PLCK G165.7+67.0: Analysis of a Massive Lensing Cluster in a Hubble Space Telescope Census of Submillimeter Giant Arcs Selected Using Planck/Herschel

We obtained imaging of six Planck/Herschel-selected fields between 2015 December and 2016 July with the HST Wide Field Camera 3 IR detector (WFC3-IR) in Cycle 23 (GO-14223; PI: Frye). The fields are PLCK G145.2+50.9 (G145), PLCK G244.8+54.9 (G244), PLCK G165.7+67.0 (G165), PLCK G045.1+61.1 (G045), PLCK G080.2+49.8 (G080), and PLCK G092.5+42.9 (G092). The imaging is composed of one orbit each in the F110W and F160W filters. Table 1 gives the observing details.

The WFC3-IR images are redrizzled using the software package DrizzlePac (Fruchter et al. 2010). We adopt values for the photon-sensitive effective size of a pixel to its real size (final_pixfrac) and a final pixel scale (final_scale) of 0.85 and 006, respectively. We checked the redrizzled images by computing the FWHM of a few stars in each field. In some cases, such as the G165 field, there were only two isolated, unsaturated stars within the field of view, so we substituted a compact and isolated elliptical galaxy as a third source. Redrizzling of the data in each case resulted in a 3%–10% improvement in image quality (FWHM) over the pipeline products. The final reduced images reach comparable depths to the CLASH clusters. For one representative case, G165, we compute 10σ limiting magnitudes of F110W_AB = 26.9 mag and F160W_AB = 26.2 mag for point sources inside $0\buildrel{\prime\prime}\over{.} 4$ apertures. We find that the image depth and filters are sufficient to make NIR detections of the strongly lensed DSFG in each of our sample fields. We also identify other examples of giant arcs and/or image multiplicities in some cases. In Figure 2, we present the HST color images of the central regions for each of the six fields. We refer the reader to Appendix A for further details regarding the search for the NIR counterparts.

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The WFC3 F160W images are used as detection images for the matched aperture photometry. We custom-built our code to cope with the unusual morphologies peculiar to arcs in the central regions of massive lensing clusters. We detect sources by applying a σ-clipping algorithm with respect to the local background rms values. The local background, in turn, is estimated following a similar approach to that in SExtractor (Bertin & Arnouts 1996). Briefly, the image is divided into patches of 100 × 100 pixels, with the background in each patch represented by the σ-clipped median. The local background is then estimated by a smooth 3 × 3 spline interpolation over these patches. To ensure robust detection of objects, we smooth the image with a Gaussian filter of FWHM ∼ 02. Objects are deblended using the watershed PYTHON algorithm in astropy.photutils (The Astropy Collaboration et al. 2018). Artifacts such as diffraction spikes are visually identified and removed.

We assign apertures to each galaxy image by measuring the semimajor/minor axis sizes at 3 times the FWHM lengths of the detected objects, typically amounting to 06. Elliptical annuli are used to get the best estimate of the background, with an inner radius equal to the photometric aperture and an outer radius equal to 1.2 times the inner radius. We compute the aperture flux and then subtract the area-scaled local background level within the annuli. The flux uncertainty is computed as the quadratic sum of the local smooth background rms value only. We note that aperture corrections are minimal owing to our large extraction aperture of >04. In three fields, G145, G045, and G080, the multiple images of the single DSFG are typically too faint and/or blended with the halos of bright cluster members near in projection to measure a flux. In these cases, a 1σ upper limit on their fluxes is reported. In Table 2 we present the photometric catalog of the lensed DSFGs for our sample. The magnification factor, μ, of the lensed DSFG was measured using our light-traces-mass lens model. The effective Einstein radius at the redshift of the lensed source, ${\theta }_{E}=\sqrt{A/\pi }$, was measured from our lens model.

Table 2.  The Sample of HST Lensed DSFGs

Arc ID	R.A.	Decl.	F110WAB	F160WAB	Magnification	Lens Sizea	Spectroscopic Redshift
	(J2000)	(J2000)			(μ)	(arcsec)	zlens	zDSFG
G145_DSFG_1a	10:53:22.250	+60:51:48.95	>26.9	>26.2	12 ± 1	5.9	0.837b	3.6c
G145_DSFG_1b	10:53:22.563	+60:51:44.03	>26.9	>26.2	5 ± 1	''	''	''
G244_DSFG_1	10:53:53.107	+05:56:18.44	${22.1}_{-0.1}^{+0.1}$	${21.0}_{-0.1}^{+0.1}$	7-36d	1.4d	1.525d	3.005d
G165_DSFG_1a	11:27:14.731	+42:28:22.56	${23.0}_{-0.1}^{+0.1}$	${22.2}_{-0.1}^{+0.1}$	≳30	13	0.351b	2.2357e
G165_DSFG_1b	11:27:13.917	+42:28:35.56	>26.5	$\gt 25.6$	∼8	''	''	''
G045_DSFG_1a	15:02:36.012	+29:20:50.51	>26.9	${25.5}_{-0.2}^{+0.2}$	>9f	8	0.549c	3.427g
G045_DSFG_1b	15:02:36.479	+29:20:47.90	>27.0	${25.3}_{-0.2}^{+0.2}$	>9f	''	''	''
G045_DSFG_1c	15:02:36.921	+29:20:47.96	>26.7	${25.8}_{-0.3}^{+0.3}$	>7f	''	''	''
G080_DSFG_1a	15:44:33.202	+50:23:43.53	>27.1	>26.5	∼20	7	0.670c	2.6c
G080_DSFG_1b	15:44:32.483	+50:23:41.69	>27.5	>26.5	∼20	''	''	''
G092_DSFG_1ag	16:09:17.842	+60:45:19.41	${24.2}_{-0.1}^{+0.1}$	${23.0}_{-0.1}^{+0.1}$	∼20	⋯	0.45i	3.256e
G092_DSFG_1bg	16:09:17.693	+60:45:22.31	${25.0}_{-0.2}^{+0.2}$	${23.7}_{-0.1}^{+0.1}$	∼20	⋯	''	''

Notes.

^aThe effective Einstein radius is reported, defined as ${\theta }_{E}=\sqrt{A/\pi }$, where A is the area inside the critical curve (e.g., Acebron et al. 2018). ^bThe spectroscopic redshift comes from this paper. ^cThe spectroscopic redshift comes from Cañameras et al. (2015). ^dThe lensed image is only partially resolved in our HST image (Figure 2). These values for the magnification factor, the size of the Einstein radius, and the redshift are drawn from the ALMA data in Cañameras et al. (2017a, 2017b). ^eThe spectroscopic redshift comes from Harrington et al. (2016). ^fMagnification estimates for the three brightest emission-line regions of this arclet family were first reported in Nesvadba et al. (2016) as μ = 10–22. ^gThe spectroscopic redshift comes from Nesvadba et al. (2016). ^hWe find that these two images are likely to originate from two different sources at a similar redshift. ⁱThe spectroscopic redshift comes from SDSS DR14 data.

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We acquired imaging of G165 in K band using the LBT Advanced Rayleigh Ground layer adaptive Optics System (ARGOS; Rabien et al. 2018) during instrument commissioning time in 2016 December (2016B; PI: Frye). ARGOS corrects ground-layer distortions in the imaging of the two 8.4 m apertures using two three-beam constellation lasers as guide stars that are fixed to each aperture. The ARGOS instrumentation operates through the LUCI imager and multislit spectrometer. High-quality corrections of up to FWHM ≈ 025 at K are achievable across a large field of view ($4^{\prime} \times 4^{\prime}$) at a native pixel scale of 012 pixel⁻¹. We acquired LBT/LUCI +ARGOS data in monocular mode on two separate nights: 46 minutes of observation using LUCI2 on 9 December and 42 minutes using LUCI1 on 2016 December 15. We note that the LUCI1 set of observations have a slightly shorter exposure time and, in turn, a slightly higher per-pixel rms uncertainty. However, they yield a fainter point-source detection limit owing to the lower FWHM as measured in isolated and unsaturated stars. We choose to analyze the data separately from each night and only to combine the photometric measurements at the last step.

Random dithers of up to 40'' are imposed between individual exposures to optimize the sky subtraction in the crowded cluster regions and to eliminate detector artifacts. Such large dithers require high point-source stability across the field. As a check, we estimate the pointing error at each dither position by stacking the object frames and then measuring the positional centroids of 13 pre-selected cluster members that span the full field of view and that are isolated from bright sources. We find that the typical translational shift between images is ∼2 pixels, or ∼025, with negligible rotation. The WCS information in each object frame is updated accordingly. At this point we resample the images onto the same pixel grid using the flux-conserved, overlapping pixel-area method in the Python routine astropy.reprojection, as needed.

