Galaxy Clusters Selected via the Sunyaev–Zel'dovich Effect in the SPTpol 100-square-degree Survey

The SPT is a 10 m diameter telescope located within 1 km of the geographic South Pole, at the National Science Foundation's Amundsen–Scott South Pole Station, one of the premier sites on Earth for mm-wave observations. The 10 m aperture results in a diffraction-limited angular resolution of ∼1' at 150 GHz, which is well matched to the angular size of high-redshift galaxy clusters. Combined with the redshift-independent surface brightness of the SZE, this makes the SPT a nearly ideal instrument for discovering high-redshift clusters through the SZE. The first receiver on the SPT was used to conduct the 2500-square-degree SPT–SZ survey. The resultant cluster catalog contains 42 clusters above z = 1 with typical masses of $3\times {10}^{14}{M}_{\odot }$, the most extensive sample of massive, high-redshift systems selected via ICM observables in the literature (Bleem et al. 2015b, hereafter B15).

The SPTpol receiver (Austermann et al. 2012), installed on the telescope in 2012, consists of 1536 detectors, 1176 configured to observe at 150 GHz, and 360 configured to observe at 95 GHz. The first SPTpol observing season and part of the second season were spent observing a roughly 100-square-degree field centered at R.A. 23^h30^m, decl. −55° (bounded by 23^h < R.A. < 24^h, −60° <  decl. < −50°, the same definition as the ra23h30dec−55 field in B15). This is referred to as the SPTpol 100-square-degree field. It was actually observed as two separate subfields: a "lead" field and a "trail" field. This strategy was adopted to mitigate the effects of ground-based signals. No ground signals were ever detected, so we analyze both fields as one. Observations occurred between March and November of 2012 and in March and April of 2013. Of approximately 6600 observations of the field, 6150 observations at 95 GHz and 6040 observations at 150 GHz are used in this work. Maps made from the weighted sum of all SPTpol observations of this field have rough noise levels (in CMB temperature fluctuation units) of 6.5 μK-arcmin at 150 GHz and 11.2 μK-arcmin at 95 GHz, a factor of 3–4 lower than the typical noise levels for the SPT–SZ maps used in B15, but over a much smaller area.⁵¹ We thus expect a lower total number of clusters compared to B15 but a higher density and a larger fraction of systems at high redshift.

The mapmaking procedure followed in this work is nearly identical to that in B15. We summarize the procedure briefly here and point readers to B15, Reichardt et al. (2013), and Schaffer et al. (2011) for more detail. The data from every individual observation of the field at each observing frequency is calibrated, filtered, and binned into 025 map pixels using the Sanson–Flamsteed projection (Calabretta & Greisen 2002). The filtering includes removing the best fit to a set of Legendre polynomials, sines, and cosines from the time-ordered data of each detector, low-pass filtering the data, and removing the mean and a spatial gradient across the detector array from each time sample. The equivalent Fourier-domain filtering from each of these steps is a high pass in the scan direction with a cutoff of angular multipole ℓ ∼ 400, a low pass in the scan direction with a cutoff of ℓ ∼ 20,000, and an isotropic high pass with a cutoff of ℓ ∼ 200, respectively. The low-pass filter is set well above the resolution of the SPT and is only used to prevent aliasing of high-frequency time-domain noise. In the two high-pass filtering steps, compact emissive sources with flux density greater than 6.4 mJy at 150 GHz are masked to avoid filtering artifacts (the same sources were masked in B15).

The filtered, time-ordered data from each detector are inverse-noise weighted, and the weighted data are binned and averaged into pixels. The maps from each individual observation are then combined using the total pixel weights into a single full-depth map at each observing frequency. The pixel weight is the sum of the weights for every time-ordered datum that contributes to the pixel.

