GEMINI/GMOS SPECTROSCOPY OF 26 STRONG-LENSING-SELECTED GALAXY CLUSTER CORES^*

The targeted strong-lensing clusters were initially identified in one of several visual searches for giant arcs in an exhaustive sample of red-sequence-selected (Gladders & Yee 2000) clusters in the SDSS and RCS-2 surveys. Our visual searches produced three distinct giant arc samples, each of which has different visual selection criteria. The SDSS "Visual" sample (M. D. Gladders et al. 2011, in preparation) is composed of candidate strong-lensing clusters that were identified in the relatively shallow SDSS survey imaging. We confirmed the lensing interpretation in follow-up g-band imaging on ∼2–4 m class telescopes. The SDSS "Blind" sample consists of strong-lensing clusters that were identified in follow-up g-band imaging of the most massive ∼200 clusters, as selected by the red sequence from the SDSS photometry (Hennawi et al. 2008). The RCS-2 giant arc sample (M. B. Bayliss et al. 2011, in preparation) is defined in the same way as the SDSS Visual sample, but uses imaging data that is ∼2 mag deeper than the SDSS, with a median seeing of ∼07, and therefore facilitates morphological classifications on par with the follow-up imaging of the SDSS giant arcs. See Gilbank et al. (2010) for a detailed description of the RCS-2 data.

We have adopted a naming convention for giant arcs discovered in the SDSS—Sloan Giant Arc Survey (SGAS) Jhhmmss+ddmmss (Koester et al. 2010)—and giant arcs discovered in the RCS-2—Red-Sequence Cluster Survey Giant Arc (RCSGA) Jhhmmss+ddmmss (e.g., Wuyts et al. 2010). These two surveys for giant arcs have produced hundreds of strong-lensing clusters, and we followed-up a subset of these systems spectroscopically. We observed a sample of 26 clusters with the Frederick C. Gillett Telescope (Gemini North) between 2008 February and 2010 June as part of Gemini programs GN-2008A-Q-25 and GN-2009A-Q-21. Some of our 26 target strong-lensing clusters have been previously identified as strong lenses in the literature: A1703, GHO 132029+315500, RXC J1327.0+0211, SDSS J1115+5319, SDSS J1446+3033, SDSS J1527+0652, SDSS J1531+3414, and SDSS J2111−0114 (Hennawi et al. 2008); SDSS J0957+0509, SDSS J1226+2152, SDSS J1621+0607, and SDSS J2238+1319 (Wen et al. 2009); SDSS J1209+2640 (Ofek et al. 2008); SDSS J1343+4155 (Diehl et al. 2009; Wen et al. 2009); SDSS J1038+4849 (Belokurov et al. 2009; Kubo et al. 2009); SDSS J2243−0935 (Horesh et al. 2010); and SDSS J0915+3826 (Bayliss et al. 2010). Several detailed studies of the strong-lensing properties of A1703 can be found in the literature (Limousin et al. 2008; Oguri et al. 2009; Richard et al. 2009, 2010). The remaining 9/26 of the clusters discussed in this paper are previously unpublished strong lenses.

Analyses of a subset of the Gemini spectroscopy presented here have been published in several recent papers. Oguri et al. (2009) conducted a weak-lensing analysis of SDSS J2111−0114, SDSS J1446+3033, SDSS J1531+3414, and A1703. Gemini spectroscopic redshifts of the clusters and lensed images were used as constraints in a joint strong plus weak-lensing analysis. Our more careful analysis of these clusters has revealed additional redshifts of candidate lensed background sources. Bayliss et al. published the discovery of two bright, strongly lensed Lyα emitting galaxies at z ∼ 5 in SDSS J1343+4155 and SDSS J0915+3826 in Bayliss et al. (2010). In addition, Koester et al. (2010) presented the discovery of two bright, strongly lensed Lyman break galaxies (LBG) at z ∼ 3 lensed by SDSS J1527+0652 and SDSS J1226+2152.

