A SUNYAEV–ZEL'DOVICH-SELECTED SAMPLE OF THE MOST MASSIVE GALAXY CLUSTERS IN THE 2500 deg² SOUTH POLE TELESCOPE SURVEY

The SPT, a 10 m off-axis Gregorian design with a 1 deg² field of view, has been searching for galaxy clusters in the mm-wave sky since its commissioning in 2007. The SPT is located within 1 km of the geographical South Pole. At an altitude of 2800 m above sea level, the South Pole is one of the premier locations for mm-wave astronomy. The high altitude and low temperatures ensure an atmosphere with low water-vapor content and excellent transparency. Meanwhile, the location near Earth's rotational axis allows 24 hr access to the target fields.

The SZ receiver currently mounted on the telescope consists of 960 transition-edge-sensor bolometers (Lee et al. 1998), cooled to a temperature of 280 mK. These bolometers are split into six wedges each containing 160 detectors. The sensitivity and configuration of these wedges have changed over the four years of scientific operation. In 2007, we fielded a preliminary array with wedges at all three frequencies but with limited sensitivity. In 2008, the array contained a single 95 GHz wedge, three 150 GHz wedges, and two 220 GHz wedges. The 95 GHz wedge did not produce science-quality data, but the 150 and 220 GHz wedges performed to specification. In 2009, the 95 GHz wedge was replaced with a wedge with much higher sensitivity, and one of the 220 GHz wedges was replaced by a 150 GHz wedge, resulting in an array with one wedge at 95 GHz, four wedges at 150 GHz, and one wedge at 220 GHz. The focal plane configuration has remained the same since 2009. The 10 m primary is conservatively illuminated, resulting in beam sizes (FWHM) of approximately 16, 11, and 10 at 95, 150, and 220 GHz, respectively.

The SPT team has previously published two SZ-selected cluster samples: Staniszewski et al. (2009, hereafter S09) presented four clusters (including three newly discovered clusters) selected from ∼40 deg² of 2007 and 2008 150 GHz data, while Vanderlinde et al. (2010, hereafter V10) presented 21 clusters (including 12 new discoveries beyond S09) selected from 150 GHz data in the full 200 deg² of 2008 observations.

The SPT-SZ survey area is a contiguous 2500 deg²  region defined by the boundaries 20^h ⩽ R.A. ⩽ 20^h, 0^h ⩽ R.A. ⩽ 20^h, and −65° ⩽ δ ⩽ −40°. This region comprises the majority of the low-dust-emission southern sky below δ = −40°. Observing fields north of this declination becomes difficult with the SPT because of the increased atmospheric loading and attenuation at low elevation. We split the survey region into 19 fields, ranging in size from ∼70 deg² to ∼230 deg². Single observations of fields of this size can be completed in an hour or two, allowing a regular schedule of interleaved calibrations (see S09; Carlstrom et al. 2011 for details). The exact size, shape, location, and order of observation of these fields are determined by a combination of factors including availability of data at other wavelengths, sun avoidance (some of our observations take place during the Austral spring and summer), and the desire to have a final survey area that is easy to define. The location, year of observation and size for each field are shown in Table 1. Figure 1 shows the full survey region and the individual field borders overlaid on the 100 μm dust map from Schlegel et al. (1998).

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The standard operating mode of the SPT is to observe a target field by scanning back and forth in azimuth across the field followed by a step in elevation. These steps are large compared to the beam size, so subsequent observations of the field have a small offset in elevation applied in order to oversample the sky. Certain fields were observed in what is called a "lead-trail" mode. In this observing mode, the lead half of a field was scanned followed by the trail half, as opposed to scanning the entire azimuth range of the field in a single scan. This strategy was employed to safeguard against possible ground contamination, but we see no evidence of such contamination on the angular scales of interest to this work. Approximately two-thirds of the ra21hdec-50 observations³⁴ were taken using an elevation scan mode rather than scanning in azimuth. In this mode, the telescope was parked at a fixed azimuth and scanned up and down in elevation, allowing the sky to drift through the field of view. We include data from both azimuth and elevation scans on this field. We have investigated the effects of these different scan strategies on noise properties and cluster finding and found these effects to be negligible.

As mentioned in the introduction, observations have been completed to full survey depth (a noise level of 18 μK arcmin at 150 GHz) for roughly 1500 deg² of the SPT survey region. Initial preview observations of the remaining ∼1000 deg²  were performed in late 2010, to a noise level of 54 μK arcmin  at 150 GHz, or three times the full-depth noise level. The results presented in this work are based on data from both the full-depth and preview-depth fields.

