RELICS: A Strong Lens Model for SPT-CLJ0615–5746, a z = 0.972 Cluster

SPT0615 was observed with HST as part of the RELICS (GO14096; PI: Coe) Treasury HST program, which aimed to discover a statistically significant samples of galaxies at high redshift (z > 6; Salmon et al. 2017). The cluster selection process is described in detail in Cerny et al. (2018) and D. Coe et al. (2018, in preparation), and strong lensing analyses for other RELICS clusters were published in Cerny et al. (2018), Acebron et al. (2018), and Cibirka et al. (2018). SPT0615 was observed for two orbits with the Wide Field Camera 3 (WFC3) in F105W, F125W, F140W, and F160W and for one orbit with the Advanced Camera for Survey (ACS) in F435W. All clusters in the program were imaged over two epochs to allow for variability searches. Additional archival ACS imaging in F606W and F814W were available from GO12757 (PI: High) and GO12477 (PI: Mazzotta). GO12477 obtained one pointing of F814W imaging and a 2 × 2 mosaic in F606W. GO12757 obtained a 2 × 2 mosaic in F814W, including overlapping area for deeper imaging in the strong lensing region. Because the length of the exposure time varies in F814W, the depth of the field varies from ${m}_{814,{AB}}=27.99$ at the very center of the field to ${m}_{814,{AB}}=27.19$ at the shallowest part of the field. These are the 5σ limiting magnitudes in an r = 02 circular aperture. The center of the field will have a deeper limiting magnitude. The wavelength coverage spans 0.4–1.7 μm. Table 1 summarizes the observations.

Calibrated images from all available programs, including archival programs, were obtained from the Mikulski Archive for Space Telescopes (MAST).¹⁷ Individual frames were then visually inspected to ensure that the quality is acceptable for science. Satellite trails and other image artifacts were manually masked out. Additionally, the WFC3/IR images have persistence that was masked out using products supplied by the WFC3 team. A custom pixel mask provided by G. Brammer (2016, private communication) removes hot pixels not in the pipeline mask. The ACS images were corrected for charge transfer inefficiency losses using the method described in Anderson & Bedin (2010). Subexposures in each filter were combined to form a deep image using the AstroDrizzle package (Gonzaga et al. 2012) using PIXFRAC = 0.8. The images in different filters were aligned to the same reference frame, and the astrometry was matched to the Wide-field Infrared Survey Explorer point source catalog (Wright et al. 2010). The final, reduced images are made available to the public as high-level science products through MAST.¹⁸ The public release includes photometric catalogs of all the fields, including photometric redshift estimates using the Bayesian Photometric Redshifts method (BPZ; Benítez 2000).

Ground-based spectroscopic observations were obtained using the upgraded Low Dispersion Survey Spectrograph (LDSS3-C) on the Magellan Clay telescope using the University of Arizona (PI: Stark) allocation. SPT0615 was observed on 2017 March 30 for a total exposure time of one hour. Average seeing was 06–07 throughout the night. Slits were placed on candidate lensed galaxies. The VPH-ALL grism was used, which has coverage between 4250 Å < λ < 10000 Å. A 1'' slit was used on all objects, with spectral resolution R 450–1100 across the wavelength range. The detector is 64 in spatial extent. A full description of the RELICS Magellan/LDSS3 follow-up results will be presented in a future paper (R. Mainali et al. 2018, in preparation).

We first consider a model that includes all of the images from systems 1 and 2 and three images from system 3. This model has one cluster-sized halo and contributions from cluster-member galaxies as described above. We fix the cut radius of this halo to 1500 kpc but allow all other parameters to vary. Because of the proximity of the images in system 1 to the central cluster galaxies, we allow the velocity dispersion of three of the central cluster galaxies to vary (shown in Figure 5), but we fix all other parameters to those determined by scaling relations. This is the model with the minimum BIC, −48.00, indicating that it is the best model by the standards of that criterion (see Table 3). Compared to the other models, ΔBIC > 10, meaning that the evidence in favor of this model is very strong. It is also the best model using the AICc; none of the others are likely when compared to Model 1. The critical curves for this model are shown in Figure 6. The model parameter results are shown in Table 4.