We obtained pre-imaging of 20 of the 26 clusters in gri with the Gemini Multi-Object Spectrograph (GMOS; Hook et al. 2004) in queue mode in order to facilitate mask design. The Gemini imaging data consist of 2 × 150 s dithered exposures, with one exposure at an initial pointing position for a given cluster, and the other exposure at a position corresponding to the "nod" in our planned spectroscopic observations (see Section 2.3). All GMOS images were taken with the detector binned 2 × 2 for a scale of 01454 pixel⁻¹. Gemini/GMOS-North imaging data were reduced using the Gemini IRAF⁶ package. The pre-imaging have approximate point source 3σ limiting magnitudes of g ≲ 25.5, r ≲ 25.8, and i ≲ 25.5. For four of the 26 clusters—SDSS J2111−0114, SDSSJ 1446+3033, SDSS J1531+3414, and A1703—we have only r-band pre-imaging from Gemini and rely on deep gri imaging from Subaru (Oguri et al. 2009) to determine color information for sources in these fields. Photometric catalogs for the 24 clusters with pre-imaging were derived from the available multi-band imaging data using object-finding and aperture photometry routines from the DAOPHOT Package. For the remaining two clusters—SDSS J0957+0509 and SDSS J1527+0562—we have g-band imaging from the 2.5 m Nordic Optical Telescope (NOT) on La Palma and the 3.5 m WIYN Telescope on Kitt Peak, respectively. The g-band data from NOT consist of 2 × 300 s exposures taken with the MOSaic CAmera (MOSCA), which is an array of four 2k × 2k CCDs. Data were taken binned 2 × 2 resulting in 0217 pixel⁻¹. The g-band data from WIYN are similar; we took 2 × 300 s exposures with the Orthogonal Parallel Transfer Imaging Camera (OPTIC), which is an array of two 2k × 4k CCDs. These data were unbinned for a scale of 014 pixel⁻¹. The deeper g-band images were used to place slits targeting the bright arcs manually, and photometric catalogs from the SDSS DR7 (Abazajian et al. 2009) were used to identify cluster member galaxies by their presence on the red sequence.

Spectroscopic masks for each cluster were designed using object positions and colors from the photometric catalogs. The highest priority slits were manually placed on candidate lensed background sources as identified by color and morphology, and then the mask was filled in with lower priority slits placed on red-sequence-selected cluster members with r_AB ⩽ 22.5 in the photometric catalogs. This flux limit corresponds to a luminosity limit of ∼0.1–0.6 L* for each cluster, depending on the cluster redshift.

All spectroscopic observations were carried out with GMOS using the custom slit masks described above. Spectra were taken using the macroscopic nod-and-shuffle (N&S) mode available on GMOS. The use of macroscopic N&S allows for small slits and increases the density of slits that we can place in the cores of the target clusters. We use a modified version of the standard macroscopic N&S mode wherein we shuffle the charge by one-third of the detector along the spatial axis, while nodding the telescope on the sky by one-sixth of the detector. A mask is designed to cover the central third of the detector that is effectively a combination of two "sub-masks," each of which primarily targets a region on the sky approximately one-sixth the size of the detector. With the nod distance set to one-sixth of the detector size, the targeted region on the sky is nodded from one spectroscopic sub-mask to the other, such that we collect science spectra for this region during 100% of the total exposure time of the observation. Our strategy avoids the 50% overheads that are necessary for a simple macroscopic band N&S observation by enabling us to design two independent masks covering the central sixth of the detector along the spatial axis. The two sub-masks are optimized to place slits on as many candidate strong-lensing features as possible, with slits often placed on the most prominent arcs in both sub-masks to gather data on those sources for the full exposure time of the observations. Additionally, the sub-masks can include slits targeting sources located in an area equal to the size of one-sixth of the detector to either side of the central region. These regions include red-sequence-selected cluster members that we use to fill in gaps in the slit mask after placing slits on all candidate strong-lensing features. Figure 1 shows the Gemini/GMOS r-band pre-imaging data for SDSS J1138+2754 with the N&S spectroscopic mask slits overplotted and each of the pointing and nod positions to illustrate our observing strategy.

