 M ⊙ . Note that the light profile parameters for J091305.0 − log (R e / 1kpc) α This workSLACS (Auger et al. 2010b)SL2S only (Sonnenfeld et al. 2013) log [ M Tot (R e / 1kpc) -2 ] α Re/2
Figure 4.
Correlation between total mass density profile slope, α ,and effective radius, R e , ( top panel ) and average projected totalsurface mass density within R e / bottom panel ). In both panels,the Sa lens J091305.0 − σ error envelope. correlated with the average surface mass density containedwithin R e /
2. In Figure 4, we plot these correlations forour lenses. The top panel shows the density profile slope, α , plotted against effective radius. For our four early-typelenses, we obtain a straight line fit of α = 2 . ± . − (0 . ± .
47) log(R e / σ error envelope. This com-pares to the fit α = 2 . ± . − (0 . ± .
12) log(R e / α =2 . ± . − (0 . ± .
20) log(R e / .In the bottom panel of Figure 4, we plot α against theaverage total surface mass density within half the effectiveradius, as quantified by the ratio M TotR e / / (R e / . Weobtain a straight line fit of α = 11 . ± .
11 + (0 . ± .
22) log(M
TotR e / / (R e / ) which compares to the gra-dient of d α/ d log[M TotR e / / (R e / ] = 0 . ± .
19 for theSLACS lenses as measured by Auger et al. (2010b).
As the preceding section has shown, in all observational di-agnostics and trends we have considered, bar the correlationbetween f DM and R e , the H-ATLAS lenses are more similarto the SL2S lenses than those of SLACS. This is perhaps notsurprising when one considers the following characteristicmedian values expressed in order SLACS, SL2S, H-ATLAS: e R e ≃ e M ∗ ≃ . M ⊙ , 10 . M ⊙ ,10 . M ⊙ ; e M TotR e / ≃ . M ⊙ , 10 . M ⊙ , 10 . M ⊙ . It ap-pears to be the case therefore, at least in the SDP data, thatthe H-ATLAS lenses populate the low-mass tail of the SL2Slens sample.Despite these obvious differences and despite our verysmall sample of lenses at present, we still detect many of thecorrelations found in the various other aforementioned stud-ies. These studies have taken care to ensure that the trendsthey detect are not the result of selection biases or system-atic effects. In a similar vein, a potential systematic effect tobe considered when comparing our results with these is thatour lensing analysis does not incorporate any additional con-straints from dynamical measurements. This means that theslope is measured in the vicinity of the Einstein ring, whereasin analyses using lensing and dynamics, the average slope in-terior to the Einstein ring is measured. Therefore, a changein slope with radius could potentially introduce a system-atic offset in the slopes determined in the present work with Here, we have taken a slice through the 4-dimensional planethat Sonnenfeld et al. fit to the density profile slope by assuminga redshift of 0.3 and a stellar mass of log(M ∗ / M ⊙ ) = 11 . (cid:13) , 1–14 -ATLAS: Modelling the first lenses respect to those from lensing and dynamics. However, as pre-viously mentioned, on the scales probed by strong lensing,the slope appears not to exhibit any significant dependencyon radius since there is no apparent trend in slope with theratio of Einstein radius to effective radius (Koopmans et al.2006; Ruff et al. 2011).This is related to the effect reported in (Ruff et al.2011) and (Bolton et al. 2012) that the ratio of the Einsteinradius to the lens galaxy’s effective radius increases with in-creasing lens redshift. This is due to the redshift dependenceof the angular diameter distance ratios which govern thelensing geometry and the fact that a fixed physical size re-duces in angular extent with increasing redshift (at least outto the lens redshifts in this work). This has the result thatas redshift is increased, the density profile is measured byour lensing-only analysis at a radius which is an increasingmultiple of the effective radius. A change in slope with ra-dius would therefore mimic a change in slope with redshift.However, in addition to the observational evidence that theslope is not seen to depend on radius on strong lensing scales,on much larger scales, the slope is expected to steepen withincreasing radius according to simulations and the require-ment that the total halo mass converges. Therefore, even ifthis steepening were to influence our slope measurements,our detection of the rate at which slopes become less steepwith increasing redshift must be a lower limit to the intrinsicrate.In terms of a physical interpretation of observed vari-ations in the density profile slope, the picture is somewhatunclear. Simulations by Dubois et al. (2013) reproduce theobserved steepening with decreasing redshift and find thatfeedback from active galactic nuclei (AGN) modifies theslope. This work indicates that AGN feedback is requiredto reproduce the near-isothermal profiles (i.e., α ≃
2) ob-served in low redshift early type galaxies. However, thesimulations of Remus et al. (2013) indicate that whilst acombination of dry minor and major mergers produce near-isothermality at low redshifts, the slopes are significantlysteeper at higher redshift. Confounding this is the simu-lation work of Nipoti, Treu & Bolton (2009) which showsthat the total mass profile of early types is not modified atall by dry mergers.Turning to the projected dark matter fraction withinhalf the effective radius, f DM , Dubois et al. (2013) claimthat AGN feedback is required to reproduce the observedfractions and that without it, the fraction of stellar mass istoo high. The SLACS work reports a 5 σ detection of increas-ing f DM with effective radius. This compares to our marginaldetection (2 . σ ) and a null detection in the SL2S lenses.If this trend is real, an obvious interpretation might bethat star formation efficiency reduces as halo mass increases.Another possibility is presented by Nipoti, Treu & Bolton(2009) who predict that the fraction of dark matter withinthe effective radius increases as a result of mergers.Instead of investigating how f DM varies with effectiveradius, an alternative is to test whether f DM changes withredshift since this is another diagnostic which can be pro-vided by simulations.Figure 5 shows this plot for the H-ATLAS lenses (ex-cluding J091305.0 − f DM = 0 . ± .