We design our own reduction pipeline to ensure high flatness across the chip and to maximize the signal-to-noise ratio of the data. As a first step, we subtract the dark frames from all object frames. We then proceed to find the best estimate of the background. Within a single exposure, the sky background varies by ∼100 ADUs, comparable to the integrated flux of some of the fainter cluster members. Therefore, instead of creating sky frames by taking the median at multiple pointings directly, we apply a "normalizing-rescaling" approach, in which we construct the master sky frames using exposures adjacent in time, which are then scaled to the background level of each object frame prior to the subtraction.

We designate each dither pointing "i" as the co-addition of 24 individual object frames in 5 s exposures, all taken at the same position (120 s total science time), plus ∼0 s readout time owing to nondestructive readouts. The 5 s exposure was chosen to be small to avoid persistence and nonlinearity effects. We find that a reasonable compromise in image combination is to collect the temporally closest five dither pointings about each ith dither pointing in a running boxcar, equating to a total clock time of ∼14 minutes including overheads. The result of including more dither pointings is a slight improvement in the background noise but a degradation in image flatness. We mask out the bright sources in all the frames of the running boxcar to avoid biasing the result, or "master background," upward of its true value with unwanted cluster halo light. Before dividing this master frame into the ith dither pointing, we divide the dither pointing frame by its five-pass, 3σ clipped median value¹⁸ to obtain the mean image of these "normalized" object frames. As a last step, we scale this new running master background frame to the 3σ clipped median of this ith dither pointing to match the sky-background level at the exact time of the exposure. Our background-subtracted dither pointings yield the "first-stage" result shown in Figure 3.

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Following an iterative approach, we introduce two additional stages to the background subtraction, each time using the previous stage result as a starting point. The main difference is that we continue to extend the bright object mask into the fainter outskirts of the masked sources. We avoid aggressively expanding the bright source mask, as increasing the number of masked pixels improves the flatness, but at the expense of the noise level, as fewer frames are available from which to estimate the background. The "third-stage" result is obtained by performing another iteration of the "second-stage" result. To assess image quality after each reduction stage, we compute the background rms values inside of seven test boxes of size 50 × 200 pixels located in regions isolated from bright sources. We find the background rms to decrease on average by 9% following the first stage and to converge to the ≲1% level following the second stage (see Figure 3).

To make corrections for pixel-to-pixel variations, we first tried applying a flat field to the data in the usual way prior to subtracting off the background. The result was unsatisfactory because image artifacts remained in the data. On reversing the order of these two operations, we found an improvement in the image flatness and the removal of the image artifacts. This improvement arises because our master flat field is constructed by combining local sky frames generated as a natural part of our background subtraction algorithm. Finally, we stacked the sky-subtracted and flat-fielded object frames to produce our final data product. We report a mean K-band FWHM of $0\buildrel{\prime\prime}\over{.} 53$ for the 2016 December 9 run (LUCI2) and $0\buildrel{\prime\prime}\over{.} 29$ for the 2016 December 15 run (LUCI1). In all, for the 2016 December 9 and 2016 December 15 runs, we reach a 10σ limiting magnitude of K_AB = 22.6 mag and K_AB = 23.5 mag inside apertures of 4 × FWHM, respectively. We do not combine the final images from the two different detectors, because the 2016 December 15 data have better spatial resolution (Figure 4). We emphasize, however, that our photometry is measured using both nights of data and weighted by an inverse-variance-weighted mean of the two fluxes, as described in Section 4.1.

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The large aperture of LBT and the high resolution of LUCI+ARGOS have enabled rare detections of dozens of arcs in a ground-based image. Moreover, a side-by-side comparison of our K-band image and our HST WFC-IR images allows identifications of single galaxy images that appear in multiple positions in the image plane, or "arclet families." By this approach, we confirm the image position of the lensed DSFG, Arc 1a, and make the first detection of its counterimage, Arc 1b, at its model-predicted location (Figure 5). Until now, we were unable to detect Arc 1b in our HST images, as the arc was too faint and too red. The K-band detection of this doubly imaged source with a known spectroscopic redshift is impactful because it allows us to break the mass-sheet degeneracy to construct a robust mass map. In all, 11 arclet family members are detected in five separate arclet families. Thus, the LBT/LUCI+ARGOS K imaging data effectively extend the wavelength reach of HST, thereby opening up new discovery space that favors the redder galaxy populations. For additional details regarding the performance of the LBT/LUCI+ARGOS instrument, see Rabien et al. (2018).

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We acquired imaging in the G165 field on 2016 February 2 using the Spitzer InfraRed Camera (IRAC) in the 3.6 μm and 4.5 μm channels as part of a larger program (Cy13, GO-13024; PI: Yan) to image the fields of massive lensing clusters that would make good targets for JWST. The on-target exposure time was set to 12,000 s in each of the two channels. The Spitzer Science Center (SSC) processed these data using the standard SSC pipeline, and we made the final image mosaics based on these products. A detailed analysis of the data set of this entire program will appear in a separate paper (H. Yan et al. 2018, in preparation). We also refer the reader to the description in Griffiths et al. (2018), where the reduction of their IRAC data from the same Spitzer program is discussed. In Figure 5, we show the 3.6 μm IRAC mosaic of this field (right panel). The two images of the DSFG, G165_DSFG_1a and G165_DSFG_1b, are both bright, with S_3.6,AB ≈ 19.1 mag and S_3.6,AB ∼ 19.9 mag, respectively.

We obtained spectroscopy in the field of G165 on 2015 February 14 using MMT/Hectospec (Fabricant et al. 2013), as a part of a larger program (2015A; PI: Frye). Hectospec is a multifiber spectrograph that assigns optical fibers on the sky with minimum allowed separations of ≳20''. To maximize the wavelength range for measuring redshifts, we selected the 270 groove mm⁻¹ grism, which covers a wavelength range of 3700–9150 Å at a dispersion of 1.21 Å pixel⁻¹. We chose to position 23 fibers (20 galaxy targets plus 3 standard stars) with priorities set to the positions of the brighter examples of prominent giant arcs and cluster members, as selected by their NIR photometric redshift estimates made using Canada–France–Hawaii Telescope (CFHT) plus Spitzer/IRAC imaging. We refer to Cañameras et al. (2018) for details on the photometric analysis and photometric redshifts. Note that as the planning for this observing run took place prior to receiving the HST data set, we were not able to fine-tune the target list to include new arclet family members. The observations were composed of a single Hectospec pointing with 7 × 1020 s exposures taken under variable seeing conditions of ∼1''–2''. This was sufficient for our science goal given the 15 fiber widths and the relatively bright magnitudes of the targets of i_AB ≃ 18–22 mag.

The reductions proceeded in a standard fashion using the IDL/Hectospec Reduction Software package (HSRED) obtained from the Smithsonian Astrophysical Observatory Telescope Data Center.¹⁹ We removed cosmic rays using the code "LA Cosmic" (van Dokkum 2001). Corrections for pixel-to-pixel variations, fringe corrections, and fiber identifications are accomplished using a dome flat. Background subtractions were made after first averaging together the spectra set to blank-sky positions, taken under the same conditions as the science data. The wavelength solution is found in two ways, using both an HeNeAr lamp exposure and the positions of prominent night-sky lines. We co-added the individual exposures to yield the final reduced spectra.

Secure spectroscopic measurements are made for 19 objects, which we define as the high-significance detection of two or more spectral features (>2σ level in the continuum). Our catalog results in measurements for five new cluster members with z = 0.326–0.376 and 11 new sources with redshifts 0.388 < z < 0.622. Three galaxies have MMT/Hectospec redshifts that place them in the foreground. See Section 4.2 for additional details and the redshift catalog.

We obtained further spectroscopy in the field of G165 using the Gemini-North Multi-Object Spectrograph (GMOS) as a part of a larger program (GN-2016A-Q-30; PI: Frye). The observations took place on 2016 April 27. We selected the B600 line mm⁻¹ grating, which has a wavelength coverage measured from our data of a total of 2975 Å about the central wavelength for each slitlet at a dispersion of 0.92 Å pixel⁻¹. As we did not have the HST images in time to plan this observing run, we populated the slit masks first with prominent arcs selected from the CFHT image from Cañameras et al. (2015), followed by cluster members selected from our Gemini pre-imaging data. We chose 1'' slits to match typical seeing on-site. We acquired six science exposures of 1200 s, two each at central wavelengths of 645 nm, 650 nm, and 655 nm to correct for chip gaps. Arc spectra were obtained within ±1 night of the observations using the CuAr lamps at similar central wavelengths. Dispersed flat-fields were taken at each of the three central wavelength (and hence grating tilt) configurations.