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N&S offers several benefits that are especially advantageous for pursuing redshifts of candidate strongly lensed sources. First, N&S provides for better sky subtraction (Glazebrook & Bland-Hawthorn 2001; Abraham et al. 2004), especially at lower spectral resolutions, than traditional long-slit or multi-slit spectroscopy. Excellent sky subtraction over a large range of wavelengths is crucial for identifying galaxy redshifts at z ≳ 1.0, which often relies on spectral lines that are redshifted into the red (i.e., ∼7000–10000 Å) where sky lines are numerous. Second, a macroscopic N&S strategy allows us to cut slits matching the sizes of target sources, as small as 1'' × 1'' microslits, which can be densely packed into the cores of our strong-lensing clusters to target as many arcs, arclets, and cluster members as possible. Our modified N&S approach complements the size of the GMOS detector very nicely. The GMOS detector array is approximately ∼56 × 56 in size; this means that we can optimize slit placement in the central ∼1' of the target clusters, which corresponds well with the core regions probed by strong lensing.

All spectra taken as a part of the GN-2008A-Q-25 program used the R150_G5306 grating in first order with the detector binned 2 × 2, producing an average dispersion of 3.5 Å per image pixel and a six-pixel spectral resolution element. The resulting spectral FWHM is ∼940 km s⁻¹, corresponding to a spectral resolution, $R \equiv \frac{\lambda }{\delta \lambda } \simeq 320$, and covers a spectral range, Δλ ∼ 4000–9500 Å, with our highest sensitivity in the interval, Δλ ∼ 5500–9000 Å. Our effective spectral range is limited at both the blue and red ends by the sensitivity of both the GMOS CCDs and the transmission efficiency of the grating. The masks for GN-2008A-Q-25 spectroscopy were designed using only slitlets of 1'' × 1'', many of which could be placed along the longest arcs. The N&S cycle time for all 2008A spectra was 60 s.

Analysis of the GN-2008A-Q-25 spectra motivated us to change the instrumental setup for GN-2009A-Q-21 spectroscopy. We no longer restricted ourselves to only 1'' × 1'' microslits, but instead increased the spatial extent of our slits along the arcs and occasionally tilted them to better cover an arc or achieve optimal slit packing. All spectra taken in the GN-2009A-Q-21 program used the R400_G5305 grating in first order, in conjunction with the GG455_G0305 longpass filter, and with the detector binned by 2 in the spectra direction and unbinned spatially. This configuration produces a dispersion of 1.34 Å per (binned) spectral pixel and a spectral resolution of ∼310 km s⁻¹ or R ≃ 960 with a wavelength coverage, Δλ ∼ 4200 Å. The observed wavelength range for slits located near the centers of our masks is ∼5200–9400 Å. Given the performance of the GMOS CCDs at the very blue and red ends, we find that the R400_G5305 grating loses very little effective wavelength coverage compared with the R150_G5306 grating, while improving the quality of the N&S sky subtraction as well as our ability to measure reliable absorption line redshifts for arcs located in the redshift desert.

A persistent problem in our 2008A observations was systematics in the N&S sky subtraction caused by charge traps. The amount of trapped charge depends sensitively on the detector binning and the amount of charge shuffling (i.e., the N&S cycle length). After conducting experiments with dark frames we found that the detector binned by 2 in the spectral direction and unbinned spatially provided the best compromise between trapped charge and increased read noise. We also experimented with two different N&S cycle lengths, 60 s and 120 s, the former of which optimizes sky subtraction and the later of which minimizes the negative impact of charge traps. We obtained test observations for one of our masks with both cycle lengths and found that the quality of the N&S sky subtraction was not significantly diminished for the 120 s cycles, which we opted to use throughout the remainder of our 2009A observations.

Table 1 shows which targets were observed from Gemini North in 2008A and 2009A, along with the integration times for each mask. Sky subtraction of N&S data is achieved by simply differencing the two shuffled sections of the detector. All of our spectra were wavelength calibrated, extracted, stacked, flux normalized, and analyzed using a custom data reduction pipeline which we developed based on the XIDL⁷ and the SDSS idlspec2d⁸ software packages. We extract individual spectra and perform all stacking in one dimension using a rejection algorithm to exclude cosmic rays and hot pixels. Our masks were not observed at the parallactic angle, and we relied on archival standards in the GMOS data archive to determine the sensitivity function, thus our flux calibration is only approximate.

