GALAXY CLUSTERS DISCOVERED VIA THE SUNYAEV–ZEL'DOVICH EFFECT IN THE FIRST 720 SQUARE DEGREES OF THE SOUTH POLE TELESCOPE SURVEY

SPT is a 10 m telescope designed to survey a large area of the sky at millimeter wavelengths with arcminute angular resolution (Ruhl et al. 2004; Padin et al. 2008; Carlstrom et al. 2011). The first SPT receiver was a three-band (95, 150, and 220 GHz) bolometer camera optimized for studying the primary CMB anisotropy and the tSZ effect. From the time the SPT was commissioned through the end of 2011, the majority of observing time was spent on the recently completed 2500 deg² SPT survey. The cluster catalog presented in this paper is derived from the first 720 deg² of this survey. This area was observed during the Austral winters of 2008 and 2009. In addition to the early SPT galaxy cluster results discussed in Section 1, science results from early subsets of the survey data have included measurements of the primary and secondary CMB anisotropy (Keisler et al. 2011; Lueker et al. 2010; Shirokoff et al. 2011; Reichardt et al. 2012), a measurement of gravitational lensing of the CMB (van Engelen et al. 2012), and the discovery of a new population of extremely bright submillimeter galaxies (Vieira et al. 2010).

For cluster-finding, we use data from the SPT 95 GHz and 150 GHz frequency bands. The effective band centers for a non-relativistic tSZ spectrum are 97.6 GHz and 152.9 GHz. The 220 GHz band is centered near the tSZ null, so it contains effectively no SZ cluster signal; the 220 GHz data is also too shallow to effectively subtract the CMB. In the 2008 observing season, the 480 detectors at 150 GHz performed well, but the 95 GHz detectors did not meet specifications. The receiver was reconfigured for the 2009 observing season with 640 detectors at 150 GHz and 160 new detectors at 95 GHz. We observed roughly 170 deg² in two fields in 2008 and 550 deg² in three fields in 2009. Each field was observed to a minimum depth of 18 μK_CMB-arcmin at 150 GHz.³⁴ The 2009 fields were observed to a minimum depth of 44 μK_CMB-arcmin at 95 GHz. The SPT map of the first of the two 2008 fields is publicly available (Schaffer et al. 2011).

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 (Schaffer et al. 2011). One field (ra21hdec-50) was observed with a hybrid scan strategy including scans at both constant elevation and constant azimuth. This scan strategy changes the filtered point spread function for this field compared to the rest of the data, which affects the SPT signal-to-noise ratio (S/N) to cluster mass scaling relations presented in Section 6.2.

The SPT beams have been measured using a combination of bright active galactic nuclei (AGNs) in the survey fields and targeted observations of planets (Shirokoff et al. 2011; Keisler et al. 2011). The SPT beam can be described by a main lobe and a diffuse sidelobe. For compact sources such as galaxy clusters, the effect of the sidelobe is degenerate with a calibration factor, and we choose to fold it into the calibration. The SPT main lobe beam is well-described by a Gaussian with FWHM = 16 and 119 at 95 and 150 GHz, respectively. The 2009 data in this work are calibrated using observations of RCW38, a galactic H ii region (Staniszewski et al. 2009, W11), while the 2008 data are calibrated by cross-correlating dedicated SPT observations of large patches of sky with WMAP observations of those same regions (V10).

The pointing model is determined using daily observations of galactic H ii regions and sensors on the telescope structure sensitive to temperature and mechanical movement (Schaffer et al. 2011). The final pointing in the maps is checked against the positions of radio sources in the Australia Telescope 20 GHz survey (AT20G, Murphy et al. 2010), which has positional accuracy to better than 1 arcsec. The absolute SPT pointing measured in this way is accurate to 3 arcsec. The rms pointing uncertainty in the maps is 7 arcsec.

The map-making algorithm for the SPT data has been described in detail in Lueker et al. (2010), Shirokoff et al. (2011), and V10. In overview, the first step is to apply a relative calibration to the time-ordered data (TOD) and then bandpass filter the TOD. Correlated atmospheric signals are removed by subtracting the mean signal across a set of adjacent bolometers. We mask bright point sources detected at >5 σ at 150 GHz (> ∼ 6 mJy) before filtering. The pointing for each detector is reconstructed, and the data from each detector are co-added into a map with inverse-noise weighting.

The maps (and cluster list) for the 2008 season are identical to those presented by V10. Maps for the 2009 season have several small differences in the filtering detailed below.

• 1.  
  In V10, the bandpass filter was set by a high-pass filter (HPF) at 0.25 Hz and a low-pass filter at 25 Hz. In 2009, different fields were observed at different scan speeds, so we choose to define the HPF with respect to angular multipole ℓ. The HPF of the 2009 data is at ℓ = 400; the V10 HPF corresponds to ℓ ≃ 350. As in V10, the HPF is implemented by removing a set of sines and cosines from each scan across the field. We supplement the Fourier mode removal by first fitting and removing a 9th order Legendre polynomial from each scan. The higher order (V10 used first order) is necessitated by the large atmospheric modulation introduced by the subset of observations which scan in elevation. Depending on the observation, this filter acts as a high-pass filter in either the R.A. or decl. direction.
• 2.  
  V10 removed both the mean and slope across the two-dimensional array of all detectors at a single frequency. The 2009 data have four times as many 150 GHz detectors as 95 GHz detectors so the V10 scheme would result in different common mode removal at each frequency. Instead, we follow the treatment in Shirokoff et al. (2011) and remove the mean across sets of neighboring detectors. The 150 GHz detectors are divided into four sets based on their position in the focal plane and the 95 GHz detectors are treated as a single set. This filter set choice produces nearly identical filtering at 95 and 150 GHz.

We use simulations to determine priors on the SZ scaling relations discussed in Section 6.2 as well as the expected false detection rate for the sample. Simulated sky realizations are filtered to match the real data, and noise realizations based on the measured map noise properties are added.

Each simulated sky is a Gaussian realization of the sum of the best-fit lensed WMAP7 ΛCDM primary CMB model, a kSZ model, and point source contributions. The kSZ power spectrum is taken from the Sehgal et al. (2010) simulations and has an amplitude, D_l = l(l + 1)C_l, of 2.05 μK² at ℓ = 3000. We include both Poisson and clustered point sources. The Poisson contribution reflects both radio source and dusty, star-forming galaxy (DSFG) populations. The amplitude of the radio source term is set by the de Zotti et al. (2005) model source counts to an amplitude D^r₃₀₀₀ = 1.28 μK² at 150 GHz with an assumed spectral index of α_r = −0.6 (defined by flux ∝ν^α). The amplitude of the Poisson DSFG term at 150 GHz is D^p₃₀₀₀ = 7.7 μK². Finally, the clustered DSFG component is modeled by a D_ℓ∝ℓ term normalized to D^c₃₀₀₀ = 5.9 μK² at 150 GHz. The DSFG terms have an assumed spectral index of 3.6. The amplitude of each component was selected to be consistent with the Shirokoff et al. (2011) band powers.

For the determination of the SZ detection significance to cluster mass scaling, we also add a map of the tSZ effect; this tSZ map is not included when estimating the false detection rate. The tSZ map is drawn from a 4000 deg² simulation by Shaw et al. (2010). Note that the limited sky area in this simulation means that we reuse the same tSZ maps between different fields in order to get 100 realizations. This limitation does not exist for the Gaussian realizations.

We use the simulations described above, omitting the tSZ component, in order to estimate the rate of false detections arising from noise and non-cluster astrophysical signals. The resulting rates are shown in Figure 1. As expected, the false detection rate is essentially indistinguishable between the fields; there are the same number of Nσ noise fluctuations per unit area. The simulations lead to a prediction of 6.4 false detections in the >5 σ catalog and 59 false detections in the >4.5 σ catalog.

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For each cluster candidate, we estimate the integrated Comptonization by fitting the cluster to a projected spherical β-model with β = 1

$$\begin{equation} Y(\theta) = y_0 \left(1+\frac{\theta ^2}{\theta _c^2} \right)^{-1}, \end{equation} \tag{ 3 }$$

where y₀ is peak Comptonization and θ_c is the angular radius of the cluster core. The integrated Comptonization is defined as

$$\begin{equation} Y_{\theta _I} = 2\pi \int _0^{\theta _I} Y(\theta) d\theta. \end{equation} \tag{ 4 }$$

In Table 6, we set θ_I = 1' and report $Y_{1^{\prime }}$. We expect measurements of $Y_{1^{\prime }}$ to be robust despite the well known degeneracy between θ_c and the central Compton parameter y₀ for observations that do not resolve the cluster core (e.g., Planck Collaboration et al. 2011).