The initial calibrations of bias subtraction and flat-fielding proceeded in the standard way using the IRAF Gemini reduction package.²⁰ We removed cosmic rays prior to the background subtraction using the IRAF task GEMCRSPEC. For the wavelength calibration, there is a tendency for the IRAF algorithm to introduce wavelength offsets of the stacked spatial rows, especially for the smaller spectral "boxes." To avoid introducing this undesirable spatial feature into the data, we chose instead to use a pipeline written in IDL by one of us (B.L.F.). The IDL pipeline includes the tasks mentioned below and is discussed elsewhere (Frye et al. 2002, 2007, 2008). Briefly, the IDL pipeline avoids repixelization by identifying the flexure-induced instrumental curvature imprinted onto the individual spectrum box edges between the 2D spectra. This curvature amounts to 1–3 pixel shifts from the center to edge of the CCD, which are easily fit by low-order polynomials. We then wavelength-calibrate the data in two ways: using the arc lamps and using the night-sky lines. As both outputs had an rms on the wavelength fit of <0.5 Å, we choose to use the sky lines for the potential benefit that the wavelength references are embedded directly onto the data at the time of the observations.

Cosmic-ray hits on the object were removed in 1D by a comparison of the stacked spectra from the six different exposures using our IDL task SPADD (Frye et al. 2002, 2007, 2008). Thresholds are set for the acceptable number of cosmic-ray hits per pixel in the stack to avoid removal of real spectral features. We measured redshifts for the 1D co-added spectra using our IDL task SPEC (Frye et al. 2002, 2007, 2008). Our catalog results in spectroscopic measurements for 32 galaxies in the G165 field. Of these, we find nine cluster members that are new with 0.326 < z < 0.376 and 18 new lensed sources with 0.386 < z < 1.065. Five galaxies have Gemini/GMOS redshifts that place them in the foreground of the lens. We refer to Section 4.2 for additional details and the full redshift catalog.

To include the LBT/LUCI + ARGOS data in our catalog alongside the HST photometry, we first translate the central locations of our photometric apertures defined by the F160W image onto the K band using the WCS information. Although the FWHM resolution of our LUCI1 K-band data ($\mathrm{FWHM}\sim 0\buildrel{\prime\prime}\over{.}$29) is higher than that of our two HST bands ($0\buildrel{\prime\prime}\over{.} 22$ and $0\buildrel{\prime\prime}\over{.} 18$ for F110W and F160W bands, respectively), we do not alter the aperture sizes and ellipticities, as there is adequate matching to detect the vast majority of the sources. The data from LUCI1 and LUCI2 are obtained under different weather conditions, and the field orientation angles and plate scales are slightly different for LUCI1 and LUCI2. As a result, we opt to conduct K-band photometry separately for LUCI1 and LUCI2 images and only afterward to compute the aperture fluxes by applying an inverse-variance-weighted mean of the two values.

Table 3 gives the complete photometric catalog for all 11 arclet families. As the photometric depth at K is shallower than for the HST J- and H-band data, the aperture fluxes for some sources and arclets fall below their 1σ uncertainties. In such cases, we report the detection limit of the aperture fluxes. The redshift, z_pred, gives the predicted value for the redshift using our lens model. Notably, 11 arclet family members are detected in our LBT LUCI+ARGOS K-band image. They are Arcs 1a, 1b, Arcs 2a, 2b, 2c, Arcs 3a, 3b, 3c, Arcs 4a, 4b, 4c, and Arc 6b. The lensed DSFG, G165_DSFG_1a, has F110W_AB = ${23.0}_{-0.2}^{+0.2}$ mag, F160W_AB = ${22.2}_{-0.2}^{+0.2}$ mag, and K_AB = ${18.9}_{-0.2}^{+0.2}$ mag, bright enough to make ground-based spectroscopic follow-up feasible.

Table 3.  The PLCK_G165.7+67.0 (G165) Lensed DSFG and the Arclet Families

Arc	R.A.	Decl.	F110WAB	F160WAB	KAB	zpreda
ID	(J2000)	(J2000)	(mag)	(mag)	(mag)
G165_DSFG_1a	11:27:14.731	+42:28:22.56	${23.0}_{-0.2}^{+0.2}$	${22.2}_{-0.2}^{+0.2}$	${18.9}_{-0.2}^{+0.2}$	2.2357b
G165_DSFG_1b	11:27:13.917	+42:28:35.54	>26.5	>25.6	${22.6}_{-0.2}^{+0.2}$	2.2357
G165_2a	11:27:15.962	+42:28:29.00	${22.8}_{-0.1}^{+0.1}$	${21.4}_{-0.1}^{+0.1}$	${18.5}_{-0.1}^{+0.1}$	1.7
G165_2b	11:27:15.606	+42:28:34.18	${22.8}_{-0.1}^{+0.1}$	${21.3}_{-0.1}^{+0.1}$	${18.3}_{-0.1}^{+0.1}$	''
G165_2c	11:27:15.325	+42:28:41.32	${22.8}_{-0.1}^{+0.1}$	${21.4}_{-0.1}^{+0.1}$	${18.5}_{-0.1}^{+0.1}$	''
G165_3a	11:27:14.146	+42:28:32.00	${25.0}_{-0.1}^{+0.1}$	${24.3}_{-0.1}^{+0.1}$	${21.6}_{-0.1}^{+0.1}$	2.7
G165_3b	11:27:14.330	+42:28:30.36	${25.6}_{-0.2}^{+0.2}$	${25.1}_{-0.2}^{+0.2}$	${22.3}_{-0.2}^{+0.3}$	''
G165_3c	11:27:14.969	+42:28:17.34	${25.3}_{-0.2}^{+0.2}$	${24.6}_{-0.2}^{+0.2}$	${21.9}_{-0.3}^{+0.3}$	''
G165_4a	11:27:14.059	+42:28:32.73	${26.1}_{-0.2}^{+0.3}$	${24.8}_{-0.1}^{+0.1}$	${22.7}_{-0.3}^{+0.4}$	2.7
G165_4b	11:27:14.372	+42:28:29.00	${25.8}_{-0.2}^{+0.2}$	${24.7}_{-0.2}^{+0.2}$	${22.2}_{-0.2}^{+0.2}$	''
G165_4c	11:27:14.909	+42:28:17.33	>26.9	${26.0}_{-0.2}^{+0.2}$	>23.6	''
G165_5a	11:27:13.187	+42:28:25.83	${25.8}_{-0.2}^{+0.2}$	${25.7}_{-0.2}^{+0.3}$	>23.0	4.3
G165_5b	11:27:13.188	+42:28:24.67	${25.7}_{-0.2}^{+0.2}$	${25.5}_{-0.2}^{+0.2}$	>23.4	''
G165_6a	11:27:13.924	+42:28:32.79	${25.8}_{-0.2}^{+0.2}$	${24.7}_{-0.1}^{+0.1}$	>23.2	2.7
G165_6b	11:27:14.358	+42:28:27.72	${25.8}_{-0.2}^{+0.2}$	${24.5}_{-0.1}^{+0.1}$	${23.2}_{-0.4}^{+0.7}$	''
G165_6c	11:27:14.836	+42:28:16.88	>26.3	${25.1}_{-0.2}^{+0.2}$	>23.2	''
G165_7a	11:27:15.300	+42:28:38.35	>26.2	${25.6}_{-0.3}^{+0.4}$	>23.5	1.7
G165_7b	11:27:15.397	+42:28:35.96	>26.9	${25.2}_{-0.2}^{+0.3}$	>23.5	''
G165_7c	11:27:16.083	+42:28:25.84	${26.2}_{-0.3}^{+0.4}$	${25.7}_{-0.4}^{+0.5}$	>23.5	''
G165_8a	11:27:15.210	+42:28:40.85	>26.0	>25.3	>23.0	1.7
G165_8b	11:27:15.581	+42:28:32.37	>26.3	>25.5	>23.0	''
G165_8c	11:27:15.834	+42:28:28.36	>26.8	>26.2	>23.0	''
G165_9a	11:27:15.423	+42:28:40.59	${26.5}_{-0.3}^{+0.4}$	>25.6	>22.9	1.5
G165_9b	11:27:15.568	+42:28:36.06	>26.4	>25.6	>22.4	''
G165_9c	11:27:16.096	+42:28:28.03	>26.6	>25.6	>22.7	''
G165_10a	11:27:15.171	+42:28:38.92	>26.3	${26.2}_{-0.3}^{+0.5}$	>22.8	1.7
G165_10b	11:27:15.453	+42:28:32.90	${26.5}_{-0.3}^{+0.3}$	${25.9}_{-0.3}^{+0.3}$	>23.0	''
G165_11a	11:27:15.761	+42:28:42.28	${24.7}_{-0.1}^{+0.1}$	${24.5}_{-0.1}^{+0.1}$	>22.0	2.1
G165_11b	11:27:15.784	+42:28:40.45	${25.0}_{-0.1}^{+0.1}$	${24.8}_{-0.2}^{+0.2}$	>22.0	''
G165_11c	11:27:16.510	+42:28:26.12	${25.0}_{-0.1}^{+0.1}$	${24.7}_{-0.1}^{+0.1}$	>22.7	''

Notes.

