Spectroscopic Confirmation of Five Galaxy Clusters at z > 1.25 in the 2500 deg² SPT-SZ Survey

The 2500 deg² SPT-SZ survey (Carlstrom et al. 2011), completed in 2011, discovered 37 galaxy clusters with high significance at z > 1, via the SZE. These clusters were detected via the SPT-SZ campaign that observed the CMB at frequencies of 95, 150, and 220 GHz. The full cluster catalog, B15, is ∼100% complete at z > 0.25 for a mass threshold of M_500c ≥ 7 × 10¹⁴ M_⊙ ${h}_{70}^{-1}$. Survey strategy and analysis details can be found in previous works by the SPT collaboration (Staniszewski et al. 2009; Vanderlinde et al. 2010; Williamson et al. 2011; Reichardt et al. 2013).

For optical and near-IR (NIR) photometric follow-up of this cluster sample, several programs were initiated (see Song et al. 2012 and B15 for details on observational strategies). Optical photometry in the griz bands was obtained for the sample clusters using either the CTIO (4 m) facility, ESO/New Technology Telescope (NTT, 3.58 m) or the Magellan/Baade Telescope (6.5 m) in Chile to depths that can detect galaxies at 0.4L_∗ at z = 0.75 at 5σ in red bands. This was followed up by Spitzer/IRAC observations in the 3.6 and 4.5 μm bands for NIR photometry, which is crucial for observations of higher redshift clusters for member galaxy candidate selection. The final NIR images detect z = 1.5 0.4L_* galaxies at a 10σ significance.

The IR and optical photometry is complemented by observations in the J, H, H-long and K_s bands (the last two being modified versions of the standard H and K filters, respectively), using the wide-area near-IR instrument FOURSTAR on the Magellan/Baade telescope (Foreman-Mackey et al. 2013). Data were acquired between 2014 January and 2016 January; the data used here are a small subset of the overall data set, with details of the reduction and analysis to be provided in a future paper (M. B. Bayliss et al. 2018, in preparation). Deep optical photometric follow-up was also acquired for four of the five clusters discussed in this paper using the simultaneous griz imager Magellan/PISCO (Stalder et al. 2014) on 2016 November 2. Deep HST/WFC3 photometry in the F814W and F140W filters (PI: Strazzullo, HST Cycle 23 program) is available for the fifth cluster, SPT-CL J0607-4448. RGB images for the sample clusters are shown in Figure 1.

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The cluster subsample analyzed in detail here comprises five of the eight most massive z > 1.2 clusters from the SPT-SZ sample, all of which have deep Chandra X-ray imaging (McDonald et al. 2017). The remaining three are SPT-CL J2040-5541 (spectroscopically confirmed at z = 1.478 in Bayliss et al. 2014), SPT-CL J0205-5829 (spectroscopically confirmed at z = 1.322 in Stalder et al. 2013), and SPT-CL J0459-4947, for which current data provide an X-ray spectroscopic redshift of 1.70 ± 0.02 (A. B. Mantz et al. 2018, in preparation, with a past published redshift of 1.85 in McDonald et al. 2017). This total sample is referred to as the "SPT High-z Cluster" sample.

In Section 2.2, we describe the spectroscopic optical observations of this five-cluster subsample. The cataloged properties of these five clusters, and the further three systems that complete the set of the most massive high-redshift clusters in the SPT-SZ sample, are reproduced from B15 in Table 1. The photometric data used for constructing RGB images in this work are summarized in Table 2.

Table 1.  Galaxy Clusters in the SPT-SZ High-z Cluster Sample^a

Cluster ID	R.A.	Decl.	ξa	Redshift	M500c
(SPT Cat.)	J2000	J2000	(SZ Significance)	(Photometric or Previously Published)	1014 ${h}_{70}^{-1}$ M⊙
(1)	(2)	(3)	(4)	(5)	(6)
SPT-CL J2341-5724	355.3568	−57.4158	6.87	1.38 ± 0.08	3.05 ± 0.60
SPT-CL J0156-5541	29.0449	−55.6980	6.98	1.22 ± 0.08	3.63 ± 0.70
SPT-CL J0640-5113	100.0645	−51.2204	6.86	1.25 ± 0.08	3.55 ± 0.70
SPT-CL J0607-4448	91.8984	−44.8033	6.44	1.43 ± 0.09	3.14 ± 0.64
SPT-CL J0313-5334	48.4809	−53.5781	6.09	1.37 ± 0.09	2.97 ± 0.64
SPT-CL J0205-5829	31.4428	−58.4852	10.50	1.322b	4.74 ± 0.77
SPT-CL J2040-4451	310.2483	−44.8602	6.72	1.478c	3.33 ± 0.66
SPT-CL J0459-4947	74.9269	−49.7872	6.29	1.70 ± 0.02d	2.67 ± 0.55

Notes. Galaxy clusters in bold are analyzed in this paper.