One field, the ra23h30dec-55 field, was observed in both 2008 and 2010. Given the higher quality of the 95 GHz wedge in 2010, that year's data are used in preference to the 2008 data, which were used in Vanderlinde et al. (2010). For this reason, the properties of SPT-CL J2337-5942 are not identical to those reported in Vanderlinde et al. (2010). We choose not to combine the 2008 and 2010 data in order to reduce the number of different map depths considered.

The data reduction pipeline applied to the SPT data is very similar to that described in previous SPT papers such as S09, Vanderlinde et al. (2010), and Shirokoff et al. (2010). An overview of the processing is presented here, highlighting differences with earlier SPT releases. The same data-processing and map-making procedure is used for each field, with minor adaptations in filtering to produce uniform map properties regardless of scan strategy.

The first steps in processing are to flag regions of compromised data (for instance, time samples with cosmic ray events) and to reconstruct the pointing for each detector. We then calibrate the time-ordered data (TOD) to CMB temperature units. As in S09, this calibration is based on observations of a galactic H ii region (RCW38). The TOD is filtered and co-added into the final single-frequency map with inverse-noise weighting.

The filtering consists of bandpass filtering the TOD and removing correlated noise between detectors. The high-pass filter is implemented by removing a ninth-order Legendre polynomial and a set of Fourier modes from each scan. The highest-frequency Fourier modes removed correspond to an angular frequency of k = 400 in the scan direction.³⁵ Depending on the scan strategy used for the observation, this filter acts as a high-pass filter in the R.A. or decl. direction. This differs slightly from Vanderlinde et al. (2010) where only a first-order polynomial was removed, and the set of Fourier modes removed was defined by temporal frequency (f <.25 Hz) rather than angular frequency (k < 400). The cutoff definition was altered to handle variable scan speeds. For the 2008 scan speeds, 0.25 Hz corresponds to k ≃ 360, which means that the k-space high-pass cutoff is slightly higher in this work than in Vanderlinde et al. (2010). A low-pass filter was also applied (with a cutoff at k ∼ 30, 000) to avoid aliasing of high-frequency TOD noise when the data are binned into a map.

Atmospheric noise is correlated across the entire focal plane. Vanderlinde et al. (2010) removed the mean and slope across all detectors in a frequency band at each time sample. However, the number of detectors at the two frequencies used in this work (95 and 150 GHz) differs by a factor of four, so this scheme would filter different spatial modes on the sky at each frequency. Instead, as was done in Shirokoff et al. (2010), the mean of the TOD across a geometrically compact set of one quarter of the 150 GHz detectors or all the 95 GHz detectors (i.e., across one detector wedge) is subtracted at each time sample. This acts as an isotropic high-pass filter with a cutoff at roughly k = 500.

As discussed in Section 2.2, most of the SPT fields have been observed in three frequency bands, centered at 95, 150, and 220 GHz. Multiple sky signals and sources of noise contribute to each single-frequency co-added map of a field, and each of these contributions has unique spatial and spectral properties. Primary CMB fluctuations, emissive point sources, and noise (both atmospheric and instrumental) contribute to the maps at all three frequencies. A small signal from the kinetic SZ (kSZ) effect (due to the interaction between CMB photons and free electrons with a bulk velocity) also contributes to all three frequencies. Most importantly for this work, the 95 GHz and 150 GHz maps contain an additional signal due to the tSZ effect from clusters. Because we can predict the spectral signature of the tSZ effect (up to a small relativistic correction), we can combine the maps from the three bands to maximize sensitivity to tSZ and minimize noise and other contaminants. Furthermore, we can use the fact that the galaxy clusters we expect to find have a different spatial profile than other signals and noise to construct a spatial filter that maximizes sensitivity to cluster-shaped signals.

As shown by Melin et al. (2006) and others, the optimal³⁶ way to extract a cluster-shaped tSZ signal from our data is to construct a simultaneous spatial-spectral filter. We begin by assuming that the maps are fully described by

$$\begin{eqnarray} T(\mathbf {x},\nu _i) &=& B(\mathbf {x},\nu _i) * [ f_\mathrm{{{SZ}}}(\nu _i) \mbox{$T_{\rm{CMB}}$}y_\mathrm{{{SZ}}}(\mathbf {x}) + n_\mathrm{astro}(\mathbf {x},\nu _i)] \nonumber\\ && + n_\mathrm{noise}(\mathbf {x},\nu _i), \end{eqnarray} \tag{ 1 }$$