09 + (0 . ± . z . In comparison, thesimulations of Dubois et al. (2013) predict that the fraction z d f D M Figure 5.
Variation of the fraction of dark matter within halfthe effective radius, f DM , for a Salpeter IMF with redshift. Thegrey shading depicts the 1 σ error region for the straight line fit. of dark matter within 10% of the virial radius decreases withincreasing redshift when AGN feedback is present, or, thatthis fraction remains constant with redshift if AGN feedbackis not present. If the fraction of dark matter within 10% ofthe virial radius scales in the same way as f DM , then thisis in contrast to our findings. However, since f DM dependson the size of the stellar component and the virial radiuseffectively does not, there is still the possibility that the tworesults are consistent if the stellar mass increases in spatialextent relative to the dark matter with increasing redshift.Important clues also come from comparing the mor-phology of the visible component of the lenses with that ofthe dark matter halo. We find significant discrepancies in thealignment and ellipticity between the stellar component andthe total mass in some lenses. The discrepancies are consis-tent with what has been measured in the SL2S sample butlarger than those found in SLACS. This may be a combi-nation of the fact that both the H-ATLAS and SL2S lenseshave a higher average ratio of Einstein radius to effective ra-dius than the SLACS lenses and that the baryonic morphol-ogy correlates less strongly with that of the dark matter atlarger radii (e.g. Bett et al. 2010; Skibba & Macci`o 2011).In order to proceed with a more robust interpretation ofthese findings, more input is required from simulation workalthough as we previously discussed, present indications arethat such large morphological differences between the darkand baryonic components are to be expected. In this paper, we have modelled the first five strong gravita-tional lens systems discovered in the H-ATLAS SDP data.To directly compare with other lensing studies, we havemodelled the lenses with elliptical power-law density pro-files and searched for trends in the power-law slope and thefraction of dark matter contained within half the effectiveradius. We have found consistency with almost all existinglens analyses, although with our present sample of only fivelenses, we lack high statistical significance in our measuredtrends. The main results of this paper are that: c (cid:13) , 1–14 S. Dye et al. • the slope of the power-law density profile varies withredshift according to α = 2 . ± . − (0 . ± . z . • the H-ATLAS lenses have a mean projected dark matterfraction within half the effective radius of f DM = 0 .
46 witha scatter of 0.10, for a Salpeter IMF. • the dark matter fraction within half the effective radiusscales with effective radius as f DM = − . ± .
20 + (1 . ± .
46) log(R e / • the slope of the power-law density profile scaleswith effective radius as α = 2 . ± . − (0 . ± .
47) log(R e / TotR e / / (R e / as M TotR e / / (R e / . • f DM scales with redshift as f DM = 0 . ± .
09 + (0 . ± . z .The modelling in this paper used near-IR HST data.Whilst the HST provides the high resolution imaging nec-essary for modelling of high redshift lenses, not all of theH-ATLAS lensed sources will be as readily detected inthe near-IR as the SDP lenses considered herein. Beingsubmm selected systems, submm and radio interferometryis the ideal technology for obtaining the required signal tonoise and image resolution. This has been demonstrated byBussmann et al. (2013) who have used the SMA to imageseveral tens of lenses detected by the Herschel Space Ob-servatory. ALMA has also been used to image some of theSPT lenses (see, for example Hezaveh et al. 2013). How-ever, the true power of this facility will not be realised untilit operates with its full complement of antennae. At thispoint, ALMA will begin to deliver the high signal-to-noiseand high resolution images required by source-inversion lensmodelling methods, necessary for the strongest possible con-straints on galaxy mass profiles. Furthermore, spectral lineimaging with ALMA will open up the possibility of recon-structing lensed source velocity maps to probe the dynamicsof high redshift submm galaxies.The H-ATLAS lens sample is very much in its infancy.As the size of the sample grows and begins to populate the z d ≃ APPENDIX A: LENS PARAMETERCONFIDENCE PLOTS
In this appendix, we plot the confidence contours for allparameter combinations for each lens (apart from the lensposition parameters x c and y c since we did not detect anysignificant offsets between the lens mass centre and the cen-troid of the lens galaxy light). In each plot, the contourscorrespond to the 1, 2 and 3 σ confidence levels. ACKNOWLEDGEMENTS
The work in this paper is based on observations made withthe NASA/ESA Hubble Space Telescope under the HSTprogramme
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