DISCOVERY OF A STRONG LENSING GALAXY EMBEDDED IN A CLUSTER AT z = 1.62^*

Using the Keck/LRIS, we carried out a spectroscopic survey of the cluster IRC 0218 on 2012 October 19 and 20 (NASA/Keck Program ID 48/2012B). Targets were selected from the Williams et al. (2009) catalog of the UDS taken as part of the UKIRT Infrared Deep Sky Survey (Lawrence et al. 2007). The K-selected catalogs reach 5σ-limiting magnitudes in 175 diameter apertures of B < 27.7, R < 27.1, i < 26.8, z < 25.5, J < 23.9, and K < 23.6.

We use the 600/4000 grism for the blue side and the 600/10000 grating for the red side of LRIS. With 1'' slit widths, the resolutions are 4.0 Å and 4.7 Å, respectively. Observing conditions were excellent with ∼06 median seeing. The total integration time on the lens is 9 hr. We reduce the spectra following Tran et al. (2007), using IRAF¹¹ routines with custom software provided by D. Kelson (Kelson 2003). The wavelength coverage of the extracted spectra is 3800–5800 Å (blue side) and 7000–10000 Å (red side). A full analysis of this redshift survey will be presented in K.-V. H. Tran et al. (in preparation).

We use XCSAO (Kurtz et al. 1992) with various templates for Lyman-break and Lyα emitting galaxies from Shapley et al. (2003) to measure a redshift for the blended spectrum composed of the lens galaxy and the lensed source. The strong emission detected at 3957 Å (Figure 1, top) has the asymmetric profile characteristic of Lyα (Shapley et al. 2003) and corresponds to a redshift of z_S = 2.25384 ± 0.00003. The observed Lyα equivalent width (EW), derived for a continuum fit between 1180–1250 Å rest frame, is 129.4 ± 4.6 Å.

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The UDS cluster falls in a legacy field that has extensive multi-wavelength observations, including deep HST imaging from CANDELS (006 pixel⁻¹; Grogin et al. 2011; Koekemoer et al. 2011) and G141 spectroscopy from 3D-HST (Brammer et al. 2012). Additional HST imaging and G102 spectroscopy were obtained in GO-12590 (PI: C. Papovich). Figure 1 shows the total fluxes measured for the more massive of the two brightest cluster galaxies (BCGs) from the 3D-HST catalog of the UDS field (Skelton et al. 2014), which includes Spitzer/IRAC. Hereafter, the BCG refers to this more massive galaxy unless otherwise stated. The BCG shows excess flux at λ < 5000 Å due to emission from the lensed source. At longer wavelengths, the lens galaxy dominates. Grism spectroscopy confirms the BCG redshift of $z_{\rm L}=1.6406^{+0.0018}_{-0.0050}$. We attribute the redshift difference between the BCG and cluster to peculiar velocities due to the unrelaxed nature of the cluster (e.g., Martel et al. 2014), consistent with the high fraction of star-forming members (Tran et al. 2010). We use z = 1.62 as the lens redshift for cosmological calculations.

The lens and source are blended in ground-based observations, but HST's resolution (Figure 2) separates the system into the BCG, an arc (object A), and a counterimage (object B). In the grism spectra, the BCG shows strong continuum. Approximately 05 above the BCG in the G141 spectrum is a compact emission line corresponding to [O iii] λλ4959, 5007 at z_S = 2.2623 ± 0.0002 from object A. We also detect [O iii] λλ4959, 5007 corresponding to object B once we remove the lens galaxy's light (I. G. Momcheva et al. in preparation). The faint object C shows weak [O iii] λλ4959, 5007 in the grism spectrum consistent with a redshift of z_S = 2.26.

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Taking a 27 × 27 pixel region around the lens, we utilize the deepest HST images spanning the widest wavelength range: ACS/F475W, ACS/F814W, WFC3/F125W, and WFC3/F160W (Figure 3, top rows). We model the lens galaxy as an elliptical singular power-law mass distribution with the mass profile slope parameterized as Γ = (γ' − 1)/2 (where the three-dimensional mass density is $\rho (r)\propto r^{-\gamma ^{\prime }}$). We adopt a uniform prior of 0.2 ⩽ Γ ⩽ 0.8. The projected axis ratio b/a has a uniform prior (0.3 ⩽ b/a ⩽ 1) with the position angle as a free parameter. The normalization of the mass profile is set by the Einstein radius θ_E, which is also a free parameter. We adopt a Gaussian prior on the mass centroid with a width of σ = 005 (see Koopmans et al. 2006) that is centered on the fitted light centroid of the lens galaxy in the WFC3/F160W image (λ_rest  ∼  0.6 μm).

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We first remove the lens galaxy's light using a single Sérsic profile, as this is sufficient to describe the lens light in the region of the lensed images. In F814W, we exclude the annular region containing the lensed images (objects A and B; Figure 2) when fitting the lens light profile. Because the lens is considerably brighter than the counterimage (object B; Figure 2) in F125W and F160W, we exclude only the half-annulus around arc A when fitting the lens light profile.