In addition to the Gemini/GMOS-North spectroscopy, we supplement our data set with cluster member redshift measurements made at the 3.5 m Astrophysical Research Consortium (ARC) Telescope at Apache Point Observatory in New Mexico, using the Dual Imaging Spectrograph (DIS) in long-slit mode. The APO+DIS observations were taken using the B400 and R300 gratings on the red and blue sides, respectively, and a 15 slit. Science exposures were accompanied by HeNeAr arc calibrations and quartz lamp flat-field exposures at the same orientation in order to minimize systematic errors due to instrument flexure. The resulting data were reduced, calibrated, sky-subtracted, extracted, and stacked using custom IDL scripts that incorporate procedures from the XIDL software package. All redshifts measured from the APO+DIS data came out of the red side spectra, which cover a wavelength range Δλ ≃ 5500–9500 Å at a dispersion of ∼2.3 Å pixel⁻¹, resulting in spectral resolution R ≃ 1100. We observed RCS2 J1055+5547 on the night of 2007 March 17 at two different orientations selected to simultaneously put 1–2 bright red-sequence-selected cluster member candidates and 1–2 arc candidates within the slit. At each orientation we collected 3 × 900 s integrations and from these data we measure redshifts for the Brightest Cluster Galaxy (BCG), which is also present in the SDSS DR7 spectroscopic catalog (Abazajian et al. 2009) as well as redshifts for two additional cluster members. On the night of 2008 June 3 we observed SDSS J1621+0607 at a single orientation with 3 × 1800 s integrations, from which we measure a redshift for the BCG.

All spectra were examined by eye and compared to a variety of spectral line lists spanning a broad rest-frame wavelength range. We assigned redshifts to individual spectra by identifying a set of lines at a common redshift, fitting a Gaussian profile to each line to identify the central wavelength for each line, and taking the mean redshift of the entire set of lines. Redshifts for cluster member galaxies are derived from at least three lines, the most commonly used of which are strong stellar photospheric lines that are characteristic of older stellar populations (e.g., Ca ii H&K λ3934, 3969, g-band λ4306, Mg i λ5169, 5174, 5185, and Na i λ5891, 5894, 5897). Redshifts for putative strongly lensed sources were measured in the same way as the cluster members, though the specific lines used vary significantly among the different lensed source spectra. A large majority of our strongly lensed sources are very blue in the available photometry, implying that they are actively forming stars. Given our spectral coverage we expect to observe one or more prominent emission lines (e.g., [O ii] λ3727, H-βλ4862, [O iii] λ4960, 5007, and H-αλ6563) for star-forming galaxies at z ≲ 1.5, with some slight variation from source to source depending on the limit in our red coverage for a given science slit. For strongly lensed sources at z ≳ 1.5 we must rely on rest-frame UV features to identify redshifts. In some cases we observe Lyα λ1216 in emission, accompanied by a break in the continuum, but for many sources we measure redshifts from systems of UV metal absorption lines, including but not limited to Mg ii λ2796, 2803, Fe ii λ2344, 2372, 2384, 2586, 2600, C iv λ1548, 1551, Si ii λ1260, 1527, and Si iv λ1394, 1403. Redshift solutions were also checked against spectral templates, namely, the Shapley et al. (2003) LBG composite spectrum and the Gemini Deep Deep Survey composite late-, intermediate-, and early-type spectra (Abraham et al. 2004).

Redshift errors result primarily from a combination of the uncertainty in our wavelength calibrations and the statistical uncertainty in the identification of line centers. The measured locations of bright sky lines in wavelength-calibrated data taken across different nights are stable within the calibration uncertainties discussed above, indicating that there are no systematic velocity offsets introduced in comparisons of data taken on different dates. Typical total redshift uncertainties in the case of high signal-to-noise data—both cluster member galaxies and background sources—are ±0.0007 for spectra taken with the R150 grating/2008A data and ±0.0003 for spectra taken with the R400 grating/2009A data. Lower signal-to-noise data, including approximately half of the spectra for strongly lensed sources, tend to have slightly larger uncertainties: as large as ±0.001 for R150/2008A spectra and ±0.0006 for R400/2009A spectra. We also note that redshifts for some of our background sources that are measured from only a few features in the rest-frame UV can often be subject to additional systematic uncertainty due to the inherent velocity offsets that are typically observed between absorption and emission features in star-forming galaxies at high redshift (e.g., Shapley et al. 2003).