^aUnless otherwise noted, these redshifts are predictions drawn from our strong-lensing model that await spectroscopic confirmation. ^bThe spectroscopic redshift for G165_DSFG_1a comes from Harrington et al. (2016).

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The catalog for all 62 objects in the G165 field with measured redshifts is given in Table 4 and presented as a redshift histogram in Figure 6. All objects in our redshift catalog are secure, by which we mean that we require that two or more spectroscopic features be detected at the ≳2σ level relative to the continuum. In the case of a single emission line, we require also the detection of a second significant feature such as a continuum break. We did not encounter any lone emission lines in this census. Hypothetically, if we did detect a single emission line blueward of Hα without a continuum break, then we would flag it as an Lyα candidate line. This is because a single emission line shortward of the rest-frame wavelength of Hα will likely be [O iii] λλ4959, 5007, [O ii] λλ3727, 3729, or Lyα. In the first case, we would resolve both lines of the doublet. In the second case, the redshift would be sufficiently small, z ≲ 0.8, that we would also detect [O iii] λλ4959, 5007 in our spectral bandpass for both the MMT/Hectospec and Gemini/GMOS data sets. In the event that none of the above cases are encountered, then this would leave the likely identification of such a feature as Lyα. However, we do not detect any high-redshift candidates in this particular data set.

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Table 4.  Spectroscopic Redshifts in the G165 Field^a

Source ID	R.A.	Decl.	zspec	Ref	${i}_{\mathrm{SDSS},\mathrm{AB}}$	F110WAB	F160WAB
	(J2000)	(J2000)			(mag)	(mag)	(mag)
s1	11:26:36.173	+42:30:08.42	0.621	S	18.99	⋯	⋯
s2	11:26:43.968	+42:31:05.16	0.274	S	18.17	⋯	⋯
s3	11:26:45.732	+42:28:15.65	0.121	S	17.05	⋯	⋯
s4	11:26:46.387	+42:26:51.81	0.412	S	18.76	⋯	⋯
s5	11:26:48.850	+42:28:33.05	0.471	S	19.59	⋯	⋯
s6	11:26:59.151	+42:30:11.10	0.412	H	21.34	⋯	⋯
s7	11:26:59.471	+42:28:10.81	0.346	H	18.74	⋯	⋯
s8	11:26:59.999	+42:27:03.71	0.388	H	19.77	⋯	⋯
s9	11:27:00.233	+42:31:03.06	0.232	H	17.84	⋯	⋯
s10	11:27:02.557	+42:29:12.35	0.445	H	19.68	⋯	⋯
s11	11:27:02.667	+42:27:20.19	0.348	G	20.02	⋯	⋯
s12	11:27:04.239	+42:29:32.38	0.399	G	21.46	⋯	⋯
s13	11:27:04.785	+42:31:21.53	0.389	H	20.15	⋯	⋯
s14	11:27:05.558	+42:25:55.06	0.445	G	21.42	⋯	⋯
s15	11:27:05.754	+42:27:34.60	0.623	G	⋯	⋯	⋯
s16	11:27:06.732	+42:27:50.40	0.275	G	17.50	⋯	⋯
s17	11:27:06.787	+42:27:23.25	0.623	G	⋯	⋯	⋯
s18	11:27:07.552	+42:28:22.50	0.622	H	20.35	⋯	⋯
s19	11:27:09.420	+42:30:38.23	0.624	G	21.01	⋯	⋯
s20	11:27:09.564	+42:30:10.90	0.358	G	⋯	⋯	⋯
s21	11:27:10.774	+42:30:14.15	0.033	S	14.71	⋯	⋯
s22	11:27:11.137	+42:26:50.88	0.412	H	18.56	⋯	⋯
s23	11:27:12.283	+42:28:23.88	0.353	H	21.08	20.2	19.9
s24	11:27:13.046	+42:27:09.58	0.386	G	21.25	21.4	21.3
s25	11:27:13.133	+42:31:09.47	0.510	S	19.29	⋯	⋯
s26	11:27:13.300	+42:30:27.68	0.347	G	21.30	⋯	⋯
s27	11:27:13.444	+42:27:00.54	0.411	G	20.46	⋯	⋯
s28	11:27:13.653	+42:30:39.21	0.374	G	21.29	⋯	⋯
s29	11:27:13.680	+42:28:22.44	0.348	S	18.33	18.7	18.3
s30	11:27:14.803	+42:27:37.58	0.135	H	19.06	18.6	18.2
s31	11:27:15.312	+42:29:00.99	0.305	G	20.18	22.0	21.7
s32	11:27:15.370	+42:27:35.60	1.065	G	19.06	22.0	21.9
s33	11:27:16.596	+42:28:40.99	0.348	S	18.00	18.3	17.9
s34	11:27:16.664	+42:27:23.07	0.720	G	22.24	⋯	⋯
s35	11:27:16.692	+42:28:38.15	0.338	S	17.16	⋯	⋯
s36	11:27:16.894	+42:31:08.83	0.508	G	21.35	⋯	⋯
s37	11:27:17.145	+42:26:07.18	0.146	G	21.62	⋯	⋯
s38	11:27:17.928	+42:27:20.43	0.193	H	18.41	⋯	⋯
s39	11:27:18.027	+42:26:48.30	0.368	G	20.23	⋯	⋯
s40	11:27:18.501	+42:26:02.94	0.623	G	⋯	⋯	⋯
s41	11:27:18.594	+42:29:29.25	0.471	G	⋯	22.9	22.7
s42	11:27:18.652	+42:28:09.81	0.354	G	⋯	21.6	21.3
s43	11:27:18.879	+42:29:55.38	0.254	G	21.44	⋯	⋯
s44	11:27:19.394	+42:29:50.95	0.346	H	20.28	⋯	⋯
s45	11:27:19.452	+42:27:01.73	0.723	G	-	⋯	⋯
s46	11:27:19.908	+42:30:18.18	0.351	G	20.59	⋯	⋯
s47	11:27:20.146	+42:29:18.46	0.275	G	20.40	24.2	24.0
s48	11:27:20.379	+42:30:28.11	0.999	G	20.97	⋯	⋯
s49	11:27:20.386	+42:30:51.64	0.443	H	⋯	⋯	⋯
s50	11:27:20.458	+42:27:59.16	0.345	H	19.17	18.7	18.4
s51	11:27:20.509	+42:29:01.78	0.414	G	-	⋯	⋯
s52	11:27:22.652	+42:31:08.80	0.344	H	19.54	⋯	⋯
s53	11:27:23.369	+42:29:53.01	0.348	G	21.04	⋯	⋯
s54	11:27:23.383	+42:26:27.56	0.914	G	20.12	⋯	⋯
s55	11:27:23.685	+42:26:49.52	0.916	G	⋯	⋯	⋯
s56	11:27:23.833	+42:28:42.64	0.0b	H	18.51	⋯	⋯
s57	11:27:24.564	+42:29:48.99	0.347	G	21.06	⋯	⋯
s58	11:27:24.695	+42:29:04.92	0.759	G	21.72	⋯	⋯
s59	11:27:25.340	+42:27:43.93	0.395	H	22.12	⋯	⋯
s60	11:27:26.521	+42:26:58.02	0.347	H	19.55	⋯	⋯
s61	11:27:29.150	+42:30:23.45	0.544	S	19.36	⋯	⋯
s62	11:27:31.872	+42:27:41.04	0.522	S	19.60	⋯	⋯

Note.

