DISCOVERY AND COSMOLOGICAL IMPLICATIONS OF SPT-CL J2106-5844, THE MOST MASSIVE KNOWN CLUSTER AT z>1

Currently, the SPT has been used to complete observations of 1500 deg² to full survey depth of 18 μK arcmin at 150 GHz and an additional 1000 deg² has been surveyed to a "preview" depth of 54 μK arcmin, where the unit K refers to equivalent fluctuations in the CMB temperature. By the end of the 2011 observing season, we expect the full 2500 deg² survey region to be complete to full depth. Details of the survey strategy and data processing are described in Staniszewski et al. (2009), Vanderlinde et al. (2010), and Williamson et al. (2011). The 2009 observations that yielded the discovery of SPT-CL J2106-5844 included measurements at 95, 150, and 220 GHz to a noise level of 42, 18, and 85 μK arcmin.

SPT-CL J2106-5844 was detected in maps of 2009 SPT data created using time-ordered data processing and map-making procedures equivalent to those described in Vanderlinde et al. (2010). Two different cluster extraction pipelines were used to detect and characterize clusters in these SPT maps. Both pipelines use a multi-scale matched-filter approach similar to the one described in Melin et al. (2006). One pipeline, used to extract clusters from single-band 150 GHz data, is identical to the cluster extraction procedure described in Vanderlinde et al. (2010). The other pipeline, used to extract clusters from multi-band SPT data, is identical to that described in Williamson et al. (2011). The final SZ observable produced by both pipelines is ξ, the detection significance maximized across all filter scales. SPT-CL J2106-5844 was detected at ξ = 18.5 by the single-band pipeline and at ξ = 22.1 by the multi-band pipeline.

An image of the filtered, multi-band SPT data—using the filter that maximized ξ, and centered on SPT-CL J2106-5844—is shown in the left panel of Figure 1. Detection significance contours from this same filtered map are overlaid in Figures 1 and 4.

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In 2009 June, we obtained griz imaging of SPT-CL J2106-5844 with the Inamori Magellan Areal Camera and Spectrograph (IMACS; Dressler et al. 2006) and Low Dispersion Survey Spectrograph (LDSS3 ³¹ ) on the twin Magellan 6.5 m telescopes. We obtained additional I-band imaging with FORS2 (Appenzeller et al. 1998) on the Very Large Telescope (VLT) 8 m telescope in 2010 September. See High et al. (2010) for a description of our observation strategy and reduction procedure.

SPT-CL J2106-5844 was observed at the CTIO 4 m Blanco telescope using the NEWFIRM imager (Autry et al. 2003) on 2010 July 28. Data were obtained in the J and K_s filters under photometric conditions. All images were acquired using a 30 point random dither pattern. At each dither position, six frames with 10 s exposure times were co-added, providing 60 s total exposure per position. The dither pattern was repeated as necessary to achieve total exposure times of 7200 s in J and 4440 s in K_s .

NEWFIRM data were reduced using the FATBOY pipeline, originally developed for the FLAMINGOS-2 instrument, and modified to work with NEWFIRM data in support of the Infrared Bootes Imaging Survey (A. H. Gonzalez 2011, in preparation). Individual processed frames are combined using SCAMP and SWARP (Bertin et al. 2002), and photometry is calibrated to 2MASS (Skrutskie et al. 2006). The final images in both filters have FWHM of 13.

Mid-infrared Spitzer/IRAC imaging was obtained in 2009 September 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. ³² 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 following the method of Ashby et al. (2009). Briefly, we correct for column pulldown and residual images, mosaic the individual exposures, resample to 086 pixels (half the solid angle of the native IRAC pixels), and reject cosmic rays.