Each redshift measurement falls into one of four classifications (0–3) which describe the confidence level of the redshift. Class 3 redshifts are the highest confidence measurements and are typically measured from systems of ⩾6 absorption and emission features. These redshift measurements are secure with essentially no chance of misinterpretation, and the large majority of the redshifts reported here are of this classification. Figure 2 shows examples of six class 3 spectra. Class 2 redshifts are medium-confidence measurements that are based on at least two high-significance lines and/or a larger number of low-significance features. The redshifts reported here as class 2 are very likely the real redshifts of the corresponding sources, but there is a small chance that any given class 2 redshift might have been misidentified. Two example class 2 spectra are shown in Figure 3. Class 1 redshifts are low-confidence measurements that were made using only a few low-significance spectral features and represent a "best-guess" redshift using the available spectral data along with color information in the pre-imaging data. Figure 4 shows two example class 1 spectra.

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Class 0 indicates a redshift failure for a particular slit; some objects labeled class 0 exhibit low signal-to-noise continuum flux but lack sufficiently strong lines or dominant features to facilitate a redshift measurement. Class 0 spectra correspond to objects that are good candidates to be strongly lensed background sources based on their color, location, and morphology that were targeted by our spectroscopic masks. We report all background source redshifts measured for each of our 26 strong-lensing clusters, with each redshift tied to a source on the sky by its foreground cluster name and a two character object label, where the first character of the label indicates a unique background source and the second character of the label indicates a slit placed on that background source. All cluster member galaxies and background sources with redshifts as well as class 0 candidate strongly lensed sources are presented in Table 4 with labels that correspond to the label markers in Figures 5–11. Figures 5–11 are color images of each lensing cluster field with the object labels overplotted to indicate the source locations. In many cases our spectroscopic masks had more slits than are indicated in the color images, but we combined spectra for slits that were directly adjacent to one another and those slits which contained spectra from different pieces of what is clearly the same extended source.

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In total our Gemini spectroscopy includes a total of 1126 science spectra on 26 different masks (≃43 slits per mask). In many cases there are multiple slits on a mask that target a single background lensed source. This occurs in some masks where we place slits on sources at both the pointing and nod positions to collect science spectra for 100% of our exposure time. Most masks have multiple slits placed on separate images of the same multiply imaged source, or multiple slits placed along different pieces of a continuous giant arc; this last case is demonstrated in the mask displayed in Figure 1. In addition to the Gemini/GMOS-North spectroscopy, we also present analysis of a few cluster member spectra obtained on the ARC 3.5 m telescope, with DIS. Redshifts from APO/DIS spectra were measured in the same way as the Gemini/GMOS redshifts. Combining all cluster member spectra results in a total of 262 spectroscopic cluster member redshifts. We supplement our own measurements with 26 cluster member redshifts from the SDSS DR7 spectroscopic catalog in order to characterize the dynamical properties of the strong-lensing clusters with an average sample size of 11 spectroscopic members per cluster.

From the slits placed on candidate strong-lensing features, we identify 126 spectra with redshifts that place them behind the foreground galaxy clusters and associate these spectra with 69 unique background galaxies, many of which are obviously strongly lensed and/or multiply imaged, and all of which are likely magnified significantly. We divide these 69 individual lensed background sources into three distinct samples: primary giant arcs, secondary strongly lensed sources, and tertiary background sources. Primary giant arcs are those giant arcs that were initially used to identify a given cluster as a strong lens in the SDSS imaging data. There is typically one primary giant arc per cluster lens, though some systems, such as SDSS J1038+4849 and SDSS J1446+3033, have multiple, distinct primary giant arcs that are visible in the SDSS survey data. Secondary strongly lensed sources are objects which either form arcs, or are multiply imaged, such that we identify them follow-up imaging but lack sufficient brightness and/or morphology to be identified as arcs in the raw SDSS survey imaging. Primary and secondary sources are likely magnified by factors of ≳10× (e.g., Richard et al. 2009; Bayliss et al. 2010; Koester et al. 2010). Tertiary background sources are sources or arclets that are located behind one of our cluster lens targets but which do not appear to be strongly lensed based on the available data. Tertiary background sources are likely magnified by anywhere between a few tens of percent and factors of a few due to their location near the core of the foreground cluster lenses (Smail et al. 2002).