For SPTpol, we measure the instrument response as a function of angle (i.e., instrument beams) on planets, particularly Mars. The main lobe of the beam at both frequencies is well approximated by an azimuthally symmetric Gaussian, with FWHM ∼ 16 and ∼11 at 95 and 150 GHz, respectively. Uncorrected shifts in absolute pointing between individual-observation maps lead to a further smearing of the beam in coadded maps, resulting in a final beam FWHM of ∼17 and ∼12 at 95 and 150 GHz. In the matched filter described in the next section, we use a Gaussian approximation to the beam at each frequency.

The relative calibration among detectors in the SPTpol focal plane and the absolute calibration used in this work are derived using a combination of detector response to an internal thermal source and to the Galactic Hii region RCW38. We use a calibration procedure identical to that described in Schaffer et al. (2011), and we refer the reader to that work for details. We apply an additional calibration factor to our simulations to account for any discrepancies between the RCW38-based calibration and absolute calibration against SPT–SZ maps (see Section 3.2).

The SPTpol maps contain signals from several classes of sources, each of which has its own spatial and spectral characteristics. We first describe the spatial behavior of these sources. At large angular scales, our maps are dominated by the CMB. On the smallest scales, power comes mostly from point sources, such as dusty galaxies and radio-bright sources. Galaxy clusters populate the intermediate regime, between the large-scale CMB fluctuations and the point sources.

The intensity of these signals also varies by observing frequency. The amplitude of the CMB and kinematic SZE is preserved across observing frequencies, because the maps are calibrated in CMB temperature units. Radio-loud active galactic nuclei appear with a falling spectrum, while dusty galaxies have a rising spectrum. Finally, the SZE spectrum is given in Equation (3). For a given cluster, the magnitude of the SZE is greater at 95 GHz than 150 GHz. We model the map as follows:

$$\begin{eqnarray}&&\begin{array}{l}T\left(\vec{\theta },{\nu }_{i}\right)\,=\,B(\theta ,{\nu }_{i})* \left[{\rm{\Delta }}{T}_{{\rm{sz}}}\left(\vec{\theta },{\nu }_{i}\right)+{N}_{\mathrm{astro}}\left(\vec{\theta },{\nu }_{i}\right)\right]\\ \,+\,{N}_{\mathrm{noise}}\left(\vec{\theta },{\nu }_{i}\right)\end{array}\end{eqnarray} \tag{ 4 }$$

where $\vec{\theta }$ is the position on the sky, ν_i is the observing band, ${\rm{\Delta }}{T}_{{\rm{sz}}}$ is the SZE as defined in Equation (1), N_astro is all other signals fixed on the sky (such as emissive point sources), ${N}_{\mathrm{noise}}$ is any noise term not fixed on the sky (such as instrumental noise), B(θ, ν_i) represents the effects of the SPTpol beam, as well as filtering operations applied during mapmaking, and ∗ is the convolution operator.

Using the known spatial and spectral forms of the astrophysical noise terms described above and the measured nonastrophysical noise (see Section 3.2), we construct a simultaneous spatial–spectral filter to optimally extract the cluster signal. The process is similar to that described in Melin et al. (2006). In the Fourier domain, the filter takes the form

$$\begin{eqnarray}&&{\boldsymbol{\psi }}(l,{\nu }_{{\boldsymbol{i}}})={\sigma }_{\psi }^{2}\sum _{{\boldsymbol{j}}}{{\boldsymbol{N}}}_{{\boldsymbol{ij}}}^{-1}(l){{\boldsymbol{f}}}_{\mathrm{SZ}}({\nu }_{{\boldsymbol{j}}}){{\boldsymbol{S}}}_{\mathrm{filt}}({\boldsymbol{l}},{\nu }_{{\boldsymbol{j}}})\end{eqnarray} \tag{ 5 }$$

where ${\sigma }_{\psi }^{2}$ is the predicted variance of the filtered map, given by

$$\begin{eqnarray}&&{\sigma }_{\psi }^{-2}=\int {d}^{2}l\sum _{i,j}{f}_{{\rm{sz}}}({\nu }_{i}){S}_{\mathrm{filt}}({\boldsymbol{l}},{\nu }_{i}){{\boldsymbol{N}}}_{{ij}}^{-1}({\boldsymbol{l}}){f}_{{\rm{sz}}}({\nu }_{j}){S}_{\mathrm{filt}}({\boldsymbol{l}},{\nu }_{j}).\end{eqnarray} \tag{ 6 }$$