The likelihood of a set of cluster model parameters $\mathcal {H}$ given our set of observed maps $D_{\nu }(\bar{x})$ is defined as

$$\begin{eqnarray} \log (&P&(D|\mathcal {H})) = \nonumber\\ && -\frac{1}{2}\sum _{\bar{k},\nu 1,\nu 2}\frac{(\widetilde{D}_{\nu _1}(\bar{k})-\widetilde{s}^{\mathcal {H}}_{\nu _1}(\bar{k}))(\widetilde{D}_{\nu _2}(\bar{k})-\widetilde{s}^{\mathcal {H}}_{\nu _2}(\bar{k}))^*}{N_{\nu _1 \nu _2}(\bar{k})}, \end{eqnarray} \tag{ 5 }$$

where $\widetilde{D}_{\nu }(\bar{k})$ is the Fourier transform of the map for frequency ν, $\widetilde{s}^{\mathcal {H}}_{\nu }$ is the frequency-dependent Fourier transform of the cluster model for parameters set $\mathcal {H}$ which we define as ($\bar{x}, \theta _c, y_0$), and $N_{\nu _1\nu _2}(\bar{k})$ is the frequency-dependent covariance matrix of the set of maps which accounts for the same noise and astrophysical components used in the matched filter analysis. For the cluster profile, we use the projected spherical β-model defined above. We only fit the profile within θ < 5θ_c.

We use the Rapid Gridded Likelihood Evaluation (RGLE) method (T. Montroy et al., in preparation) to evaluate the cluster likelihood and compute $Y_{1^{\prime }}$. The RGLE method is based on computing the likelihood for each cluster candidate on a fixed grid in parameter space. In this case, it is a four-dimensional grid over the parameters set $\mathcal {H}$. We define the extent of the grid as follows. The 2D position, $\bar{x}$, is constrained to be within 15 of the matched filter position. The central decrement is allowed to range from −4.3 × 10⁻⁴ to 2.2 × 10⁻³; this prior does not impact the results. The core radius, θ_c, is required to be between 0' and 75. For cluster candidates at z > 0.125, we additionally limit the physical core radius (r_c) of the cluster to be less than 1 Mpc. We translate between r_c and θ_c based on the redshift of each cluster candidate (or redshift lower limit if unconfirmed). A core radius of 1 Mpc is much larger than the typical cluster size, so this limit allows full exploration of the likelihood degeneracy between Y₀ and θ_c while reducing the chance of bias due to noise fluctuations on scales much larger than the expected cluster size.

To compute the probability distribution for $Y_{1^{\prime }}$, we first marginalize the four-dimensional grid over position (i.e., $\bar{x}$) to determine the two-dimensional likelihood surface for (θ_c, y₀). The value of $Y_{1^{\prime }}$ at each (θ_c, Y₀) is calculated from Equation (4) with θ_I = 1'. Formally, the likelihood for a given value of $Y_{1^{\prime }}$ can be computed by integrating the likelihood surface over curves of constant $Y_{1^{\prime }}$,

$$\begin{equation} P(D|Y_{1^{\prime }} = Y_i) = \int dY_0 d \theta _c P(D|Y_0,\theta _c) \delta (Y_{1^{\prime }}(Y_0,\theta _c)-Y_i). \end{equation} \tag{ 6 }$$

The median value and 68% confidence intervals for $Y_{1^{\prime }}$ are determined from this likelihood function.

When applying the RGLE method to the SPT maps in order to estimate $Y_{1^{\prime }}$, we use the calibration and beam shapes reported in Reichardt et al. (2012). We note that for the 2009 data, these are slightly different from the calibration and beam model described in Section 2.1 and used in cluster finding in this work. We use maps at 95 GHz (where available) and 150 GHz to estimate the cluster properties. To limit contamination from point sources, we use maps where previously identified point sources have been subtracted. The point source amplitudes are estimated using a variant of the RGLE which fits for the point source amplitudes given the beam shape. The point source subtraction significantly changes $Y_{1^{\prime }}$ for very few clusters since all affected point sources are at least 8' away from any cluster candidate.

The RGLE method was previously used in Story et al. (2011) to compute integrated Comptonization for SPT follow-up observations of Planck ESZ cluster candidates (Planck Collaboration et al. 2011). The method has been verified by extensive simulations; we have also checked that the RGLE method produces comparable results to an alternative method based on Markov Chain Monte Carlo based sampling of the likelihood surface (B. Saliwanchik et al., in preparation).

Every SPT-selected cluster candidate is followed up with optical imaging observations, and many candidates are also targeted with NIR imaging. Our strategy has evolved over time in order to utilize limited telescope resources to measure redshifts for the majority of cluster candidates. Briefly, the SPT candidates are pre-screened with Digitized Sky Survey (DSS) data. Candidates that appear to be at low redshift are followed up with the 1 m Swope telescope. Candidates that appear to be at high redshift (i.e., that do not appear in DSS images) are targeted with the 4 m Blanco telescope at CTIO or the 6.5 m Magellan telescopes at Las Campanas Observatory. The 4–6 m class observing is performed using an adaptive strategy, wherein candidates are imaged for a short time in three bands, then with a second pass in two bands if the cluster has not been detected. The second-pass imaging is designed to reach depths sufficient to confirm a z ∼ 0.9 cluster. Given weather and other constraints, not all candidates were observed to full depth.

Space-based NIR observations with Spitzer/IRAC were obtained at 3.6 μm and 4.5 μm for the subset of candidates that were both above a given significance threshold and not identified as low-redshift clusters in DSS data. The significance threshold was ξ ⩾ 4.5 for 350 deg² of SPT coverage and ξ ⩾ 4.8 for the remaining 370 deg² of SPT coverage. Candidates that were not imaged with Spitzer—and for which redshifts could not be estimated from the acquired optical data—were targeted with K_s-band observations with the NEWFIRM camera on the Blanco 4 m.

A number of clusters were also observed using either long-slit or multi-slit spectrographs in subsequent follow-up projects. A robust biweight location estimator (Beers et al. 1990) is used to determine the cluster spectroscopic redshifts from ensemble spectra of member galaxies. Of the clusters in this work, 57 have spectroscopic redshifts, either from the literature or from our targeted observations. The redshifts are shown in Table 6, and the source for every spectroscopic redshift is presented by S12.

All optical images are processed using the PHOTPIPE analysis pipeline (Rest et al. 2005; Miknaitis et al. 2007), as was done in previous SPT optical follow-up analyses (High et al. 2010; Williamson et al. 2011; Story et al. 2011). A separate reduction of the optical data from the Blanco Mosaic-II imager is performed using a version of the Dark Energy Survey (DES) data management pipeline (Mohr et al. 2008; Desai et al. 2012), which will eventually be used for analysis of data once the DES begins. The Spitzer/IRAC imaging data are processed from the standard online pipeline system and analyzed as described in Ashby et al. (2009); NEWFIRM data are reduced using the FATBOY pipeline (Eikenberry et al. 2006).

Redshifts are estimated for each candidate using three methods as described by S12. The first two methods are based on the identification of red-sequence overdensities and are described in detail in High et al. (2010) and Song et al. (2012a), respectively. The third method estimates photometric redshifts for individual galaxies using the ANNz algorithm (Collister & Lahav 2004), and cluster redshifts are estimated by measuring a peak in a manually selected red galaxy photometric redshift distribution. For a given cluster candidate, redshift estimates from the three methods are compared, outliers are flagged, and a combined redshift estimate is produced. In cases where only the Spitzer/IRAC 3.6 μm and 4.5 μm data are deep enough to detect the cluster, we use the High et al. (2010) method to estimate the redshift. Tests confirm this to be reliable at z > 0.7 and a similar method is described in Stern et al. (2005) and Papovich (2008). These redshifts and associated uncertainties are shown in Table 6. If none of the three methods is successful at estimating a redshift for a given candidate, we report a lower redshift limit based upon the depth of the follow-up imaging.

4.3.1. Dedicated X-Ray Observations of SPT Clusters

4.3.2. ROSAT Counterparts

As discussed in Section 3, any cluster detections within 8' of an emissive point source detected above 5σ at 150 GHz are rejected. We do this because residual source flux or artifacts due to the masking of these point sources can cause spurious decrements when the maps are filtered. A total area of ∼50 out of 770 deg² (∼6.5%) was excluded from cluster finding for this reason. This conservative procedure is appropriate for constructing a cluster catalog with a clean, easy-to-define selection function and a mass-observable relation with minimal outliers. However, it is likely that several massive clusters will lie within the exclusion region, and some of those clusters might be only minimally affected by the nearby emissive source. If we assume no spatial correlation between sources and clusters, we would expect roughly eight missed clusters above ξ = 5.

As in W11, we re-ran the cluster-finding algorithm on all the fields used in this work with only the very brightest sources masked. For this work we used a bright-source threshold of S_150 GHz > 100 mJy, compared to the normal threshold of ∼6 mJy, resulting in a total masked area of <3 deg². Each detection with ξ ⩾ 5 from the originally masked area was visually inspected (below the ξ = 5 threshold, it becomes too difficult to distinguish visually between real clusters and artifacts), and the vast majority were rejected as obvious point-source-related artifacts. Some detections, however, did appear to be significant SZ decrements only minimally affected by the nearby source. These objects are listed in Table 3. We find six objects above ξ = 5, consistent within Poisson uncertainties with the expected number. One of these objects, SPT-CL J2142-6419, was also identified in the auxiliary detection procedure in W11. Two of the six objects (SPT-CL J2154-5952 and SPT-CL J2154-5936) are unusually close to one another on the sky (165 separation), but visual inspection shows nothing out of the ordinary about either candidate beyond its proximity to an emissive source.