Table 2 contains a list of all unique background sources with secure redshifts from GMOS spectroscopy. Sources are listed as either primary, secondary, or tertiary objects. Primary giant arcs are listed with measurements of the length-to-width (l/w) ratio, the average radial separation between the arc and the cluster center (R_arc), and the total integrated AB magnitudes in the g band, or in one of the r or i bands if a given arc has poor signal-to-noise in our g-band imaging data. We also report l/w ratio estimates and integrated AB magnitudes for secondary strongly lensed sources, and integrated AB magnitudes for tertiary sources. This table does not include any sources for which we do not have precise redshift measurements, and so the primary arcs around some clusters—SDSS J1028+1324, SDSS J1115+5319, SDSS J1152+0930, GHO 132029+315500, SDSS J1446+3414, and SDSS J1456+5702—do not appear in Table 2. Similarly there are dozens of putative secondary strongly lensed sources apparent in the GMOS pre-imaging that are not listed in Table 2 because the spectroscopy did not yield redshifts. Some arcs without precise redshifts are addressed in Bayliss et al. (2011) and have "redshift desert" constraints placed on the strongly lensed sources.

Table 2. Individual Lensed Sources

Cluster Core	Source Labela	Redshift	l/wb	Rarcc	AB Mag	Classificationd
SDSS J0851+3331	A	1.6926	16	23''	g = 21.88	Primary
SDSS J0851+3331	B	1.3454	6	...	g = 24.08	Secondary
SDSS J0851+3331	C	1.2539	...	...	g = 23.46	Tertiary
SDSS J0915+3826	A	1.501	8	12''	g = 22.60	Primary
SDSS J0915+3826	B	5.200	4	...	i = 23.34e	Secondary
SDSS J0915+3826	C	1.4358	...	...	g = 24.85	Tertiary
SDSS J0957+0509	A	1.8198	11	8''	g = 20.69	Primary
SDSS J0957+0509	B	1.0067	...	...	g = 22.79	Tertiary
SDSS J0957+0509	C	1.9259	...	...	g = 22.29	Tertiary
SDSS J1038+4849	A	2.198	14	12''	g = 21.24	Primary
SDSS J1038+4849	B	0.9657	12	11''	g = 21.28	Primary
SDSS J1038+4849	C	2.783	10	85	g = 22.48	Primary
SDSS J1038+4849	D	0.8020	8	...	r = 23.55	Secondary
RCS2 J1055+5547	A	1.2499	15	16''	g = 22.33	Primary
RCS2 J1055+5547	B	0.9359	3	...	g = 23.01	Secondary
RCS2 J1055+5547	C	0.7769	...	...	r = 21.31	Tertiary
SDSS J1115+5319	D	1.234	...	...	g = 24.63	Tertiary
SDSS J1138+2754	A	0.9089	7	9''	g = 21.44	Primary
SDSS J1138+2754	B	1.3335	17	...	g = 21.84	Secondary
SDSS J1138+2754	C	1.455	17	...	g = 23.65	Secondary
SDSS J1152+3313	A	2.491	13	85	g = 20.84	Primary
SDSS J1152+3313	B	4.1422	1f	...	r = 23.40	Secondary
SDSS J1152+0930	A	0.8933	5	...	g = 22.15	Secondary
SDSS J1152+0930	B	0.9760	...	...	g = 24.28	Tertiary
SDSS J1209+2640	A	1.018	21	11''	g = 21.04	Primary
SDSS J1209+2640	B	0.879	6	...	r = 23.45	Secondary
SDSS J1209+2640	C	3.949	7	...	r = 24.77	Secondary