Images generated from the OIR data are presented in Figure 1. From the deep optical-only images (gri), it is difficult to see any indication of a cluster. However, the addition of infrared data shows a clear overabundance of very red galaxies clustered near the peak of the SZ decrement. The overabundance of galaxies that are spatially coincident and have similar colors is a clear indication of a cluster of galaxies. Color–magnitude diagrams (CMDs) for galaxies within the imaging field of view (FOV; Figure 2) show an overabundance of very red galaxies and a probable red sequence. These data are consistent with the spectroscopic redshifts described below.

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We obtained low-resolution spectra of several cluster members of SPT-CL J2106-5844 with the Gladders Image-Slicing Multislit Option (GISMO; M. D. Gladders et al. 2011, in preparation) module on IMACS mounted on Magellan in 2010 June; however, these spectra did not yield a definitive cluster redshift. Magellan slit masks were designed using galaxies selected from deep optical and MIR imaging compatible with the red sequence expected at z ≳ 1.2, as this was the initial redshift approximation from the photometry. The selection was similar to that of Brodwin et al. (2010). This technique gives higher priority to brighter galaxies with colors consistent with the red sequence. If there is a region without a suitable red-sequence target, blue galaxies were selected with the idea that they may be emission-line cluster galaxies. The Magellan observations were obtained using the f/2 camera with the 300 l/mm "red" grism and the WB6300–9500 filter. A total of sixteen 1800 s exposures were obtained on June 6 and 7. The combination of moderate seeing and a non-optimal filter choice for the actual redshift likely caused the low yield from these observations.

The VLT observations were obtained with the GRIS_300I grism combined with the OG590 blocking filter. Two VLT/FORS2 masks were designed using galaxies selected from deep I-band VLT pre-imaging and the Spitzer IRAC imaging to have colors compatible with the red sequence expected at z ≈ 1.2–1.3, which was initially indicated by the photometry. Each mask was populated with approximately 30 slitlets of typical length 10''. This target was originally accepted as Priority B for VLT/FORS2 spectroscopy as part of a larger SPT spectroscopy campaign. In late 2010 November, Chandra X-ray spectroscopy gave an initial redshift from the Fe K line (see Section 2.4). After this result when it became clear that there was a significant chance of it not being observed in Fall 2010, we submitted a special request to the ESO Director to raise this target to Priority A. That proposal was successful, and on each of three nights in early 2010 December a single 2700 s exposure was obtained for a total exposure time of 8100 s on one of the two masks. These observations were taken under excellent seeing conditions (05 to 08) but at high airmass between 1.5 and 1.7. These data were immediately reduced to reveal redshifts of 15 cluster members, enabling a robust cluster redshift.

Spectroscopic reductions proceeded using standard CCD processing with IRAF and the COSMOS reduction package (Kelson 2003) for the VLT and Magellan data, respectively. The data were extracted using the optimal algorithm of Horne (1986). Flux calibration and telluric line removal were performed using the well-exposed continua of spectrophotometric standard stars (Wade & Horne 1988; Foley et al. 2003).

Three independent redshift determinations were performed using a cross-correlation algorithm (IRAF RVSAO package; Kurtz & Mink 1998), a template fitting method (SDSS early-type PCA templates), and a χ² minimization technique by comparing to galaxy template spectra. There were only minor differences in the final results from the three methods. In total, we have obtained secure redshifts, consistent with membership in a single cluster, for 18 galaxies. Two of these galaxies have obvious [O ii] emission, while the others have SEDs consistent with passive galaxies with no signs of ongoing star formation.

A 3σ clipping was applied around the peak in redshifts to select spectroscopic cluster members. Representative spectra of cluster members and a redshift histogram of cluster members are presented in Figure 3. Redshift information for cluster members is presented in Table 1. A single galaxy was observed and has a secure redshift from both Magellan and VLT. Although the VLT spectrum shows clear Ca H&K absorption lines and the Magellan spectrum only shows the D4000 break, the measured redshifts are consistent.

