PLCK G165.7+67.0: Analysis of a Massive Lensing Cluster in an Hst Census of Submillimeter Giant Arcs Selected Using Planck/Herschel
We investigate the physical properties of the galaxy cluster PLCK G165.7+67.0 (G165), as a part of an HST WFC3-NIR imaging survey in the fields of six strongly-lensed Dusty Star Forming Galaxies (DSFGs) at - 4 identified by color through a new cluster search method using Planck/Herschel. We detect NIR counterparts for all six DSFG submillimeter sources, and undertake strong lensing analyses. In particular, G165 at =0.351 stands out for its exceptional lensing properties. After combining the color and morphological information, we find eleven background galaxies that are multiply imaged. One of these, the bright DSFG visible in the Planck/Herschel data, splits into two images: a giant arc with a spatial-extent of 45 that is merging with the critical curve, and a lower magnification counter-image that is detected in our new longer wavelength ground- and space-based imaging data. From a spectroscopic redshift census, we calculate a dynamical mass from our 18 cluster members of M within 250 kpc, or a factor of 3 higher than the lensing mass to fixed radius. Our spectroscopy reveals a velocity gradient across the bimodal mass structure. This gradient suggests that the dynamical mass estimation may be biased high due to projection effects. Taken altogether, we suggest that this cluster with its high dark matter concentration, relatively weak X-ray flux and low SZ decrement may be explained as a pre-merger for which the intra-cluster gas is diluted along the line-of-sight, while the integrated surface mass density is supercritical to strong lensing effects.
Clusters of galaxies with masses M are extremely useful but rare tracers of the distribution of mass in the universe (Bahcall, 1977; Mo & White, 1996). Finding galaxy clusters, and establishing cluster properties and cluster scaling relations, are fundamental to cosmology studies (Vikhlinin et al., 2009; Mantz et al., 2010; Rozo et al., 2010; Allen et al., 2011; Benson et al., 2013; Hasselfield et al., 2013; Planck Collaboration et al., 2014). As ensembles of discrete galaxies, they can be discovered in optical and near-infrared wide-area surveys such as the Sloan Digital Sky Survey (SDSS) (i.e., Koester et al., 2007a, b; Rykoff et al., 2014, 2016).
Although originally discovered at optical wavelengths, galaxy clusters with masses of 1 - 10 10 M will almost always contain a massive component of hot intra-cluster gas which makes them distinct X-ray sources. This reservoir of hot baryons is a salient feature of massive clusters, as there is no physical mechanism to dissipate it. To take advantage of this requisite feature, the ROSAT archives offer the all-sky advantage to efficiently detect the most extreme sources of X-ray emission produced by thermal bremsstrahlung and line emission in the intra-cluster gas (Rosati et al., 1998; Ebeling et al., 2007, 2010).
A galaxy cluster bound by gravity also has a distinct signature at radio wavelengths. This is because the same large reservoirs of intra-cluster gas which give rise to the X-ray flux also distort the cosmic microwave background radiation (CMB) by inverse Compton scattering. From the ground, searches for galaxy clusters by detection of this Sunyaev-Zel’dovich (SZ) effect using the South Pole Telescope (SPT; Carlstrom et al., 2011) yield hundreds of candidates (Bleem et al., 2015). Targeted searches using the Atacama Cosmology Telescope (ACT; Fowler et al., 2007) that employ a similar technique are also successful (Sehgal et al., 2011, 2013). From space, Planck High Frequency Imager (HFI) data is used to extend the search for the SZ decrement to all available extragalactic sky (Lamarreet al., 2003; Planck Collaboration et al., 2016a).
To complement the cosmological SZ approach, the detection of galaxy over-densities by the astronomical technique of color-selection has recently been explored. Ultra-bright infrared galaxies are targeted, such as the Dusty Star Forming Galaxies (DSFGs) which produce stars at rates of up to 1000 yr and yield prodigious amounts of dust. This warm dust radiates as a modified blackbody spectrum with a prominent peak in the rest-frame far-infrared. Submillimeter data are well-suited to conduct the color search for the DSFGs because this wavelength range corresponds to the observed-frame thermal dust peak at redshifts typical of DSFGs of 2 - 4 (Casey et al., 2014; Planck Collaboration, 2015, and reference therein). In this regime, there is the unusual advantage that one records the flux density of the DSFGs closer to the peak of their rest-frame SED as their redshift increases. As a result, the benefit of the high flux density of DSFGs largely compensates for the cosmological dimming (Blain, 1999; Planck Collaboration, 2015), thereby gaining leverage for the detection of high-redshift objects.
A Planck/HFI census was undertaken to find DSFGs by color using the cleanest 26% of the data, or 10,000 deg. To be selected by Planck/HFI, the DSFGs had to be separately detected in each of the cleaned 857 GHz and 353 GHz maps, be compact at Planck resolution (5), and have flux density ratios in the 353, 545, and 857 GHz maps consistent with being red and dusty sources (Planck Collaboration, 2015). These so-called ‘cold’ sources in the CMB are extremely rare, with number densities of 1 per tens of square degrees, requiring the wide-field survey area of Planck/HFI. We flag the brightest 228 of these cold sources as the candidate DSFGs. To classify the sources, follow-up observations are made of this sample higher spatial resolution using the Herschel/SPIRE. Details and initial results are discussed elsewhere (Planck Collaboration, 2015, 2016). In sum, 15 of the 228 sources are discovered to be individual DSFGs boosted in brightness as a result of gravitational lensing (Planck Collaboration, 2015; Cañameras et al., 2015).
In this paper, we present new HST imaging and lensing analysis for six of the 15 strongly-lensed Planck/Herschel-selected sources. We focus our study on one particular object in our sample, namely, PLCK G165.7+67.0 (hereafter G165). To better understand the properties of this one field, we acquire multi-wavelength imaging and spectroscopic follow-up observations which will be discussed in detail.
This paper is organized as follows. In §2 we compare our sample of strongly-lensed DSFGs with others in the literature. In §3 we present new HST imaging data for our sample of six Planck/Herschel-selected strongly-lensed DSFGs. We also present new ground- and space-based observations of the high mass cluster, G165. In §4 we describe the data reduction and analysis of the follow-up data obtained for G165. In §5, we construct the strong lensing model for G165. This analysis is followed by a discussion in §6 in which we make independent determinations of its mass, its lensing strength, and the properties of its low inferred cluster gas pressure. In §7 we summarize our results. An Appendix is provided to describe the imaging and lensing analysis of all six fields in our HST sample. We assume throughout a CDM cosmology with km s Mpc, , (Planck Collaboration et al., 2016b).
2 Strongly-Lensed DSFGs
Although the details of the search strategies for strongly-lensed DSFGs differ, most algorithms set a high 350 m flux density (), or a high 500 m flux density () cut of 100 mJy. To date, dozens of strongly-lensed DSFGs in the redshift range 2 4 satisfy these criteria. In Figure 1 we assemble the set of lensed DSFGs for the surveys or subsets thereof for which there are Planck flux densities, spectroscopic redshifts for the lens and the lensed sources, and images of the lensed sources. For each DSFG, the symbol size is proportional to the size of the Einstein radius we estimated from the resolved image of the lensed source. For reference, Einstein radii of 1, 5, and 10 are used, which are typical of individual massive galaxy lenses (), galaxy group lenses (), and galaxy cluster lenses (), respectively. The legend gives the color-coded references. The brightest lensed DSFG, the “Cosmic Eyebrow” (), stands out for its high submillimeter flux density ( mJy). It was found by cross-correlating the sources in the WISE all-sky source catalog “AllWISE,” with infrared-bright galaxies in the Planck compact source catalog (brown circle in Figure 1; Díaz-Sánchez et al., 2017). Note that the peak submillimeter flux density of the Cosmic Eyebrow is measured from Planck/HFI data, which has higher uncertainty by a factor of 10 than the Herschel/SPIRE photometry used for the other comparison samples in Figure 1.