^aFrom Bleem et al. (2015). See Section 2.1 for more details. ^bSpectroscopic follow-up in Stalder et al. (2013). ^cSpectroscopic follow-up in Bayliss et al. (2014). ^dPreliminary result from A. B. Mantz et al. (2018, in preparation).

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2.2.1. Spectral Observations

2.2.2. Designing Spectroscopic Masks

The spectra were processed using The Carnegie Observatories System for Multi-Object Spectroscopy (COSMOS)²⁵ reduction package, which is specifically designed to reduce raw spectra acquired using the Magellan Telescopes.

We describe the data reduction briefly below. All images were de-biased using bias frames acquired each afternoon. We used a HeNeAr comparison arc line for wavelength calibration. The analysis is focused on the range where the VPH-red grism is most sensitive and over which we expect useful features from red member galaxies: 7500–10000 Å. A flat-field image acquired temporally adjacent to each science frame was used to define the spectral trace for each slit. This flat image was also used to flat-field the slit response. Sky subtraction was performed by fitting a one-dimensional third-order spline along the dispersion axis, following the techniques outlined in Kelson (2003). Different exposures of the sky-subtracted science spectra were stacked and 2D cosmic-ray cleaning was performed by outlier rejection. COSMOS also generates a noise image that is dominated by photon noise in bright sky lines at these wavelengths.

Figure 2 shows examples of 2D sky-subtracted spectra from four potential member galaxies of the galaxy cluster SPT-CL 0156–5541. The y-axis depicts the spatial width of individual slits, against the horizontal dispersion axis (or wavelength), over the wavelength range 8500–9200 Å. Emission features ([O ii] λ3727, 2729 doublet) and a strong spectral continuum can be clearly seen in some cases. It is crucial to note that there are sections of the spectra in the wavelength range of interest that are dominated by poor sky subtraction with significant systematics. A thorough exploration of the tunable parameters available in the COSMOS reduction package did little to ameliorate this—the poor sky subtraction is not due to an insufficient description of the slit geometry. In principle, fringing could contribute to this effect, but the LDSS3C detector is a thick, fully depleted CCD, the same as the chips used in the Dark Energy Camera (Flaugher et al. 2015), and is not expected to show fringing at this level. Our current understanding is that these artifacts are predominantly the result of slit roughness and are not fully removed by flat-fielding because the roughness produces both a transmission variation and small-scale variation in the wavelength solution. The quality of 2D spectra is a major factor in selecting analysis strategies for 1D spectra, which are described in the following sections.

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Two-dimensional spectra are condensed into one-dimensional spectra for analysis using the IRAF/NOAO package apall that fits polynomial functions to the spectral continuum (along the dispersion axis) in individual 2D spectra. Along the spatial axis, the process involved clipping slit edges for defects and fitting a boxcar model to the counts distribution. At any wavelength, the root mean square (rms) of the sky-subtracted residuals defines the uncertainties.

Due to suboptimal sky subtraction in the LDSS3 pipeline, the resulting 1D wavelength-calibrated (albeit not flux-calibrated) spectra are dominated by systematic noise at some wavelengths and are not suitable for sophisticated spectral analysis techniques that can be employed to analyze galaxy spectra (e.g., principal-component analysis). Several strong spectral features are apparent in some spectra, and we base much of the analysis that follows on the detection of these features, namely the [O ii] λλ3727, 3729 doublet emission lines and Ca ii H&K λλ3968, 3934 absorption lines. Atomic spectral features like [O ii], [O iii], and Hβ (more on this in Section 5.5) trace the direct light from excited nebular gas around young O, B stars that is unobscured by dust in star-forming regions in galaxies. Atomic Ca ii H&K and molecular CN ((0, 0) violet 3850–3880 Å; also discussed in Section 5.5) features are pronounced in K stars in galaxies, tracing older stellar populations in galactic environments. For more details, we refer the reader to Bruzual & Charlot (1993).