where y_SZ is the true tSZ sky signal in units of the Compton y parameter, $\mbox{$T_{\rm{CMB}}$}$ is the mean temperature of the CMB, f_SZ encodes the frequency scaling of the tSZ effect relative to primary CMB fluctuations (e.g., Carlstrom et al. 2002), n_astro and n_noise are the astrophysical signals and instrument/atmospheric noise we wish to de-weight, $B(\mathbf {x},\nu _i)$ encodes the instrument beam and any filtering applied in the analysis, and "*" denotes convolution. Given this assumption, the matched spatial-spectral filter is given by

$$\begin{equation} {\it \Psi }(k_x,k_y,\nu _i) = \sigma _\psi ^{-2} \ \sum _j \mathbf {N}_{ij}^{-1}(k_x,k_y) f_\mathrm{{{SZ}}}(\nu _j) S_\mathrm{filt}(k_x,k_y,\nu _j). \end{equation} \tag{ 2 }$$

Here, σ⁻²_ψ is the predicted variance in the filtered map

$$\begin{eqnarray} \sigma _\psi ^{-2} &=& \sum _{i,j} f_\mathrm{{{SZ}}}(\nu _i) S_\mathrm{filt}(k_x,k_y,\nu _i) \ \mathbf {N}_{ij}^{-1}(k_x,k_y) \nonumber\\ &&\times f_\mathrm{{{SZ}}}(\nu _j) S_\mathrm{filt}(k_x,k_y,\nu _j), \end{eqnarray} \tag{ 3 }$$

and S_filt is the assumed cluster profile convolved with $B(\mathbf {x},\nu _i)$. The k_x and k_y arguments are included explicitly in S_filt because, while the underlying cluster profile is assumed to be azimuthally symmetric, the filtering described in Section 2.3 is anisotropic. The ν argument is included explicitly to account for the fact that the filtering and instrument beam can be different in the different SPT bands. $\mathbf {N}$ is the band–band, pixel–pixel covariance matrix describing the noise and non-tSZ signal:

$$\begin{eqnarray} \mathbf {N}_{{\rm abij}} &=& \langle \left[ B(\mathbf {x}_a,\nu _i) * n_\mathrm{astro}(\mathbf {x}_a,\nu _i) + n_\mathrm{noise}(\mathbf {x}_a,\nu _i) \right] \nonumber\\ &&\times [ B(\mathbf {x}_b,\nu _j) * n_\mathrm{astro}(\mathbf {x}_b,\nu _j) + n_\mathrm{noise}(\mathbf {x}_b,\nu _j) ] \rangle. \end{eqnarray} \tag{ 4 }$$

Under the assumption that these components are translationally invariant, the pixel–pixel part of this matrix will be diagonal in the Fourier domain, which is why we only include the band indices in Equation (2). This also means that Ψ can be evaluated separately at each value of {k_x, k_y}, and the largest matrix that needs to be inverted is N_bands-by-N_bands.

There should be no correlation between the astrophysical signals and instrumental/atmospheric noise, in which case $\mathbf {N}$ can be separated into $\mathbf {N}_\mathrm{astro}$ and $\mathbf {N}_\mathrm{noise}$. Furthermore, the instrumental noise should be uncorrelated between bands, although the atmospheric noise may have correlations. We have performed correlation analyses on SPT maps similar to those used in this work and found little, if any, noise correlation between bands, which is expected because the correlated part of the atmospheric emission is largely removed in the filtering described in Section 2.3. In this case, we can estimate $\mathbf {N}_\mathrm{noise}$ individually in each band. We do so using the jackknife procedure described in Vanderlinde et al. (2010) and S09.

Our model for $\mathbf {N}_\mathrm{astro}$ is a combination of primary and lensed CMB fluctuations, point sources below the SPT detection threshold, kSZ, and tSZ from clusters below the SPT detection threshold. The power-spectrum shapes and 150 GHz amplitudes for these components are identical to those used in Vanderlinde et al. (2010). The spectral behavior of the primary CMB, kSZ, and tSZ components are known (up to the relativistic correction for tSZ, which we ignore). The spectral behavior of the point sources is assumed to be such that the flux density of a given source follows a power law in frequency (ν/ν₀)^α, with α = 3.6. This is consistent with the behavior of dusty, star-forming galaxies (DSFGs) below the SPT detection threshold. Radio sources below the SPT detection threshold are expected to contribute negligibly to the map rms compared to noise (Hall et al. 2010; Shirokoff et al. 2010).