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Table 4.  Model Parameters

Object	ΔR.A.	ΔDecl.		θ	rcore	rcut	σ
	(kpc)	(kpc)		(°)	('')	('')	(km s−1)
Model 1
Halo 1	${0.40}_{-0.96}^{+0.41}$	${3.63}_{-0.81}^{+1.16}$	${0.55}_{-0.05}^{+0.01}$	${124.2}_{-1.8}^{+1.4}$	${17.5}_{-3.0}^{+0.5}$	[1500]	${1350}_{-60}^{+50}$
Halo 2	[0.00]	[0.00]	[0.13]	[−89.0]	${2.62}_{-0.81}^{+0.11}$	[45.89]	680a
Halo 3	[−0.21]	[−1.98]	[0.43]	[−23.7]	[0.16]	[41.60]	${50}_{-5}^{+70}$
Halo 4	[0.86]	[−2.87]	[0.01]	[24.3]	[0.07]	[19.13]	${100}_{-30}^{+50}$
Model 4
Halo 1	${0.58}_{-1.96}^{+0.03}$	${7.64}_{-1.27}^{+1.67}$	${0.71}_{-0.01}^{+0.10}$	${109.7}_{-1.1}^{+7.7}$	${9.8}_{-1.1}^{+5.5}$	[1500]	${740}_{-70}^{+240}$
Halo 2	[0.00]	[0.00]	[0.13]	[−89.0]	${2.57}_{-0.67}^{+0.04}$	[45.89]	${660}_{-70}^{+20}$
Halo 3	[−0.21]	[−1.98]	[0.43]	[−23.7]	[0.16]	[41.60]	${80}_{-40}^{+30}$
Halo 4	[0.86]	[−2.87]	[0.01]	[24.3]	[0.07]	[10.13]	${90}_{-20}^{+40}$
Halo 5	$-{0.96}_{-6.58}^{+3.74}$	$-{18.76}_{-3.83}^{+2.81}$	${0.70}_{-0.15}^{+0.01}$	${143.0}_{-1.5}^{+5.7}$	${46.6}_{-6.3}^{+2.3}$	[1800]	${1800}_{-140}^{+40}$

Note. Values in brackets were held fixed during fitting. Halos 2, 3, and 4 are galaxy scale. They are labeled in cyan in Figure 5. Halo 5 takes into account the foreground structure, although it is projected to the same redshift as SPT0615, and thus the velocity dispersion is not indicative of its mass. ΔR.A. and Δdecl. are measured in the image plane. The ellipticity, , is that of the mass distribution, while θ is the position angle of the potential, measured counterclockwise from horizontal.

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Model 1 predicts three additional arc candidates in system 3. Candidate 3.3 is predicted to be ∼1 magnitude fainter than arcs 3.1 and 3.2, but ∼1.6 magnitudes brighter than 3.5. Candidate 3.4 is predicted to be 1.75 magnitudes brighter than arc 3.5. Arc 3.1 has m_F814W = 25.52, and Arc 3.2 has ${m}_{{\rm{F}}814{\rm{W}}}\,=25.49$. Arc 3.5 could not be deblended from the neighboring source and thus we were unable to measure its magnitude. Candidate 3.3 has ${m}_{{\rm{F}}814{\rm{W}}}=27.50$. There are no predictions for the brightness of candidate 3.4 relative to arcs 3.1 and 3.2; however, we measure its magnitude to be ${m}_{{\rm{F}}814{\rm{W}}}=26.40$. Candidate 3.6 is predicted to be 0.1 magnitudes fainter than arc 3.1 and 0.6 magnitudes fainter than arc 3.2. It is predicted to be 2.2 magnitudes brighter than arc 3.5. We measure candidate 3.6 to be ${m}_{{\rm{F}}814{\rm{W}}}=25.70$. We searched the regions of these predictions and found objects that were similar in color and morphology to the images with secure detections. Model 2 includes all six of these images, but is otherwise the same as Model 1. Table 3 shows the results of the statistical tests. Using both the BIC and AICc, this model is considered the worst of those tested. The χ² value for this model is also ∼10× higher than the χ² value for any of the other models, and as such we do not consider it further, even taking into account the increased complexity of the model as compared to model 1. As shown below, these constraints only make sense with a second halo to account for the foreground structure.

In this model, we attempt to account for the line-of-sight structure by adding a second cluster-sized halo to the single effective lens plane. This line-of-sight structure is not associated with SPT0615, so this is not a full multiplane analysis but rather an approximation. Distance is degenerate with normalization, and with so few constraints it is difficult to disentangle the two. This approximation ignores the higher order effects discussed in McCully et al. (2014), but does approximate the amplitude and direction of the shear that a second cluster-sized halo induces. We fix the cut radius of this halo at 1800 kpc and allow all other parameters to vary. The model puts this new halo directly to the south of the first cluster-sized halo. The χ² value for this model is comparable to that of Models 1 and 4. It is the third most likely model of the four described here.