The band–band, pixel–pixel covariance matrix is represented by ${\boldsymbol{N}}$, and S_filt is the Fourier transform of the search template convolved with B(θ, ν_i). We use an isothermal projected β-model (Cavaliere & Fusco-Femiano 1976) with β fixed at 1 for the SZ surface brightness template:

$$\begin{eqnarray}&&{\boldsymbol{S}}={\boldsymbol{\Delta }}{{\boldsymbol{T}}}_{0}{\left(1+{\theta }^{2}/{\theta }_{c}^{2}\right)}^{-\tfrac{3}{2}\beta +\tfrac{1}{2}}.\end{eqnarray} \tag{ 7 }$$

The normalization (ΔT₀) is a free parameter, and we search over a range of core radii (θ_c). V10 explored the use of more sophisticated models, but found no significant improvement.

The covariance matrix N is constructed using model power spectra for the astrophysical terms and measured noise properties for the remaining terms. The astrophysical portion is made up of the lensed CMB, point sources, and kinematic and thermal SZE from unresolved sources. The CMB power spectrum is calculated using the best-fit WMAP7 + SPT ${\rm{\Lambda }}\mathrm{CDM}$ parameters (Keisler et al. 2011; Komatsu et al. 2011). The thermal SZE background is taken to be flat in l(l + 1) space, with the level taken from Lueker et al. (2010). The kinematic SZE spectrum is taken from Shirokoff et al. (2011). While newer results are available for these spectra (e.g., George et al. 2015; Planck Collaboration et al. 2018), the matched filter is insensitive to the details of the spectra at this level. The combination of instrumental and atmospheric noise is measured from the data (see Section 3.2).

Before applying the matched filter, we mask point sources above 6.4 mJy (at 150 GHz) with a radius of 4' from the source center. This reduces spurious detections caused by ringing around the brightest sources. We also apply an additional 8' veto around these sources, in which we reject any candidate objects. A small number of spurious detections are still included, which we remove via visual inspection.⁵² After masking, the total search area is 94.1 deg².

We use 12 different filters, with θ_c evenly spaced between 025 and 30. After applying the filter in the Fourier domain, we transform back to map space to locate cluster candidates. Candidates are selected by their signal-to-noise ratio (S/N). Our observation strategy causes small variations in noise in both R.A. and decl. The overlap region between the lead and trail fields is somewhat deeper than the nonoverlapping regions, and instrumental and atmospheric noise is larger closer to the equator. Our simulations (see Section 3.2) naturally include both noise variations. We account for the decl. dependence of the noise by splitting the field into 90' strips of constant decl. and ignore the R.A. dependence when calculating the S/N of cluster candidates. Both variations are small (typically ≤5%), so this will not bias our mass estimation (see Section 3.4).

In each strip, we fit a Gaussian to the distribution of all unmasked pixel values within 5σ of the mean. We use the standard deviation of the fitted Gaussian as our measure of noise. The pixel distribution is highly Gaussian within 4σ of the mean, and the fitted standard deviation varies only a small amount when fitting all pixels within 2–5σ of the mean. Therefore, we expect that using the Gaussian approximation of our noise distribution will be sufficiently accurate. This was changed from previous SPT analyses, which used the rms of the strip. For each strip, we divide the filtered map by the noise, resulting in an S/N map. The updated method of measuring the noise typically results in a 6–10% increase in the S/N at the locations of clusters. Galaxy cluster candidates are found using a SExtractor-like algorithm (Bertin & Arnouts 1996) on each filtered map. For each candidate, we maximize the S/N (ξ) over R.A., decl., and filter scale. The matched filter and the results of applying it to a small section of the maps used in this work are shown in Figure 1.