SDSS J1226+2152	A	2.9233	12	12''	g = 21.61	Primary
SDSS J1226+2152	B	1.3358	...	...	r = 24.24	Tertiary
SDSS J1226+2152	C	0.7278	...	...	r = 23.70	Tertiary
SDSS J1226+2152	D	0.7718	...	...	r = 22.08	Tertiary
SDSS J1226+2152	E	0.7323	...	...	r = 23.64	Tertiary
SDSS J1226+2149	A	1.6045	8	20''	g = 22.44	Primary
SDSS J1226+2149	B	0.8012	3	...	g = 22.62	Secondary
SDSS J1226+2149	C	0.9134	7	...	g = 23.43	Secondary
SDSS J1226+2149	D	1.1353	...	...	g = 24.48	Tertiary
A1703	A	0.889	8	5''	g = 21.93	Primary
GHO 132029+315500	B	0.8473	4	...	r = 23.27	Secondary
GHO 132029+315500	C	1.1513	...	...	g = 24.16	Tertiary
GHO 132029+315500	D	0.8121	...	...	g = 24.34	Tertiary
RXC J1327.0+0211	A	0.991	8	10''	g = 20.73	Primary
RXC J1327.0+0211	B	1.476	...	...	g = 23.77	Tertiary
RXC J1327.0+0211	C	1.602	...	...	g = 23.10	Tertiary
SDSS J1343+4155	A	2.091	25	13''	g = 20.88	Primary
SDSS J1343+4155	B	4.994	2	...	i = 23.78e	Secondary
SDSS J1343+4155	C	1.2936	...	...	r = 24.60	Tertiary
SDSS J1343+4155	D	0.9516	...	...	g = 24.20	Tertiary
SDSS J1420+3955	A	2.161	7	22''	g = 21.85	Primary
SDSS J1420+3955	B	3.066	12	35''	g = 21.87	Primary
SDSS J1446+3033	A	1.006	...	...	g = 24.11	Tertiary
SDSS J1446+3033	B	0.579	...	...	g = 22.97	Tertiary
SDSS J1446+3033	C	1.441	...	...	g = 24.47	Tertiary
SDSS J1456+5702	B	0.8327	7	...	r = 22.54	Secondary
SDSS J1456+5702	C	1.141	...	...	g = 24.49	Tertiary
SDSS J1527+0652	A	2.760	10	17''	g = 20.90g	Primary
SDSS J1527+0652	B	1.283	...	...	r = 22.70	Tertiary
SDSS J1531+3414	A	1.096	9	11''	g = 22.32	Primary
SDSS J1531+3414	B	1.300	6	13''	g = 22.15	Primary
SDSS J1531+3414	C	1.027	...	...	g = 22.86	Tertiary
SDSS J1621+0607	A	4.134	8	16''	r = 22.28	Secondary
SDSS J1621+0607	B	1.1778	5	...	r = 21.21	Primary
SDSS J2111−1114	A	2.858	18	11''	g = 21.18	Primary
SDSS J2111−1114	B	1.476	...	...	g = 22.56	Tertiary
SDSS J2111−1114	C	1.152	...	...	g = 23.96	Tertiary
SDSS J2238+1319	A	0.724	15	10''	g = 21.73	Primary
SDSS J2238+1319	B	0.980	3	...	g = 24.22	Secondary
SDSS J2243−0935	A	2.091	12	10''	g = 21.31	Primary
SDSS J2243−0935	B	1.3202	4	...	g = 22.65	Tertiary
SDSS J2243−0935	C	0.7403	6	...	r = 23.20	Tertiary

Notes. ^aSource labels matching those in Figures 5–11 and Table 4. ^bLength-to-width ratios are all estimated from ground-based imaging with variable seeing. In the case of multiple arcs/images, the largest l/w ratio is given. ^cR_arc here is the mean distance from a giant arc to the BCG of the lensing cluster. ^dPrimary, secondary, or tertiary background source identification, as discussed in Section 3.1. ^eFrom Bayliss et al. (2010). ^fThis object has l/w = 1, but we spectroscopically confirm multiple images of the source separated by ∼13''. ^gFrom Koester et al. (2010).