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A robust biweight estimator was applied to the spectroscopic sample to determine a mean redshift of z = 1.131^+0.002 _−0.003 and a velocity dispersion of σ_v = 1230⁺²⁷⁰ ₋₁₈₀ km s⁻¹. The uncertainty in both quantities is determined through bootstrap resampling. Since the dynamics of passive and star-forming galaxies within clusters are different, with passive galaxies assumed to be a better tracer of the cluster potential (e.g., Fadda et al. 1996; Girardi et al. 1996; Mohr et al. 1996; Koranyi & Geller 2000), we also provide the mean redshift and velocity dispersion of only the passive galaxies, z = 1.132^+0.002 _−0.003 and σ_v = 1270⁺³²⁰ ₋₂₁₀ km s⁻¹, respectively.

The velocity distribution of spectroscopic members relative to the mean velocity (Figure 3) is skewed. The bootstrap resampling produced a positive skewness in 89% of the samples, which indicates that it is not very statistically significant given our sample size. However, this may be an indication of substructure, consistent with the possible merger seen in the X-ray image (see Section 2.4). There is no spatial segregation of galaxies clustered in velocity space; however, the number of spectroscopic members is still small.

As part of a program to follow up the most massive, high redshift clusters detected with the SPT in 2009, we have obtained a 25 ks X-ray observation of SPT-CL J2106-5844. These data were obtained through a combined Chandra High Resolution Camera and Advanced CCD Imaging Spectrometer Guaranteed Time Observation program. Data reduction was performed with the method described by Andersson et al. (2010). The observation resulted in 1425 source counts within r₅₀₀ in the 0.5–7.0 keV band, corresponding to a flux, F_X (0.5–2.0 keV) = (2.58 ± 0.15) × 10⁻¹³ erg cm⁻² s⁻¹. A 2'' × 2''-binned X-ray image was produced using the X-ray events in the 0.7–4.0 keV band (Figure 4). The observation reveals an X-ray luminous cluster with pronounced asymmetry in the surface brightness distribution (see Figure 4), indicating that it may be in a merging state. In particular, we note that a bright concentration of gas is offset ∼10'' east of the main cluster centroid.

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X-ray observations of SPT-CL J2106-5844 were used to measure the gas temperature, T_X , and the X-ray analog of Comptonization, Y_X = M_gas × T_X . The cluster mass can then be inferred with the M–Y_X and M–T_X relations of Vikhlinin et al. (2009). The r₅₀₀ radius is derived iteratively from the M–Y_X scaling relation as described in Andersson et al. (2010). See Section 3.3 for details regarding the X-ray mass estimates. A spectrum is extracted from the data within the derived r₅₀₀ radius, excluding the core within 0.15 r₅₀₀. The spectrum is fit, keeping the absorbing hydrogen column fixed at the galactic value n_H = 4.32 × 10²⁰ cm⁻², and the metal abundance fixed at 0.3 solar. Fixing the redshift to the mean spectroscopic redshift, z = 1.132, results in a best-fit T_X = 11.0^+2.6 _−1.9 keV and Y_X = (14.3 ± 3.4) × 10¹⁴  M_☉ keV. Within r₅₀₀ (117''), including the cluster core, SPT-CL J2106-5844 has a luminosity of L_X (0.5–2.0 keV) = (13.9 ± 1.0) × 10⁴⁴ erg s⁻¹, comparable to the luminosity of the Bullet cluster (Markevitch et al. 2002).

An X-ray spectrum was produced from the data within 20'' (0.17 r₅₀₀), where the metal abundance of the gas is likely to peak. The resulting spectrum is shown in Figure 5 with a model folded through the detector response. The strong 6.7 keV Fe K line is present in the spectrum at approximately 3 keV. This spectrum indicates z = 1.18 ± 0.03, a metal abundance Z = 1.44^+0.66 _−0.51  Z_☉, and a central temperature T_X = 6.5^+1.7 _−1.1 keV. Notably, this measurement was the first robust spectroscopic redshift measurement for this cluster.