As in Vanderlinde et al. (2010) and S09, the source template S is described by a projected spherical β-model, with β fixed to 1,

$$\begin{equation} \Delta T = \Delta T_0 \big(1+\theta ^2/\theta _c^2\big)^{-1}, \end{equation} \tag{ 5 }$$

where the normalization ΔT₀ and the core radius θ_c are free parameters. As in Vanderlinde et al. (2010) and S09, 12 different matched filters were constructed and applied to the data, each with a different core radius, spaced evenly between 025 and 30. As in Vanderlinde et al. (2010), point sources detected above 5σ were masked out to a radius of 4', with the value inside that radius set to the average of the surrounding pixels. For extended sources, a custom mask was applied, covering the shape of the emission. In both cases, cluster detections inside the masked region or within 4' of the outer edge of the masked region were rejected, meaning that any detection within 8' of a masked point source was rejected.

The method of extracting clusters from the filtered maps in this work (including S/N estimation and peak detection) is identical to that used in Vanderlinde et al. (2010). As in V10, we refer to the detection significance maximized across all 12 matched filters as ξ and use ξ as the primary SZ observable.

We have measured the performance of the multi-band cluster detection algorithm relative to single-band detection and found significant improvement when we add the 95 GHz data—which has roughly a factor of two higher noise in CMB fluctuation temperature than the 150 GHz data—over 150 GHz data alone. We find very little further improvement when we add the 220 GHz data, which has a factor of five higher noise than the 150 GHz data. As the 220 GHz SPT maps are not currently deep enough to add significantly to the cluster detection efficiency, we use only 95 and 150 GHz data for all the results presented in this work.

For one field, ra5h30dec-55, only 150 and 220 GHz data exist, and we only perform single-frequency 150 GHz cluster finding on this field's map (with results indistinguishable from those reported in Vanderlinde et al. 2010). Using the measured improvement in cluster S/N in multi-band versus single-band data (roughly 20% averaged across all redshifts and cluster sizes), we determined that the most significant cluster in this field would not have made it into the catalog in this work even if we had 95 GHz data on this field (see Section 3 for details of the selection of clusters for this work).

Of the 26 clusters reported in this paper, 12 are new discoveries, one was previously reported in V10, and 13 others have been identified in other optical, X-ray, and SZ cluster catalogs, with 7 having multiple identifications. The previously identified clusters include seven clusters in the optical Abell catalog (Abell et al. 1989), nine clusters in the X-ray ROSAT-ESO Flux Limited X-ray Galaxy cluster survey catalog (REFLEX; Böhringer et al. 2004), and six clusters in the mm-wave ACT catalog (Marriage et al. 2010). These cross-associations and alternative identifications are noted in Table 6. In this section, we discuss particularly notable clusters in the SPT catalog.

SPT-CL J0102-4915. This cluster was first reported in Marriage et al. (2010). It is the most significant detection to date in the full SPT survey by nearly a factor of two. It has a comparable X-ray luminosity and beam-averaged SZ decrement to the Bullet cluster and AS1063, whose SZ significances should be similar when the SPT survey is completed to full depth. Given the redshift of this cluster (z = 0.78), it is expected to be one of the rarest objects in the SPT survey (see Figure 5).

SPT-CL J0615-5746. This cluster has the second highest redshift of any cluster in this paper, with a redshift of z = 0.972. Based on its ROSAT faint source catalog counterpart, it is measured to be the fourth most X-ray luminous cluster in this catalog (see Section 6).

SPT-CL J0658-5556. This cluster is the well-known Bullet cluster, otherwise known as 1ES 0657-558. It has been extensively studied in multiple wavelengths (e.g., Clowe et al. 2006) and is known to be one of the most massive and X-ray luminous clusters in the universe. It is expected to be the most massive cluster in the final SPT catalog.

SPT-CL J2106-5844. Multi-wavelength observations of this SPT-discovered cluster are discussed in detail in Foley et al. (2011). This is the highest-redshift cluster (z = 1.132) spectroscopically confirmed in the SPT survey. X-ray observations from Chandra measure an X-ray luminosity of L_X(0.5–2.0 keV) = 13.9 × 10⁴⁴ erg s⁻¹ (Foley et al. 2011), comparable to the X-ray luminosity of the Bullet cluster. The mass we report in Table 6 for SPT-CL J2106-5844 is slightly (5%–10%) discrepant with the SZ mass reported in Foley et al. (2011), although the difference is much smaller than either value's 1σ uncertainty. The difference arises because Foley et al. (2011) use the single-band 150 GHz ξ and the exact V10 scaling relation to derive the mass, whereas this work uses the multi-band ξ and the multi-band scaling relation developed specifically for this work. (See Section 4.1 and V10 for details on the mass estimation and scaling relations.)

SPT-CL J2248-4431. This cluster is also known as AS1063. It is the second most X-ray luminous cluster in the REFLEX X-ray survey (Böhringer et al. 2004), even more luminous than the Bullet cluster. It has the second highest estimated mass for any cluster in this paper.