This model is the same as model 2 but adds an additional cluster-sized halo to account for the foreground structure. As with model 3, we fix the cut radius of this second cluster-sized halo at 1800 kpc and allow all other parameters to vary. If these three additional images are indeed part of system 3, as is indicated by their color and morphology, the separation is larger than expected in a typical lensing configuration, which could be caused by the presence of the foreground structure. This is the second most probable model; however, using the relative likelihood estimator described above, it is only 0.02% as likely as model 1 to be the best model. The parameters of this model are shown in Table 4.

We calculate the projected mass of the cluster using the mass map generated by Lenstool (Figure 7, left). To calculate the 1σ error bars, we generate 100 maps from parameter sets sampled from the MCMC analysis and calculate the standard deviation of the distribution of calculated masses. Strong lensing mass calculations are most accurate in the region where there are constraints. Our convention is as follows: we use R for the 2D projected radius and r for the 3D spherical radius. For SPT0615, there are constraints out to R ∼ 25''. We find the total projected mass density within R = 267 to be $M={2.51}_{-0.09}^{+0.15}\times {10}^{14}$ M_☉. We also extrapolate a mass measurement to R₅₀₀ (the dashed black line in Figure 7, right) so that we may compare to other studies of this cluster. In particular, we compare our constraints to the weak lensing analysis conducted by Schrabback et al. (2018a), which is based on the mosaic ACS observations of the cluster. When centering their weak lensing measurements onto the Chandra X-ray centroid and correcting for the corresponding miscentering and mass modeling bias, these authors constrain the cluster mass to ${M}_{500,\mathrm{WL}}={5.5}_{-2.3}^{+2.6}\times {10}^{14}\,{M}_{\odot }$. Assuming the Diemer & Kravtsov (2015) concentration–mass relation, their best-fitting mass corresponds to a spherical overdensity radius of ${r}_{500,\mathrm{WL}}=108^{\prime\prime}$. This WL mass constraint agrees within 2σ with the SZ constraint ${M}_{500,\mathrm{SZ}}=10.53\pm 1.55\times {10}^{14}\,{M}_{\odot }$, which Bleem et al. (2015) obtain when assuming a mass-observable scaling relation for which the SPT cluster counts fit a ΛCDM cosmology best (Reichardt et al. 2013). We compare these estimates of the spherical overdensity mass, plotted at the WL-estimated ${r}_{500,\mathrm{WL}}$, to the enclosed mass from our extrapolated SL model in the right panel of Figure 7. Noting that the enclosed mass at R₅₀₀ is generally higher than a spherical overdensity mass at r₅₀₀ given the projection, we conclude that the different mass measurements are broadly consistent. Again, we emphasize that we are unable to constrain the mass slope with strong lensing this far outside the region of the strong lensing constraints. The statistical errors grossly underestimate the true uncertainties at these projected radii, and thus these estimates should be used with caution.

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At M ∼ 10¹⁵ M_☉, SPT0615 is one of the most massive high-redshift clusters known. The only other cluster in the RELICS sample with z > 0.7 is ACT-CLJ0102−49151 ("El Gordo"). It is at z = 0.870 and has ${M}_{200,\mathrm{SZ}}=2.16\pm 0.32\times {10}^{15}\,{h}_{70}^{-1}$ M_☉ (Menanteau et al. 2012). A strong lensing analysis by Zitrin et al. (2013) found a lower limit of M ∼ 1.7 × 10¹⁵ M_☉, in good agreement with the SZ mass. The strong lensing analysis by Cerny et al. (2018) finds that $M(\lt 500\,\mathrm{kpc})=11.0\pm 0.7\,\times {10}^{14}$ M_☉, also in good agreement. Other strong lensing clusters with complete models in this high-redshift regime include RCS 0224-0002 (z = 0.773; Gladders et al. 2002; Smit et al. 2017) with ${M}_{200,\mathrm{SL}}=1.9\pm 0.1\times {10}^{14}$ M_☉ (Rzepecki et al. 2007), and RCS2 J232727.6-020437 (z = 0.7; Gilbank et al. 2011; Menanteau et al. 2013; Hoag et al. 2015) with ${M}_{200}\sim 2\mbox{--}3\,\times {10}^{15}\,{h}_{70}^{-1}\,{M}_{\odot }$ (Sharon et al. 2015; Schrabback et al. 2018b). High-redshift clusters that show evidence of strong lensing but do not have complete models include RCS 231953+0038.0 (z = 0.897; Gladders et al. 2002) and IDCS J1426.5+3508 (z = 1.75; Gonzalez et al. 2012). RCS 231953+0038.0 is part of a supercluster, along with two other cluster components (Gilbank et al. 2008). It has an X-ray mass of ${M}_{200,{\rm{X}}}\,={6.4}_{-0.9}^{+1.0}\times {10}^{14}$ M_☉ (Gilbank et al. 2008; Hicks et al. 2008) and a weak lensing mass of ${M}_{200,\mathrm{WL}}={5.8}_{-1.6}^{+2.3}\times {10}^{14}$ M_☉ (Jee et al. 2011). The cluster IDCS J1426.5+3508 is the most massive cluster known at z > 1.4. Gonzalez et al. (2012) use the presence of a giant strong lensing arc to calculate the cluster mass enclosed within the arc. Extrapolating, they find ${M}_{200,\mathrm{SL}}\,\gt {2.8}_{-0.4}^{+1.0}\times {10}^{14}$ M_☉. Comparing SPT0615 to the other known strong lensing clusters at high redshift, we conclude that it is not a mass outlier in the group of known strong lensing clusters.