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Merger simulations suggest that high-redshift cool-core clusters should be rare (Gottlöber et al. 2001), and previous observations have indicated a steep decline in the number of cool-core clusters at high redshift (e.g., Vikhlinin et al. 2007). However, other analyses have found that the cool-core fraction varies significantly between different high redshift X-ray selected samples (e.g., Santos et al. 2010). Future work comparing these results to the cool-core fraction in SZ selected samples should help to understand the role of selection in these results. Regardless of the abundance at high redshift, SPT-CL J2106-5844 is one of the few high-redshift cool-core galaxy clusters known.

An SZ-based cluster mass estimate is produced following Vanderlinde et al. (2010), using the single-band (150 GHz) detection significance ξ as a mass proxy. We direct the reader to that work for details. Briefly, an SZ-mass scaling relation, derived from the simulations of Shaw et al. (2009) and constrained though a cosmological analysis, is used to estimate a set of conditional probabilities P(ξ|M), taking into account the measurement noise and the intrinsic scatter in the scaling relation. A posterior mass estimate is then calculated through application of a mass prior. The systematic errors are estimated by linearly expanding the mass estimate as a function of the scaling relation parameters and using the marginalized uncertainties on these parameters.

The SZ detection of this cluster is from an untargeted survey, allowing us to take the halo mass function of Tinker et al. (2008) as a prior on its mass. We assume the WMAP 7-year preferred ΛCDM parameters (Larson et al. 2011) when calculating this prior; marginalizing over the ΛCDM cosmological parameter uncertainties was found to have a negligible impact on the effect of this prior. SPT-CL J2106-5844 has a single-band 150 GHz significance of ξ = 18.5, which results in an unbiased posterior SZ-derived mass estimate of M_SZ,200 = (1.06 ± 0.23) × 10¹⁵ h⁻¹ ₇₀  M_☉.

We also report (see Section 3.4 and Table 2) a biased SZ mass estimate, using a flat mass prior; we present it here for completeness only. It is important to note that this mass is not directly comparable to other flat-mass-prior estimates (e.g., the masses estimated in Sections 3.2 and 3.3). The SZ observation was drawn from an untargeted survey and hence from the entire underlying population of clusters (given by the halo mass function), while the targeted observations were conducted with a priori knowledge that a massive cluster was present; these two different modes of observation draw from different populations and thus will exhibit different levels of Eddington bias. To reiterate, naively using any mass estimate without understanding the selection of the observed population can result in biased measurements.

The dynamical mass of SPT-CL J2106-5844 can be estimated from the velocity dispersion using the M–σ_v calibration of Evrard et al. (2008). Numerical simulations indicate that galaxies are likely to exhibit velocity bias compared to the dark matter velocity field (e.g., Biviano et al. 2006; White et al. 2010). Mock observations of simulated clusters that model the galaxy selection within follow-up observations like those reported here enable these biases to be quantified and corrected (A. Saro et al. 2011, in preparation). Published results suggest these biases are at the level of 10% in the dispersion (White et al. 2010). Here, we attempt no correction to the dispersion but account for this additional systematic uncertainty in the mass estimator.

As the dynamical mass estimate arises from a targeted follow-up observation, the underlying mass distribution can be well defined (and accounted for) only in the context of the SZ-based selection. Such a joint estimate of mass is presented below in Section 3.4; here, we report an independent (hence biased) dynamical mass estimate using a flat prior on the mass.

Using the velocity dispersion from all 18 spectroscopic cluster members gives M_dyn,200 = 1.3^+1.4 _−0.5 × 10¹⁵ h⁻¹ ₇₀  M_☉. Using the velocity dispersion from only the passive galaxies provides a very similar result, M_dyn,200 = 1.4^+1.7 _−0.8 × 10¹⁵ h⁻¹ ₇₀  M_☉). In both cases, the uncertainty takes into account the statistical uncertainty of the velocity dispersion, an additional 13% intrinsic scatter of the velocity dispersion due to the orientation of the velocity ellipsoid along the line of sight (White et al. 2010), the 4% intrinsic scatter of the Evrard et al. (2008) M–σ_v relation, and a 10% estimate of the systematic uncertainty in the dispersion that arises from the currently uncertain kinematic relationship between the galaxies and the underlying dark matter.