SPT-CL J2344-4243. From its redshift and its ROSAT bright source catalog counterpart (see Section 6), this cluster is measured to have the largest X-ray luminosity of any cluster in this paper. A bright Type 2 Seyfert galaxy at redshift 0.5975, 2MASX J23444387-4243124, is located 19'' from the SZ cluster centroid. This redshift is consistent with our photometric red-sequence redshift estimate of 0.62 for the cluster (see Section 5), suggesting that this galaxy may be in or near this cluster.

As discussed in Section 2.4, emissive sources above 5σ are masked in the cluster-finding procedure, and any cluster detections within 8' of a masked point source are rejected, because residual source flux or artifacts due to the masking can cause spurious decrements when the maps are filtered. However, this rather conservative procedure can result in rejecting a cluster detection that was only marginally affected by the nearby emissive source.

To test this scenario, we re-ran the cluster-finding algorithm on all the fields used in this work with only the very brightest (S_150 GHz > 50 mJy) sources masked (as compared to the 5σ thresholds of roughly 6.4 and 17 mJy in the full-depth and shallow fields). Each detection above the ξ threshold for this paper was visually inspected, and the vast majority were rejected as obvious point-source-related artifacts. However, two objects were clearly real detections. One of these detections, with ξ = 19.3 (in a full-depth field), is a known cluster (AS0295), and we include it in our catalog as SPT-CL J0245-5302. There are two >5σ sources within 8 arcmin of this cluster, but neither is strong enough to affect the ξ measurement by more than 1σ or 2σ. Furthermore, the sources lie to the north and south of the cluster, and wings from the matched filter are predominantly along the scan direction (east–west in all SPT fields but one). However, because this cluster was not found by the original version of the cluster-finding algorithm, we do not include it any cosmological analysis.

The other detection, ξ = 13.3 (full-depth), has an 8σ source almost directly to the east. Because this cluster (SPT-CL J2142-6419, which will likely appear in a future catalog) could have been bumped over our ξ = 13 full-depth threshold by the filtering wing of the point source, we choose not to include it in this work.

A number of different techniques are available for obtaining cluster mass estimates from SZ measurements. The integrated SZ flux, Y, is expected to be a tight proxy for the cluster mass (Barbosa et al. 1996; Holder & Carlstrom 2001; Motl et al. 2005; Nagai et al. 2007; Shaw et al. 2008; Stanek et al. 2009). Unfortunately, the difficulty in determining the correct filter scale θ_c from SPT data alone adds significant scatter to the scaling relation of mass with Y (see V10 for details).³⁷ In simulations, the SPT significance ξ has a smaller scatter than our current integrated Y estimates, and, as in V10, we use the significance as a mass proxy.

Due to the significant impact of noise biases, a direct ξ–M scaling relation is complex and difficult to characterize. Instead, following the prescription of Vanderlinde et al. (2010), we introduce an unbiased significance ζ, whose scaling with mass M₂₀₀(ρ_mean) takes the form

$$\begin{equation} \zeta = A \left(\frac{M}{5\times 10^{14}\,M_\odot \, h^{-1}}\right)^B \left(\frac{1+z}{1.6}\right)^C, \end{equation} \tag{ 6 }$$

where A is a normalization, B a mass evolution, and C a redshift evolution.³⁸ In simulated maps of both depths, ζ was calculated for each cluster as in V10, by determining the preferred filter scale and cluster position in the absence of noise then averaging the detection significance at that filter scale and position over many noise realizations. Mass scaling relations were fit to the subset of these with M > 2 × 10¹⁴ h⁻¹ M_☉ and z > 0.3 by minimizing the residual logarithmic scatter in ζ about the relation.³⁹ These relations are given in Table 2. As these are based on the same SZ simulations used in Vanderlinde et al. (2010), they can be viewed as equivalent to the relations presented in that work.

Uncertainties in the SZ modeling lead to significant systematic uncertainties on these scaling relation parameters. Following Vanderlinde et al. (2010), we apply conservative 30%, 20%, 50%, and 20% Gaussian uncertainties to A, B, C, and scatter, respectively.