In the redshift range 2 4, a search for lensed DSFGs within the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS) using as a discriminator yields 22 lensed DSFGs covering a search area of 14.4 deg (Harris et al., 2012; Bussmann et al., 2013; Calanog et al., 2014; Negrello et al., 2017). This same approach applied to the Herschel Multi-tiered Extragalactic Survey (HerMES) field extends the areal coverage by a factor of 7, resulting in 13 new lensed sources (Wardlow et al., 2013; Bussmann et al., 2013; Calanog et al., 2014; Nayyeri et al., 2016). By applying similar flux density cuts to the Herschel Stripe 82 Survey (Hers82), an additional three lensed DSFGs are found (Nayyeri et al., 2016).
From the ground, South Pole Telescope (SPT) data enables the selection of strongly-lensed DSFGs based on the ratio of flux densities at 1.4 and 2.0 mm , which are consistent with thermal emission by dusty galaxies (Vieira et al., 2010; Carlstrom et al., 2011). The brightest sources in the sample are then followed-up at higher resolution using most notably the SubMillimeter Array (SMA) and the Atacama Large Millimeter Array (ALMA). A total of 26 strongly-lensed DSFGs are identified, which tend toward higher redshifts owing to their selection at longer wavelengths, and whose identifications are typically explained as galaxy-galaxy lensing events (Weiß et al., 2013; Vieira et al., 2013).
The Planck collaboration used Planck/HFI data to extend the search for lensed DSFGs to all available sky. This enables the detection of the most rare and extreme sources picked out by the detection of the thermal dust peak. To focus detection on only the most extreme sources, a strict flux density criterion is imposed that exceeds 500 mJy at 545 GHz. The expectation is that the brightest sources that are also compact at Planck resolution will be too faint to be explained by a single field DSFG. These sources are most likely: (1) multiple DSFGs, or (2) a single strongly-lensed DSFG. The latter case would flag the presence of a large foreground mass. On follow-up at higher resolution using Herschel/SPIRE, the vast majority of sources resolve out into clumps of several submillimeter bright objects in close projected proximity (Planck Collaboration, 2015, 2016). These are candidate galaxy over-dense regions which are potentially the high redshift predecessors of massive lensing clusters at lower redshifts (Planck Collaboration, 2015; Flores-Cacho et al., 2016; Martinache et al., 2018; Kneissl et al., 2018).
At the same time, a small minority of 15 of 228 sources remained isolated, while also meeting additional flux density thresholds of mJy and/or mJy. These sources show signatures of individual DSFGs that are boosted in brightness as a result of strong lensing. Of these, 11 sources could be followed-up at higher resolution using observing facilities from the northern hemisphere. Spectroscopic measurements of the lens and source redshifts, and identification of giant arc structures, strengthen the lensing interpretation (solid red disks in Figure 1, Cañameras et al., 2015; Nesvadba et al., 2016; Cañameras et al., 2017a, b).
The Harrington et al. (2016) sample (black-and-red-dashed circles) is closely related to the (Cañameras et al., 2015) sample. Their selection also relies on color using a combination of Planck and Herschel, yet the intersection is incomplete owing to the use of different Planck catalogs. Harrington et al. (2016) select sources by cross correlating Herschel/SPIRE with: Planck PCCS (6 candidates), Planck HerMes (1 candidate), and Planck HerS-82 (1 candidate). The selection of the Planck/Herschel sample (Cañameras et al., 2015) was made by applying color criteria to: Planck PCCS and Herschel/SPIRE (6 candidates), and to Planck OT2 and Herschel/SPIRE (five candidates). In sum, 3 of 8 of the Harrington et al. (2016) lensed DSFGs are new.
|Lensing Field||Exp. (s)||Exp. (s)|
|PLCK G145.2+50.9 (G145)||2808||2736|
|PLCK G244.8+54.9 (G244)||2592||2484|
|PLCK G165.7+67.0 (G165)||2664||2556|
|PLCK G045.1+61.1 (G045)||2556||2556|
|PLCK G080.2+49.8 (G080)||2664||2664|
|PLCK G092.5+42.9 (G092)||2808||2736|
In sum, there is a tendency for Planck/Herschel selected sources to have higher flux densities and larger Einstein radii than those drawn from the literature. The cluster scale of the lens may partially explain this difference, in that a larger magnification factor () can be achieved, especially in the case of an Einstein ring such that , where is the mass of the lens. The wider areal coverage of a factor of 10 relative to the SPT and a factor of 100 or more relative to H-ATLAS, HerMES and Hers82 surveys also helps by allowing to set higher flux density thresholds resulting in the identification of larger lenses in some cases.
3 Observations and Reduction
We present new observations using HST/WFC3-IR for the six fields in our sample. We present also new observations covering the G165 field using LBT/LUCI + ARGOS, Spitzer/IRAC, Gemini/GMOS, and MMT/Hectospec.
3.1 Hst Observations
We obtained imaging of six Planck/Herschel selected fields between December 2015 and July 2016 with the HST Wide Field Camera 3 IR detector (WFC3-IR) in Cycle 23 (GO-14233, 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 comprised of one orbit each in the and filters. See Table 1 for the observing details.
The WFC3/IR images are re-drizzled 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 and , respectively. The results of re-drizzling the data in each case show improvements in image quality over the pipeline products of up to 10%. The final reduced images reach comparable depths to the CLASH clusters. For one representative case, G165, we compute 10 limiting magnitudes of 26.9 mag and 26.2 mag for point sources inside 04 apertures. We find that the image depth and bandwidth 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.
The WFC3 images are used as detection images for the matched aperture photometry in both bands. We custom-built our own code to cope with the unusual morphologies peculiar to arcs in the central regions of massive lensing clusters. We detect sources by applying a -clipping algorithm with respect to the local background RMS values. The local background, in turn, is estimated following a similar approach as in SExtractor (Bertin & Arnouts, 1996). Briefly, the image is divided into patches of pixels, with the background in each patch represented by the -clipped median. The local background is then estimated by a smooth spline interpolation over these patches. To ensure robust detection of objects, we smooth the image with a Gaussian filter of FWHM 2. Objects are de-blended 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 semi-major/minor axis sizes at 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 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 . In three fields, G145, G045, and G080, the DSFG arclet family members are too faint and/or blended with the halos of bright cluster members near in projection to measure a flux. In these cases, an upper limit on their fluxes is reported. In Table 2 we present the photometric catalog of the lensed DSFGs for our sample. The columns are: Arc ID, RA (J2000), DEC (J2000), and mag, the magnification factor of the lensed DSFG as measured by our mass-traces-light lens model, the effective Einstein radius in arcseconds as measured from our lens model, the redshift of the lens, and the redshift of the lensed source.