To constrain the lens mass parameters, we use image pixels in the annular regions in F475W and F814W and the half-annular regions in F125W and F160W (Figure 3, second row) that contain the lensed images. We construct weight images for each filter by adding Poisson noise from sources to the inverse variance images, as outlined in Koekemoer et al. (2011) for CANDELS. Glee simultaneously models across the four bands and reconstructs the source onto a grid of 20 × 20 pixels with a resolution of ∼005. Our lens model also requires a point source convolved with the point-spread function (PSF) coincident with the peak surface brightness in image A (Figure 2). The position of this point source is the same across all filters and fit simultaneously with the lens model parameters. The counterimage of the point source is not modeled separately given its low magnification.

The lens galaxy is embedded in a cluster, and the overdense environment may affect the lens model (e.g., Momcheva et al. 2006; Wong et al. 2011). We model cluster galaxies within 2' of the lens as singular isothermal spheres truncated at r₂₀₀ and estimate their virial masses assuming the stellar-to-halo mass relation of Moster et al. (2013). We parameterize the cluster's dark matter halo as a spherical Navarro–Frenk–White (NFW) profile (Navarro et al. 1996) with a mass of 7.7 × 10¹³ M_☉ centered at the peak of the X-ray emission (source 12A in Pierre et al. 2012) and a concentration calculated using the mass–concentration relation of Zhao et al. (2009).

In addition to this fiducial model, we run an extensive suite of models to test environmental contributions to the lens. We explore multiple permutations with and without: (1) nearby cluster galaxies; (2) the cluster dark matter halo; (3) additional external shear; (4) galaxies along the line of sight, assumed to be in the lens plane. We also run test models that allow the cluster halo centroid to vary by the 25'' uncertainty on the X-ray emission centroid (Pierre et al. 2012), as well as models where we double the cluster mass.

In exploring this wide variety of models, we find that they provide fits of comparable quality, and the inferred parameters (e.g., θ_E) among the different models agree to within their statistical uncertainties. We adopt our fiducial power-law ellipsoid lens model with a fixed NFW halo for the cluster and fixed isothermal halos for the cluster galaxies because it is realistic and has the fewest additional free parameters.

With our fiducial lens model, we measure an Einstein radius of $\theta _{\rm E} = 0.38^{+0.02}_{-0.01}$ arcsec ($3.2_{-0.1}^{+0.2}$ kpc) and total mass enclosed within θ_E of $1.8^{+0.2}_{-0.1}\times 10^{11}$ M_☉. From our environment model, we estimate that the cluster halo and other cluster members contribute ∼10% of this enclosed mass (∼7% and ∼3%, respectively), consistent with results at z ≲ 0.5 (Treu et al. 2009). Increasing the environment contribution would increase this fraction (e.g., a cluster halo with double the mass would contribute ∼15% of the enclosed mass), but θ_E remains robust to within the model uncertainties. The lens galaxy's mass within θ_E is thus ∼1.6 × 10¹¹ M_☉.

Following Papovich et al. (2012), we now model the lens light in F160W with a two-component model using an n = 4 bulge and n = 1 disk. The arc is masked, although the source flux is negligible compared to the lens flux (<3%). Papovich et al. (2012) measure the total stellar mass assuming a Chabrier (2003) IMF with solar metallicity. We integrate the light profile and calculate the stellar mass within θ_E to be $1.3_{-0.2}^{+0.5} \times 10^{11}\, M_{\odot }$, corresponding to a dark matter fraction of $f_{\rm DM}^{{\rm Chab}} {(<} \theta _{\rm E}) = 0.3_{-0.3}^{+0.1}$. If we use a Salpeter (1955) IMF, which seems to be preferred for ETGs at z < 1 (e.g., Auger et al. 2010; Cappellari et al. 2012; Sonnenfeld et al. 2012; Conroy et al. 2013), the enclosed stellar mass is $2.2_{-0.4}^{+0.9} \times 10^{11}\, M_{\odot }$ and is larger than the enclosed total mass ($f_{\rm DM}^{{\rm Salp}} ({<}\theta _{\rm E}) = -0.3_{-0.5}^{+0.2}$), albeit at marginal significance. This is an upper limit on the dark matter fraction of the galaxy, as the environment contributes ∼10% of the total mass within θ_E.

In the three reddest filters (the lens is undetected in F475W), the centroids of the lens light profile and of the mass model are offset by as much as ∼1.5 pixels (∼01; Figure 3). Studies of z ≲ 0.5 ETGs do not find significant offsets between their mass and light (Koopmans et al. 2006). However, the lens light centroid shifts among different bands, suggesting that the youngest stars are displaced from the older population. The different stellar populations may not all directly trace the dark matter.