As described in Section 2.4, the X-ray observations of SPT-CL J2106-5844 were used to measure the gas temperature, T_X , and the X-ray analog of Comptonization, Y_X = M_gas × T_X . Following the methodology of Andersson et al. (2010), the data were iteratively fit to determine r₅₀₀, T_X , and Y_X . Using the scaling relations of Vikhlinin et al. (2009), these values provide estimates of the gas and total mass of the cluster, M_gas,500 = (1.27 ± 0.07) × 10¹⁴ h⁻¹ ₇₀  M_☉ and $M_{Y_{X},\,500} = (0.93 \,{\pm}\, 0.19) \,{\times}\, 10^{15}$ h⁻¹ ₇₀  M_☉, respectively. Estimating the cluster mass from the gas temperature, we find a similarly high mass of $M_{T_{X},\, 500} = (0.92 \,{\pm}\, 0.37) \,{\times}\, 10^{15}$ h⁻¹ ₇₀  M_☉, where we have increased the mass by 17% according to the recipe in Vikhlinin et al. (2009) because of the large degree of asymmetry in the surface brightness distribution, indicative of merging activity.

For both mass estimates above, we have adopted a systematic uncertainty of 9% for the mass calibration of the scaling relations. The uncertainty on the self-similar evolution of these relations was estimated using the simulation informed estimate of 5% and 7% uncertainty on the normalization at z = 0.6 for the M–Y_X and M–T_X , respectively. This uncertainty on the evolutionary term was extrapolated to the cluster redshift. For further discussion on these uncertainties, see Vikhlinin et al. (2009); the appropriate mass prior to account for Eddington bias is only well-defined in the context of SZ-based selection.

The X-ray, SZ, and optical redshift data can each be used to produce an estimate of the mass of SPT-CL J2106-5844. We list our estimates for the mass of SPT-CL J2106-5844 from each of these observables in Table 2. Note that we have converted the $M_{Y_{X},\, 500}$ mass to $M_{Y_{X},\, 200}$ assuming a Navarro–Frenk–White density profile and the mass-concentration relation of Duffy et al. (2008). $M_{T_{X},\, 500}$ is not used in the combined mass estimate since it is correlated with $M_{Y_{X},\,500}$ and has a larger uncertainty. Similarly, M_dyn, 200 is not used in the combined mass estimate because of its large uncertainty.

We assume for the purposes of the combined mass estimate that the uncertainties are uncorrelated between the two masses. In principle, the different observables could have correlated scatter in their scaling with mass; however, this is expected to be negligible at the current S/N of the observables. This simplification allows us to write the posterior mass distribution as a product of the two independent conditional probabilities,

$$\begin{equation} P(M|\xi, Y_{X}) \propto P(M) \cdot P(\xi | M) \cdot P(Y_{X} | M), \end{equation} \tag{ 1 }$$

where P(M) is again the halo mass function of Tinker et al. (2008), evaluated at the WMAP 7-year preferred point in ΛCDM parameter space. Functionally, this reduces to a product of two probability density functions, the unbiased SZ mass estimate and the flat-prior Y_X mass estimate. We find the combined, unbiased, mass estimate from the two observables to be M₂₀₀ = (1.27 ± 0.21) × 10¹⁵ h⁻¹ ₇₀  M_☉.

All mass estimates are consistent and very high for a cluster at this redshift. Each individual mass estimate, as well as the combined estimate, indicates that SPT-CL J2106-5844 is the most massive cluster yet discovered at z>1. It is ∼60% more massive than SPT-CL J0546-5345 (Brodwin et al. 2010) at z = 1.07, the second most massive galaxy cluster at z>1.