Twenty-eight out of forty-four galaxies were confirmed via Ca ii H&K, while 16 redshifts were measured via [O ii] as the principal spectral feature. In the case of some passive galaxies, a modest Hδ 4102Å line corresponding to the Ca ii H&K-based redshifts may also be observed, but not extracted independently. These spectral features were first identified visually in both 2D and 1D spectra and analyzed using two separate methods that are described below. It is important to note that spectral features and redshifts can robustly be identified without flux calibration of spectra (see further discussion in Section 5).

3.3.1. Redshifts from Cross-correlation: RVSAO

3.3.2. Redshifts from Line Identification

Table 3 contains galaxy coordinates and spectroscopic redshifts for all galaxies being considered as member galaxies for our five sample clusters. Also mentioned are the spectral features that were used to characterize the redshift. The total number of target galaxies upon which slits were placed is 109, excluding objects that serendipitously fell onto the slit. Of these, we consider 39 redshifts to be of high confidence. In addition, we include four galaxies with lower confidence redshifts that correspond to measurements with higher uncertainties than are usual for spectroscopic redshifts for galaxies (Δz > 0.002). We also include the moderately robust redshift for the BCG in SPT-CL J0607-4448 (see Section 5.2 for a detailed discussion). Inclusion of these five galaxies does not affect the scientific results of this analysis.

Figure 3 shows examples of one-dimensional spectra of four member galaxies of SPT-CL J0156-5541 at z = 1.2935, 1.2802, 1.2980, and 1.2900, along with 1σ pixel errors as a function of wavelength. The absorption features corresponding to Ca ii H&K can be observed, indicating the presence of a dominant older stellar population.

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Some of the spectra correspond to non-member galaxies (foreground or background) as well as stars. We describe non-member galaxy spectra in Table 4. This list of galaxies includes a z = 2.48 background galaxy with potential Fe ii/Mg ii outflows. This galaxy sits at a projected distance of 12'' from the SZ center of SPT-CL J0640-5113; given the mass of the cluster, this implies at least modest magnification due to lensing, though there is no indication in present data of significant shear or other suggestions of strong lensing effects. Of all the background galaxies identified, this galaxy has the most favorable geometry for strong lensing, and so we note it here for future reference. One field galaxy shows signatures of [Ne iii] that may be associated with AGN activity. Another background galaxy that was spectroscopically confirmed in the field of SPT-CL J0313-5334 is a distant Lyα emitter (LAE) at z = 6.15; this galaxy shows little continuum in available imaging and was found as an additional source in a slit targeting a potential cluster member (itself not confirmed by these data). The observed serendipitous line shows the asymmetry typical of distant LAEs and that location on the slit shows no other spectral features, making a distant LAE the most likely interpretation.

Many of the extracted 1D spectra have significant sky-subtraction residuals. Thus, a differentiation between statistical and systematic errors across the different analysis methods is needed to comprehensively quantify the redshifts.

The median cross-correlation uncertainty reported by RVSAO is ${\rm{\Delta }}z\sim {10}^{-5}\mbox{--}{10}^{-4}$, whereas the combined median line fit uncertainty (from customcode) is ${\rm{\Delta }}z\sim {10}^{-4}\mbox{--}{10}^{-3}$. The specific value and the ratio of uncertainties from the two methods for an individual spectrum depends on the S/N of the spectrum. Uncertainties in flat-fielding and wavelength calibration for these spectra also contribute to systematic uncertainties (Δz ∼ 10⁻⁴ each). The RVSAO code is known to underpredict uncertainties by at least a factor of 2 even absent any systematic uncertainties (Quintana et al. 2000; Bayliss et al. 2016).

Accounting for the systematic uncertainties involved requires a discussion of the RVSAO pipeline. Details of the functioning of RVSAO and physical motivations behind the algorithm are given in Kurtz & Mink (1998) and Tonry & Davis (1979), but it is worth revisiting some aspects of the pipeline and choice of parameters that are relevant to the redshift extraction at hand. RVSAO calculates redshifts based on a modified maximum-likelihood estimator that generates errors based on a cross-correlation peak width obtained from processing an input spectrum. RVSAO assumes every spectral pixel contains a flux value with uniform uncertainty, which limits our ability to interpret RVSAO output uncertainties physically, since our observed spectra have uncertainties that vary significantly with wavelength.