^aThis object is a star.

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Typical absorption- and emission-line features identified in our data (depending on the redshift and type) are Fe ii λλ2587, 2600, Mg ii λλ2796, 2803, Mg i λ2852, [O ii] λλ3727, 3729, Ca H and K, G band, [O iii] λλ4959, 5007, Mg i $\lambda \lambda \lambda$5167, 5173, 5184, NaD, Balmer family (Hα through Hθ), and [S ii] λλ6716, 6731. See Figure 7 for sample spectra. Note that all 50 secure redshifts obtained from our spectroscopy and reported in this paper with an "H" for Hectospec or "G" for Gemini/GMOS are new to the literature.

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We specify cluster membership in the standard way, by requiring the redshifts to be in the range 0.326 < z < 0.376, which corresponds to ±3σ with respect to the mean of z = 0.351. In total, we have spectroscopic redshifts for 18 galaxies in the cluster. Of these, six cluster members are drawn from our MMT/Hectospec data, and an additional nine cluster members come from our Gemini/GMOS data. The information for the remaining three cluster members comes from all other available sources, which for this field is only SDSS (DR14). Those cluster members in common with the smaller HST field fall reasonably well onto the red sequence of the color–magnitude diagram (CMD; see Section B.1). Five galaxies with spectroscopic redshifts extending behind the cluster and in the range 0.412 ≤ z ≤ 0.414 are not included in this cluster member set, yet they may be members of an unrelated background galaxy group (Figure 6, inset).

To cope with the small sample size, we choose to measure the velocity dispersion using the Gapper method (see Hou et al. 2009 for details). We compute a velocity dispersion of σ = 2400 ± 620 km s⁻¹ from the 18 cluster members, corresponding to a large value for the virial mass of ${M}_{V}=(9.1\pm 0.4)\times {10}^{15}$ M_⊙ within 1 Mpc. If we now restrict the angular extent to match the scale of our HST observations of θ = 50'', or ≈250 kpc, then 13 cluster members are removed. The velocity dispersion for this smaller redshift set is σ = 2000 ±300 km s⁻¹, yielding again a large value for the mass of ${M}_{V}={1.3}_{-0.70}^{+0.04}\times {10}^{15}$ M_⊙. The uncertainties on the velocity dispersion are found by summing up the uncertainties in the galaxy redshifts in quadrature. The value for the dynamical mass within the cluster core is not uncommon for massive clusters (Girardi et al. 1993), and at the same time it is higher than the mean value for CLASH clusters by a factor of three (Siegel et al. 2016).

We emphasize that our values for σ, and hence also for M_V, will be biased upward relative to the true value if the line-of-sight velocities are enhanced relative to those in the transverse direction. It is relevant here to consider a nonspherical velocity structure, as a bimodal mass distribution is evident in the imaging data. The cluster galaxies separate out naturally into two main mass concentrations: a northeast (NE) and a southwest (SW) region. We take the cluster center to be situated at the center of this bimodal mass distribution, with a positional uncertainty that depends on the relative masses. Given that the two mass regions produce similar numbers of arcs and arclet families, conservatively we expect the mass ratio to be ≲10. The uncertainty on the cluster center translates into an uncertainty in the virial radius, and none of the above takes into account the potentially large systemic errors due to the unknown true radial and velocity structure of the cluster. We return to the discussion of the cluster kinematics in Section 6.1.

We perform a strong-lensing analysis for the fields in our sample by an approach that relies on the assumption that the light approximately traces the mass, or "LTM," such that the galaxies are biased tracers of the dark matter. A similar LTM methodology has been used to constrain the 2D mass distribution for cluster lenses extending back to some of the first examples of image multiplicities in cluster environments, such as A2390 (Frye & Broadhurst 1998) and Cl0024 (Broadhurst et al. 2000). This lensing analysis was subsequently extended to accommodate the properties of the first cluster field to show large numbers of arclet families, namely, the HST Advanced Camera for Surveys (ACS) image of A1689 (Broadhurst et al. 2005). To construct our mass maps, we use the well-tested implementation of the LTM pipeline by Zitrin et al. (2009, 2015). We also refer to Acebron et al. (2018) and Cibirka et al. (2018) for additional descriptions.

In the LTM model, the lensing galaxies are assigned a power-law mass density distribution scaled in proportion to their luminosities. The power-law index is left as a free parameter and is the same for all lensing galaxies. The superposition of the mass distributions of the individual lensing galaxies, which makes up the initial 2D mass distribution, is then smoothed by a Gaussian kernel to approximate the dark matter distribution, whose width is the second free parameter of the model. The dominant dark matter and galaxy distributions are, in turn, summed up with a relative weight, which adds another free parameter of the model, and then they are normalized (to a specific source redshift), which necessitates the fourth free parameter. Finally, the model accommodates a two-parameter external shear to provide additional flexibility. The values for these six parameters are constrained by the positions, orientations, and relative brightnesses of the arclet families. The best-fit model and errors are optimized through a Monte Carlo Markov Chain using thousands of steps.

The exquisite spatial resolution of HST makes feasible the designation of arclet families based on morphology and color. Moreover, the HST images show obvious axes of symmetry superimposed onto the field (see example in Figure 5), which allow for the identification of image multiplicities even without the aid of measured redshifts in some cases. Arclet families, in turn, constrain the model by imposing the condition that each family member image originates from the same source. The best-fit model is the one that minimizes the angular separations between the observed and predicted (relensed) image positions in the image plane. Notably, in addition to providing confirmation of the locations of the counterimages, the strong-lensing model also has predictive power to locate new image counterparts that can be searched for in the data to iteratively improve on the model result. Because secure spectroscopic redshifts are not available for every arclet family, the ratios of the relative angular diameter distances of the lens to the source, d_LS, and of the observer to the source, d_S, are left as free parameters to be optimized in the minimization of the model. In such cases, we allow a wide range of relative values of ${d}_{{LS}}/{d}_{S}=\pm 0.12$, which equates roughly to a redshift range of z ≃ 1.5–7. We expect the redshifts of the arcs roughly to coincide with the star formation rate density peak of the universe of z = 2–3 (Madau & Dickinson 2014). Even so, this broader redshift accounts for the potential outliers, as recommended in Johnson & Sharon (2016) for the case of limited spectroscopic redshift information and also found to be a useful constraint in Cibirka et al. (2018) and Cerny et al.(2018).

The lens model for the G165 cluster field is discussed in detail below, and a lensing analysis for the other five fields appears in Section B.1. We emphasize that all arclet families discovered in this study are supported by our LTM model.

The cluster members form a pattern on the CMD referred to as the red sequence (Gladders & Yee 2000). The G165 field shows a prominent red sequence characterized by very little scatter, making the designation of the cluster members especially straightforward by applying a color cut in the usual way. At the same time, the amount of scatter increases toward fainter sources owing to the larger photometric errors. To reduce the risk of contamination by objects outside the cluster, we also impose a conservative upper magnitude limit of F160W_AB = 21.0. The initial selection flagged two objects that were found by inspection not to be bona fide cluster members and so were removed. The first was a star, and the second was galaxy "s30" with a spectroscopic redshift of z = 0.135, which places it in the foreground of the cluster. Our final catalog for G165 uses 38 cluster members in the lens model. The cluster members within the central region found by our blind selection algorithm appear as plus signs in Figure 8. We refer to Appendix B for additional details regarding the cluster member selection.

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On the lensing constraints, our HST image is replete with giant arcs and arclet families. The presence of giant arcs, as well as structures consisting of several giant arcs, has been noted before (Cañameras et al. 2015). A preliminary mass model for G165 was made using ground-based CFHT data available at the time (Cañameras et al. 2015, 2018). In total, we present here 11 designations of arclet families, all of which are new to the literature (Table 3). The reference center for our lensing analysis is set to the location of the lensed DSFG at (R.A., decl.) = (11:27:14.731, +42:28:22.56). By using the positions and brightnesses of the cluster members as constraints in our LTM algorithm, we construct a mass map that is subject to the arclet family constraints. Our model uncovers the two mass peaks evident in the imaging and reproduces all lensed galaxy images with respect to their locations (rms ∼ 065). The arclet families are marked on a color image along with the critical curve in Figure 8. Postage stamp images of the arclet family members appear in Figure 9 organized by family name. Below we give a description of each of the 11 arclet family systems, whose properties are also summarized in Table 3.