We have not yet attempted to obtain redshifts for these six cluster candidates, and they are not included in the cosmological analysis or in the total number of candidates quoted in the rest of the text. We perform the same search for counterparts to these six candidates in other galaxy cluster catalogs as we do for the main sample. We find no galaxy cluster matches, though we do find X-ray sources within 5 arcmin of SPT-CL J0334-6008 and within 2 arcmin of SPT-CL J0434-5727, SPT-CL J0442-5905, and SPT-CL J2154-5936.

Following Vikhlinin et al. (2009b) and B11, we use Y_X as an X-ray proxy for cluster mass, M₅₀₀. We assume a Y_X − M₅₀₀ relation of the form

$$\begin{equation} \frac{\mbox{$M_{\mbox{\scriptsize 500}}$}}{ 10^{14}\,M_{\odot }\,h^{-1} } = \left(A_X h^{3/2}\right)\! \left(\frac{Y_X}{3 \times 10^{14}\,M_{\odot }\,{\rm keV}} \right)^{B_{X}}\!\! \left(\frac{H(z)}{ H_0}\right)^{C_{X}}, \end{equation} \tag{ 7 }$$

parameterized by the normalization A_X, the slope B_X, the redshift evolution C_X, and a log-normal scatter D_X on Y_X. We express the mass in units of M_☉ h⁻¹ to match the ζ − M₅₀₀ relation in Section 6.2. For our cosmological analysis, we assume the same Gaussian priors on the scaling relation parameters as B11. The priors are motivated by constraints from X-ray measurements by Vikhlinin et al. (2009a) and simulations, and are discussed in detail by B11. The Gaussian priors are A_X = 5.77 ± 0.56, B_X = 0.57  ±  0.03, C_X = −0.4  ±  0.2, and D_X = 0.12  ±  0.08. We do not see movement away from these priors (i.e., evidence for tension between the prior and data) in the MCMCs presented in later sections. The scaling relation has more freedom that required by the data; if all parameters except A_X are fixed, the cosmological results are unchanged.

As in V10 and B11, we estimate galaxy cluster masses according to an SZ S/N to mass scaling relation. Following those works, we introduce the unbiased significance, ζ, since the relation between ξ and halo mass is complicated by the comparable effects of intrinsic scatter and instrumental noise. The unbiased significance is defined to be the average detection S/N of a simulated cluster, measured across many noise realizations, and related to the detection significance ξ as follows:

$$\begin{equation} \zeta = \sqrt{\langle \xi \rangle ^2-3} \end{equation} \tag{ 8 }$$

at ξ > 2. The detection significance ξ is maximized across possible cluster positions and filters scales, effectively adding three degrees of freedom to the fit. The unbiased significance ζ removes this maximization bias.

The specific form of the scaling relation is

$$\begin{equation} \zeta = A_{{\rm SZ}} \left(\frac{\mbox{$M_{\mbox{\scriptsize 500}}$}}{3 \times 10^{14}\,M_{\odot }\,h^{-1}} \right)^{B_{{\rm SZ}}} \left(\frac{H(z)}{H(0.6)}\right)^{C_{{\rm SZ}}}, \end{equation} \tag{ 9 }$$

where A_SZ is a normalization, B_SZ a mass evolution, and C_SZ a redshift evolution. The method to go from simulations to an SZ S/N to mass scaling relation is described in more detail by V10.

As described more fully in V10, this scaling relation is based on SZ simulations of approximately 4000 deg² of sky. The simulations used in this work are described in Section 3.1. The intrinsic scatter, D_SZ, was measured to be 24% in these simulations. The main uncertainty for cosmological purposes is on the mass normalization, A_SZ, which is assumed to be uncertain at the 30% level (V10).

Note that the dusty galaxies, radio galaxies and the kSZ effect in these simulations are not correlated with the tSZ effect. B11 argue that the level of correlated emission from dusty or radio galaxies is negligible; these arguments apply equally well to this sample since the mass and redshift ranges are similar. The probability of a chance superposition from a bright point source (≳ 6 mJy) is negligible given the sky density of sources (∼1 deg²; Vieira et al. 2010). We have tested whether including the correlation between the kSZ and tSZ signals would impact the predicted scaling relation. We find only small changes to A_SZ, <3% which is less than 0.1 σ for the prior. There is also a small increase in the scatter of less than 0.2 σ of the prior width. As these corrections are tiny compared to the overall prior uncertainties, we do not include them in this analysis.

Unlike V10, this analysis includes fields with substantially different noise levels. We have repeated the simulations (see Section 3.1) on each field, and find the main effect is an overall rescaling of the expected SZ S/N for a given cluster mass, i.e., a change to A_SZ. There is a slight change to the redshift evolution between fields as well, but neglecting this results in an additional percent level scatter which is completely negligible given the overall 24% scatter in the scaling relation. We have also checked the simulations by adding known cluster profiles to the real maps, applying the cluster-finding algorithm and checking the recovered S/N. This semi-analytic test agrees well with the results of the simulations. We apply a fixed rescaling of A_SZ to each field, as tabulated in Table 4. The normalization of the rescaling is chosen such that the ra5h30dec-55 field is unity. We use simulations of all five fields to estimate the parameters A_SZ, B_SZ, C_SZ, and D_SZ for the combined scaling relation, and determine values of 6.24, 1.33, 0.83, and 0.24 respectively. Uncertainties in the SZ modeling lead to significant systematic uncertainties on these scaling relation parameters. Following V10, we apply conservative 1.872, 0.266, 0.415, and 0.048 (30%, 20%, 50%, and 20%) Gaussian uncertainties to A_SZ, B_SZ, C_SZ, and D_SZ, respectively.

We have written a module extension to CosmoMC to calculate the cluster likelihood function. In essence, this module uses the Cash statistic (Cash 1979) to compare the observed number counts to a known Poisson distribution at each step in the MCMC. The method closely mirrors that presented by B11, to whom we refer the reader for a complete description. Briefly, we use the Tinker mass function (Tinker et al. 2008) to calculate the mass function based on the cosmological parameters and associated matter power spectra estimated by CAMB (Lewis et al. 2000) at 20 logarithmically spaced redshifts between 0 < z < 2.5. The mass function is calculated for an over-density of 500 times the critical density. Using the scaling relation parameters at that step of the MCMC, the mass function is translated from the native M₅₀₀-z space into the three-dimensional observable space, with axes corresponding to the SZ detection significance ξ, the X-ray parameter Y_X, and the optically derived redshift z. The observed number counts are compared to the expectation values in this three dimensional space to evaluate the likelihood for that step of the MCMC.

There are two differences between the likelihood function used in this work and that presented by B11. The most significant of these is the field-dependent SZ scaling relation described in Section 6.2. In practice, this means that the above calculation is done separately for each of the five fields, and the resulting log likelihoods are summed.

The treatment of unconfirmed cluster candidates is the second, more minor difference between this work and B11. B11 left unconfirmed clusters out of the analysis; this is appropriate given the extremely high redshift lower limit on the single unconfirmed (and almost certainly false) cluster candidate in that cluster sample. A more rigorous treatment includes the likelihood of each unconfirmed candidate, using the expectation value of the candidate being either a higher redshift cluster or a false detection. This expectation value is the sum of the expected number of false detections at a given detection significance and a redshift-dependent selection function convolved by the mass function. In practice, the treatment of unconfirmed clusters is nearly negligible since the S/N > 5 sample used to derive cosmological constraints has high purity and the precision of the cosmological constraints is currently limited by the systematic mass calibration uncertainty.

With this in mind, we make two simplifying approximations in our implementation. First, we neglect any cosmological dependence in the false detection rate—the simulations used to calculate the false detection rate are only run for one cosmological model. This effect should be negligible since the CMB and foreground power levels are well-known. Second, we treat the redshift selection function for unconfirmed candidates as a Heaviside function at the quoted redshift limit for that cluster candidate. The chance of detecting a cluster out to this redshift is nearly unity with the current optical and NIR observations. We have tested shifting the Heaviside function to z > 1.5 or z > 2 and find no impact on the cosmological constraints. This can be understood intuitively because (1) the overall purity is high, and (2) the expected number of unconfirmed, real, high-redshift clusters is small compared to the expected number of false detections.

In a ΛCDM model, cluster samples primarily constrain σ₈ and Ω_m (see e.g., B11, Rozo et al. 2010). As was done by B11, we look at "cluster-only" constraints based on ${\rm SPT_{{\rm CL}}}$+BBN+H₀ with the reionization optical depth fixed to τ = 0.08. The external data and τ prior are required since cluster abundances are insensitive to several ΛCDM parameters, including τ. We see a substantial improvement in the ${\rm SPT_{{\rm CL}}}$+BBN+H₀ constraints with the expanded cluster catalog from this work; the allowed likelihood volume is reduced by approximately a factor of two (compare the filled red/orange contours and black contours in Figure 5).

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Adding the new SPT cluster sample to the WMAP7 and SPT CMB power spectrum data improves the constraints on Ω_m, Ω_ch², σ₈, and h by roughly a factor of 1.5 over the CMB alone. The constraints are listed in the first two columns of Table 5. The cluster data modestly tightens constraints on the amplitude of the primordial power spectrum as well. The uncertainty on the amplitude is reduced by 24% from ln(10¹⁰A_s) = 3.196 ± 0.042 to 3.176 ± 0.034.