This is best observed in our analysis if each galaxy spectrum is run through RVSAO over multiple trials, in which most parameters are kept fixed except for the following: number of columns in which the data is rebinned in Fourier space, number of times the template spectrum is required to pass through the input galaxy spectrum, wavelength range in which cross-correlation is to be considered, initial redshift guess, and selection cutoffs for Fourier modes to be considered (highest and lowest). The results can be sensitive to these parameters, and the scatter across redshift solutions is expected to reasonably sample the systematic uncertainty. We ran multiple RVSAO trials with all parameters fixed, except cross-correlation wavelength range and initial redshift guess.

Each unique wavelength range corresponds to a single trial, used as an input to RVSAO, with different output cross-correlation peaks. Moreover, in trials with relatively small wavelength ranges, care is taken to eliminate wavelength regions of high noise.

The median scatter in output redshifts observed across multiple trials for the same galaxy spectrum is Δz ∼ 10⁻³, which matches the statistical uncertainties obtained from the customcode analysis. Keeping the wavelength range and initial redshift guess intact while changing the template spectrum (e.g., SAO's habtemp90) returns a similar range of uncertainties.

As mentioned above, in the presence of these limitations, we quote the most conservative uncertainties for individual redshifts. We start with considering median redshifts from multiple RVSAO cross-correlation trials. For RVSAO, we quote the rms uncertainties from multiple cross-correlation trials. In the few cases where [O ii] emission was observed, we then consider the median of RVSAO cross-correlation and [O ii] emission-line redshifts, with rms errors.

The results from the above analysis are then compared with the customcode uncertainties. To be consistent with our approach of reporting the most conservative errors due to presence of unquantifiable sky subtraction systematics, the largest of the three—RVSAO+[O ii] uncertainties, customcode uncertainties, and the difference in redshift solutions from the two sets of analyses—is taken as the galaxy redshift uncertainty. RVSAO's ability to observe spectral features across different pixel scales (or Fourier modes) in a galaxy spectrum, the agreement in redshifts from three independent analyses, and the confirmation of redshift results by visual inspection of these spectra give us confidence in our redshift estimates and the characterization of redshift uncertainties. Moreover, individual galaxy redshift uncertainties do not have a significant effect on the primary scientific result of this work, which is the cluster redshifts.

Redshift estimation in this work follows the same procedure as all previous SPT follow-up studies, described in Ruel et al. (2014). It involves using the bi-weight location estimator to calculate the average redshift, ${\overline{z}}_{\mathrm{cluster}}$, assuming a redshift sample drawn from a Gaussian distribution. For the calculation of velocity dispersion, the bi-weight estimator is robust and resistant to outliers and low number statistics. However, in cases of very small samples (N ≤ 15), the gapper estimator is preferred and is used in this work. We calculate ${\overline{z}}_{\mathrm{cluster}}$ as best determined using the procedure formulated in Beers et al. (1990). The line-of-sight velocity for individual galaxies is computed using the following relationship:

$$\begin{eqnarray}&&{v}_{i}=c\displaystyle \frac{({z}_{i}-{\overline{z}}_{\mathrm{cluster}})}{(1+{\overline{z}}_{\mathrm{cluster}})}\end{eqnarray} \tag{ 1 }$$

where ${\overline{z}}_{\mathrm{cluster}}$ is the bi-weight location-estimated mean redshift, and the denominator accounts for the difference between the emitter's rest frame and the cosmological expansion of the universe. The list of velocities v_i is used as an input to the gapper estimator to calculate the line-of-sight velocity dispersion σ_v, once ${\overline{z}}_{\mathrm{cluster}}$ is finalized. This gives us an initial estimate of ${\sigma }_{v,G}$. We then account for outliers/interlopers in velocity space by making a hard ±3σ cut on the distribution of ${\sigma }_{v,G}$ and ejecting them from the next iteration of calculations until convergence is reached (also see Section 5.4.2). Uncertainties on ${\overline{z}}_{\mathrm{cluster}}$ are calculated using the following expression in Ruel et al. (2014) for estimating standard deviation (once again, assuming the measured redshifts are close to a normal distribution):

$$\begin{eqnarray}&&{\rm{\Delta }}z=\displaystyle \frac{1}{c}\displaystyle \frac{{\sigma }_{v}(1+{\overline{z}}_{\mathrm{cluster}})}{\sqrt{{N}_{\mathrm{members}}}}\end{eqnarray} \tag{ 2 }$$

where ${\sigma }_{v}={\sigma }_{v,G}$ is the relevant gapper velocity dispersion, 1 + z is needed because ${\sigma }_{v,G}$ is defined in the rest frame, and 1/c converts velocity to redshift. Jackknife and bootstrap estimates of this uncertainty also converge to this expression (Ruel et al. 2014). Confidence intervals on velocity dispersions are estimated to be

$$\begin{eqnarray}&&{\rm{\Delta }}{\sigma }_{v}=\displaystyle \frac{\pm C}{{\sigma }_{v}\sqrt{{N}_{\mathrm{members}}-1}}\end{eqnarray} \tag{ 3 }$$