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In order to characterize our detection algorithm, we use simulated maps of the sky. Each map has several components:

• CMB: The Code for Anisotropies in the Microwave Background (CAMB; Lewis et al. 2000) is used to generate CMB spectra from the WMAP7+SPT best-fit ${\rm{\Lambda }}\mathrm{CDM}$ parameters (Keisler et al. 2011; Komatsu et al. 2011). These are used to generate Gaussian random fields for the CMB realizations.
• Radio Sources: We generate point sources at random locations, with fluxes at 150 GHz based on the model from De Zotti et al. (2005). We assume 100% spatial correlation between 95 and 150 GHz and a spectral index α_radio = −0.9 (George et al. 2015) with Gaussian scatter of 0.47 (Mocanu et al. 2013).⁵³ Sources have fluxes between 1.0 and 6.4 mJy. The upper cutoff was chosen to match the masking threshold used on the real data.
• Dusty Sources: Dusty sources are modeled as two Gaussian random fields: one for the Poisson contribution, and another for the clustered term. We again assume 100% spatial correlation between bands. We adopt the model from George et al. (2015) and use the best-fit values for spatial and spectral behavior from that work: the Poisson term is assumed to be of the form ${C}_{{\ell }}=\mathrm{const}.$ and is normalized such that ${D}_{{\ell }}={\ell }\left({\ell }+1\right)/\left(2\pi \right){C}_{{\ell }}=9.16\,\mu {{\rm{K}}}^{2}$ at ℓ = 3000 in the 150 GHz band; the clustered term is normalized such that ${D}_{3000}=3.46\,\mu {{\rm{K}}}^{2}$ at 150 GHz and ${D}_{{\ell }}\propto {{\ell }}^{0.8}$. George et al. (2015) finds the best-fit spectral indices to be α_clustered = 3.27 and α_poisson = 4.27.
• Thermal SZE: N-body simulations are used to project SZE halos onto simulated skies. Halo locations and masses are taken from the Outer Rim N-body simulation (Heitmann et al. 2019). We use the method described in Flender et al. (2016) to map halos to a location on the sky. The pressure profile described in Battaglia et al. (2012) is added at the location of each halo to create a map of the SZE. The simulated maps contain contributions from halos with ${M}_{500c}\gt 6.25\times {10}^{12}{M}_{\odot }{{h}}_{70}^{-1}$, spanning a redshift range from z = 0.01 to z = 3.0.⁵⁴ These maps contain a sufficient number of low-mass clusters to reproduce a power spectrum consistent with George et al. (2015). While the amplitude of the kinematic SZE is similar to that of the thermal SZE, we neglect the kinematic SZE because it is much smaller than other noise terms.
• Noise: The instrumental and atmospheric noise terms are not simulated. Instead, we use noise realizations calculated from the data. Noise realizations are generated by splitting the maps into equal-weight halves and then differencing them. We split the data into halves containing different maps for each noise realization, and we normalize based on the number of input maps.

We do not account for any spatial correlation between simulated components. In particular, this leads to an underestimate of the number of SZE decrements that are partially filled by radio sources. Bleem et al. (2019) performed an analysis of the radio intensity at the locations of SZE-selected galaxy clusters and found that this is not a large effect. However, this work uses deeper mm-wave data, so the Bleem et al. (2019) result should be considered a lower limit to the radio contamination. The effects of lensing dusty sources and CMB on cluster catalogs was studied in Hezaveh et al. (2013). They conclude that lensing has little to no effect on the source density in SZE-selected cluster surveys. Finally, we have not included the kinematic SZE at all. However, we have tested its impact using the simulations from Flender et al. (2016), and we find that it adds variance but no bias. We find that the kinematic SZE is responsible for ∼5% of the intrinsic scatter in the scaling relation between S/N and mass (see Section 3.4).