However, these constraints are only marginally better than those presented by B11. As shown in Figure 5, the ${\rm SPT_{{\rm CL}}}$ constraints in the Ω_m − σ₈ plane are most improved along a direction well constrained by the CMB data. For constraints in the perpendicular direction, the ${\rm SPT_{{\rm CL}}}$ data are limited by the current mass calibration uncertainty, determined from the Y_X − M scaling relation which is unchanged from B11. The mass calibration uncertainty would need to be reduced by a factor of ∼2.5 to be comparable to the statistical uncertainty. A better mass calibration will be essential to realize the full potential of cosmological constraints from galaxy clusters.

7.1.1. Comparison to Expected Number Counts

7.1.2. Mass Estimates

We present mass estimates based on the posterior probability distributions for all optically confirmed clusters in Table 6. In all cases, we quote M₅₀₀, as defined in Section 5. For the 15 clusters with X-ray data from A11, these are joint X-ray and SZ mass estimates. Only the SZ data are used for the other clusters. We calculate a probability density function on a mass grid at each point in the CMB+BAO+SN+H₀+${\rm SPT_{{\rm CL}}}$ parameter chain for a ΛCDM cosmology. The allowed ΛCDM parameter ranges for this data set are essentially unchanged from the CMB+${\rm SPT_{{\rm CL}}}$ data set. These probability density functions are combined to obtain a mass estimate that has been fully marginalized over all cosmological and scaling relation parameters.