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The magnitudes given in Table 2 are simple integrated aperture magnitudes of the brightest contiguous image or arc for a given background source, where apertures are drawn by eye to match the morphology of the arcs/sources. The photometry is calibrated relative to stars in the SDSS and are intended only to give a rough sense of the brightness for a given source. These magnitude measurements have typical errors of ∼±0.1 mag, and we emphasize that the aperture magnitudes can be misleading in some cases. For example, the large arc around SDSS J1456+5702 that covers an approximate area on the sky of ∼60–70''² (see Figure 10).

Results from spectroscopy of the 26 cluster lenses are summarized in Table 3. There are 18 clusters in our sample with N_spec ⩾ 10 spectroscopically confirmed cluster members which we take as the minimum number of cluster members that can produce a velocity dispersion estimate that is robust against large biases due to small sampling. The velocity dispersion of individual galaxies within galaxy clusters is a cluster mass observable that has a long history in astronomy (e.g., Smith 1936; Zwicky 1937) and remains a viable method for estimating the total masses of cluster by its dynamics. Estimates of the variance of poorly sampled distributions can be easily biased and require algorithms beyond the simple median and standard deviation. We use the bi-weight estimator of Beers et al. (1990) to determine the redshifts and velocity dispersions for our cluster sample and compute the errors on the velocity dispersion by calculating the bi-weight estimate of the dispersion for many bootstrapped realizations of the velocity data for each cluster and identifying the upper and lower 68% confidence intervals. Velocity histograms for the 18 strong-lensing clusters with N ⩾ 10 spectroscopic members are plotted in Figure 12, along with best-fit Gaussian models.

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Computing the dynamical mass from cluster member velocities requires some understanding of the relationship between the velocity dispersion of dark matter in the clusters and the velocity dispersion individual member galaxies, often parameterized as the velocity bias, b_v = σ_gal/σ_dm. Here, σ_gal and σ_dm are the one-dimensional velocity dispersions of member galaxies and dark matter particles, respectively. Measuring the velocity bias is difficult because it requires two independent mass estimates for a sample of clusters, one dynamical, and in reality all available mass observables are subject to significant systematics and errors. Studies of numerically simulated halos can also be used to predict what the velocity bias should be for a given population of halos in a given cosmology by identifying and tracking the velocities of "subhalos" within clusters, where the subhalos presumably host cluster member galaxies.

Efforts to make such predictions have produced estimates of the velocity bias in the range b_v ∼ 1.0–1.3 (Colín et al. 2000; Ghigna et al. 2000; Diemand et al. 2004; Faltenbacher et al. 2005). More recent work indicates that the way in which subhalos are tracked and defined in a simulation affects the resulting velocity bias prediction, and studies in which subhalos are treated correctly produce a velocity bias that is consistent with little or no significant bias (Faltenbacher & Diemand 2006; White et al. 2010). Based on these recent results, we assume no velocity bias (b_v = 1) between the galaxy and dark matter velocity dispersion for each cluster in our sample. White et al. (2010) also investigated the relationship between σ_gal and σ_dm for individual simulated halos as a function of the number of available spectroscopic cluster members. Their results suggest that for the best cases, N_members ⩾ 50, there is an intrinsic scatter of ∼15% between σ_gal and σ_dm for a given halo, and that this scatter is much worse—as high as ∼20%—when as few as 10 cluster members are used. We conservatively fold an additional 20% fractional uncertainty into our dynamical mass calculations to reflect the scatter between the galaxy velocity dispersion and the true dark matter velocity dispersion for our clusters. To calculate M₂₀₀ we apply the σ_dm–M₂₀₀ relation from Evrard et al. (2008) for the 18 of our strong-lensing clusters with N ⩾ 10 spectroscopic members (Figure 13). Our dynamical data are based on small numbers of spectroscopic members and the resulting M₂₀₀ values lack precision. However, we can use our data to get a general sense of the mass scale of the halos that we are probing with strong-lensing-selected clusters. The expectation is that mass is the dominant property in determining the likelihood of a given cluster to produce giant arcs (e.g., Hennawi et al. 2007). Observational results comparing the fraction of X-ray versus optically selected clusters which produce giant arcs are consistent with this general expectation (Horesh et al. 2010).

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