These simulations are used to characterize both the expected number of false detections and the normalization when calculating cluster mass. In order to properly account for the SPTpol beams and calibration, we first filter a map containing all of the simulated components with the SPTpol filter transfer function and the beam. For this step, we use the measured beam instead of the Gaussian approximation that is used when constructing the matched filter. Then we apply an overall calibration factor to the map for each band. This calibration factor is calculated via comparisons to calibrated SPT–SZ maps of the same field (see Keisler et al. 2015). Finally, the instrumental and atmospheric noise is added.

We expect some fraction of our cluster candidates to be false detections caused by astrophysical and instrumental noise. In order to estimate the rate of false detections, we create a set of simulated sky maps containing all noise terms but no SZE signal. While, in principle, this means we are missing a noise term from subthreshold galaxy clusters, the power in the SZE is much smaller than other noise terms on the spatial scales that the matched filter is sensitive to. Furthermore, at current noise levels, chance associations of below-threshold clusters that overlap to form an apparently higher significance cluster are very rare. We search for clusters in these maps using the procedure described above (including by-eye cleaning of spurious detections associated with bright point sources). The remaining detections are assumed to be representative of the false detections we find in the real data. At our cutoff of $\xi \gt 4.6$, we expect 91% purity (i.e., eight false detections). See Section 5 for more details on the cutoff. The false-detection rate is shown as a function of cutoff significance in Figure 2.

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We estimate masses for each cluster based on its detection significance (ξ) in SPT maps. Our method for estimating masses is described in detail in Reichardt et al. (2013), Benson et al. (2013), and Bocquet et al. (2019). In this section, we briefly describe the method.

For each galaxy cluster, we calculate the posterior probability for mass:

$$\begin{eqnarray}&&P\left(M| \xi \right)={\left.\displaystyle \frac{{dN}}{{dMdz}}\right|}_{z}P\left(\xi | M,z\right)\end{eqnarray} \tag{ 8 }$$

where ξ is the measured S/N of the cluster, $\tfrac{{dN}}{{dMdz}}$ is the assumed mass function (Tinker et al. 2008), and $P(\xi | M)$ is the ξ–mass scaling relation. As discussed in V10, ξ itself is a biased mass estimator, so we introduce the unbiased SPT detection significance ζ:

$$\begin{eqnarray}&&\zeta \equiv \sqrt{{\left\langle \xi \right\rangle }^{2}-3}.\end{eqnarray} \tag{ 9 }$$

For $\left\langle \xi \right\rangle \gt 2$, this removes bias caused by the maximization over three degrees of freedom (R.A., decl., and filter scale) performed when producing the catalog. Here, $\left\langle \xi \right\rangle$ is the mean significance with which a cluster would be detected in an ensemble of SZE surveys. For each cluster, we assume that P(ξ) is a Gaussian distribution with unit width, centered on the measured S/N, and we marginalize over the scatter. Finally, we parameterize the relationship between the unbiased detection significance and cluster mass as

$$\begin{eqnarray}&&\zeta ={A}_{{\rm{sz}}}{\left(\displaystyle \frac{{M}_{500c}}{3\times {10}^{14}{M}_{\odot }{{h}}_{70}^{-1}}\right)}^{{B}_{{\rm{sz}}}}{\left(\displaystyle \frac{E(z)}{E(0.6)}\right)}^{{C}_{{\rm{SZ}}}}\end{eqnarray} \tag{ 10 }$$

with normalization ${A}_{{\rm{sz}}}$, slope ${B}_{{\rm{sz}}}$, and redshift evolution ${C}_{{\rm{sz}}}$. We assume a log-normal scatter ${\sigma }_{\mathrm{ln}\zeta }$ on the ζ − M scaling relation.