3.2 LBT Observations
We acquired imaging of G165 in -band using the LBT Advanced Rayleigh Ground layer adaptive Optics System (ARGOS) during instrument commissioning time in December 2016 (Rabien et al. 2018). ARGOS corrects ground-layer distortions in the imaging of the two 8.4-m apertures using two 3-beam constellation lasers as guide stars that are fixed to each aperture. The ARGOS instrumentation operates through the LUCI imager and multi-slit spectrometer. High-quality corrections of up to FWHM 025 in -band are achievable across a large field of view () at a native pixel scale of 012 pix. We acquired LBT/LUCI + ARGOS data in monocular mode on two separate nights: 46 min of observation using LUCI2 on 9 December and 42 min using LUCI1 on 15 December. 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, due 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.
|Arc ID||RA||DEC||Magnification||Lens Size||Spectroscopic Redshift|
|(J2000)||(J2000)||(AB mag)||(AB mag)||()||()|
Random dithers of up to 40 are imposed 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 pix, 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 designed our own reduction pipeline so that will be optimized to ensure high flatness across the chip and to maximize the signal-to-noise 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 to construct master sky-frames taken from neighboring exposures, which are then scaled to the background level of each object frame prior to the subtraction.
We designate each dither pointing “” as the coaddition of 24 individual object frames in s exposures, all taken the same position (120 s total science time) plus 0 s readout time owing to non-destructive readouts. The 5 s exposure was chosen to be small to avoid persistence and non-linearity 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 min including other 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 5-pass, 3- clipped median value111When computing the sigma-clipped statistics of an image, we cut the borders by 300 pixels to minimize the bias due to the hot/cold edges of infrared detectors. to obtain the mean image of these “normalized” object frames. As a last step, we scale this new running master background frame to the 3- clipped median of this th dither pointing to match the sky-background level at the exact time of the exposure. Our background-subtracted dither pointings yield the “1st stage” result (Figure 3).
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 “3rd Stage” result is obtained by performing another iteration of the “2nd Stage” result. To assess image quality after each reduction stage, we compute the background RMS values inside of seven test boxes of size pixels located in regions isolated from bright sources. We find the background RMS to decrease on average by 9 % following stage one, and to converge to the 1% level following stage two (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 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. We then stacked the sky-subtracted and flat-fielded object frames to produce our final data product. We report a mean -band FWHM of 053 for the 9 Dec 2016 run (LUCI2), and 029 for the 15 Dec 2016 run (LUCI1). In all, for the 9 Dec 2016 and the 15 Dec 2016 runs, respectively, we reach a 10 limiting magnitudes of 22.6 mag and 23.5 mag inside apertures of 4 FWHM. We do not combine the final images from the two different detectors as the 15 Dec 2016 data has higher 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 §4.1.
Dozens of arcs appear in this high spatial resolution -band image, which we use in combination with our HST data to make identifications of single galaxy images that appear in multiple positions in the image plane, or “arclet families.” The exquisite quality of our LBT/LUCI + ARGOS images can be seen when combined side-by-side with our HST images as in Figure 5. For more details, see Rabien et al. (2018).
3.3 Spitzer Observations
We acquired imaging in the G165 field on 2 February 2016 using the Spitzer InfraRed Camera (IRAC) in the 3.6 m and 4.5 m 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 seconds 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 full data set of this entire program will appear in an upcoming paper (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 m IRAC mosaic of this field (right panel). The doubly-imaged DSFG, G165_DSFG_1a and G165_DSFG_1b, is strongly-detected in both Spitzer/IRAC channels ( and ).
3.4 MMT Observations
We obtained spectroscopy in the field of G165 on 14 Feb 2015 using MMT/Hectospec (Fabricant et al., 2013), as a part of a larger program (2015A; PI: Frye). Hectospec is a multi-fiber 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 grooves mm grism, which covers a wavelength range of 3700 9150 Å at a dispersion of 1.21 Å pixel. 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 near infrared (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. The observations comprised 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 relatively bright magnitudes of the targets of - 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:
(https://www.mmto.org/node/536). 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 a HeNeAr lamp exposure, as well as the positions of prominent night-sky lines. We coadded the individual exposures to yield the final reduced spectra. 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.
Secure spectroscopic measurements are made for 19 objects, which we define as the high significance detection of two or more spectral features (2 level in the continuum). Our catalog results in measurements for five new cluster members with = 0.326 - 0.376, and eleven new sources with redshifts 0.388 0.622. Three galaxies have MMT/Hectospec redshifts that place them in the foreground. See §4.2 for additional details and the redshift catalog.
3.5 Gemini Observations
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 27 April, 2016. We selected the B600 line mm 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. 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.222IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. 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 switched to using a pipeline written in IDL by one of us (BLF). The IDL pipeline includes the tasks mentioned below and is discussed elsewhere (Frye et al., 2002, 2007, 2008). Briefly, the IDL pipeline avoids re-pixelization by identifying the flexure-induced instrumental curvature imprinted onto the slitlet edges between the 2D spectra. This curvature amounts to 1-3 pixel shifts from 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 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 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 , and 18 new lensed sources with . Five galaxies have Gemini/GMOS redshifts that place them in the foreground of the lens.
4 Analysis and Results for G165
We describe our algorithms for performing the matched photometry for the HST plus LBT imaging. We then analyze the combined results of the MMT, Gemini, and archival ground-based spectroscopy.
4.1 The Photometry
To include the LBT/LUCI + ARGOS data into our catalog alongside the HST photometry, we first translate the central locations of our photometric apertures defined by the image onto the -band using the WCS information. Although the FWHM resolution of our LUCI1 -band data (29) is higher than that of our two HST bands (022 and 018 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 opted to conduct -band photometry separately for LUCI1 and LUCI2 images, and only then to compute the aperture fluxes by applying an inverse variance-weighted mean of the two values.
As the photometric depth at is shallower than for HST data, the aperture fluxes for some sources and arclets fall below their 1- uncertainties. In such cases, we report the 10 detection limit of the aperture fluxes. Table 3 gives the complete photometric catalog for all eleven arclet families. The columns are: Arc ID, RA(̃J2000), DEC(̃J2000), mag, mag and mag. The lensed DSFG, G165_DSFG_1a, has = 23.0, = 22.2, and = 18.9, bright enough to make ground-based spectroscopic follow-up feasible.
4.2 The Spectroscopy: G165 Cluster Members
The catalog for all 62 objects in the G165 field with measured redshifts is given in Table 4. The columns are: Source ID, RA (J2000), DEC (J2000), redshift (), Reference (MMT/Hectospec: H; Gemini/GMOS: G, or SDSS: S), SDSS mag, mag, and mag. Only objects with secure redshifts appear in the table, i.e., we require that two or more spectroscopic features be detected at the 2 level relative to the continuum In the case of a single emission line, we require that it be detected blueward of rest-frame H, and also show a continuum break.
In total, we now 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 remaining three cluster members are drawn from the literature (SDSS, DR13). We specify cluster membership by requiring the redshifts to be in the range 0.326 0.376, equating to 3 with respect to the mean of . Five galaxies with spectroscopic redshifts extending outside of this range (0.388 0.399) are not included in this set. This group of more distant objects have a mean redshift of =0.391 and a velocity dispersion of 1600 km s, making them members of a potential background galaxy group.
The cluster members in common with the smaller HST field, and with 20 mag, all fall reasonably well onto the red sequence of the color-magnitude diagram (CMD; see §B.1 in the Appendix). The velocity dispersion based on all the cluster members is = 2,600 50 km s, equating to a large dynamical mass of M within 1 Mpc. If we restrict the angular extent to match the scale of our HST observations of = 50 or 250 kpc, then 13 cluster members are removed. The velocity dispersion for this smaller galaxy set is = 1,600 km s, equating again to a large mass, M. Note that this mass may be biased upward as a result of a line-of-sight arrangement of mass (see §6.1 for a comparison of the various mass estimates).