Mass estimates are constructed as in Vanderlinde et al. (2010) with slight modifications to account for the different field depths. Details of the conversion from ξ to mass are given in Appendices B and D of V10. Briefly, we calculate the conditional probability of detecting a cluster of mass M at a given value of ξ, P(ξ|M), and then apply a mass function prior to create the posterior probability P(M|ξ). This procedure accounts for two types of bias in the mass estimate, the first due to the fact that we have maximized ξ over many filter choices and positions in the map, and the second due to the combination of the steepness of the cluster mass function and observational noise or scatter in the mass-observable scaling relation. The latter effect, which results in more low-mass systems scattering up into a given ξ bin than high-mass systems scattering down, is related to the phenomenon of Eddington bias⁴⁰ (Eddington 1913). For the very high detection significances used in this work, the maximization bias is completely negligible compared to the bias due to this asymmetric scatter. As in V10, we use the Tinker et al. (2008) mass function evaluated at the maximum likelihood point in the WMAP7+V10 chain as our prior. This method produces unbiased posterior estimates for cluster masses, assuming the validity of the simulations and of the various priors applied.

In Andersson et al. (2010), we compared SZ-inferred masses calculated with this method to X-ray mass estimates for the 15 clusters from V10 that had X-ray measurements. Overall, we found agreement between the SZ and X-ray mass estimates near the quoted level of the systematic uncertainties of the SZ mass estimates. However, there was a significant statistical offset, with the SZ-inferred masses lower by a factor of 0.78 ± 0.06 averaged over the sample, which we do not correct for in the masses in Table 6. This factor could have a redshift or mass dependence and naively applying a correction factor would ignore these effects. There was some evidence for this in Andersson et al. (2010), where the lowest redshift and most massive cluster had the most discrepant SZ- and X-ray-inferred masses. We are currently pursuing an analysis that jointly constrains the SZ and X-ray mass-observable relations with cosmology (B. A. Benson et al. 2011, in preparation), which will more accurately quantify any systematic offset between the SZ and X-ray mass estimates. For this work, we consider the quoted uncertainty of the SZ mass estimates to be a reasonable estimate of the systematic uncertainty, and note that there is some evidence that the SZ mass estimates are low by ∼25%. We show in Section 7 that none of the conclusions in our cosmological analyses would change if we naively applied this scaling factor.

Finally, we note that, although the scaling relation fits were only performed on simulated clusters above z = 0.3, we nevertheless report SZ-derived masses for several z < 0.3 clusters in Table 6. These mass estimates are extrapolations of the scaling relations to areas of parameter space in which they have not been tied to simulations and may therefore be subject to further systematic uncertainties. For this reason, we do not use any clusters at z < 0.3 in the likelihood calculations described in Section 7.2.

To test the likelihood of false detections, simulated observations were generated omitting the SZ signal and run through the cluster-finding pipeline. The false detection rate was found to be a rapidly falling function of the detection threshold. No false detections were found above a significance of ξ = 6 in simulations of 4000 deg² at either depth. Given that the lowest threshold used in generating the catalog presented in this work is ξ ⩾ 7, it is highly improbable that it contains any false detections. This is confirmed by the multi-band followup, which shows counterparts for each cluster in the catalog.

The catalog is complete above threshold ξ values by construction. As discussed in Section 3, two factors make it difficult to quantitatively convert this into a mass and redshift completeness. The clusters in this catalog lie at the extreme high-mass end, and, as such, are rare in the simulated skies, yielding insufficient statistics to obtain a robust estimate of their detectability. Furthermore, there is large uncertainty associated with modeling the gas attached to halos in the simulation that makes any threshold uncertain at the ∼30% level. Figure 2 shows our best estimate of 50% and 90% completeness for the two sets of field depths and ξ thresholds. We note that, as the same simulated SZ skies were used for both depths, the variance due to the limited sample size will appear as a coherent shift, rather than a scatter, between the two sets of curves

The previously unknown clusters in this catalog were imaged with the cameras shown in Table 4. The Swope 1 m at Las Campanas Observatory, equipped with the SITe3 CCD detector and BV RI filters, provided sensitivity to clusters at z ≲ 0.7. We chose at least two passbands that spanned the 4000 Å break, as determined initially using cluster redshifts estimated by eye from Digitized Sky Survey images. We required a detection of 0.4L* early-type cluster galaxies at about 5σ. We then iterated on this strategy: if the cluster was still not sufficiently detected in the initial set of exposures, we updated our best redshift estimate using the new data, if possible, and reobserved.