As defined, ${A}_{{\rm{sz}}}$ is dependent on the noise levels in the maps. In order to use the same scaling relation for a variety of fields, we redefine ${A}_{{\rm{sz}}}\to {\gamma }_{\mathrm{field}}{A}_{{\rm{sz}}}$. To find γ_field, we run a modified version of the cluster extraction algorithm. We filter 10 simulated maps, using all of the components (noise and SZE) described above. We also filter the maps containing only the SZE (signal-only maps). Instead of running the source extraction on the S/N maps, we divide the signal-only maps by the noise (calculated as described in Section 3.1). This gives us a direct measure of $\left\langle \xi \right\rangle$ instead of ξ, by removing the scatter associated with the noise terms, and reduces the number of simulations required. To construct a catalog, we maximize the S/N over the filter scale at the central pixel of each halo. We fit the scaling relation using all halos with ${M}_{500c}\gt 2\,\times {10}^{14}{M}_{\odot }{{h}}_{70}^{-1}$ and z > 0.25 to match the SPTpol cluster sample. Note that the size of the cluster on the sky becomes comparable to CMB fluctuations for galaxy clusters at z ≤ 0.25, and our mass estimates may be systematically low at these redshifts.

In previous SPT publications, we have calculated γ_field from a common set of simulations. We use a different set of cluster simulations to calculate γ_field in this work than have been used in previous SPT publications. To account for this, we recalculate γ_field for each of the 19 subfields in the SPT–SZ observing region using our new simulations, and we compare these results to the SPT–SZ values of γ_field published in de Haan et al. (2016). The ratios of the SPT–SZ field scalings in de Haan et al. (2016) to those calculated using our new simulations agree at the percent level among the 19 fields, and we take the median of this ratio and apply it to the γ_field we calculate for the SPTpol 100-square-degree field. This results in a final scaling for the SPTpol 100-square-degree field of γ_field = 2.66. Because γ_field is defined relative to V10, this implies that for the same cluster detected in this data and in V10, we should find a value of ξ that is 2.66 times larger here. A quick check using the most significant object in both catalogs, SPT–CL J2337-5942, bears this out: that cluster is detected in this work with ζ = 38.9 and in V10 with ζ = 14.8 (a factor of 2.63 smaller).

In order to provide consistent, comparable mass estimates between cluster catalogs produced by the SPT collaboration, we adopt the mass estimation method used in B15. In this method, the cosmological parameters are held fixed and only the scaling-relation parameters are varied (such that the fitting procedure becomes equivalent to abundance matching to the fixed cosmology). The cluster catalog we use for the scaling-relation fit is the updated B15 catalog presented in Bocquet et al. (2019).⁵⁵ The resulting best-fit parameters are ${A}_{{\rm{sz}}}=4.07$, ${B}_{{\rm{sz}}}=1.65$, ${C}_{{\rm{SZ}}}=0.63$, and ${\sigma }_{\mathrm{ln}\zeta }=0.18$. As a check, we run the same fit using only the cluster sample presented in this work. As expected, the constraints are not as tight as those provided by the fit using the B15 sample, but they are consistent.

The optical imaging for this work was primarily conducted using the Parallel Imager for Southern Cosmology Observations (PISCO; Stalder et al. 2014), a simultaneous four-band (griz) imager with a 9' field of view mounted on the 6.5 m Magellan/Clay telescope at Las Campanas Observatory. The simultaneous imaging in multiple bands allows PISCO to provide efficient follow-up of faint targeted sources such as galaxy clusters.

PISCO data were reduced using a custom-built pipeline that incorporates standard image processing corrections (overscan, debiasing, flat-fielding, illumination), as well as additional PISCO-specific corrections that account for nonlinearities introduced by bright sources. Reduced images are further processed through the PHOTPIPE pipeline (Rest et al. 2005; Garg et al. 2007; Miknaitis et al. 2007) for astrometric calibration and to prepare for coaddition, which is performed with the SWarp algorithm (Bertin et al. 2002). Astrometry is tied to bright stars from the Dark Energy Survey public release (Dark Energy Survey Collaboration et al. 2018) and sources from the second Gaia data release (Gaia Collaboration et al. 2018). Sources are identified in the coadded imaging data utilizing the SExtractor algorithm (Bertin & Arnouts 1996; v 2.8.6) in dual-image mode, star-galaxy separation is accomplished using the SG statistic introduced in Bleem et al. (2015a), and photometry is calibrated using the Stellar Locus Regression (SLR; High et al. 2009).