Table 6. Galaxy Clusters Above 4.5σ in 720 deg² Observed by the SPT

ID and Coordinates			YSZ × 106	Significances			Best		Redshift	M500
SPT ID	R.A.	Decl.	(arcmin2)	θc = 05	15	25	ξ	θc		(1014 h−170 M☉)
SPT-CLJ0000-5748*	0.2496	−57.8066	107 ± 24	5.48	4.84	4.38	5.48	0.50	0.7019	4.29 ± 0.71
SPT-CLJ0201-6051	30.3933	−60.8592	73 ± 19	4.44	3.50	2.39	4.83	0.25	>1.05a	...
SPT-CLJ0203-5651	30.8309	−56.8612	74 ± 19	4.78	4.02	2.45	4.98	0.25	>1.00a	...
SPT-CLJ0205-5829	31.4437	−58.4856	185 ± 19	10.39	8.96	7.19	10.54	0.25	1.3220	4.79 ± 1.00
SPT-CLJ0205-6432	31.2786	−64.5461	103 ± 19	6.02	5.04	3.91	6.02	0.50	0.7440	3.29 ± 0.79
SPT-CLJ0209-5452	32.3491	−54.8794	83 ± 21	4.52	4.40	4.05	4.52	0.50	0.42 ± 0.03	2.46 ± 0.89
SPT-CLJ0211-5712	32.8232	−57.2157	66 ± 21	4.65	3.66	3.05	4.77	0.25	>1.03a	...
SPT-CLJ0216-5730	34.1363	−57.5100	85 ± 20	4.72	4.48	3.79	4.72	0.50	>1.03a	...
SPT-CLJ0216-6409	34.1723	−64.1562	94 ± 19	5.53	4.92	4.27	5.54	0.25	0.64 ± 0.03	3.07 ± 0.86
SPT-CLJ0218-5826	34.6251	−58.4386	78 ± 20	4.48	4.15	3.17	4.54	0.25	0.57 ± 0.03	2.36 ± 0.86
SPT-CLJ0221-6212	35.4382	−62.2044	65 ± 19	4.53	3.66	2.96	4.71	0.25	>1.20a	...
SPT-CLJ0230-6028	37.6410	−60.4694	98 ± 19	5.79	4.87	3.84	5.88	0.25	0.74 ± 0.08	3.21 ± 0.79
SPT-CLJ0233-5819	38.2561	−58.3269	131 ± 20	6.34	6.44	5.67	6.64	1.25	0.6630	3.71 ± 0.86
SPT-CLJ0234-5831	38.6790	−58.5217	270 ± 19	14.65	13.03	10.54	14.65	0.50	0.4150	7.64 ± 1.50
SPT-CLJ0239-6148	39.9120	−61.8032	74 ± 19	4.50	3.46	2.75	4.67	0.25	>1.06a	...
SPT-CLJ0240-5946	40.1620	−59.7703	169 ± 19	8.99	8.64	7.63	9.04	0.75	0.4000	5.29 ± 1.07
SPT-CLJ0240-5952	40.1982	−59.8785	74 ± 19	4.53	3.64	2.50	4.65	0.25	0.62 ± 0.03	2.43 ± 0.86
SPT-CLJ0242-6039	40.6551	−60.6526	90 ± 20	4.87	4.77	4.26	4.92	1.00	>1.50a	...
SPT-CLJ0243-5930	40.8616	−59.5132	126 ± 19	7.30	6.23	5.18	7.42	0.25	0.65 ± 0.03	4.18 ± 0.89
SPT-CLJ0249-5658	42.4068	−56.9764	96 ± 20	5.37	5.21	4.48	5.44	0.75	0.23 ± 0.02	3.32 ± 0.89
SPT-CLJ0253-6046	43.4605	−60.7744	86 ± 21	4.61	4.73	4.27	4.83	1.25	0.44 ± 0.02	2.71 ± 0.86
SPT-CLJ0254-5857	43.5729	−58.9526	295 ± 22	13.61	14.42	13.82	14.42	1.50	0.4380	7.46 ± 1.46
SPT-CLJ0254-6051	43.6015	−60.8643	127 ± 21	6.35	6.59	5.75	6.71	1.00	0.44 ± 0.02	4.00 ± 0.93
SPT-CLJ0256-5617	44.1009	−56.2973	136 ± 19	7.54	6.98	5.83	7.54	0.50	0.63 ± 0.03	4.25 ± 0.89
SPT-CLJ0257-5732	44.3516	−57.5423	95 ± 19	5.28	4.53	3.51	5.40	0.25	0.4340	3.14 ± 0.86
SPT-CLJ0257-5842	44.3924	−58.7116	105 ± 21	5.35	5.19	4.71	5.38	1.00	0.42 ± 0.02	3.14 ± 0.86
SPT-CLJ0257-6050	44.3354	−60.8450	96 ± 23	4.46	4.68	4.32	4.76	1.25	0.48 ± 0.03	2.64 ± 0.86
SPT-CLJ0258-5756	44.5562	−57.9438	95 ± 22	4.06	4.50	4.18	4.50	1.50	>1.05a	...
SPT-CLJ0300-6315	45.1430	−63.2643	73 ± 22	3.61	4.29	4.85	4.88	2.75	>1.50a	...
SPT-CLJ0301-6456	45.4780	−64.9470	78 ± 20	4.79	4.07	2.99	4.94	0.25	0.65 ± 0.03	2.61 ± 0.82
SPT-CLJ0307-6226	46.8335	−62.4336	156 ± 20	8.15	8.09	6.94	8.32	0.75	0.61 ± 0.03	4.68 ± 0.96
SPT-CLJ0311-6354	47.8283	−63.9083	136 ± 20	7.06	7.11	6.29	7.33	1.00	0.30 ± 0.02	4.46 ± 0.96
SPT-CLJ0313-5645	48.2604	−56.7554	90 ± 20	4.70	4.50	3.82	4.82	0.75	0.63 ± 0.03	2.54 ± 0.82
SPT-CLJ0316-6059	49.2179	−60.9849	92 ± 19	4.45	3.95	3.28	4.59	0.25	>1.50a	...
SPT-CLJ0317-5935	49.3208	−59.5856	100 ± 19	5.80	5.00	4.00	5.91	0.25	0.4690	3.46 ± 0.89
SPT-CLJ0320-5800	50.0316	−58.0084	74 ± 21	3.93	4.47	4.42	4.54	2.25	>0.99a	...
SPT-CLJ0324-6236	51.0530	−62.6018	163 ± 19	8.59	8.01	6.82	8.59	0.50	0.74 ± 0.03	4.68 ± 0.96
SPT-CLJ0328-5541	52.1663	−55.6975	151 ± 23	6.71	6.98	6.75	7.08	1.75	0.0844	4.50 ± 1.00
SPT-CLJ0333-5842	53.3195	−58.7019	81 ± 21	4.43	4.54	4.31	4.54	1.50	0.49 ± 0.04	2.43 ± 0.86
SPT-CLJ0337-6207	54.4720	−62.1176	89 ± 21	4.32	4.84	4.75	4.88	1.75	>1.28a	...
SPT-CLJ0337-6300	54.4685	−63.0098	84 ± 20	5.27	4.80	4.34	5.29	0.25	0.46 ± 0.03	3.07 ± 0.86
SPT-CLJ0341-5731	55.3979	−57.5233	95 ± 19	5.33	4.57	3.45	5.35	0.25	0.64 ± 0.02	2.96 ± 0.82
SPT-CLJ0341-6143	55.3485	−61.7192	119 ± 25	4.22	5.01	5.34	5.60	3.00	0.63 ± 0.03	3.11 ± 0.82
SPT-CLJ0343-5518	55.7634	−55.3049	104 ± 19	5.82	4.88	3.47	5.98	0.25	0.49 ± 0.02	3.50 ± 0.86
SPT-CLJ0344-5452	56.0926	−54.8725	96 ± 19	5.30	4.25	3.08	5.41	0.25	1.01 ± 0.07	2.68 ± 0.75
SPT-CLJ0344-5518	56.2101	−55.3037	94 ± 24	4.95	4.99	4.85	5.02	1.75	0.36 ± 0.02	2.89 ± 0.89
SPT-CLJ0345-6419	56.2518	−64.3326	93 ± 19	5.50	4.95	4.04	5.57	0.25	0.93 ± 0.07	2.86 ± 0.79
SPT-CLJ0346-5839	56.5745	−58.6535	87 ± 20	4.95	4.44	3.50	4.96	0.25	0.74 ± 0.07	2.57 ± 0.79
SPT-CLJ0351-5636	57.9312	−56.6099	88 ± 21	4.44	4.52	4.24	4.65	0.75	0.38 ± 0.03	2.61 ± 0.89
SPT-CLJ0351-5944	57.8654	−59.7457	76 ± 21	4.46	4.73	4.38	4.61	1.75	>0.99a	...
SPT-CLJ0352-5647	58.2366	−56.7992	127 ± 20	7.02	6.97	6.25	7.11	0.75	0.66 ± 0.03	4.00 ± 0.86
SPT-CLJ0354-5904	58.5611	−59.0740	133 ± 22	6.20	6.30	5.72	6.49	1.25	0.41 ± 0.03	3.89 ± 0.89
SPT-CLJ0354-6032	58.6744	−60.5386	68 ± 19	4.38	3.13	2.25	4.57	0.25	1.06 ± 0.07	2.04 ± 0.75
SPT-CLJ0402-6129	60.7066	−61.4988	96 ± 22	4.81	4.76	4.33	4.83	1.00	0.53 ± 0.04	2.64 ± 0.86
SPT-CLJ0403-5534	60.9479	−55.5829	92 ± 21	4.44	4.78	4.67	4.88	1.75	>1.50a	...
SPT-CLJ0403-5719	60.9670	−57.3241	98 ± 19	5.71	5.07	4.18	5.75	0.25	0.43 ± 0.02	3.39 ± 0.89
SPT-CLJ0404-6510	61.0556	−65.1817	113 ± 29	4.28	4.58	4.59	4.75	2.25	0.15 ± 0.02	2.86 ± 0.93
SPT-CLJ0406-5455	61.6922	−54.9205	100 ± 21	5.77	4.85	4.04	5.82	0.25	0.73 ± 0.03	3.18 ± 0.82
SPT-CLJ0410-5454	62.6154	−54.9016	87 ± 21	4.93	4.17	3.24	5.06	0.25	>0.98a	...
SPT-CLJ0410-6343	62.5158	−63.7285	101 ± 19	5.79	5.27	4.31	5.79	0.50	0.49 ± 0.02	3.36 ± 0.86
SPT-CLJ0411-5751	62.8432	−57.8636	95 ± 21	4.71	5.04	4.69	5.16	1.25	0.75 ± 0.02	2.71 ± 0.79
SPT-CLJ0411-6340	62.8597	−63.6810	106 ± 19	6.28	5.63	4.80	6.41	0.25	0.14 ± 0.02	4.04 ± 0.96
SPT-CLJ0412-5743	63.0245	−57.7203	98 ± 21	5.11	5.24	4.87	5.29	1.25	0.38 ± 0.03	3.11 ± 0.89
SPT-CLJ0416-6359	64.1618	−63.9964	107 ± 20	6.03	5.63	4.85	6.06	0.75	0.30 ± 0.02	3.68 ± 0.89
SPT-CLJ0423-5506	65.8153	−55.1036	68 ± 22	4.06	4.42	3.91	4.51	1.25	0.21 ± 0.04	2.61 ± 0.89
SPT-CLJ0423-6143	65.9366	−61.7183	76 ± 20	4.46	4.03	3.12	4.65	0.25	0.71 ± 0.04	2.36 ± 0.79
SPT-CLJ0426-5455	66.5205	−54.9201	163 ± 19	8.86	7.94	6.70	8.86	0.50	0.63 ± 0.03	4.93 ± 1.00
SPT-CLJ0428-6049	67.0291	−60.8302	89 ± 21	4.74	4.89	4.20	5.06	1.25	>1.11a	...
SPT-CLJ0430-6251	67.7086	−62.8536	86 ± 19	5.16	4.56	3.48	5.20	0.25	0.38 ± 0.04	3.04 ± 0.89
SPT-CLJ0431-6126	67.8393	−61.4438	321 ± 54	4.24	5.48	6.36	6.40	3.00	0.0577	4.11 ± 0.96
SPT-CLJ0433-5630	68.2522	−56.5038	102 ± 21	5.02	5.34	5.27	5.35	1.75	0.6920	2.89 ± 0.82
SPT-CLJ0441-5859	70.4411	−58.9931	88 ± 22	3.89	4.36	4.52	4.54	2.25	>1.06a	...
SPT-CLJ0444-5603	71.1130	−56.0566	88 ± 19	5.19	4.21	3.12	5.30	0.25	0.98 ± 0.07	2.61 ± 0.75