The uncertainties are obtained by a bootstrapping technique, in which we compute the velocity dispersion of all the combinations of data sets formed by extracting one source and then sampling by replacement. We take the bootstrap uncertainty to be the 14% and 86% confidence levels. The cluster separates out naturally into two main mass concentrations, which we refer to as the Northeast (NE) and Southwest (SW) regions. We take the cluster center to be situated at the center of this bimodal mass, with a positional uncertainty that depends on the relative masses. Given that each of the two mass regions produce similar numbers of arcs and arclet families, conservatively we expect the mass ratio to be . 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 radial and velocity structure of the cluster.
The value for the dynamical mass within the cluster core is relatively common for massive clusters (Girardi et al., 1993), and at the same time is higher than the mean value for CLASH clusters by a factor of three (Siegel et al., 2016). Our values for and hence also for are potentially inflated owing to the likely presence of radial substructure in the line-of-sight direction. We return to the discussion of biases in the determination of the dynamical mass in §6.1.
5 Strong Lens Modeling
5.1 The Approach
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 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, 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 our LTM model, the lensing galaxies are assigned a power law mass density distribution scaled in proportion to their galaxy 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 is also a free parameter of the model, and then normalized (to a specific source redshift), which adds a fourth free parameter to the model. 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 exquisite spatial resolution of HST makes feasible the designation of arclet families based on morphology and color. By good fortune, the HST images show obvious axes of symmetry superimposed onto the field (see 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 counter-images, the strong lensing model also has the predictive power to locate new image counterparts which can be searched for in the data to iteratively improve on the model result. As spectroscopic redshifts are not available for every arclet family, some redshifts may be left as free parameters to be optimized in the minimization of the model. In such cases, we typically assume a redshift prior of =2 - 3 to align approximately with the peak in the star-formation rate density (Madau & Dickinson, 2014). The best-fit model and errors are optimized through a Monte-Carlo Markov Chain using thousands of steps.
The lens model for the G165 cluster field is discussed in detail below, and a lensing analysis for the other five fields appears in §B.1 of the Appendix. We emphasize that all arclet families discovered in this study are supported by our physical LTM model. The lensed DSFG spectroscopic redshifts and other relevant information can be found in Table 2 and references therein.
Our HST image is rich with giant arcs and arclet families. The presence of giant arcs, and 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, 2016; Cañameras et al., 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 (RA, DEC) = (11:27:14.731,+42:28:22.56). By inputting the positions and brightnesses of the cluster members into our LTM lensing algorithm we construct a mass map that is constrained by the arclet family information. Our model 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 7. Postage stamp images of the arclet family members appear in Figure 8 organized by family name. Below we give a description of each of the 11 unique arclet families.
G165_DSFG_1 (Arcs 1a, 1b) Arc 1a is the NIR counterpart of the lensed DSFG at = 2.2 detected in the submillimeter data set (Cañameras et al., 2015). This giant arc, which orthogonally bridges the critical curve, has a NIR angular extent of 5 Our model estimates for Arc 1a to be a merging image with a high areal magnification factor of 30 that varies along the long axis of the arc. A counter-image is predicted which is detected only in our redder LBT/LUCI + ARGOS -band image at the model-predicted location. A bright image at the exact model-predicted location is also seen in our Spitzer/IRAC imaging data. We designate this arc as the counter-image G165_DSFG_1b (see Figure 5). Interestingly, while the - color is consistent between the two images, the - color differs by a large 2.6 mag. This color difference is owing 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 an arc that is merging. As such, the background source crosses a cluster caustic such that G165_DSFG_1a represents only a region (and only a portion of the starlight) of that background source, while 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 -band magnitudes for each of the three arcs of 18.5 mag, making them also excellent sources for follow-up spectroscopy to measure the redshift. Here we leave the redshift to be optimized in the modeling, with a most likely prior in the range of = 2 - 3. The bluer arclet trio that make up Arcs 8, which are situated near in projection, are undetected at . Arcs 2a & 2b and Arcs 8a & 8b fold about an axis of symmetry, as do Arcs 7a & 7b and Arcs 10a & 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 & 6b are compact arcs which are consistent with an interpretation as a background spheroidal galaxy. These arcs 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 & 4b present more extended morphologies. Coincident with Arcs 4a & 4b, the bright family members Arcs 3a & 3b describe a fold arc conjoined at the axis point. The third image of each of these families, Arcs 3c, 4c, and 6c, appear at an an angular separation of 14 This set of third images for each family retains similar colors as well as 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 & 5b are two merging images folded about the critical curve. Meanwhile, the dashed circle labeled as “5c?” marks the position of a candidate counter-image that awaits confirmation pending additional model constraints.
G165_7a,7b,7c (Arcs 7a, 7b, 7c); G165_10a,10b (Arcs 10a, 10b) Arcs 7a & 7b and Arcs 10a & 10b project onto an arc-like structure that is parallel to Arcs 2a, 2b, and 2c. Arcs 7a & 7b are especially red and low in surface brightness. The counter-image which we designate as Arc 7c appears southward at the model-predicted location. The candidate counter-image labeled as “10c?” appears near to its expected location but at a different color and so 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 & 9b are split by an axis of symmetry. Arc 9c appears at the model-predicted location at an angular separation of 10 Note two other candidate counter-images are marked in Figure 7 on the opposite side of the gravitational potential, which await confirmation as additional model constraints become available.
G165_11a,11b,11c (Arcs 11a, 11b, 11c) The blue Arcs 11a & 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 15 at = 2.2 and 17 at = 9. By integrating up the mass surface density, we measure a lensing mass of M within a 250 kpc radius. We refer to §6 for independent measurements of the mass and estimates of the lensing strength. Our lens model is consistent with that of the nonparametric Weak and Strong Lensing Analysis Package (WSLAP) model of Diego et al. (2007). A detailed comparison of the two models especially in light of additional model constraints will appear in an upcoming paper (Pascale et al. 2018, in preparation). Note given the significant visibility of both G165_DSFG_1a and G165_DSFG_1b in the -band and Spitzer/IRAC, the James Webb Space Telescope (JWST) resolution and sensitivity will be needed at 1 - 4 m to significantly refine these models.
6.1 The Mass of G165
We recount the estimate the lensing mass from our strong lensing model. We then make two independent estimates of the lens mass from our spectroscopy.
6.1.1 Lensing mass
We measure a lensing mass of M within 250 kpc by applying the constraints imposed by the eleven arclet families (§4.2). Of these, we have spectroscopic confirmation only for G165_DSFG_1a of =2.2357 (Harrington et al., 2016). We choose to allow the redshifts of other arclet families to vary as free parameters with values of = 2 - 3. While the approach works reasonably well in that it yields accurate model predictions of the counter-images, nevertheless, the lack of redshifts is non-ideal. This is because uncertainties in the lensed galaxy redshifts translate into uncertainties on the normalization of the lens model, which in turn lead to changes in the value for the total mass of dark plus visible matter. Additional spectroscopy of arclet families is needed in this field. We find the mass density to fall off rapidly beyond 250 kpc, and to reach M within 1 Mpc.