The high mass of SPT0615 is likely a contributing factor to its success as a lensing cluster, as it has the second-highest number of high-redshift (z > 5.5) galaxy candidates in the RELICS sample. El Gordo also has a significant number of high-redshift candidates, coming in fourth in the RELICS sample (Salmon et al. 2017). While a systematic search for high-redshift galaxy candidates has not been undertaken for the other clusters mentioned in this section, it is likely that the combination of the their high mass and high redshift combine to make them good candidates for searching for high-redshift galaxy candidates in their fields.

SPT0615-JD is a candidate z ∼ 10 (z_phot = 9.9 ± 0.6) galaxy gravitationally lensed into an arc spanning 25 in the field of SPT0615. It was found as part of a systematic search for high-redshift galaxies in the RELICS fields (Salmon et al. 2018). It is not visible in bands blueward of F140W.

The left panel of Figure 8 shows the location of this galaxy, along with the predicted locations of counterimages. The right panel shows the magnification map produced by our lens model for z = 9.9. The counterimage in the upper right corner is predicted to be ∼1 magnitude fainter than the original arc, placing it below the detection level of HST. Its location next to a large star also makes it difficult to search for.

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Using our best-fit model, the counterimage in the east is predicted to be 0.04 magnitudes fainter than SPT0615-JD, which should be visible at the depth of our images; however, a search in that region has not yielded a counterimage. The arc is aligned with the direction of the shear. We note that all of the models predict counterimages in the same location and with approximately the same magnification, with the exception of Model 3, which only predicts one counterimage to the northwest. A GLAFIC model (Oguri 2010; S. Kikuchihara et al. 2018, in preparation) and Light Traces Mass (Zitrin et al. 2015) model both predict counterimages in the same location (see Salmon et al. 2018 for more details). The right panel of Figure 8 shows that SPT0615-JD is magnified by ∼8× the intrinsic brightness, while the predicted counterimage would be magnified by 3–6× the intrinsic brightness of the galaxy.

We present a strong lens model for the cluster SPT-CLJ0615−5746 (also known as PLCKG266.6−27.3) based on the presence of three multiply imaged background galaxies. Two of these multiply imaged families have confirmed spectroscopic redshifts from our observations with Magellan. The best model using the statistical results from the BIC and AICc is Model 1, which optimizes one cluster-sized dark matter halo and three smaller galaxy-sized halos, in addition to cluster-member galaxies whose mass is determined from their light through scaling relations. This model includes the secure observations of system 3, as well as the secure images from families 1 and 2. There are additional predicted images of system 3; however, these need spectroscopic confirmation before including them in the model.

The lens model is complicated by the presence of a foreground structure, estimated to be at a photometric redshift z ∼ 0.4. This is not surprising, given the prevalence of line-of-sight structure (Bayliss et al. 2014). We made versions of the lens model including this foreground structure, but the statistical analysis did not favor either version. Our analysis was not a full multiplane analysis, however, which is currently not fully supported by Lenstool. Such analysis would also benefit from spectroscopic confirmation of both the foreground candidates and multiply imaged background galaxies.

SPT0615 is a massive high-redshift cluster, with a strong lensing mass of M₅₀₀ = 10.62 ± 0.77 × 10¹⁴ M_☉. Our strong lensing mass is comparable to the SZ determined mass. It is similar in mass to other strong lensing clusters in the z > 0.8 regime and has been shown to have magnified a high number of high-redshift background galaxies into our detection limit (Salmon et al. 2017). The field also contains a high-redshift galaxy candidate with a photometric redshift z = 9.93 (Salmon et al. 2018).

SPT0615 is included in the RELICS program, and as such the data for this lens model are available through MAST. This data includes reduced images, catalogs, and lens models.