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G165_DSFG_1 (Arcs 1a, 1b).—Arc 1a is the NIR counterpart of the lensed DSFG at z = 2.2 detected in the submillimeter data set (Cañameras et al. 2015). This giant arc, which orthogonally bridges the critical curve, has an NIR angular extent of ∼5 Our model estimates that Arc 1a is a merging image with a high areal magnification factor of ≳30 that varies along the long axis of the arc. The large areal extent on the sky yields the potential to study properties within its interstellar medium, on physical scales of ≲1 kpc. In particular, two compact and bluer sources appear superimposed onto Arc 1a, which are situated on opposite sides of the critical curve at the redshift of the DSFG. These may potentially be images of star-forming knots within the DSFG that are multiply imaged, thereby yielding still higher magnification factors (see Figure 5). Spectroscopy is required to determine the relation of these two blue images to Arc 1a. Arc 1a is bright, ${K}_{{AB}}={18.74}_{-0.02}^{+0.02}$ mag, and well suited for spatially resolved spectroscopic follow-up observations.

A counterimage is also predicted, which is not detected in our HST data set but is detected in the LBT/LUCI + ARGOS K-band image at the model-predicted location. A bright image at the exact model-predicted location is also detected in our Spitzer/IRAC imaging data. We designate this arc as the counterimage G165_DSFG_1b (see Figure 5). Interestingly, while the F160W_AB–K_AB color is consistent between the two images, there is an offset in the F160W_AB–${S}_{3.6,{AB}}$ color by a large ≳2.6 mag. This color difference is due at least in part to contamination. G165_DSFG_1b appears to be situated behind a bluer and lower-redshift galaxy, which influences the photometry and therefore renders the color unreliable (see Figure 5). G165_DSFG_1a is also a merging pair. As such, the background source crosses a cluster caustic such that G165_DSFG_1a represents only a region of that background source and only a portion of the starlight. At the same time, G165_DSFG_1b unveils the entire source and thus the total integrated galaxy light. It is noteworthy that G165_DSFG_1 is the only arclet family in this field to have a measured spectroscopic redshift. This family is used for the internal minimization or "anchor" of our model.

G165_2a, 2b, 2c (Arcs 2a, 2b, 2c) and G165_8a, 8b, 8c (Arcs 8a, 8b, 8c).—The Arc 2 family members are the brightest in the field, with K_AB magnitudes for each of the three arcs of ≈18.5 mag, making them also excellent sources for follow-up spectroscopy to measure the redshift. For this object, we leave the redshift to be optimized in the modeling. The bluer arclet trio that makes up Arcs 8, which are situated near in projection, is undetected at K. Arcs 2a and 2b and Arcs 8a and 8b fold about an axis of symmetry, as do Arcs 7a and 7b and Arcs 10a and 10b discussed below.

G165_3a, 3b, 3c (Arcs 3a, 3b, 3c); G165_4a, 4b, 4c (Arcs 4a, 4b, 4c); and G165_6a, 6b, 6c (Arcs 6a, 6b, 6c).—For the following description we refer to the close-up image in Figure 5. The family members Arcs 6a and 6b are red and compact arcs that are situated on opposite sides of an axis of symmetry, as marked. Adjacent in projection on the sky, the slightly redder family members Arcs 4a and 4b present more extended morphologies. Coincident with Arcs 4a and 4b, the bright family members Arcs 3a and 3b describe a fold arc conjoined at the axis point. The third image of each of these families, Arcs 3c, 4c, and 6c, appears at an an angular separation of ≈14''. This set of third images for each family retains similar colors and image morphologies and relative image placements.

G165_5a, 5b (Arcs 5a, 5b).—These faint and blue galaxy images are situated just inside the critical curve and are the only secure arclet family members to reside on the opposite side of the gravitational potential. Arcs 5a and 5b are two merging images folded about the critical curve. Meanwhile, the dashed circle labeled as "5c?" marks the position of a candidate counterimage that awaits confirmation pending additional model constraints.

G165_7a, 7b, 7c (Arcs 7a, 7b, 7c); G165_10a,10b (Arcs 10a, 10b).—Arcs 7a and 7b and Arcs 10a and 10b project onto an arc-like structure that is parallel to Arcs 2a, 2b, and 2c. Arcs 7a and 7b are especially red and low in surface brightness. The counterimage that we designate as Arc 7c appears southward at the model-predicted location. The candidate counterimage labeled as "10c?" appears near to its expected location but at a different color, and so it is not included in our lens model.

G165_9a, 9b, 9c (Arcs 9a, 9b, 9c).—This arclet family trio is distinctively blue and compact. Arcs 9a and 9b are split by an axis of symmetry. Arc 9c appears at the model-predicted location at an angular separation of $10\buildrel{\prime\prime}\over{.}$ Note that two other candidate counterimages are marked in Figure 8 as "9d?" and "9e?" on the opposite side of the gravitational potential, which await confirmation as additional model constraints become available. Although situated near in projection to bright central elliptical galaxies, Arcs 9d? and 9e? are clearly identified in our galaxy-subtracted image using Galfit (Peng et al. 2010) in Figure 9.

G165_11a, 11b, 11c (Arcs 11a, 11b, 11c).—The blue Arcs 11a and 11b are images that merge across the critical curve as indicated by the pair of star-forming knots within Arc 11a that appears again in Arc 11b with reverse parity. Arc 11c appears at the model-predicted location southeast of the other two arclet family images at an angular separation of 18''.

From our lens model we compute a large effective Einstein radius of 13'' at z = 2.2 and 16'' at z = 9. By integrating up the mass surface density, we measure a lensing mass of (2.6 ± 0.11) × 10¹⁴ M_⊙ within a ∼250 kpc radius. By summing up the total area on the magnification map binned by the magnification factor, we compute A(> μ) as a function of μ. Our profile of this cumulative areal magnification is similar to that of the Weak and Strong Lensing Analysis Package (WSLAP) model of Diego et al. (2007), to within ∼30%. Note that given the significant visibility of both G165_DSFG_1a and G165_DSFG_1b in the K band and Spitzer/IRAC, the James Webb Space Telescope (JWST) resolution and sensitivity will be needed at 1–4 μm to significantly refine these lens models. We refer to Section 6 for independent measurements of the mass and estimates of the lensing strength and also to Appendix B for the magnification map.

The difference in our values between the lensing and the dynamical masses merits further investigation. Here we discuss our three independent estimates of the mass.

6.1.1. Lensing Mass

6.1.2. Dynamical Mass

Our value for the dynamical mass of ${1.3}_{-0.70}^{+0.04}\times {10}^{15}$ M_⊙ is a factor of ∼5 higher than that of the lensing mass within 250 kpc. By making use of our entire spectroscopic data set, which extends to 1 Mpc, our value for the dynamical mass remains high, M_V = (9.1 ± 0.4) × 10¹⁵ M_⊙. Relevant to this discussion, the imaging uncovers an obvious bimodal mass structure (Figure 8). If the mass is elongated along the line of sight, then the velocities will also be higher in this direction. In this case the erroneous assumption that the line-of-sight velocity is spherically symmetric will lead to an overestimate of the virial mass. Bimodal masses are not uncommon in massive lensing clusters (e.g., Cerny et al. 2018; Cibirka et al. 2018; Mahler et al. 2018). For example, in Mahler et al. (2018), the two mass peaks appearing in the image of the cluster A2744 are identified spectroscopically in the redshift histogram of 156 cluster members as two velocity peaks separated by 5000 km s⁻¹ (their Figure 9). We cannot perform this exercise in our current sample, given the lower numbers of spectroscopic redshifts by an order of magnitude. Instead, we undertake a search for any velocity gradient across the cluster.