6.1.2 Dynamical mass
Our value for the dynamical mass is a factor of 3.5 higher than that of the lensing mass at a fixed radius of 250 kpc. At the same time, the redshifts of only five cluster members enter into the computation (compared to 18 cluster members extending out to the virial radius). We find that the bias imposed by the small numbers is made evident in the choice of the aperture size when estimating the velocity dispersion, and hence on the enclosed mass. For example, for an aperture of 103 or 0.5 Mpc, we compute a velocity dispersion for the six cluster members of = 1600 200 km s and a corresponding dynamical mass of M. This value is unchanged from the dynamical mass contained within 250 kpc. If we now push the aperture size out by only another 10 to 300 kpc, the addition of the two cluster members skews the value for the velocity dispersion of the cluster members upward to = 2600 50 km s, equating to M. This amounts to a factor of three difference in mass from the value measured within 250 kpc. As the true velocity dispersion should not correlate with a change in aperture size in the far-field (Girardi et al., 1993), our mass value is uncertain based on the radial velocities of the cluster members. We infer from this that our information on the cluster is redshift-limited. In general, it is expected that 10 - 20 spectroscopic redshifts of cluster members are needed to obtain a robust value for the velocity dispersion (i. e., Girardi et al., 1993).
It is natural to ask if the velocity structure may be skewed from a spherical distribution, especially given the obvious bimodal distribution of the cluster members into a northeastern (NE) and a southwestern (SW) region (see Figures 7 and 9). It is useful to introduce a “bifurcation” line drawn normal to the line connecting the NE and the SW regions at its mid-point. We plot the projected distance of the cluster members residing in the NE and SW regions relative to this bifurcation line as a function of the relative radial velocity in Figure 9. We find that the two cluster members with the largest projected distances from the bifurcation line of 800 and 1050 km s also have some of the highest negative relative velocities (two green hollow squares). These two cluster members are two of only three objects in our spectroscopic sample that show nebular emission lines indicative of ongoing star formation. It is tempting to ascribe this behavior to that of galaxies situated behind the cluster that are falling into the gravitational potential well.
We find the trend that the cluster members situated in the NE half are preferentially redshifted relative to the SW half. This results in an elongation of the velocity structure. If true, then the implication is that the cluster velocity dispersion obtained from this non-spherical mass distribution is inflated relative to its true value. Additional spectroscopy is needed to fill in the sparse redshift sampling of the cluster members to obtain a larger, more representative set of cluster members out to the far-field. This discussion relates also to the question of cluster gas pressure, which is given in §6.3.
6.1.3 Caustic mass
We have spectroscopy for seventeen galaxies that reside within 5000 km s from the mean cluster redshift of =0.351. This redshift information provides the means 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 as a function of line-of-sight velocity with respect to the cluster median redshift ). On the assumption of a virialized cluster, this distribution resembles the bell of a trumpet (with the spread in increasing at low ), 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 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 1.5 is within a projected distance of , where is the velocity dispersion (Jaffé et al., 2015). Indeed, the vast majority of cluster members (black dots in Figure 10), fits well within this radius (grey shaded region, Figure 10). 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 . In practice, we impose the condition of spherical symmetry by rewriting this density threshold into a symmetric version about the line. To do this, we check the absolute values of 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 = 0 line to construct the “tuning fork” shape (green contour). The amplitude of the caustic is then related to the cluster mass such that .
By applying this estimator, we measure a mass of M within 0.8 Mpc. The uncertainty on this value is derived by a “jacknife” 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 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 value is a factor of 5 higher than the value for the lensing mass extrapolated out to 1 Mpc, and a factor of 3 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 §6.1), then this value will be an overestimate.
In a recent paper, Hayashi et al. (2017) point out that new cluster members undergoing infall show high line-of-sight velocities at all radii. This is potentially insightful for the G165 field, for which there is a bimodal segregation of cluster members. Most of our spectroscopy of the cluster members show the features of red elliptical galaxies as expected for the central region of a galaxy cluster. At the same time, the two galaxies with the highest velocities of and 1750 km s are also two of only three galaxies showing nebular emission line features (magenta diamond-shaped symbols) indicative of recent star formation. This finding of higher star formation in the high velocity outliers is consistent with the picture that these two objects are infalling members, with star formation potentially induced by interactions with other cluster members.
6.2 G165 as a Lens
We compare the lensing strength of G165 with that of another massive lensing cluster at a similar lens redshift, the Hubble Frontier Fields cluster Abell 2744 (HFFs; PI: J. Lotz, GO-13495). Abell 2744 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 5- limits in each filter of 29 mag (Mahler et al., 2018). These limits are 2 and 3 AB mag deeper than the 10- limiting magnitude for G165 for the and filters, respectively (see §3.1). 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 Abell 2744 is from Zitrin et al. (2014). We show the lens models in two left-most panels in Figure 11. We find in both cases a similar elongated shape and similar effective critical curve size of 15 for the two fields. 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 objects (right panel in Figure 11).
G165 is an ideal lens through which to investigate high- objects ( = 9 - 12). This owes in part to the relatively low redshift of the lens plane of = 0.351 for which the level of the intra-cluster light (ICL) contamination at the NIR wavelengths corresponding to the Lyman-break for 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. On imaging, the lens size is ideal for JWST/NIRCam observations as the lens fills (but does not overfill) the field of view out to 2 - 3 times its Einstein radius. Note that for relatively shallow exposures typical of a JWST short program reaching limiting fluxes of 27 mag, JWST will not have an advantage over HST at 1 - 1.6 m. For such cases, the improvement of JWST will come from imaging at the longer wavelengths ( 1.6m), which enable robust detections of the stellar continuum of any new high redshift galaxy candidates situated behind lensing clusters.
We emphasize that this cluster is an excellent candidate to monitor caustic crossing events. Stars from the ICL (see Mihos, 2016, and reference therein) are the primary obstacles to detect bright caustic crossing events, since the ICL limits the maximum magnification factors to 10,000. When these microlenses are not present, the maximum magnification can reach factors of 10, allowing us to see the effects of the much more numerous (but fainter) and smaller stars. The ICL at the position of G165_DSFG_1a is small but still considerable. Deep imaging at optical wavelengths bluer than the cluster member starlight will yield a constraint on the colors that can be converted into an estimated stellar mass per unit area that can come from the ICL.
6.3 The G165 Cluster Gas Pressure
Given our different 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 for 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 most a low luminosity X-ray source with an upper limit on the flux computed from the RASS diffuse map of counts s arcmin. 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 which may represent a weak detection of intercluster gas, or it may be noise given the detection is only at the 1-2 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. As DSFG_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 to 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. This division of mass is strengthened by our glimpses into the velocity structure, in which the cluster members show a velocity gradient between the SW and NE sides (see Figure 9). There are examples of post-mergers that produce significant enhancements of X-ray flux such as the well-studied Bullet cluster (Bradač et al., 2006; Clowe et al., 2006), and the “El Gordo” cluster (Menanteau et al., 2012). 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 as well as the X-ray emission hence reducing the SZ decrementȦt the same time, the surface mass densities integrated along the line-of-sight are still supercritical to strong lensing effects. Additional spectroscopy of cluster members is needed to test the hypothesis that cluster orientation explains the low inferred cluster gas pressure.
Searching wide-field imaging data sets for giant arcs is now fairly common, yet conducting searches for unresolved giant arcs at submillimeter wavelengths is still relatively rare. We obtained HST WFC3-NIR imaging of the fields of six lensed DSFGs selected in a novel search by their rest-frame FIR color and compactness using Planck/Herschel data. We conduct a more detailed analysis of the G165 field which shows spectacular examples of giant arcs and arclet families. We find:
Each of our six sample fields shows the NIR counterpart of the strongly-lensed DSFG. In four fields, the DSFG image appears in more than one location in the image plane as an arclet family at HST resolution (G165, G045, G145 and G080).
