SPT-CL J0205−5829: A z = 1.32 EVOLVED MASSIVE GALAXY CLUSTER IN THE SOUTH POLE TELESCOPE SUNYAEV–ZEL'DOVICH EFFECT SURVEY

SPT-CL J0205−5829 was initially discovered in the SPT-SZ survey and reported in R12, as part of the cluster catalog identified from the 720 deg² surveyed during the 2008–2009 SPT observing seasons. The survey strategy and data analysis are detailed in the previous SPT-SZ survey papers Staniszewski et al. (2009), Vanderlinde et al. (2010), Williamson et al. (2011, W11), and R12. The SPT-SZ survey was completed in 2011 November, and covers an area of 2500 deg² in three frequency bands at 95, 150, and 220 GHz.

As described in R12, cluster candidates were identified using a multi-band matched-filter approach, similar to that first described by Melin et al. (2006). The significance of a cluster detection (maximized across spatial filter scales and position in map), ξ, is used to identify cluster candidates. For the survey field containing SPT-CL J0205−5829, only the 95 and 150 GHz data were used, the SPT maps have noise levels of 45 and 16 μK arcmin in CMB temperature units at 95 and 150 GHz, respectively. In this data, SPT-CL J0205−5829 was detected with ξ = 10.5 and is among the 5% most significant detections in the R12 catalog. An image of the filtered SPT map is shown in Figure 1.

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We obtained griz imaging using the MOSAIC2 imager on the CTIO 4 m Blanco telescope on UT 2010 July 18, 25 and UT 2011 July 4 with mediocre to bad seeing (11–22) and occasional light clouds. Total integration times were 300, 300, 2350, and 1050 s to 10σ point-source depths of 23.8, 23.2, 22.2, and 21.1 AB magnitudes in g, r, i, and z, respectively. We also acquired 1800 s of deep i-band imaging of SPT-CL J0205−5829 on UT 2011 January 31 with the Inamori Magellan Areal Camera and Spectrograph (IMACS; Dressler et al. 2006) on the Baade Magellan 6.5 m telescope to 24.0 AB magnitude depth in mediocre seeing (12–15). The observation strategy and reduction procedure are described in High et al. (2010, H10), W11, and Song et al. (2012, S12) using the PHOTPIPE pipeline (Rest et al. 2005).

SPT-CL J0205−5829 was also observed with the NEWFIRM imager (Autry et al. 2003) at the CTIO 4 m Blanco telescope on UT 2010 November 6. Data were obtained in the K_s filter under photometric conditions with a 10σ point-source depth of 19.1 Vega magnitudes. At each dither position, 6 frames with 10 s exposure times were co-added at 18 random positions providing a total exposure time of 1080 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. Gonzalez 2011, private communication). Individual processed frames are combined using SCAMP and SWARP (Bertin et al. 2002), and photometry is calibrated to Two Micron All Sky Survey (Skrutskie et al. 2006). The final image has an FWHM of 096.

Infrared Spitzer/IRAC imaging was obtained in 2011 during Cycle 7 as part of a larger program to follow up clusters identified in the SPT survey. IRAC imaging is particularly important for the confirmation and study of high-redshift SPT clusters such as SPT-CL J0205−5829 where the optically faint members are strongly detected in the infrared. The on-target observations consisted of 8 × 100 s and 6 × 30 s dithered exposures in bands [3.6] and [4.5] to 10σ depths of 20.3 and 18.8 Vega magnitudes, respectively. The deep [3.6] 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.

Multislit spectroscopic observations were acquired for SPT-CL J0205−5829 on the 6.5 m Baade Magellan telescope on UT 2011 September 25–26 using the f/2 camera on the IMACS spectrograph for a total integration time of 11 hr. The strategy and procedure were as described in Brodwin et al. (2010), with the same 300 l mm⁻¹ "red" grism and WB6300-9500 filter, but without the GISMO module (in order to increase throughput). The galaxy target selection was based on the optical and infrared photometry; see Section 3. Twenty-two 30 minute exposures were made in excellent to moderately good seeing (04–07) using one slit mask. The resolution of the observations, as measured from the sky lines, was 5.2 Å. In a procedure identical to J. Ruel et al. (2013, in preparation), the COSMOS reduction package was used for standard CCD processing, resulting in wavelength-calibrated two-dimensional spectra. The one-dimensional spectra were then extracted from the sum of the reduced data. Spectral features were identified by eye from inspection of the two-dimensional and one-dimensional spectra, and redshifts were then obtained by using RVSAO routines.