We introduce a bifurcation line drawn normal to the line connecting the NE and SW mass peaks at its midpoint (see Figures 8 and 10). We then compute the radial velocities on either side of this line to search for evidence of two velocity peaks to match the incidence of the two mass peaks (Figure 10). But do the velocities give a fair representation of the kinematical structure of the cluster? In a recent paper, Hayashi et al. (2017) report that new cluster members undergoing infall show high line-of-sight velocities at all radii. This is potentially insightful for the G165 field, in which two cluster galaxies have high measured velocities of v_los ≈ 950 and 1750 km s⁻¹ (green open squares in Figure 10). These are also two of only three galaxies showing nebular emission line features indicative of recent star formation. These galaxies have a potentially larger peculiar velocity component and elevated star-forming activities, two attributes that are consistent with the picture that these objects are infalling members. On consideration of all but these two outliers, there is a hint of a redshift of the NE mass peak relative to the SW one. However, given the small mean velocity difference between the two peaks of ≲2000 km s⁻¹ and the dearth of spectroscopic redshifts, we are unable to constrain the cluster velocity configuration with the current data set. Additional spectroscopy is needed to fill in the sparse redshift sampling to obtain a larger, more representative set of cluster members. We refer to Section 6.3 for the discussion of how the cluster configuration relates to the cluster gas pressure.

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6.1.3. Caustic Mass

In keeping with the limits typically imposed for the caustic mass estimates, we set a velocity cut of ±5000 km s⁻¹ from the mean cluster redshift of z = 0.351. The redshift information for the 17 of 18 cluster members meeting this requirement provides the input to measure the caustic mass in a formalism developed in Diaferio & Geller (1997) and Diaferio (1999) (see also Serra et al. 2011; Alpaslan et al. 2012; Windhorst et al. 2018). The approach is to estimate the mass of a cluster of galaxies out to the virial radius by analyzing the distribution of its constituent galaxies in redshift space (i.e., projected separation from the cluster center R as a function of line-of-sight velocity with respect to the cluster median redshift v_los). On the assumption of a virialized cluster, this distribution resembles the bell of a trumpet (with the spread in v_los increasing at low R), whose area can be related to the gravitational potential (and hence mass) of the cluster.

It is useful to work in phase space by depicting v_los as a function of their projected distances from the cluster center. We adopt the virialized region from the prescription in Jaffé et al. (2015), such that v_los ≤ 1.5 σ is within a projected distance of R₂₀₀, where σ is the velocity dispersion. Indeed, the vast majority of cluster members (black circles in Figure 11) fit well within this radius as depicted by the gray shaded region. We convert our redshift catalog of cluster members into a continuous density field by using an adaptive density kernel. The contour (black curve) identifies the region in the redshift-space distribution that corresponds to the escape velocity of the cluster (assuming spherical infall), which in turn is related to its gravitational potential as ${v}_{\mathrm{esc}}^{2}=-2\phi (r)$. In practice, we impose the condition of spherical symmetry by rewriting this density threshold into a symmetric version about the ${v}_{\mathrm{los}}=0$ line. To do this, we check the absolute values of v_los for this double-valued function in small increments of radius along the density threshold contour. The caustic equates to the minimum of those two absolute values and is reflected along the v_los = 0 line to construct the "tuning fork" shape (green contour). The amplitude of the caustic ${ \mathcal A }(r)$ is then related to the cluster mass M such that ${GM}\propto {\int }_{0}^{r}{{ \mathcal A }}^{2}(r){dr}$.

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By applying this estimator, we measure a mass of ≈(1.9 ±0.18) × 10¹⁵ M_⊙ within 0.8 Mpc. The uncertainty on this value is derived by a "jackknife" resampling approach consisting of making 20 realizations in which two galaxies at a time are removed at random and the mass recomputed. Analysis of this set yields the stated estimate in the uncertainty of the mass. Note that the mass has been rescaled to be median biased with respect to the dynamical mass, which is calibrated as a function of redshift and cluster richness of comparable systems in Alpaslan et al. (2012). This mass value is a factor of ∼5 higher than the value for the lensing mass extrapolated out to 1 Mpc and a factor of ∼5 lower than the value for the dynamical mass computed within 1 Mpc. If G165 does have an aspherical mass distribution elongated along the line of sight (see Section 6.1), then this value will be an overestimate.

We compare the lensing strength of G165 with that of another massive lensing cluster at a similar lens redshift, the Hubble Frontier Fields cluster A2744 (HFFs; PI: J. Lotz, GO-13495). A2744 provides a useful benchmark for its well-constrained lens model and similar size of its effective Einstein radius. Its strong-lensing model is well constrained with 29 arclet families identified from deep HST imaging in seven bands with 5σ limits in each filter of m_AB ∼ 29 mag (Mahler et al. 2018). These limits are ∼1.3 and ∼1.8 AB mag deeper than the 5σ limiting magnitudes for G165 of F110W_AB = 27.7 mag and F160W_AB = 27.0 mag. For consistency, we construct the models for both clusters by our LTM approach, where the lens model for G165 comes from this paper and the one for A2744 is from Zitrin et al. (2014). We show the lens models in the two leftmost panels in Figure 12. In both cases we find a similar elongated shape and effective z = 9 critical curve size of ∼16''. To compute the lensing strengths, we assume the same background luminosity function (Finkelstein 2016) and then compare the number distribution of lensed background galaxies in the two fields. Overall, the clusters G165 and A2744 yield significantly brighter objects compared to a blank field at all magnitudes. At high redshifts, the clusters G165 and A2744 yield on average similar numbers of z ≈ 9.6 objects (right panel in Figure 12).

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G165 is an ideal lens through which to investigate high-redshift objects (z = 9–12). This is in part due to the relatively low redshift of the lens plane of z = 0.351, for which the level of the intracluster light (ICL) contamination at the NIR wavelengths corresponding to the Lyman break for z > 9 galaxies is minimized (Windhorst et al. 2018). G165 also has a reasonably high ecliptic latitude of 35°, reducing its background from the peak with the zodiacal plane. The lens size is ideal for JWST/NIRCam imaging, as the lens fills (but does not overfill) the field of view out to ∼3 times its Einstein radius. Note that for relatively shallow exposures typical of a JWST short program reaching limiting fluxes of m_AB ∼ 28 mag, the improvement of JWST will be seen at all wavelengths. The imaging at λ > 1.6 μm will enable robust detections of the stellar continuum of any new high-redshift galaxy candidates situated behind lensing clusters.

We consider the potential for G165_DSFG_1a to yield caustic transit events. In its favor, two compact and bluer knots appear in projection to be within this arc that bridges the critical curve and have small angular separations from the critical curve of roughly tenths of an arcsecond (see Figures 5 and 9). Unlike distributed masses that incur magnification factors of up to μ = 40–50, compact sources such as stars and star clusters can reach magnifications of μ ≲ 10⁵ (Windhorst et al. 2018). To assess the practicality of monitoring this arc for caustic transits, we require in addition a negligible ICL component. Diego et al. (2018) showed how, if the ICL at the position of the critical curve is significant, the stars from the ICL can set an upper limit (through microlensing) on the maximum magnification of background stars during caustic crossing events to around 10⁴. Since the ICL can extend up to large distances from the center of the halos (see, e.g., Mihos 2016), even critical curves that are relatively far from the center of halos could be affected by the microlensing from the ICL stars.

Given the somewhat novel search strategy to find the G165, it is natural to ask how this massive lensing cluster compares with others selected by more commonly used methods, such as X-ray brightness or the detection of the SZ decrement. G165 has high mass and high dark matter concentration, as evidenced by the prominent displays of giant arcs and arclet families even in these relatively shallow (single-orbit) HST images. As such, we would expect G165 to be replete with large amounts of cluster gas.

G165 is in fact undetected in ROSAT imaging (R6+R7 bands, or ∼0.7–2 keV). Put another way, G165 is at best a low-luminosity X-ray source with an upper limit on its X-ray flux computed from the RASS diffuse map of $1.12\times {10}^{-4}$ counts s⁻¹ arcmin⁻². It is unusual for a truly relaxed cluster to have an X-ray flux so low as to be undetected by ROSAT at this redshift and mass scale. At the same time, at these lower luminosities, the scaling relations correlating the X-ray luminosity to cluster mass are more uncertain owing to a large intrinsic scatter in the data (Bruch et al. 2010). G165 also misses out on membership in the Planck Sunyaev–Zel'dovich (PSZ) cluster catalog as a result of its low SZ signal, which falls below the minimum detection threshold. In the Planck Compton-Y parameter map there is a small fluctuation at the position of the cluster that may represent a weak detection of intercluster gas, or it may be noise given that the detection is only at the 1σ–2σ level. This lack of a significant SZ signal might be a consequence of radio emission washing out a shallow decrement, projection effects, or an overestimation of the cluster mass.