We use the LTM approach to construct a mass map in the fields for which there is at least one arclet family seen in our data (G165, G045, G145 and G080). For the cases without arclet families that are resolved in our data set (G092, G244), we still generate a -map through the galaxy brightnesses and orientations. For G165, we estimate a lensing mass of M within 250 kpc and an effective Einstein radius of 15 at = 2.2.
For G165 we identify eleven arclet families by their similar colors, morphologies and model predictions. Obvious axes of symmetry lend additional support to our arclet family designations. The lensed DSFG (G165_DSFG_1a) appears in the NIR as a red giant arc with an angular extent of 5 and magnification factor of 30. Its counter-image, G165_DSFG_1b is fainter, and detected only in our high resolution LBT/LUCI + ARGOS -band image and in our Spitzer/IRAC images. There is a - color difference between the two images that arises because G165_DSFG_1a is a merging image and so represents only a portion of that background source, while G165_DSFG_1b uncovers the entire background source.
For G165 we present ground-based spectroscopy using MMT/Hectospec and Gemini/GMOS. We measure 51 new redshifts, which augment the spectroscopic catalog of objects in this field by a factor of five. From these data we calculate a dynamical mass of M within 250 kpc. We also estimate a caustic mass for G165, which is M within 0.8 Mpc. These masses estimates are high, possibly due to the observed aspherical distribution of mass.
The lensing properties for G165 are not far different from those of other well-studied massive lensing clusters. In a counting simulation, for G165 we predict similar numbers of high redshift object detections to 9 as A2744, another well-studied lensing cluster with similar lens redshift and dark matter properties.
Based on the 18 spectroscopic redshifts of cluster members for G165, we find hints of a velocity gradient across the cluster. Such a line-of-sight orientation will dilute the intercluster gas below the ROSAT and Planck-SZ effect detection limits, while maintaining a high surface mass density integrated over the line-of-sight that amply suffices to explain the observed strong lensing effects.
Appendix A NIR Counterparts of Our Lensed DSFG Sample
We searched for the NIR counterparts of the lensed DSFG submillimeter sources. Using the submillimeter positions as a guide, we detect red and relatively-bright NIR counterparts for all six lensed DSFGs at the expected locations with respect to their positions in the submillimeter data (Figure 2, Cañameras et al., 2015). In all cases, the lensed DSFG images in the HST images stand out as the reddest sources in the field. Note these galaxy images are significantly magnified, even if their size is smaller than or equal to the instrumental resolution of HST. Despite their small angular extents in some cases, these lensed sources are still amongst the brightest DSFGs in the sky in the NIR due to their large estimated magnification factors.
In the G145, G165, G045 and G080 fields, we detect multiple images of a single background DSFG. For G145 and G080, we find that two of the images match up with peaks in the submillimeter (the “” symbols in Figure 2). In another field, G092, the NIR counterparts are also identified, yet show different morphologies despite their similar colors. These images are more likely to be two unrelated and possibly interacting DSFGs at a similar redshift (see §5).
For G244, we detect the submillimeter arc, but do not spatially resolve the Einstein ring structure, although two sets of arclet families are identified in this field using high resolution ALMA data (Cañameras et al., 2017a, b). Finally, for G165 we find that G165_DSFG_1a bridges the critical curve. We detect another red source at the model-predicted location of the counter-image, G165_DSFG_1b that is prominent in both Spitzer/IRAC channels (dashed circle in Figure 5). The colors between the two images are different, which was initially unexpected as lensing is achromatic. At the same time, G165_DSFG_1a is an arc that is merging with an image of itself. Here, the background source is crossing a cluster caustic, such that G165_DSFG_1a represents only a portion of that background source, while G165_DSFG_1b shows the entire source (see §5.2 for more details). The estimation of the strong lensing properties appears below.
Appendix B Lensing Analysis
We apply our well-tested LTM pipeline to the G045, G145, G092, G080 and G244 fields, while the lens model for G165 was already discussed in detail in §5.2. For each field, the red lensing galaxies populate a distinctive region of the CMD. Galaxies on this “red sequence” have similar colors because they have a similar redshift and share a roughly similar star formation history. The red sequence is easily established in each of the six fields (Figure 12), where the red star-shaped symbols denote the cluster members used in our model. To reduce the chances for contamination from foreground/background objects, we impose a conservative magnitude cut on our selection of lensing galaxy members in the range of = 20 - 22 mag, depending on the field. We have spectroscopic information on cluster members within the HST field-of-view in four clusters, G165, G045, G145, and G080, which aids further in their identification (Figure 12, gold-filled circles). The positions and brightnesses of the cluster members serve as inputs to the LTM model. We emphasize that all arclet families discovered in this study are supported by our physical LTM model. Note that the spectroscopic redshifts of the lenses, the lensed DSFGs, and other relevant information can be found in Table 2 and references therein.
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 which is =0.556, based on seven redshifts in the 3- clipped range drawn from our spectroscopy which will appear in a separate paper (Frye et al. 2018b, in preparation). Of these, the redshift for one cluster member is situated within the field of view of our HST data (gold-filled circles in Figure 12). The reference center for our analysis is the location of the lensed DSFG image at (RA, DEC) = (15:02:36.012, +29:20:50.51). Our lens model recovers both the image positions and angular separations of the counter-images with an rms 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 , respectively.
The positional centroids from the submillimeter image are indicated by the gold plus symbols 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, in turn, a third image that coincides with the image in the submillimeter, but which 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 0.837, which we take to define the lens plane. This value is based on four redshifts in the 3- clipped range drawn from our spectroscopy, which all fall within the HST field of view (gold-filled circles in Figure 12). This spectroscopy will appear in a separate paper (Frye et al. 2018b, in preparation). We note that there is no spectroscopic information available from the archives or other sources. The redshifts for the four lensing members are situated within the field-of-view of our HST data (gold-filled circles in Figure 12). The reference center for our analysis is the DSFG located at (RA, DEC) = (10:53:22.249,+60:51:43.93). Our lens model recovers both the image positions and angular separations of the counter-images with an RMS of 01. In turn, we estimate magnification factors of 120.5 and 50.5 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 which are not very near in projection to the critical curve (few arcseconds). Our model yields an effective Einstein radius of 10 at the redshift of the lensed DSFG.
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 vs. clumpy components of the two images (Figure 2, inset). The measured redshift of = 3.3 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 which induces the ultra-high star-formation rates of 1000 M yr 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 ( = 0.448 from SDSS DR 14). The reference center for our analysis is the location of the DSFG at (RA, DEC) = (16:09:17.842, 60:45:19.41). Even without an established arclet family, we construct a map of the surface mass density through the cluster brightnesses and orientations of the member galaxies (see Figure 13). By adopting our best-fit scenario that these are two singly-imaged lensed sources at a similar redshift, we compute high magnification factors of 20 for each image.
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 “” symbols and labels. We designate the two NIR counterparts that we detect in our HST imaging as G080_DSFG_1a and G080_DSFG_1b. These images are red, faint and low surface brightness features that are visible only upon smoothing the background image (see inset of Figure 2). Interestingly, there is 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 compute a redshift for the lens of = 0.670 that is based on ten redshifts in the 3- clipped range drawn from our spectroscopy in this field, which will appear in a separate paper (Frye et al. 2018b, in preparation). 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 12). The reference center for our analysis is the location of the lensed DSFG image at (RA, DEC) = (15:44:33.202, +50:23:43.53). Our lens model recovers both the image positions and angular separations of the counter-images with an rms 2.2 From this analysis we estimate high magnification factors of 20 for each of the two images. An effective Einstein radius of 7 is computed at the redshift of the lensed DSFG.