This expression accurately captures the confidence interval on the total measurement. For the gapper statistic, C = 0.91.

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The final redshifts and velocity dispersions are tabulated in Table 5. Figure 5 shows the distribution of individual cluster member velocities (with an overplotted Gaussian distribution of mean 0, standard deviation σ_v,G, and an amplitude corresponding to the maxima of the histogram bin counts), where the distribution of member galaxy velocities and the estimated values of the cluster velocity dispersions are consistent with each other.

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Table 5.  Mean Redshifts, Velocity Dispersions, and Mass Comparisons of Sample Galaxy Clusters

Cluster Name	Members	z	δz	σv,Ga	${M}_{200c,\mathrm{SZ}}$ b	${M}_{200c,{\rm{X}} \mbox{-} \mathrm{ray}}$ c	${M}_{200c,\mathrm{dyn}}$ d
	(no.)			(km s−1)	(×1014 ${h}_{70}^{-1}$ M⊙)	(×1014 ${h}_{70}^{-1}$ M⊙)	(×1014 ${h}_{70}^{-1}$ M⊙)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
SPT-CL J2341-5724	10	1.2588	0.0021	941 ± 285	${4.90}_{-1.00}^{+1.00}$	${5.40}_{-1.20}^{+1.20}$	${5.10}_{-3.30}^{+5.90}$
SPT-CL J0156-5541	15	1.2879	0.0018	936 ± 228	${5.90}_{-1.20}^{+1.20}$	${6.30}_{-1.00}^{+1.00}$	${4.90}_{-2.70}^{+4.40}$
SPT-CL J0640-5113	7	1.3162	0.0031	1147 ± 426	${5.80}_{-1.20}^{+1.20}$	${4.70}_{-1.00}^{+1.00}$	${8.80}_{-6.50}^{+13.20}$
SPT-CL J0607-4448	5	1.4010e	0.0028	843 ± 383	${5.10}_{-1.10}^{+1.10}$	${4.30}_{-0.90}^{+0.90}$	${3.40}_{-2.80}^{+6.80}$
SPT-CL J0313-5334	7	1.4741	0.0018	727 ± 270	${4.90}_{-1.10}^{+1.10}$	${3.20}_{-2.50}^{+2.60}$	${2.20}_{-1.60}^{+3.20}$

Notes.

^aUsing the robust and resistant gapper estimator, recommended for $N\leqslant 15$ member galaxies, described in Beers et al. (1990) and Ruel et al. (2014). ^bSZ masses reported in B15 and scaled up to ${M}_{200c}$. ^cX-ray temperature-based masses reported in McDonald et al. (2017). ^dUsing the gapper velocity dispersion and the M–${\sigma }_{v}$ relation (see Saro et al. 2013 for details). ^eCluster redshift determined out of two redshift "groups," z = 1.40 and z = 1.48. See Section 5.2 for more details.

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SPT-CL J0607-4448 (${z}_{\mathrm{phot}}=1.43\pm 0.09$, ${M}_{500c,\mathrm{SZ}}\,\sim 3.14\pm 0.64\times {10}^{14}{h}^{-1}\,{M}_{\odot }$) was targeted for LDSS3 spectroscopy with 20 slits on a multiobject mask, with 10 delivering reliable redshifts (including two field galaxies not associated with the cluster). Eight of the resulting galaxy redshifts were found to be grouped around two redshifts—z ∼ 1.40 (1.4087, 1.4077, 1.3973, and 1.3948), and z ∼ 1.48 (1.4933, 1.4716, 1.4787, and 1.4965). These two redshift groups are separated enough along the Hubble flow that they are certainly distinct objects. However, it is unclear which object dominates the SZ signal that led to the detection of SPT-CL J0607-4448 in the SPT-SZ survey. Based on the properties of four galaxies measured in each redshift group, the velocity dispersions and member galaxy velocity distributions do not clearly favor any one candidate (σ_v,G for z ∼ 1.40 and z ∼ 1.48 are 843 ± 383 and 1587 ± 834 km s⁻¹, respectively). While the z ∼ 1.40 dynamics (namely, the numerical value of the velocity dispersion) are relatively more consistent with expectations and the other clusters measured in this paper, the associated large uncertainties need to be noted. The spatial distribution of spectroscopically confirmed galaxies in each group does not indicate a preference for one of the redshifts. However, the detailed photometric analysis of the stellar bump and red-sequence colors for SPT-CL J0607-4448 in V. Strazzullo et al. (2018, in preparation) favors the lower redshift solution.