Additional optical imaging was drawn from targeted observations with the LDSS3 camera on Magellan/Clay (five systems), as well as from a reprocessing of public data from the Blanco Cosmology Survey (Bleem et al. 2015a; five systems). These data were processed following the methods described in B15 and Bleem et al. (2015a), respectively.

Spitzer/IRAC imaging (Fazio et al. 2004) at 3.6 μm and 4.5 μm is available for the majority (91%) of the SPTpol 100-square-degree sample. These data come from both targeted imaging obtained over the course of the SPT–SZ survey (8%; see B15 for details) and data in the Spitzer-SPT Deep Field (SSDF; Ashby et al. 2013). The 94-square-degree SSDF in particular was designed to overlap with deep observations by the SPT in this 100-square-degree field, although it does not cover the entire extent of the millimeter-wave maps used in this work. Our near-infrared imaging with Spitzer is of sufficient depth to identify galaxy clusters at z ≲ 1.5.

4.2.1. Near-infrared Completeness

Cluster candidates are characterized using tools that identify excesses of red-sequence galaxies at cluster locations. These tools, as well as the models used for the colors of red-sequence galaxies as a function of redshift, are described in detail in B15; here we simply note details specific to the analysis of this SPTpol sample.

As this is one of the first analyses to make use of PISCO data to confirm and characterize SPT cluster candidates, it was necessary to calibrate the cluster red-sequence models to match the PISCO photometric system. Further details are given in Bleem et al. (2019), who perform a detailed comparison of redshifts derived from PISCO and a subsample of the B15 catalog with spectroscopic redshifts. Similar to other griz-band photometry derived from previous targeted observations of SPT clusters, we have transformed the PISCO photometric system to that of the Sloan Digital Sky Survey (Abazajian et al. 2009) using instrumental color terms in the SLR calibration process.⁵⁶ The PISCO imaging presented here was obtained as part of a broader effort to obtain high-quality data with good seeing on SPT–SZ and SPTpol clusters for a number of additional follow-up studies. In the course of this effort, imaging was obtained for a large fraction of galaxy clusters identified in the 2500-square-degree SPT–SZ survey with spectroscopic confirmations (Ruel et al. 2014; Bayliss et al. 2016); 51 of these systems were used to calibrate the red-sequence models for redshift estimation with the PISCO data. From this calibration, we determine cluster redshifts to be accurate to ${\sigma }_{z}/(1+z)\sim 0.015-0.02$.

Finally, we have also taken advantage of additional spectroscopy of high-redshift clusters obtained following the publication of B15 (e.g., Bayliss et al. 2016; Khullar et al. 2019) to improve our calibration of near-infrared color-redshift models.

In this section, we compare the catalog presented in this work with other cluster catalogs. We compare against galaxy clusters in the Simbad⁵⁸ database, as well as the second Planck cluster catalog (Planck Collaboration et al. 2016), B15, and the XXL 365 catalog (Adami et al. 2018). Two objects are considered a match if they fall within 50 of each other below z = 0.3. For higher redshift objects, we apply a threshold of 20 (except for comparisons to the Planck catalog, where we use a 40 radius to compensate for the larger Planck instrument beam). The full results can be found in Table 2. Here we highlight some recent catalogs.