We confirm the NIR counterpart of the lensed DSFG as a red and spatially-extended image, although the spectacular 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 which is 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. The expected location of the DSFG ( = 3.0) is the reference center for our analysis at (RA, DEC) = (10:53:53.107, +05:56:18.44). Without arclet families we cannot construct a lens model for this field. Nevertheless, we are able to approximate the surface mass density relative to the critical value through the galaxy brightness and its orientation to yield a -map (Figure 13). Note that this field already has a published model based on the exquisite ALMA data (Cañameras et al., 2017a, b).
Appendix C Intrinsic Properties of the Lensed DSFGs
By our estimates, the image magnification factors of all the fields in our sample range from factors of 5 - 30 or more, making these objects not intrinsically luminous. For example, the six sources in our sample have submillimeter flux densities in the range of 330 - 1054 mJy (Cañameras et al., 2015), which equate to estimated unlensed flux densities corrected by their magnification factors from our lens models of 25 - 100 mJy which are more representative of the field DSFG population. We obtain rare spatially-resolved images of the lensed DSFG in some cases, which offers a unique and high resolution view into the complex morphologies of the star forming component. For the lensed DSFGs in G092 and G045 in particular, distinct stellar clumps are detected with magnification-corrected sizes of 300 pc, similar to that expected for giant H II regions and for high redshift intensely star forming galaxies (Förster Schreiber et al., 2011). For G165, the physical and kinematical properties of the clumps within the lensed DSFG are presented in Cañameras et al. (2018).
Importantly, G165_DSFG_1a is situated on the critical curve. This offers the opportunity to search for transient lensing events in the form of compact star forming clumps traversing the critical curve, which can yield higher magnifications than cluster lensing by factors of 200 or more (Kelly et al., 2018). Such approaches may offer a viable route to access first light sources with JWST (Windhorst et al., 2018), and to constrain the amount of compact dark matter (Diego et al., 2018). G165_DSFG_1a has a very high apparent (i.e., without correcting for lensing effects) star-formation rate of 17733 171 M yr (Cañameras et al., 2015, their Table 2). Corrected by the magnification factor from our model, this becomes 590 M yr. The corrected star-formation rate is also high, and is exactly the galaxy type in which one may expect to find bright stars that undergo caustic (or micro-caustic) crossings, as they can be magnified by factors of thousands. Given the fortuitous placement of G165_DSFG_1a and the intensity of the ICL, microlensing events should be relatively common in this field. Under these circumstances, G165 is a good candidate for frequent monitoring using JWST to search for caustic crossing events.
- Acebron et al. (2018) Acebron, A., Cibirka, N., Zitrin, A., et al. 2018, ApJ, 858, 42
- Allen et al. (2011) Allen, S. W., Evrard, A. E., & Mantz, A. B. 2011, ARA&A, 49, 409. arXiv:1103.4829
- Alpaslan et al. (2012) Alpaslan, M., Robotham, A. S. G., Driver, S., et al. 2012, MNRAS, 426, 2832
- Bahcall (1977) Bahcall, N. A. 1977, ARA&A, 15, 505
- Benson et al. (2013) Benson, B. A., de Haan, T., Dudley, J. P., et al. 2013, ApJ, 763, 147. arXiv:1112.5435
- Bertin & Arnouts (1996) Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393
- Blain (1999) Blain, A. W. 1999, MNRAS, 309, 955
- Bleem et al. (2015) Bleem, L. E., Stalder, B., de Haan, T., et al. 2015, ApJS, 216, 27
- Bradač et al. (2006) Bradač, M., Clowe, D., Gonzalez, A. H., et al. 2006, ApJ, 652, 937
- Broadhurst et al. (2000) Broadhurst, T., Huang, X., Frye, B., & Ellis, R. 2000, ApJ, 534, L15
- Broadhurst et al. (2005) Broadhurst, T., Benítez, N., Coe, D., et al. 2005, ApJ, 621, 53
- Bruch et al. (2010) Bruch, S., Donahue, M., Voit, G. M., Sun, M., & Conselice, C. J. 2010, ApJ, 724, 608
- Bussmann et al. (2013) Bussmann, R. S., Pérez-Fournon, I., Amber, S., et al. 2013, ApJ, 779, 25
- Cañameras et al. (2015) Cañameras, R., McKenzie, T., König, S., et al. 2015, A&A, 581, A105
- Cañameras (2016) Cañameras 2016, https://tel.archives-ouvertes.fr/tel-01416000
- Cañameras et al. (2017a) Cañameras, R., Nesvadba, N. P. H., Kneissl, R., et al. 2017a, A&A, 600, L3
- Cañameras et al. (2017b) Cañameras, R., Nesvadba, N., Kneissl, R., et al. 2017b, A&A, 604, A117
- Cañameras et al. (2018) —. 2018, A&A, submitted
- Calanog et al. (2014) Calanog, J. A., Fu, H., Cooray, A., et al. 2014, ApJ, 797, 138
- Carlstrom et al. (2011) Carlstrom, J. E., Ade, P. A. R., Aird, K. A., et al. 2011, PASP, 123, 568
- Casey et al. (2014) Casey, C. M., Narayanan, D., & Cooray, A. 2014, Phys. Rep., 541, 45
- Cibirka et al. (2018) Cibirka, N., Acebron, A., Zitrin, A., et al. 2018, arXiv:1803.09557, ApJ, submitted
- Clowe et al. (2006) Clowe, D., Bradač, M., Gonzalez, A. H., et al. 2006, ApJ, 648, L109
- Condon et al. (1995) Condon, J. J., Anderson, E., & Broderick, J. J. 1995, AJ, 109, 2318
- Diaferio (1999) Diaferio, A. 1999, MNRAS, 309, 610
- Diaferio & Geller (1997) Diaferio, A., & Geller, M. J. 1997, ApJ, 481, 633
- Díaz-Sánchez et al. (2017) Díaz-Sánchez, A., Iglesias-Groth, S., Rebolo, R., & Dannerbauer, H. 2017, ApJ, 843, L22
- Diego et al. (2007) Diego, J. M., Tegmark, M., Protopapas, P., & Sandvik, H. B. 2007, MNRAS, 375, 958
- Diego et al. (2018) Diego, J. M., Kaiser, N., Broadhurst, T., et al. 2018, ApJ, 857, 25
- Ebeling et al. (2007) Ebeling, H., Barrett, E., Donovan, D., et al. 2007, ApJ, 661, L33