Table 4. Optical and Infrared Imagers

Aliasa	Site	Telescope	Aperture	Camera	Filtersb	Field	Pixel scale
			(m)				('')
im1	Cerro Tololo	Blanco	4	MOSAIC-II	griz	36' × 36'	0.27
im2	Las Campanas	Magellan/Baade	6.5	IMACS f/2	griz	274 × 274	0.200
im3	Las Campanas	Magellan/Clay	6.5	LDSS3	griz	83 diam. circle	0.189
im4	Las Campanas	Swope	1	SITe3	BV RI	148 × 228	0.435
im5	Paranal	VLT	8.2	FORS2	I	68 × 68	0.25
im6	Cerro Tololo	Blanco	4	NEWFIRM	JKs	28' × 28'	0.4
im7	...	Spitzer Space Telescope	0.85	IRAC	[3.6][4.5]	52 × 52	1.2

Notes. The optical and infrared cameras used. The choice of facilities and filters for any given cluster was typically optimized according to our best redshift estimate prior to observation. Not all imagers, nor all the listed filters, were used on each cluster. ^aShorthand alias used in Table 3. ^bThe filters we used, which were in general a subset of all of those available. We did not typically use all listed filters on each cluster.

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The Blanco 4 m at Cerro Tololo Inter-American Observatory and the Magellan 6.5 m telescopes at Las Campanas Observatory provided sensitivity to clusters at z ≲ 1. The Blanco/MOSAIC-II, Magellan/LDSS3, and Magellan/IMACS CCD cameras were used with griz filters. The same iterative strategy was implemented until we reached our required detection.

As detailed in Foley et al. (2011), 50 minutes of preimaging with the VLT's FORS2 camera in I provided additional broadband data for our highest-redshift cluster, SPT-CL J2106-5844, in our corresponding spectroscopic program.

All images were reduced in a uniform manner using the same software and methods described in detail in the previous, closely related work of High et al. (2010, hereafter H10). Photometry was calibrated using the Stellar Locus Regression method (High et al. 2009). The red-sequence redshifts reported in Table 3 were derived using the same red-sequence software described in High et al. (2010). These redshifts are estimated to be accurate to σ_z/(1 + z) ≈ 2%–3% (statistical plus systematic), as determined using a larger subset of clusters with added spectroscopic redshift data. An exception to this is the SWOPE derived redshifts (SPT-CL J0245-5302 and SPT-CL J0411-4819) which are accurate to σ_z/(1 + z) ≈ 4%–5%. This was due to using Johnson filters (as opposed to Gunn–Sloan filters), and calibrating the photometry with a synthetic stellar locus (rather than the median Sloan Digital Sky Survey stellar locus from Covey et al. 2007) using the PHOENIX stellar model atmosphere library (Brott & Hauschildt 2005).

A parallel reduction of the Blanco/MOSAIC-II data was performed using the Dark Energy Survey data management system (Ngeow et al. 2006; Mohr et al. 2008). Redshifts for the 12 clusters with MOSAIC-II imaging were independently measured from these data using Artificial Neural Network (ANNz; Collister & Lahav 2004) software and another red-sequence method (J. Song et al. 2011, in preparation). This independent cross-checking led to consistent redshift estimates in all cases, except for SPT-CL J0615-5746, where redshift estimates ranged from about 0.9 to 1.1 (this cluster was later spectroscopically confirmed at z = 0.972); and SPT-CL J0555-6405, where different estimates gave redshifts of 0.27, 0.35, and 0.42. In the latter case, because the red sequence appears most pronounced and unambiguous at 0.42, we report the redshift from the High et al. (2010) software only.

An additional cross-check for two of the clusters presented here is provided by Menanteau et al. (2010), who estimated photometric redshifts of 0.75 ± 0.04 for SPT-CL J0102-4915 (compare our result of 0.78) and 0.54 ± 0.05 for SPT-CL J0438-5419 (compare 0.45).

Spitzer/IRAC imaging is particularly important for the confirmation and study of high-redshift SPT clusters, such as SPT-CL J2106-5844 at z = 1.132 (Figure 26), where the optically faint members are strongly detected in the mid-infrared. Three of our catalog clusters were observed as part of a larger program to follow up clusters identified in the SPT survey. The on-target observations consisted of 8 × 100 s and 6 × 30 s dithered exposures at 3.6 and 4.5 μm, respectively. The deep 3.6 μm observations are sensitive to passively evolving cluster galaxies down to 0.1 L* at z = 1.5. The data were reduced exactly as in Brodwin et al. (2010), following the method of Ashby et al. (2009). Briefly, we correct for column pulldown and residual image effects, mosaic the individual exposures, resample to 086 pixels (half the solid angle of the native IRAC pixels), and reject cosmic rays.

Eleven of the clusters in this work have published spectroscopic redshifts, which we note in Table 3. Using the instruments listed in Table 5, we present new spectroscopic redshift measurements on five clusters, four of which have no such previously published data. The robust biweight location estimator is used to determine the cluster spectroscopic redshifts from ensembles of member galaxies.