The most directly comparable catalog is the SPT–SZ catalog presented in B15. The full SPT–SZ 2500 deg² catalog contains 0.22 confirmed clusters per square degree, while our catalog has nearly four times the density, at 0.86 clusters per square degree. The median redshifts of the two catalogs are similar (z_med = 0.60 for this work, and z_med = 0.55 in B15), but our catalog contains a much larger fraction at high redshift. We find that 18% of the clusters with measured redshifts in this work are more distant than z = 1, while only 8% of the clusters in B15 have z > 1.

The B15 catalog contains 28 candidates in the ra23h30dec−55 field, and we find 22 of them in this work. One cluster (SPT–CL J2332-5053) is optically confirmed in B15, but not included in this catalog. It is part of an interacting system with SPT–CL J2331-5052, which was also noted in previous X-ray observations (Andersson et al. 2011). Our source-finding algorithm groups all connected pixels above a fixed threshold. Because of the deeper data used in this work, there is a high-significance "bridge" that connects the two clusters detected in B15. By increasing the detection threshold above the minimum value in the bridge in our source-finding algorithm, we can force this detection to become separate objects. We find two clusters, one at (R.A., decl.) of (352.96122, −50.864841) with ξ = 19.08, and the other at (353.02512, −50.892534) with ξ = 9.59, both with θ_c = 05. Both objects are at the same redshift (the smaller object, reported only in B15, is at $z=0.56\pm 0.04$, while SPT–CL J2331-5052 is at z = 0.576). For the more massive object, R₅₀₀ ≈ 28, which is more than half the projected distance between the two objects. In Table 1 we report the single cluster SPT–CL J2331-5052. This choice is largely arbitrary for this catalog, and we have chosen to be consistent with our stated selection function. However, future catalogs will find many objects like this, and the choice to report them as single clusters or more than one must be accounted for in any cosmological analyses. Figure 6 shows a composite image with combined optical imaging and SZE contours of this system. The remaining five candidates found in B15 are not optically confirmed, which is consistent with the expected false-detection rate. Finally, one candidate (SPT–CL J2321-5418) is not optically confirmed in this catalog or B15, due to several bright stars in the foreground of the optical imaging.

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The sky coverage in this work extends slightly beyond the boundaries of the RA23H30DEC−55 field in B15, and as a result we find an additional four clusters, which are reported in different fields in the B15 catalog. This brings the total number of matching clusters in both our catalog and B15 to 26. The estimated masses for these two catalogs are consistent with the estimated errors.

The Planck galaxy cluster catalog (Planck Collaboration et al. 2016) contains four clusters in this field, all of which are included in both this catalog and the SPT 2500 deg² catalog. The cluster redshifts agree, and the scatter in mass between these clusters is consistent with the scatter between the clusters in B15 and the Planck cluster catalog. A more detailed comparison of Planck and SPTpol masses is included in Bleem et al. (2019).

The XXL is an X-ray survey performed using XMM-Newton (Pierre et al. 2017), and it is one of the deepest X-ray surveys to date. It covers 50 deg², 25 of which overlap with the sky area in this work. In the overlapping area, XXL finds 154 galaxy clusters, the majority of which are at sufficiently low mass or redshift as to be undetectable in this analysis. Fourteen of these clusters are also found in the SPTpol data. The masses of clusters in the XXL catalog are reported using two different methods. Since we report masses in ${M}_{500c}$, we compare to the XXL masses calculated using an X-ray temperature scaling relation (because these are also in ${M}_{500c}$). Of the 14 matching clusters, only 13 have scaling-relation masses reported in Adami et al. (2018). We compare the masses of the 13 clusters and find that they are statistically consistent, with a median ratio of ${1.08}_{+0.06}^{-0.04}$ and rms scatter of 41%. Dividing out the median difference yields a scatter of 38%. The scatter is dominated by the highest mass cluster, but the SPTpol mass estimate is only 1.2σ discrepant from the estimated XXL mass. The masses of the matching clusters are shown in Figure 7. We also compare redshifts between the two catalogs. Most of the redshifts are consistent, but one cluster is significantly discrepant.⁵⁹

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