- Ebeling et al. (2010) Ebeling, H., Edge, A. C., Mantz, A., et al. 2010, MNRAS, 407, 83
- Fabricant et al. (2013) Fabricant, D., Chilingarian, I., Hwang, H. S., et al. 2013, PASP, 125, 1362
- Finkelstein (2016) Finkelstein, S. L. 2016, PASA, 33, e037
- Flores-Cacho et al. (2016) Flores-Cacho, I., Pierini, D., Soucail, G., et al. 2016, A&A, 585, A54
- Förster Schreiber et al. (2011) Förster Schreiber, N. M., Shapley, A. E., Genzel, R., et al. 2011, ApJ, 739, 45
- Fowler et al. (2007) Fowler, J. W., Niemack, M. D., Dicker, S. R., et al. 2007, Appl. Opt., 46, 3444
- Fruchter & et al. (2010) Fruchter, A. S., & et al. 2010, in 2010 Space Telescope Science Institute Calibration Workshop, p. 382-387, 382–387
- Frye et al. (2002) Frye, B., Broadhurst, T., & Benítez, N. 2002, ApJ, 568, 558
- Frye et al. (2007) Frye, B. L., Coe, D., Bowen, D. V., et al. 2007, ApJ, 665, 921
- Frye et al. (2008) Frye, B. L., Bowen, D. V., Hurley, M., et al. 2008, ApJL, 685, L5
- Girardi et al. (1993) Girardi, M., Biviano, A., Giuricin, G., Mardirossian, F., & Mezzetti, M. 1993, ApJ, 404, 38
- Griffiths et al. (2018) Griffiths, A., Conselice, C. J., Alpaslan, M., et al. 2018, MNRAS, 475, 2853
- Harrington et al. (2016) Harrington, K. C., Yun, M. S., Cybulski, R., et al. 2016, MNRAS, 458, 4383
- Harris et al. (2012) Harris, A. I., Baker, A. J., Frayer, D. T., et al. 2012, ApJ, 752, 152
- Hasselfield et al. (2013) Hasselfield, M., Hilton, M., Marriage, T. A., et al. 2013, J. Cosmology Astropart. Phys, 7, 008
- Hayashi et al. (2017) Hayashi, M., Kodama, T., Kohno, K., et al. 2017, ApJ, 841, L21
- Jaffé et al. (2015) Jaffé, Y. L., Smith, R., Candlish, G. N., et al. 2015, MNRAS, 448, 1715
- Johnson et al. (2014) Johnson, T. L., Sharon, K., Bayliss, M. B., et al. 2014, ApJ, 797, 48
- Kelly et al. (2018) Kelly, P. L., Diego, J. M., Rodney, S., et al. 2018, Nature Astronomy, 2, 334
- Kneissl et al. (2018) Kneissl, R., Polletta, M. d. C., Martinache, C., et al. 2018, arXiv: 1804.06581, A&A, submitted
- Koester et al. (2007a) Koester, B. P., McKay, T. A., Annis, J., et al. 2007a, ApJ, 660, 221
- Koester et al. (2007b) —. 2007b, ApJ, 660, 239
- Lamarreet al. (2003) Lamarre, J. M., Puget, J. L., Bouchet, F., et al. 2003, New Ast, 47, 1017
- Madau & Dickinson (2014) Madau, P., & Dickinson, M. 2014, ARA&A, 52, 415
- Mahler et al. (2018) Mahler, G., Richard, J., Clément, B., et al. 2018, MNRAS, 473, 663
- Mantz et al. (2010) Mantz, A., Allen, S. W., Rapetti, D., & Ebeling, H. 2010, MNRAS, 406, 1759
- Martinache et al. (2018) Martinache, C., Rettura, A., Dole, H., et al. 2018, A&A, accepted
- Menanteau et al. (2012) Menanteau, F., Hughes, J. P., Sifón, C., et al. 2012, ApJ, 748, 7
- Mihos (2016) Mihos, J. C. 2016, in IAU Symposium, Vol. 317, The General Assembly of Galaxy Halos: Structure, Origin and Evolution, ed. A. Bragaglia, M. Arnaboldi, M. Rejkuba, & D. Romano, 27–34
- Mo & White (1996) Mo, H. J., & White, S. D. M. 1996, MNRAS, 282, 347, doi: 10.1093/mnras/282.2.347
- Nayyeri et al. (2016) Nayyeri, H., Keele, M., Cooray, A., et al. 2016, ApJ, 823, 17
- Negrello et al. (2017) Negrello, M., Amber, S., Amvrosiadis, A., et al. 2017, MNRAS, 465, 3558
- Nesvadba et al. (2016) Nesvadba, N., Kneissl, R., Cañameras, R., et al. 2016, A&A, 593, L2
- Planck Collaboration (2015) Planck Collaboration. 2015, A&A, 582, A30
- Planck Collaboration (2016) —. 2016, A&A, 596, A100
- Planck Collaboration et al. (2014) Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2014, A&A, 571, A20. arXiv:1303.5080
- Planck Collaboration et al. (2016a) —. 2016a, A&A, 594, A27
- Planck Collaboration et al. (2016b) Planck Collaboration, Adam, R., Ade, P. A. R., et al. 2016b, A&A, 594, A8
- Rabien et al. (2018) Rabien, S., Angel, R., Barl, L., et al. 2018, A&A, submitted
- Richard et al. (2014) Richard, J., Jauzac, M., Limousin, M., et al. 2014, MNRAS, 444, 268. arXiv:1405.3303
- Rosati et al. (1998) Rosati, P., Della Ceca, R., Norman, C., & Giacconi, R. 1998, ApJ, 492, L21
- Rozo et al. (2010) Rozo, E., Wechsler, R. H., Rykoff, E. S., et al. 2010, ApJ, 708, 645. arXiv:0902.3702
- Rykoff et al. (2014) Rykoff, E. S., Rozo, E., Busha, M. T., et al. 2014, ApJ, 785, 104
- Rykoff et al. (2016) Rykoff, E. S., Rozo, E., Hollowood, D., et al. 2016, ApJS, 224, 1
- Sehgal et al. (2011) Sehgal, N., Trac, H., Acquaviva, V., et al. 2011, ApJ, 732, 44
- Sehgal et al. (2013) Sehgal, N., Addison, G., Battaglia, N., et al. 2013, ApJ, 767, 38
- Serra et al. (2011) Serra, P., Amblard, A., Temi, P., et al. 2011, ApJ, 740, 22
- Siegel et al. (2016) Siegel, S. R., Sayers, J., Mahdavi, A., et al. 2016, arXiv: 1612.05377, ApJ, submitted
- Spilker et al. (2016) Spilker, J. S., Bezanson, R., Marrone, D. P., et al. 2016, ApJ, 832, 19
- The Astropy Collaboration et al. (2018) The Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, arXiv: 1801.02634
- van Dokkum (2001) van Dokkum, P. G. 2001, PASP, 113, 1420
- Vieira et al. (2010) Vieira, J. D., Crawford, T. M., Switzer, E. R., et al. 2010, ApJ, 719, 763
- Vieira et al. (2013) Vieira, J. D., Marrone, D. P., Chapman, S. C., et al. 2013, Nature, 495, 344
- Vikhlinin et al. (2009) Vikhlinin, A., Kravtsov, A. V., Burenin, R. A., et al. 2009, ApJ, 692, 1060
- Wardlow et al. (2013) Wardlow, J. L., Cooray, A., De Bernardis, F., et al. 2013, ApJ, 762, 59
- Weiß et al. (2013) Weiß, A., De Breuck, C., Marrone, D. P., et al. 2013, ApJ, 767, 88
- Windhorst et al. (2018) Windhorst, R. A., Timmes, F. X., Wyithe, J. S. B., et al. 2018, ApJS, 234, 41
- Zitrin et al. (2009) Zitrin, A., Broadhurst, T., Umetsu, K., et al. 2009, MNRAS, 396, 1985
- Zitrin et al. (2014) Zitrin, A., Zheng, W., Broadhurst, T., et al. 2014, ApJ, 793, L12
- Zitrin et al. (2015) Zitrin, A., Labbé, I., Belli, S., et al. 2015, ApJL, 810, L12