5.3.1. SPT-CL J0234-5831 and SPT-CL J0254-5857

5.3.2. SPT-CL J0615-5746

5.3.3. SPT-CL J2106-5844

5.3.4. SPT-CL J2337-5942

M11 have published fitting functions that allow us to answer the question: is this one cluster in significant tension with ΛCDM? In Figure 5, we plot the mass versus redshift for all 26 clusters and overplot exclusion curves from M11. As explained in Appendix C of M11, the mass for a given cluster that is appropriate to compare to their exclusion curves is not precisely the best posterior estimate of that cluster's mass. The masses plotted in Figure 5 are calculated using Equation (C3) from M11, using the conditional probability P(ξ|M) to estimate their M_obs and σ_ln M and using the local slope of the Tinker et al. (2008) mass function around the value of M_obs for γ. The error bars on the masses in Figure 5 are calculated by setting the fractional error (i.e., the error in ln M) equal to the fractional error of the posterior mass estimates in Table 6. We have confirmed that this is an excellent approximation to the full probability distribution of the M11-appropriate masses for the cluster sample in this work.

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The two highest exclusion curves overplotted in Figure 5 represent the mass and redshift above which an individual cluster would be less than 5% likely to be found in a given survey region in 95% of the ΛCDM parameter probability distribution. We plot one exclusion curve for the least likely cluster allowed in a 2500 deg² survey and one curve for the least likely cluster allowed in the entire sky. It is clear that, according to the formalism of M11, no cluster in our sample is individually in strong tension with ΛCDM—a conclusion that would still hold if we applied the naive scaling factor of 1/0.78 discussed in Section 4.1 to all the cluster masses.

This result can be compared to the result of Foley et al. (2011), in which the single cluster SPT-CL J2106-5844 is found to be less than 5% likely to exist in the 2500 deg² SPT survey region in 32% of the ΛCDM parameter probability distribution. There are some differences in the two analyses, the most important of which is that Foley et al. (2011) use a mass estimate that combines SZ and X-ray data, whereas this work only reports an SZ-derived mass. The central value of the Foley et al. (2011) combined SZ/X-ray mass estimate is 30% higher than the central value of the SZ-derived mass reported here. We have included the Foley et al. (2011) combined mass as a point in Figure 5 and have also plotted the M11 exclusion curve corresponding to <5% likelihood of finding a cluster in the SPT survey in 32% of parameter probability. As expected from the result in Foley et al. (2011), the p = 32% exclusion curve nearly intersects the central SPT-CL J2106-5844 mass value from that work (adjusted appropriately for the M11 plot).

While no individual cluster lies above either p = 95% exclusion line in Figure 5, there are several which come reasonably close. One might imagine that the collective "unlikelihood" of these clusters could indicate the need to go beyond the standard ΛCDM cosmological model. The most straightforward extension to ΛCDM that could explain an excess of massive clusters (including ones at high redshift) is the possibility of a non-Gaussian component to the primordial density perturbations. Different models of inflation predict different levels and types of non-Gaussianity (e.g., Bartolo et al. 2004), with the size of the leading-order non-Gaussian term described by the parameter f_NL. We have included the mass and redshift distribution of the clusters presented here in a cosmological likelihood calculation with and without f_NL as a free parameter. The likelihood calculation was implemented as in V10, with the effect of f_NL on cluster abundance added following the prescription of Dalal et al. (2008). To simplify the selection function and mass scaling part of the calculation, the preview-depth relation (see Table 2) was used for all clusters, and preview-depth values of ξ were estimated for the full-depth clusters by making co-added maps of only one-ninth of the observations and running the cluster finder on these maps. As in V10, the scaling relation is not expected to capture the correct behavior at low redshift; as in V10, we exclude this regime by applying a hard cut z > 0.3 in this analysis.

The preferred value of f_NL in the extended model is consistent with zero (f_NL = 30 ± 450 at 68% confidence). We note that this is a significantly weaker constraint than that found by Komatsu et al. (2011) using the CMB bispectrum as measured in the WMAP7 data, but that the two results are consistent with each other and with f_NL = 0. This is in tension with the recent results of Cayón et al. (2010), Hoyle et al. (2010), and Enqvist et al. (2010), who found significant evidence for non-zero f_NL based on other high-redshift galaxy clusters using a different statistical technique. In contrast to those works, this analysis uses a likelihood analysis over the full range of mass and redshift space including the SPT selection function, marginalizing over scaling relation uncertainties. This approach naturally incorporates information about both the mass and redshift distribution and the total number of clusters. Our f_NL constraints do not change appreciably and are still fully consistent with f_NL = 0 if we re-run the analysis using a prior on the ξ–M relation that incorporates the scaling between SZ and X-ray masses discussed in Section 4.1.