SPT-CLJ0446-5849	71.5160	−58.8226	136 ± 19	7.34	6.29	4.95	7.44	0.25	1.16 ± 0.07	3.68 ± 0.82
SPT-CLJ0452-5945	73.1282	−59.7622	85 ± 23	3.78	4.37	4.50	4.50	2.50	>0.66a	...
SPT-CLJ0456-5623	74.1745	−56.3869	79 ± 19	4.76	4.32	3.41	4.76	0.50	0.66 ± 0.03	2.46 ± 0.82
SPT-CLJ0456-6141	74.1496	−61.6840	80 ± 19	4.79	4.05	3.42	4.84	0.25	0.41 ± 0.03	2.71 ± 0.86
SPT-CLJ0458-5741	74.6021	−57.6952	85 ± 23	3.94	4.56	4.91	4.91	2.50	>1.03a	...
SPT-CLJ0502-6113	75.5400	−61.2315	79 ± 19	5.02	4.41	3.54	5.09	0.25	0.66 ± 0.03	2.75 ± 0.82
SPT-CLJ0509-5342*	77.3360	−53.7045	157 ± 25	6.61	6.04	5.09	6.61	0.50	0.4607	5.36 ± 0.71
SPT-CLJ0511-5154	77.9202	−51.9044	119 ± 24	5.63	4.73	3.86	5.63	0.50	0.6450	3.61 ± 0.96
SPT-CLJ0514-5118	78.6859	−51.3100	111 ± 29	4.61	4.82	4.52	4.82	1.50	>1.16a	...
SPT-CLJ0516-5430	79.1480	−54.5062	241 ± 26	9.11	9.37	8.57	9.42	0.75	0.2950	6.46 ± 1.32
SPT-CLJ0521-5104	80.2983	−51.0812	134 ± 28	5.34	5.28	4.96	5.45	1.00	0.6755	3.46 ± 0.96
SPT-CLJ0522-5026	80.5190	−50.4409	121 ± 32	4.50	4.82	4.72	4.87	1.75	0.51 ± 0.03	3.07 ± 1.00
SPT-CLJ0527-5928	81.8111	−59.4833	80 ± 25	4.52	3.66	3.14	4.71	0.25	>0.93a	...
SPT-CLJ0528-5300*	82.0173	−53.0001	110 ± 23	5.42	4.38	3.52	5.45	0.25	0.7678	3.18 ± 0.61
SPT-CLJ0529-5238	82.2923	−52.6417	86 ± 24	4.31	3.50	2.68	4.52	0.25	>1.12a	...
SPT-CLJ0532-5647	83.1586	−56.7893	99 ± 32	3.19	4.09	4.41	4.51	2.75	>0.93a	...
SPT-CLJ0533-5005*	83.3984	−50.0918	116 ± 24	5.51	5.08	4.32	5.59	0.25	0.8810	2.68 ± 0.61
SPT-CLJ0534-5937	83.6018	−59.6289	82 ± 25	4.25	3.53	2.78	4.57	0.25	0.5761	2.71 ± 1.00
SPT-CLJ0537-5549	84.2578	−55.8268	100 ± 30	3.91	4.51	4.55	4.55	2.00	>1.11a	...
SPT-CLJ0538-5657	84.5865	−56.9530	102 ± 30	3.79	4.37	4.61	4.63	2.75	>1.50a	...
SPT-CLJ0539-5744	84.9998	−57.7432	109 ± 25	5.01	4.61	3.86	5.12	0.25	0.76 ± 0.03	3.07 ± 0.93
SPT-CLJ0546-5345*	86.6541	−53.7615	173 ± 24	7.69	6.99	6.20	7.69	0.50	1.0663	5.25 ± 0.75
SPT-CLJ0551-5709*	87.9016	−57.1565	150 ± 28	6.00	6.06	5.48	6.13	1.00	0.4230	3.75 ± 0.54
SPT-CLJ0556-5403	89.2016	−54.0630	100 ± 25	4.72	4.41	3.79	4.83	0.25	0.93 ± 0.04	2.64 ± 0.93
SPT-CLJ0559-5249*	89.9245	−52.8265	228 ± 26	8.81	9.15	8.51	9.28	1.00	0.6090	6.79 ± 0.86
SPT-CLJ2002-5335	300.5113	−53.5913	75 ± 23	4.44	4.30	4.01	4.53	1.25	>1.02a	...
SPT-CLJ2005-5635	301.3385	−56.5902	80 ± 19	4.68	4.38	3.88	4.68	0.50	>0.64a	...
SPT-CLJ2006-5325	301.6620	−53.4287	86 ± 23	4.93	4.77	4.01	5.06	1.00	>1.50a	...
SPT-CLJ2007-4906	301.9663	−49.1105	87 ± 23	4.46	3.84	3.14	4.50	0.25	1.25 ± 0.07	1.93 ± 0.86
SPT-CLJ2009-5756	302.4262	−57.9480	80 ± 19	4.68	4.20	3.42	4.68	0.50	0.63 ± 0.03	2.36 ± 0.79
SPT-CLJ2011-5228	302.7810	−52.4734	75 ± 23	4.46	4.21	3.70	4.55	0.75	0.96 ± 0.04	2.25 ± 0.89
SPT-CLJ2011-5725	302.8526	−57.4214	91 ± 19	5.35	5.25	4.83	5.43	0.75	0.2786	3.18 ± 0.89
SPT-CLJ2012-5342	303.0822	−53.7137	73 ± 23	4.65	4.38	3.84	4.65	0.50	>0.68a	...
SPT-CLJ2012-5649	303.1132	−56.8308	116 ± 25	4.70	5.83	5.99	5.99	2.50	0.0552	3.71 ± 0.93
SPT-CLJ2013-5432	303.4968	−54.5445	78 ± 23	4.23	3.05	1.92	4.75	0.25	>1.02a	...
SPT-CLJ2015-5504	303.9884	−55.0715	79 ± 23	4.64	4.28	3.68	4.64	0.50	>0.61a	...
SPT-CLJ2016-4954	304.0181	−49.9122	100 ± 23	5.01	4.62	3.77	5.01	0.50	0.26 ± 0.02	3.25 ± 0.96
SPT-CLJ2017-6258	304.4827	−62.9763	117 ± 22	5.89	6.45	5.92	6.45	1.50	0.57 ± 0.03	3.61 ± 0.82
SPT-CLJ2018-4528	304.6076	−45.4807	85 ± 23	4.59	4.26	3.41	4.64	0.25	0.40 ± 0.03	2.82 ± 0.96
SPT-CLJ2019-5642	304.7703	−56.7079	94 ± 19	5.17	5.05	4.41	5.25	0.75	0.15 ± 0.03	3.11 ± 0.89
SPT-CLJ2020-4646	305.1936	−46.7702	97 ± 24	5.07	5.08	4.38	5.09	1.25	0.17 ± 0.02	3.43 ± 1.00
SPT-CLJ2020-6314	305.0301	−63.2413	82 ± 19	5.31	4.69	3.84	5.37	0.25	0.58 ± 0.02	2.89 ± 0.82
SPT-CLJ2021-5256	305.4690	−52.9439	190 ± 54	3.44	4.58	5.27	5.31	3.00	0.11 ± 0.02	3.64 ± 1.00
SPT-CLJ2022-6323	305.5235	−63.3973	106 ± 19	6.58	5.91	5.04	6.58	0.50	0.3830	3.82 ± 0.89
SPT-CLJ2023-5535	305.8377	−55.5903	282 ± 24	11.75	13.36	13.04	13.41	1.75	0.2320	7.14 ± 1.43
SPT-CLJ2025-5117	306.4837	−51.2904	183 ± 22	9.37	8.81	7.36	9.48	0.75	0.20 ± 0.02	6.29 ± 1.29
SPT-CLJ2026-4513	306.6140	−45.2256	107 ± 22	5.53	5.09	4.26	5.53	0.50	0.71 ± 0.03	3.32 ± 0.89
SPT-CLJ2030-5638	307.7067	−56.6352	100 ± 20	5.28	5.33	4.89	5.47	1.00	0.39 ± 0.03	3.14 ± 0.86
SPT-CLJ2032-5627	308.0800	−56.4557	167 ± 22	7.64	8.03	7.92	8.14	1.75	0.2840	4.79 ± 1.00
SPT-CLJ2034-5936	308.5408	−59.6007	144 ± 18	8.54	7.62	6.23	8.57	0.25	0.92 ± 0.07	4.32 ± 0.89
SPT-CLJ2035-5251	308.8026	−52.8527	205 ± 23	9.60	9.95	8.97	10.00	0.75	0.47 ± 0.02	6.18 ± 1.25
SPT-CLJ2035-5614	308.9022	−56.2407	76 ± 19	4.43	4.27	3.70	4.55	0.75	>1.02a	...
SPT-CLJ2039-5723	309.8246	−57.3871	76 ± 19	4.69	4.34	4.13	4.69	0.50	>1.25a	...
SPT-CLJ2040-4451	310.2468	−44.8599	122 ± 22	6.08	4.60	3.62	6.28	0.25	1.35 ± 0.07	3.21 ± 0.79
SPT-CLJ2040-5230	310.1255	−52.5052	76 ± 22	4.50	3.41	2.57	4.70	0.25	>1.01a	...
SPT-CLJ2040-5342	310.2195	−53.7122	107 ± 22	5.88	5.36	4.61	5.88	0.50	0.57 ± 0.04	3.68 ± 0.89
SPT-CLJ2040-5725	310.0631	−57.4287	107 ± 19	6.38	5.91	5.03	6.38	0.50	0.9300	3.25 ± 0.75
SPT-CLJ2043-5035	310.8285	−50.5929	151 ± 22	7.81	7.47	6.73	7.81	0.50	0.7234	4.71 ± 1.00
SPT-CLJ2043-5614	310.7906	−56.2351	74 ± 19	4.66	4.00	3.17	4.72	0.25	0.69 ± 0.03	2.36 ± 0.79
SPT-CLJ2045-6026	311.3649	−60.4469	67 ± 19	4.59	3.46	2.51	4.77	0.25	>0.47a	...
SPT-CLJ2046-4542	311.5620	−45.7111	92 ± 23	4.43	4.36	3.73	4.54	1.00	>1.02a	...
SPT-CLJ2048-4524	312.2268	−45.4150	89 ± 24	4.25	4.44	3.96	4.56	1.00	>0.98a	...
SPT-CLJ2051-6256	312.8027	−62.9348	83 ± 20	4.97	5.04	4.39	5.17	1.25	0.47 ± 0.02	2.86 ± 0.86
SPT-CLJ2055-5456	313.9941	−54.9366	113 ± 18	6.61	6.32	5.71	6.61	0.50	0.11 ± 0.02	4.64 ± 1.07
SPT-CLJ2056-5106	314.0723	−51.1163	89 ± 25	4.37	4.60	4.63	4.70	2.00	>1.02a	...
SPT-CLJ2056-5459	314.2199	−54.9892	102 ± 19	5.87	5.07	4.23	6.05	0.25	0.7180	3.68 ± 0.89
SPT-CLJ2057-5251	314.4105	−52.8567	69 ± 23	4.50	4.03	3.38	4.52	0.25	>1.50a	...
SPT-CLJ2058-5608	314.5893	−56.1454	78 ± 18	4.84	4.03	2.88	5.02	0.25	0.6060	2.64 ± 0.79
SPT-CLJ2059-5018	314.9324	−50.3049	91 ± 22	4.73	4.21	3.30	4.79	0.25	0.39 ± 0.02	2.96 ± 0.96
SPT-CLJ2100-4548	315.0936	−45.8057	90 ± 23	4.84	4.53	4.12	4.84	0.50	0.7121	2.71 ± 0.93
SPT-CLJ2100-5708	315.1503	−57.1347	83 ± 19	5.03	4.47	3.21	5.11	0.25	0.59 ± 0.03	2.71 ± 0.79
SPT-CLJ2101-5542	315.3106	−55.7027	115 ± 29	4.67	4.99	4.82	5.04	1.75	0.22 ± 0.02	2.93 ± 0.86
SPT-CLJ2101-6123	315.4594	−61.3972	84 ± 19	5.28	4.83	3.95	5.28	0.50	0.60 ± 0.03	2.82 ± 0.82
SPT-CLJ2103-5411	315.7687	−54.1951	78 ± 22	4.72	4.32	3.48	4.88	0.25	0.46 ± 0.02	2.96 ± 0.96
SPT-CLJ2104-5224	316.2283	−52.4044	77 ± 23	4.97	3.54	2.19	5.32	0.25	0.7991	3.04 ± 0.89