The BCG spectrum (Figure 6) does not possess a spectral feature (emission or absorption) that produced a clear spectroscopic redshift, due to the presence of particularly strong sky subtraction residuals. Both customcode and the RVSAO cross-correlation fail to converge to a reliable redshift, but considered against the two choices (z = 1.40 or 1.48), the spectrum favors a z = 1.40 solution. The black vertical lines correspond to the Ca ii H&K doublet feature redshift to z = 1.40, which is in close proximity to a potential 4000 Å feature at ∼9600 Å (as opposed to the break presenting itself at ∼9880 Å in the case of a z = 1.48 solution). Moreover, there is a potential emission feature at 8944 Å that, in isolation, is not compelling, but can be interpreted as [O ii] emission at z ∼ 1.3993. This indicates that the cluster redshift for SPT-CL J0607-4448 is z = 1.4010. The galaxies in the z ∼ 1.48 structure (which may or may not be a virialized group or cluster) are noted in Table 4.

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This sample contains five high-mass, high-redshift SPT-SZ−detected galaxy clusters that have been determined photometrically to be above z > 1.25. From the literature, we find ∼50 confirmed galaxy clusters at z > 1.15, which implies that spectroscopic confirmation of clusters in our sample increases the number of clusters in this regime by 10%. The SPT high-redshift cluster sample also lies at significantly higher masses than most spectroscopically confirmed clusters at such redshifts; in the high-mass/high-redshift space bounded by the lowest mass and lowest redshift SPT-SZ clusters in this sample, these five spectroscopic confirmations roughly double the total number of confirmed clusters from all previous work.

Figure 7 depicts the distribution of M_200c as a function of redshift (or age of the universe) of all spectroscopically confirmed galaxy clusters at z > 1.15 for which masses were reported in the literature. The census includes infrared-selected clusters from the SpARCS (Nantais et al. 2016; Noble et al. 2016), MaDCoWS (Brodwin et al. 2015; Gonzalez et al. 2015), and ISCS (Brodwin et al. 2011, 2016; Jee et al. 2011) surveys; X-ray-selected clusters from the XMM (Stott et al. 2010), XDCP (Fassbender et al. 2011), XLSS (Tran et al. 2015), and RDCS (Rosati et al. 1998) surveys; and SZ-selected clusters from the SPT-SZ survey. This census covers a mass range of M_200c ≈ 0.3–10 × 10¹⁴ M_⊙. The colors show the method used to estimate cluster mass: X-ray temperature, X-ray luminosity, SZ, and weak lensing.

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The three clusters shown by red squares without black outlines are SPT-SZ clusters spectroscopically confirmed elsewhere at redshifts greater than 1.2—SPT-CL J2040-4451 (z = 1.48, Bayliss et al. 2014), SPT-CL J0205-5829 (z = 1.32, Stalder et al. 2013), and SPT-CL J0459-4947 (X-ray spectroscopy-based redshift z = 1.70 ± 0.02; A. B. Mantz et al. 2018, in preparation). The red squares with black outlines represent the five SPT high-redshift clusters analyzed in this paper.

It is crucial to note that most of the redshifts confirmed in this work are derived from absorption features despite observational difficulties, while higher redshift clusters are typically confirmed by virtue of strong emission observed e.g., clusters JKCS 041 (z = 1.8; Andreon et al. 2014), XLSSC 122 (z = 2.0; Mantz et al. 2018), CL J1001+0220 (z = 2.5; Wang et al. 2016), and the COSMOS-ZFOURGE overdensity (z = 2.1; Yuan et al. 2014).