The source is magnified by a factor of $2.1_{-0.3}^{+0.4}$. The unlensed source has an extended profile with a bright compact region that is mapped to the outskirts of the source (Figure 3). We fit a Sérsic profile to the extended source to measure its flux. To compute the total flux (Table 1), we add the flux from the compact emission, which is determined by taking the flux of the fitted PSF component and dividing by the magnification at that location (|μ_A| in Table 1). We estimate the modeling uncertainty to be ∼0.15 mag by fitting to a subset of sources reconstructed from samples in the MCMC chain. Combined with the photometric uncertainties, the total uncertainty is ∼0.2 mag. The effective radius varies between r_eff ∼ 011–020.

Table 1. Observed Quantitiesand Lens Model Parameters

Parameter	Value
Observed quantities
α, δ (J2000)	02:18:21.5, −05:10:19.9
zL (grism)	$1.6406 ^{+0.0018}_{-0.0050}$
zS (grism)	2.2623 ± 0.0002
zS (Lyα)	2.25384 ± 0.00003
Lyα EWobserved(Å)	129.4 ± 4.6
WFC3/F125W (mag)a	21.19 ± 0.01
WFC3/F160W (mag)a	20.67 ± 0.01
M$_{\star }^{{\rm Chab}}$ (1011 M☉)b	$2.0^{+0.8}_{-0.3}$
M$_{\star }^{{\rm Salp}}$ (1011 M☉)b	$3.5^{+1.4}_{-0.6}$
Bulge + Disk profile (F160W)
Bulge (n = 4) reff ('')	$0.15_{-0.03}^{+0.04}$
Disk (n = 1) reff ('')	$0.72_{-0.07}^{+0.10}$
Lens model: Galaxy parametersc
μtot	$2.1_{-0.3}^{+0.4}$
|μA|d	$1.8_{-0.2}^{+0.3}$
|μB|d	$0.3_{-0.1}^{+0.1}$
Δx ('')e	$-0.05_{-0.02}^{+0.01}$
Δy ('')e	$-0.08_{-0.02}^{+0.02}$
θE ('')	$0.38_{-0.01}^{+0.02}$
b/a	$0.8_{-0.2}^{+0.1}$
θ(°)	$8_{-41}^{+45}$
Γ	$0.70_{-0.07}^{+0.06}$
Mtot(< θE) (1011 M☉)	$1.8_{-0.1}^{+0.2}$
$M_{\star }^{{\rm Chab}}({<}\theta _{\rm E})$ (1011 M☉)	$1.3_{-0.2}^{+0.5}$
$M_{\star }^{{\rm Salp}}({<}\theta _{\rm E})$ (1011 M☉)	$2.2_{-0.4}^{+0.9}$
$f_{\rm DM}^{{\rm Chab}} ({<}\theta _{\rm E})$	$0.3_{-0.3}^{+0.1}$
$f_{\rm DM}^{{\rm Salp}} ({<}\theta _{\rm E})$	$-0.3_{-0.5}^{+0.2}$
Reconstructed source: intrinsic valuesc
ACS/F475W (mag)	25.5 ± 0.2
ACS/F814W (mag)	25.5 ± 0.2
WFC3/F125W (mag)	25.9 ± 0.2
WFC3/F160W (mag)	25.2 ± 0.2

Notes. ^aTotal magnitudes from Skelton et al. (2014). ^bTotal stellar masses from Papovich et al. (2012). ^cFor lens model quantities, the reported values are medians, with errors corresponding to the 16th and 84th percentiles. ^dμ_A, μ_B are magnifications at the peak locations of the brighter and fainter images, respectively. ^eOffset of mass profile centroid relative to galaxy light centroid in F160W.

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There is residual image flux (Figure 3, fourth row) that we attribute to compact emission regions in the source. The residuals shift in both intensity and position among the bands, likely because of different emission lines (Figure 1, bottom): F814W samples only the continuum and has the smallest residuals, while F475W has Lyα and F160W has [O iii] λλ4959, 5007 emission. Indeed, Lyα emission can be spatially offset from continuum emission in galaxies at z > 2 (e.g., Feldmeier et al. 2013; Momose et al. 2014). We speculate that offset [O ii] λ3727 emission may be causing the weaker residual feature in F125W. Although the G141 spectrum does not show it, [O ii] λ3727 would fall in a region where the grism response is dropping, making this interpretation uncertain. These residuals cannot come from the same source position, as lensing is achromatic. The lens model uses the same position of the compact emission region (green cross, Figure 3) across the multiple bands, but because they are offset, the model compromises by placing the PSF between the peak fluxes. This results in residuals in all bands, even F814W where there is only continuum.

The largest residual is in F475W and is due to Lyα emission that is observed in both the arc and counterimage (objects A and B in Figure 2; see also Figure 3, left). To test if the bright Lyα emission is problematic for the lens modeling, we fit an additional PSF to the counterimage in F475W and subtract it a priori. Using only the upper half-annulus to model the lens, we find that the image residuals, inferred lens model parameters, and modeled source fluxes are nearly identical to that of our fiducial model.

The residuals corresponding to the emission-line regions extend in the direction of the arc (object A), i.e., tangential to the lens galaxy. This implies that the emission-line regions are elongated and/or stretched due to lensing.