SPT-CLJ2106-5820	316.5144	−58.3459	66 ± 19	4.43	2.94	1.56	4.81	0.25	>1.00a	...
SPT-CLJ2106-5844	316.5210	−58.7448	363 ± 18	21.78	18.67	14.36	22.08	0.25	1.1320	8.36 ± 1.71
SPT-CLJ2106-6019	316.6642	−60.3299	73 ± 19	4.82	3.49	2.21	4.98	0.25	0.97 ± 0.03	2.32 ± 0.75
SPT-CLJ2106-6303	316.6596	−63.0510	84 ± 20	4.56	4.82	4.24	4.90	1.25	>1.04a	...
SPT-CLJ2109-4626	317.4516	−46.4370	104 ± 21	5.32	4.33	3.24	5.51	0.25	0.98 ± 0.09	3.00 ± 0.86
SPT-CLJ2109-5040	317.3820	−50.6773	103 ± 27	4.56	5.14	5.06	5.17	2.00	0.47 ± 0.03	3.21 ± 0.93
SPT-CLJ2110-5244	317.5502	−52.7486	114 ± 22	6.22	5.82	4.79	6.22	0.50	0.61 ± 0.02	3.86 ± 0.93
SPT-CLJ2111-5338	317.9216	−53.6496	111 ± 25	5.53	5.51	4.80	5.65	1.00	0.43 ± 0.03	3.64 ± 0.93
SPT-CLJ2115-4659	318.7995	−46.9862	140 ± 34	4.98	5.40	5.48	5.60	2.25	0.34 ± 0.02	3.68 ± 0.96
SPT-CLJ2118-5055	319.7291	−50.9329	116 ± 22	5.52	4.84	3.66	5.62	0.25	0.6254	3.43 ± 0.93
SPT-CLJ2119-6230	319.8846	−62.5096	61 ± 19	4.37	3.35	2.83	4.55	0.25	0.72 ± 0.03	2.21 ± 0.79
SPT-CLJ2120-4728	320.1594	−47.4776	109 ± 21	5.87	4.82	3.61	5.98	0.25	0.99 ± 0.07	3.36 ± 0.86
SPT-CLJ2121-5546	320.2715	−55.7780	85 ± 19	4.61	4.44	3.55	4.79	0.75	>0.75a	...
SPT-CLJ2121-6335	320.4269	−63.5843	133 ± 32	3.87	5.01	5.43	5.43	2.75	0.23 ± 0.02	3.21 ± 0.86
SPT-CLJ2124-6124	321.1488	−61.4141	147 ± 21	8.08	8.18	7.70	8.21	1.00	0.4350	4.68 ± 0.96
SPT-CLJ2125-6113	321.2902	−61.2292	76 ± 19	4.74	4.55	4.27	4.74	0.50	>1.50a	...
SPT-CLJ2127-6443	321.9939	−64.7288	75 ± 22	3.81	4.44	4.53	4.54	1.75	>0.97a	...
SPT-CLJ2130-4737	322.6622	−47.6257	81 ± 23	4.51	3.37	2.18	4.83	0.25	>1.50a	...
SPT-CLJ2130-6458	322.7285	−64.9764	130 ± 20	7.31	7.31	6.43	7.57	1.00	0.3160	4.46 ± 0.96
SPT-CLJ2131-5003	322.9717	−50.0647	88 ± 23	4.83	4.50	3.98	4.83	0.50	0.45 ± 0.02	2.93 ± 0.93
SPT-CLJ2133-5411	323.2978	−54.1845	71 ± 22	4.17	3.00	1.75	4.58	0.25	>1.50a	...
SPT-CLJ2135-5452	323.9060	−54.8773	90 ± 20	4.39	4.57	4.00	4.61	1.00	>1.00a	...
SPT-CLJ2135-5726	323.9158	−57.4415	176 ± 18	10.43	9.81	8.64	10.43	0.50	0.4270	5.68 ± 1.11
SPT-CLJ2136-4704	324.1175	−47.0803	114 ± 22	6.10	5.46	4.68	6.17	0.25	0.4250	4.04 ± 0.96
SPT-CLJ2136-5519	324.2392	−55.3215	73 ± 19	4.65	3.91	3.37	4.65	0.50	>1.50a	...
SPT-CLJ2136-5535	324.0898	−55.5853	74 ± 19	4.52	4.40	3.79	4.58	0.75	>1.19a	...
SPT-CLJ2136-5723	324.1209	−57.3923	75 ± 20	4.22	4.55	4.10	4.55	1.50	>1.04a	...
SPT-CLJ2136-6307	324.2334	−63.1233	100 ± 19	6.11	5.80	4.91	6.25	0.75	0.9260	3.18 ± 0.75
SPT-CLJ2137-6437	324.4178	−64.6235	71 ± 19	4.40	4.10	3.27	4.60	0.75	0.91 ± 0.07	2.11 ± 0.75
SPT-CLJ2138-6007	324.5060	−60.1324	225 ± 19	12.39	12.41	11.14	12.64	0.75	0.3190	6.75 ± 1.32
SPT-CLJ2139-5420	324.9670	−54.3396	77 ± 24	4.69	4.69	3.92	4.81	0.75	0.24 ± 0.02	3.07 ± 1.00
SPT-CLJ2140-5331	325.0304	−53.5199	90 ± 23	4.54	4.13	3.48	4.55	0.25	0.51 ± 0.02	2.61 ± 0.96
SPT-CLJ2140-5727	325.1380	−57.4564	76 ± 19	4.90	4.01	3.14	5.08	0.25	0.40 ± 0.03	2.86 ± 0.86
SPT-CLJ2142-4846	325.5693	−48.7743	70 ± 24	4.02	4.53	4.36	4.53	1.50	>0.80a	...
SPT-CLJ2145-5644	326.4694	−56.7477	213 ± 18	12.30	11.67	10.39	12.30	0.50	0.4800	6.39 ± 1.25
SPT-CLJ2146-4633	326.6473	−46.5505	202 ± 22	9.59	8.67	6.99	9.59	0.50	0.9330	5.36 ± 1.07
SPT-CLJ2146-4846	326.5346	−48.7774	115 ± 25	5.59	5.88	5.34	5.88	1.50	0.6230	3.64 ± 0.93
SPT-CLJ2146-5736	326.6963	−57.6138	98 ± 19	5.94	5.46	4.57	5.94	0.50	0.61 ± 0.02	3.25 ± 0.82
SPT-CLJ2148-4843	327.0971	−48.7287	77 ± 23	4.19	2.88	1.81	4.64	0.25	0.98 ± 0.07	2.29 ± 0.86
SPT-CLJ2148-6116	327.1798	−61.2791	124 ± 20	6.95	7.22	6.31	7.27	1.25	0.5710	4.04 ± 0.89
SPT-CLJ2149-5330	327.3770	−53.5014	95 ± 24	4.79	4.50	4.04	4.79	0.50	0.60 ± 0.03	2.79 ± 0.93
SPT-CLJ2150-6111	327.7177	−61.1954	73 ± 21	4.12	4.50	4.70	4.70	2.50	>1.11a	...
SPT-CLJ2152-4629	328.1943	−46.4947	94 ± 21	5.45	4.56	3.26	5.60	0.25	>1.50a	...
SPT-CLJ2152-5143	328.0034	−51.7245	67 ± 24	4.45	4.33	3.79	4.53	0.75	0.41 ± 0.03	2.68 ± 0.96
SPT-CLJ2152-5633	328.1458	−56.5641	100 ± 21	5.16	5.66	5.68	5.84	1.75	>1.50a	...
SPT-CLJ2155-5103	328.8747	−51.0508	73 ± 25	4.11	4.41	4.40	4.52	1.75	>1.06a	...
SPT-CLJ2155-5225	328.8941	−52.4169	95 ± 25	4.45	4.77	4.36	4.77	1.50	0.62 ± 0.03	2.71 ± 0.93
SPT-CLJ2155-6048	328.9851	−60.8072	88 ± 20	4.87	5.19	4.56	5.24	1.00	0.5390	2.82 ± 0.82
SPT-CLJ2158-4702	329.6901	−47.0348	78 ± 23	4.50	4.38	4.17	4.56	1.00	>0.90a	...
SPT-CLJ2158-4851	329.5737	−48.8536	80 ± 23	4.28	3.38	2.20	4.61	0.25	>0.75a	...
SPT-CLJ2158-5615	329.5975	−56.2588	88 ± 20	4.28	4.42	3.93	4.54	1.25	>1.07a	...
SPT-CLJ2158-6319	329.6390	−63.3175	62 ± 19	4.33	3.43	2.64	4.54	0.25	>1.06a	...
SPT-CLJ2159-6244	329.9922	−62.7420	108 ± 21	6.02	5.98	5.54	6.08	1.00	0.43 ± 0.02	3.50 ± 0.86
SPT-CLJ2200-5547	330.0304	−55.7954	79 ± 21	3.83	4.63	4.72	4.80	2.00	>0.98a	...
SPT-CLJ2201-5956	330.4727	−59.9473	338 ± 25	11.61	13.57	13.99	13.99	2.50	0.0972	7.57 ± 1.50
SPT-CLJ2202-5936	330.5483	−59.6021	76 ± 19	4.81	4.21	3.36	4.89	0.25	0.42 ± 0.03	2.68 ± 0.82
SPT-CLJ2259-5432	344.9820	−54.5356	135 ± 38	4.56	4.71	4.65	4.78	2.00	0.46 ± 0.03	3.04 ± 1.04
SPT-CLJ2259-5617	344.9974	−56.2877	99 ± 24	5.04	4.27	3.55	5.29	0.25	0.15 ± 0.02	3.79 ± 1.07
SPT-CLJ2300-5331	345.1765	−53.5170	119 ± 27	5.24	5.02	4.65	5.29	0.25	0.2620	3.68 ± 1.04
SPT-CLJ2301-5046	345.4585	−50.7823	92 ± 24	4.58	3.83	2.82	4.58	0.50	>1.50a	...
SPT-CLJ2301-5546	345.4688	−55.7758	106 ± 25	5.19	4.93	4.62	5.19	0.50	0.7480	3.11 ± 0.96
SPT-CLJ2302-5225	345.6464	−52.4329	104 ± 29	3.77	4.24	4.60	4.60	2.50	>1.04a	...
SPT-CLJ2311-5011	347.8427	−50.1838	91 ± 29	3.40	3.85	4.42	4.64	3.00	>1.50a	...
SPT-CLJ2312-5820	348.0002	−58.3419	89 ± 24	4.66	3.75	3.11	4.78	0.25	0.83 ± 0.05	2.68 ± 0.96
SPT-CLJ2329-5831	352.4760	−58.5238	107 ± 25	4.95	4.64	3.96	4.95	0.50	0.81 ± 0.03	2.86 ± 0.93
SPT-CLJ2331-5051*	352.9584	−50.8641	166 ± 23	7.86	6.60	5.14	8.04	0.25	0.5760	5.14 ± 0.71
SPT-CLJ2332-5358*	353.1040	−53.9733	193 ± 31	7.25	7.30	6.84	7.30	1.50	0.4020	6.50 ± 0.79
SPT-CLJ2334-5953	353.6989	−59.8892	94 ± 30	2.94	3.98	4.53	4.53	2.50	>1.50a	...
SPT-CLJ2337-5942*	354.3544	−59.7052	312 ± 24	14.72	12.63	10.11	14.94	0.25	0.7750	8.14 ± 1.14
SPT-CLJ2341-5119*	355.2994	−51.3328	227 ± 24	9.48	9.02	7.74	9.65	0.75	1.0030	5.61 ± 0.82
SPT-CLJ2342-5411*	355.6903	−54.1887	132 ± 23	6.18	5.24	3.96	6.18	0.50	1.0750	3.00 ± 0.50
SPT-CLJ2343-5521	355.7574	−55.3641	130 ± 28	4.87	5.58	5.74	5.74	2.50	>1.50a	...
SPT-CLJ2343-5556	355.9290	−55.9371	106 ± 27	4.49	4.53	4.00	4.58	1.00	>1.22a	...
SPT-CLJ2351-5452	357.8877	−54.8753	151 ± 47	4.35	4.70	4.83	4.89	2.75	0.3838	3.18 ± 1.04
SPT-CLJ2355-5056*	358.9551	−50.9367	138 ± 24	5.73	5.34	4.31	5.89	0.75	0.3196	4.07 ± 0.57
SPT-CLJ2359-5009*	359.9208	−50.1600	152 ± 27	6.19	6.23	5.64	6.35	1.25	0.7750	3.54 ± 0.54