As previously discussed, obtaining redshifts for primarily passively evolving galaxies at well beyond z = 1 is difficult, and the spectra discussed here are further compromised by systematic sky-subtraction issues. We thus consider in the subsections that follow several analyses of these data beyond cluster redshift estimation, primarily to demonstrate that the redshifts derived above are consistent with expectations for high-redshift clusters.

5.4.1. Consistency of Dynamical Masses with SZE and X-ray Masses

We estimate the dynamical masses of these five galaxy clusters using the dispersion–mass scaling relation from Saro et al. (2013):

$$\begin{eqnarray}&&{M}_{200c,\mathrm{dyn}}={\left(\displaystyle \frac{{\sigma }_{\mathrm{DM}}}{A\times {h}_{70}{(z)}^{C}}\right)}^{B}{10}^{15}{M}_{\odot }\end{eqnarray} \tag{ 4 }$$

where A = 939, B = 2.91, C = 0.33, and ${M}_{200c,\mathrm{dyn}}$ is the dynamical mass within ${R}_{200c}$, defined as the radius within which the mean density ρ is 200 times the critical density ρ_c of the universe. σ_DM is the dispersion computed from galaxy clusters in dark matter simulations, where subhalos correspond to galaxies, while h₇₀(z) is the redshift-dependent Hubble constant.

It is assumed here that the average velocity dispersion of galaxies in our clusters can be substituted in the above expression, i.e., ${\sigma }_{\mathrm{DM}}\sim {\sigma }_{v,G}$, to give a crude estimate of the cluster dynamical masses, which is sufficient given the significant uncertainties associated with velocity dispersion from the small numbers of members and the uncertainty floor imposed by projection and orientation effects in individual clusters (White et al. 2010).

Additionally, other potential systematic uncertainties should be considered when comparing the dynamical mass to other estimators. An example is the conversion from ${M}_{500c,\mathrm{SZ}}$ to ${M}_{200c,\mathrm{SZ}}$ (B15 reports ${M}_{500c}$)—the scale factor is ∼1.65 in this redshift regime, assuming an NFW profile and a mass–concentration scaling relation from Duffy et al. (2008).

Table 5 reports the velocity dispersion, the implied dynamical masses, the SZ-derived masses (B15), and the X-ray-temperature derived masses (McDonald et al. 2017) for all five clusters. All masses are reported in ${M}_{200c}$, scaled where necessary. The dynamical mass to SZ mass ratio for this sample (calculated by fitting a line to the ${M}_{200c,\mathrm{dyn}}$–${M}_{200c,\mathrm{SZ}}$ plane) is 0.73 ± 0.36, and the dynamical mass to X-ray mass ratio is 0.87 ± 0.42. The uncertainty in these ratios is dominated by the high uncertainties in the dynamical masses.

Figure 8 shows the masses with uncertainties for all five clusters; the dynamical masses are uncertain, but there is no evidence of deviations from expectation that would suggest any systematic issue with the derived galaxy (and in turn, galaxy cluster) redshifts.

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5.4.2. Velocity–Radius Diagrams for a Stacked Cluster

As mentioned previously, when calculating the velocity dispersion for a single cluster, we account for outliers/interlopers in velocity space by making hard ±3σ cuts on the distribution of σ_v,G and ejecting them from the next iteration of calculations until convergence occurs.

To examine this phase space further, we create a stacked cluster from the composite distribution of all 44 member galaxy velocities and galaxy distances from the SZ centers (the caustic technique; Diaferio & Geller 1997; Gifford et al. 2013). The SZ mass is used to normalize velocities by an equivalent dispersion ${\sigma }_{200c,\mathrm{SZ}}$, calculated using the dispersion–mass scaling relation (Saro et al. 2013) from ${M}_{200c,\mathrm{SZ}}$ (scaled up from the SPT mass ${M}_{500c,\mathrm{SZ}}$) akin to the previous section. The projected radial distances of individual member galaxies are also normalized by ${R}_{200c,\mathrm{SPT}}$. The resulting phase-space diagram is shown in Figure 9, along with the peculiar velocity distribution in the "stacked cluster." The horizontal dotted lines correspond to the ±3σ threshold, while the orange dotted curve is the radially dependent ±2.7σ(R) threshold from an NFW profile, for optimal interloper rejection (Mamon et al. 2010). From Figure 9, we conclude that (a) the simple 3σ outlier rejection used in Section 5.1 is sufficient and (b) the radial profile of velocities in the stacked cluster look as expected (i.e., small at the center, rising to a maximum, and decreasing at large radii), suggesting that cluster members have been robustly measured and identified. We would like to acknowledge the possibility that this radial profile evolution exhibited within the ±3σ threshold can be attributed to the low number of member galaxies with confirmed redshifts.