Radio sources have an inverted spectrum with respect to IR sources that can counteract the SZ signal. AsDSFG_G165_1a is the one image in the field with high submillimeter flux arising from high star formation and/or AGN activity; this lensed DSFG is the most likely source to be radio-loud. There is a weak radio emitter detected near the position of the IR source. From NVSS data we measure a total flux from the cluster including this IR source of <40 mJy at 1.4 GHz (Condon et al. 1995). Although present, this modest radio signal is insufficient to compete with the SZ effect at the relevant frequencies (100–353 GHz), thereby ruling out radio contamination as an explanation for the relative SZ silence.

The last conventional explanation is the lensing configuration. The G165 field contains an obvious bimodal substructure. There are other examples of bimodal mass structures, such as the well-studied Bullet Cluster (Bradač et al. 2006; Clowe et al.2006) and the cluster known as "El Gordo" (Menanteau et al. 2012). These two clusters are classified as "post-mergers" that, in turn, produce significant enhancements of the X-ray flux. If the field is elongated along the line-of-sight direction as a series of two smaller galaxy structures, then we may be catching G165 during a less well studied evolutionary "pre-merger" phase. In this scenario, the total cluster gas pressure dilutes across the large structure, which reduces the gas pressure and the X-ray emission, hence reducing the SZ decrement. At the same time, the mass integrated along the line of sight still provides ample surface mass densities, leading to strong-lensing effects. A test of this hypothesis can be made by acquiring X-ray observations. For example, XMM imaging at the level of 20–27 ks total exposure allows us to measure the distribution and centroid and place limits on the electron temperature of the X-ray gas. If G165 deviates from a monolithic mass, then an offset will be detected, or at least an X-ray source that is marginally extended yet still potentially offset from the center of mass.

The positional centroids from the submillimeter image are indicated by the gold plus signs in Figure 2. We find NIR counterparts for two of these three peaks, which we designate as G145_DSFG_1a and G145_DSFG_1b. These two small arcs are only marginally resolved using HST. Initially, only one counterpart image was identified, DSFG_G145_1a. A careful search unveiled a second image with a similar color, at the model-predicted location, which we designate as DSFG_G145_1b. Using these two arcs as inputs, the model predicts a third image that coincides with the image in the submillimeter but is not detected by HST. The lack of a detection is not surprising, given the faintness of the other two NIR counterparts, which both hover around the limiting magnitude of our observations. The redshift distribution of galaxies in this field is broad, with a somewhat poorly defined peak at z ≈ 0.837, which we take to be the lens plane. This value is based on four redshifts in the 3σ clipped range 0.822 < z < 0.852 drawn from our spectroscopy, which all fall within the HST field of view (gold filled circles in Figure 13). This spectroscopy will appear in a separate paper. We note that there is no spectroscopic information available from data archives or other sources. The redshifts for the four lensing members that are situated within our HST field of view appear as the gold filled circles in Figure 13. Our lens model recovers both the image positions and angular separations of the counterimages with an rms of ∼01. In turn, we estimate magnification factors of 12 ± 0.5 and 5 ± 0.5 for G145_DSFG_1a and G145_DSFG_1b, respectively. We estimate the uncertainty by sampling the values for the magnification in a neighboring annular region of width 2'', an approach that works reasonably well for images that are not very near in projection to the critical curve (≳ few arcseconds). Our model yields effective Einstein radii of 10'' at the redshift of the lensed DSFG and 9'' at z = 9.

We confirm the NIR counterpart of the lensed DSFG as a red and spatially extended image, although the ring-like structure and two arclet families seen in the ALMA data are blended with the primary lens in our HST image and are thus unresolved (Figure 2). The primary lensing galaxy consists of a single object with a measured redshift of z = 1.5, which also blended with the lensed DSFG. Elsewhere in the field there are two blue arcs in the near projected proximity of the brightest cluster galaxy that appear to be unrelated images, and no other arclet families are identified. Without arclet families we cannot construct a lens model for this field. Based on this information, we are able to approximate the surface mass density relative to the critical value through the relative galaxy brightnesses and orientations to yield a κ-map (Figure 14), yet we do not cite a z = 9 critical curve radius. Note that this field already has a published model based on the ALMA data (Cañameras et al. 2017a, 2017b).

Four peaks of the lensed DSFG are detected in the submillimeter and ALMA imaging (Cañameras et al. 2015; Nesvadba et al. 2016). Of these, we find NIR counterparts for three images, which we designate here as G045_DSFG_1a, 1b, and 1c (see Figure 2). We measure a spectroscopic redshift for the lens of z = 0.556, based on seven redshifts in the 3σ clipped range 0.535 < z < 0.577 drawn from our spectroscopy, which will appear in a separate paper. Of these, the redshift for one cluster member is situated within the field of view of our HST data (gold filled circles in Figure 13). Our lens model recovers both the image positions and angular separations of the counterimages with an rms of ∼04. In turn, the model yields high magnification factors of ≳9, ≳9, and ≳7 for G045_DSFG_1a, 1b, and 1c, respectively. In an independent analysis, the magnification factors of 10–22 were measured for smaller emission-line regions within each arc (Nesvadba et al. 2016). We compute effective Einstein radii of 8'' at the lensed DSFG redshift and 10'' at z = 9.

The submillimeter imaging shows three bright peaks of this one lensed DSFG. The positional centroids of the peaks are indicated in Figure 2 by the gold plus signs and labels. We designate the two NIR counterparts that we detect in our HST imaging as G080_DSFG_1a and G080_DSFG_1b. There is considerable noise at the expected positions of the images owing to their close projected proximity to the extended halos of bright lensing galaxy members. We found that by smoothing the data we were able to take out the high-contrast noise, an exercise that enabled the detection of G080_DSFG_1a and G080_DSFG_1b (see inset of Figure 2). Interestingly, we measure a shift by up to 05 in the positional centroids of G080_DSFG_1a and G080_DSFG_1b between the SMA and HST images, equating to a physical extent in the source plane of ∼4 kpc. We find no good explanation for these positional offsets. We measure a lens redshift of z = 0.670 that is based on 10 redshifts in the 3σ clipped range $0.649\lt z\lt 0.691$ drawn from our spectroscopy in this field, whose results will appear in an upcoming paper. Of these, the redshifts of four of the cluster members are situated within the field of view of our HST data (gold filled circles in Figure 13). In general, the red sequence shows somewhat more scatter than in some of the other fields, which introduces a higher probability for misidentifying objects of roughly similar colors. To mitigate any potential contamination by galaxies external to the cluster, we make a conservative color cut, resulting in a narrow band of cluster members (red filled stars in Figure 13), yet the uncertainty on the placement of this narrow color cut ultimately limits its usefulness. Our lens model recovers both the image positions and angular separations of the counterimages with an rms of ∼22. The relatively low value of the rms uncertainty shows that the model is robust. At the same time, the rms value is higher than those computed for the other fields in our sample for two reasons: (1) there is a higher uncertainty on the positional centroids of G080_DSFG_1a and G080_DSFG_1b given their ultralow surface brightness, and (2) the high scatter in the red sequence translates into a higher probability for contamination by objects with similar colors that are not bona fide lensing galaxy members. From our lens model high magnification factors of ∼20 are measured for each of the two images. We compute effective Einstein radii of ∼7'' at the redshift of the lensed DSFG and ∼11'' at z = 9.

The single "tadpole-shaped" arc detected in the SMA imaging breaks up into two lensed sources, G092_DSFG_1a and G092_DSFG_1b, in our HST images. These arcs are not easily reproduced by our lens model despite their similar colors. A clue to their nature is given by subtracting off the light of the central elliptical galaxy using Galfit. By doing this, we uncover significant differences in the smooth versus clumpy components of the two images (Figure 2, inset). The measured redshift is z = 3.3, which is integrated over both components. Based on the available information, we infer that these two images are two different galaxies at a similar redshift. As such, this may potentially be an example of a pair of interacting galaxies that induces the ultrahigh star formation rates of ∼1000 M_⊙ yr⁻¹ obtained from correcting the value in Cañameras et al. (2015, their Table 2) by the magnification factor provided from our lens model. There is only a single available redshift in this field from the literature, which is of high value, as it corresponds to that of the central lensing galaxy (z = 0.448 from SDSS DR 14). Without an arclet family, we cannot construct a robust lens model for this field. At the same time, we are able to approximate the surface mass density relative to the critical value through the relative galaxy brightnesses and orientations to yield a κ-map (Figure 14). By adopting our best-fit scenario that G092_DSFG_1a and G092_DSFG_1b are two singly imaged lensed sources at a similar redshift, we compute high magnification factors of ∼20 for each image, and we do not cite a z = 9 critical curve radius.