Notes. Galaxy cluster candidates selected above a significance of 4.5 in the first 720 deg² of the SPT survey. Galaxy clusters marked by an "*" have X-ray data that are used in the cosmological analysis (see A11 and B11 for a description of the X-ray data). For each candidate, we report the detection significance of each candidate in the "Best" column, as well as the significances at a fixed set of three core radii (Section 3). We also report the position and (if confirmed) redshift (Section 4). Spectroscopic redshifts are quoted without uncertainties. The integrated Y_SZ is reported for a 1' aperture (Section 3.3). Finally, we report a mass estimate for each confirmed cluster marginalized over the ΛCDM chain (Section 7.1.2). ^aUnconfirmed cluster candidate which is either above the quoted redshift limit or a false detection.

A machine-readable version of the table is available.

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We next examine cosmological constraints in a wCDM cosmology. This model introduces the dark energy equation of state, w, as a free parameter (in the ΛCDM model, w is fixed to −1). The equation of state remains constant with time. The cluster abundance and the shape of the mass function depend on w through its effect on the expansion history of the universe and the growth of structure.

The best external constraints on w come from a combination of the CMB, BAO, H₀, and SNe data. Adding the SPT cluster sample to this data set reduces the uncertainty on the dark energy equation of state by a factor of 1.3 to give −1.010 ± 0.058. This value is completely consistent with a cosmological constant and within 1 σ of the no-cluster constraint of w = −1.054 ± 0.073. These results are shown in Figure 6 and tabulated in Table 5.

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The cluster data also aid in the measurement of the dark matter density and σ₈. The addition of clusters moves the preferred cold dark matter density down by nearly 1 σ from Ω_ch² = 0.1140 ± 0.0041 to Ω_ch² = 0.1104 ± 0.0029. As would be expected, the amplitude of the matter power spectrum also drops from σ₈ = 0.840 ± 0.038 to 0.807 ± 0.027. The uncertainties on both parameters are reduced by a factor of 1.4 with the addition of the SPT cluster data.

We can compare the wCDM results to those reported by B11 based on fewer clusters but the same X-ray data and mass calibration uncertainty. B11 report σ₈ = 0.793 ± 0.028 and w = −0.973 ± 0.063 for the CMB + BAO + SNe + ${\rm SPT_{{\rm CL}}}$ (B11) data. In this analysis, the median σ₈ and w values shift by ∼0.5 σ relative those presented by B11, and the uncertainties tighten slightly. These changes are primarily due to including the local measurement of H₀ in the constraints, rather than the additional clusters. We also ran chains without H₀ to parallel the B11 treatment and both differences effectively disappear.

The second extension to a ΛCDM model that we consider is a non-zero sum of neutrino masses, ∑m_ν ⩾ 0. Non-zero neutrino masses are well motivated by the measured mass differences in neutrino oscillation experiments (e.g., Ahmad et al. 2002; Eguchi et al. 2003; Ashie et al. 2004). For CMB+H₀+BAO, neutrino masses are highly degenerate with σ₈, as shown in Figure 7. Cluster abundances are an independent measure of local structure (σ₈), and thereby enable better constraints on the sum of the neutrino masses. In this work, we assume a thermal background of three degenerate mass neutrino species.

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The main results with massive neutrinos are shown in Figure 7 and tabulated in Table 5. Adding the SPT cluster sample to the CMB+H₀+BAO data leads to a small preference for a positive neutrino mass sum. If we fit the 1D posterior on the total neutrino mass with a Gaussian (avoiding the bias to the median and 68% interval values due to the positivity prior), the preferred value is ∑m_ν = 0.17 ± 0.13 eV. The uncertainties on the neutrino mass tighten with the addition of the cluster data, but the shift in the peak likelihood toward higher masses means that the 95% confidence upper limit on ∑m_ν is nearly unchanged: ∑m_ν < 0.44 eV without clusters and ∑m_ν < 0.38 eV with clusters. This improvement is largely due to the tighter constraint on σ₈ derived from the cluster data. The ${\rm SPT_{{\rm CL}}}$ data tightens the σ₈ measurement from the CMB + BAO + H₀ data from 0.775 ± 0.041 to 0.766 ± 0.028.

We again compare these results to those reported by B11. B11 report σ₈ = 0.770 ± 0.026 and a 95% CL upper limit of ∑m_ν < 0.33 eV for the CMB+H₀+BAO+${\rm SPT_{{\rm CL}}}$(B11) data. The median σ₈ value has shifted down slightly in this work leading to a higher ∑m_ν limit. The parameter uncertainties are essentially unchanged.

The cosmological results in this paper are derived from a high-purity and high-redshift subsample of the catalog consisting of 100 galaxy clusters. The full SPT survey covers approximately 3.5 times the sky area used in this work and is being used to produce a similar high-purity catalog with 3.5 times as many clusters. Realizing the scientific potential of this sample will require significant improvements to the current mass calibration. We have simulated the impact of a more accurate mass calibration on both the current catalog and the full SPT survey. A 5% mass calibration would tighten the current constraints to σ(w) = 0.043 (for ${\rm CMB {+} BAO {+} H_0 {+} SNe {+} SPT_{{\rm CL}}}$) and σ(∑m_ν) = 0.10 eV (for CMB + BAO + H₀) respectively, a factor of 1.3 better than those listed in Table 5 for the current mass calibration. Determining the mass calibration to better than 5% would have little impact with the current catalog. However, it would significantly improve constraints for the 3.5 times larger, full SPT sample and could make possible a significant detection of the sum of the neutrino masses.

As laid out by B11, four approved observation programs are being pursued by the SPT collaboration to independently test the cluster mass calibration, with the goal of reducing this uncertainty to a level ≲5%. First, X-ray observations with Chandra are scheduled for the 80 most-significant SPT cluster detections at z > 0.4. Second, we have been awarded time for weak lensing observations of ∼35 SPT-detected clusters spanning 0.30 < z < 1.3 using the Magellan and Hubble telescopes. Third, we have been awarded time for optical velocity dispersion observations of ∼100 SPT-detected clusters using the Very Large Telescope (VLT) and a large NOAO program on Gemini South. Fourth, the DES will also yield weak lensing mass estimates (S/N ∼ 1) of all SPT cluster candidates. The combination of the X-ray, velocity dispersion, and weak lensing observations will enable valuable cross-checks between these different mass estimates and should lead to significant improvements in the cluster mass calibration.