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In addition, we run a Kolmogorov–Smirnov (K-S) test on the total galaxy population's velocity distribution (gray horizontal histogram, Figure 9). The K-S statistic is 0.08, i.e., it does not reject the hypothesis that normalized galaxy velocities in our cluster sample are drawn from a Gaussian distribution. This is consistent with expectations (see Ruel et al. 2014; Bayliss et al. 2017).

We also analyze the distribution of cluster member galaxies in velocity–radius phase space by distinguishing passive (orange) from [O ii]-emitting (purple) galaxies. Nominally passive galaxies describe a more centrally condensed distribution by comparison to the more extended distribution of galaxies exhibiting [O ii] emission. This is likely a real trend and unlikely to be a simple selection effect—placing slits on bright red apparent cluster galaxies at larger radii is easier than in the cluster center due to less crowding, and there are potential red cluster members at all radii in the imaging data. Moreover, it is seen that the ratio of passive galaxy to [O ii]-emitting galaxy velocity dispersion is 0.95 ± 0.26, in good agreement with trends observed by Bayliss et al. (2017) for low- and medium-redshift SPT-discovered galaxy clusters. This projected radius and velocity segregation between passive and emission-line galaxies is thought to indicate differences in formation timescales and accretion histories into the cluster environment (see Bayliss et al. 2017 for a comprehensive discussion). That the entire galaxy population of the stacked cluster when dissected in this manner is again consistent with expectations from lower redshift clusters also indicates that cluster member redshifts have been well measured.

We construct a composite spectrum of 28 passive member galaxies across the five clusters, i.e., all galaxies for which an [O ii] emission feature was not detected. To stack, we shift each spectrum to the rest frame (based on its final reported redshift) and map it to the wavelength range 3645–4125 Å, with a flux normalization using the throughput curve for the instrument LDSS3C in this configuration. This is followed by a weighted-sum stacking of the 28 spectra, where each flux value is weighted by the error vector for each galaxy spectrum. We further exclude a portion of each spectrum from the stack; the excluded data are any pixels with uncertainties greater than 2× the mean uncertainty of the 10 least uncertain pixels in each input spectrum. This typically excludes about 30% of the input pixels, which roughly correspond to the majority of the pixels that have large sky-subtraction residuals.

A systematic uncertainty is calculated by varying the exclusion percentage upward and downward by 10% (i.e., typically from 20% to 40% of the pixels are excluded) in steps of 1% and computing a stacked spectrum at each cut. The variance at each pixel across the resulting 21 different stacks is taken as an estimate of the systematic uncertainty. The statistical uncertainty is calculated by bootstrapping the input spectra in the stacking process. The final reported uncertainty is the sum in quadrature of the systematic and statistical uncertainties, which typically are of comparable magnitude. The stacked spectrum (blue, with the 68% confidence interval in light blue) is shown in Figure 10.

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Notably, in the stacked spectra, we detect a composite [O ii] emission feature not previously detected in individual spectra. Additionally, the spectrum clearly shows a pronounced broad CN feature in the range of 3820–3850 Å, as well as Hδ absorption at 4102 Å. We also perform stellar population synthesis modeling with our stacked spectrum using the MCMC code Prospector (Conroy & Gunn 2010; Foreman-Mackey et al. 2013; Johnson & Leja 2017; Leja et al. 2017) to demonstrate that the aggregate spectrum is reasonable and as expected for cluster member galaxies at this epoch. In Figure 10, we overplot a best-fit spectrum using a simple tau (τ) model (e-folding time = 300 Myr, in orange) for a 1.7 Gyr old stellar population, at a metallicity log (Z/Z_⊙) = 0.33 with a velocity broadening over scales of 275 km s⁻¹. Dotted lines correspond to rest-frame [O ii], CN, Ca ii H&K, and Hδ features. The clear emergence of [O ii], Hδ, and CN features—which were not used to establish redshifts for any of these galaxies—and the overall good correspondence between the stacked and the quite reasonable model spectrum, is yet one more validation of the redshifts of the individual galaxies that were used in the composite stacking. A comprehensive analysis of physical properties of stellar populations in the cluster members characterized here shall be presented in a future paper (G. Khullar et al. 2018, in preparation).