A deep X-ray observation of SPT-CL J0205−5829 was obtained by the XMM-Newton observatory (ObsID: 0675010101) on UT 2011 June 19–20 using the European Photon Imaging Camera, which consists of two metal-oxide-silicon (MOS) arrays plus one fully depleted p–n (PN) junction CCD array. The total integration times were 69 ks for the MOS arrays and 65 ks for the PN array. The data reduction and analysis were performed with SAS v11.0 utilizing the XMM-Newton Extended Source Analysis Software package³⁴ (e.g., Snowden et al. 2008). The net clean exposure time is 57 and 39 ks in the MOS/PN arrays, respectively. Based on the De Luca & Molendi (2004) diagnostics, we find a ∼30%–40% background enhancement in the observation due to residual quiescent soft proton contamination. The MOS2 CCD#5 was in an anomalously high state and we have removed it from further analysis.

We have also excised all point sources identified in the source detection step. We have visually inspected the excision regions and made conservative adjustments to their size. In particular, a point source associated with a bright galaxy (bluer than the passively evolving model) was identified in the core region of the cluster (α = 02:05:45.4, δ = −58:28:58.3, ∼12'' west of the X-ray centroid) and was removed with an excision radius of ∼11'' (see Figure 3).

From the procedure described in S12, we measure a redshift based on the Spitzer IRAC photometry of z = 1.30 ± 0.12 (see Figure 2). We fit a model of passively evolved galaxies from Bruzual & Charlot (2003, BC03) to the data to determine the redshift. The optical data were not deep enough to offer any additional constraint to the redshift except for the brightest of the cluster members (see Section 3.3). The redshift estimator identified 32 galaxies with IRAC [3.6]–[4.5] colors consistent with this redshift (a 3.5σ overdensity compared to the background), shown in Figures 1 and 2. From this list, we designed a multi-slit mask for the IMACS spectroscopic observations described in Section 2.3, filling the mask with other targets, identified as galaxies with bluer colors relative to the model in the i band and Spitzer data.

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Redshifts and other spectroscopic properties of member galaxies are listed in Table 1. Of the 47 slits designed into the mask, 1 spectroscopic member was identified from an [O ii] emission line, and 8 from Ca H and K. Figure 3 shows the spectra of the 9 cluster members. The brightest cluster galaxy (BCG), defined as the brightest cluster member in [3.6], is at a redshift of z = 1.3218 ± 0.0005, and the combined robust (biweight) redshift of nine cluster members is z = 1.322^+0.001_−0.002. We do not calculate the velocity dispersion due to the overwhelming intrinsic uncertainty in the derived mass estimates with <15 members (Saro et al. 2012).

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We also estimate the star formation rate (SFR) for each cluster member from the integrated [O ii] flux which was corrected for galactic extinction (reddening) using the dust map from Schlegel et al. (1998) and scaled to match the i-band magnitude from IMACS imaging. We do not correct for source dust extinction as we lack a well-constrained NUV-Blue-continuum measurement for most of these galaxies. This is also consistent with our derived extinction from spectral energy distribution (SED) fits of the four brightest central galaxies (see Section 3.3). We measured the continuum-subtracted flux centered on the [O ii] wavelength with a bin width of 8 Å (320 km s⁻¹) and converted to luminosity using the cluster redshift. The SFR was estimated from the [O ii] luminosity using the scaling law from Kennicutt (1998). The measured [O ii] flux and SFR (or 3σ upper limits) are given in Table 1.

We selected the brightest central galaxies to be the four brightest galaxies consistent with the [3.6]–[4.5] model, within 1 arcmin of the SZ center. We then use an analysis similar to the Rosati et al. (2009) SED fitting procedure. To constrain the SFH of each of these galaxies, we fit an exponential-burst stellar population SED model at solar metallicity and Chabrier initial mass function from BC03 to the available photometry (see Figure 4), including magnitude lower limits, fix the redshift at z = 1.322, and add a source reddening model from Calzetti et al. (2000). From the fit parameters, we calculate the rest-frame K-band luminosity, stellar mass (and corresponding stellar mass-to-light ratios), and age. The uncertainties for these parameters are from the χ² 68% confidence intervals in the multi-dimensional sampled grid and checked by bootstrapping this procedure hundreds of times and were in good agreement. These parameters are presented in Table 2. We find that all models give well-constrained K-band luminosities, mainly because the observed Spitzer [4.5] filter corresponds to 2 μm in the rest frame. The 4000 Å breaks are mainly constrained by the deep IMACS i-band measurement.

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The rest-frame K-band luminosity of the brightest galaxy, at L ∼ 4 × 10¹¹ L_☉, is typical for BCGs in similar-sized clusters at z < 0.25 based on previous X-ray (Haarsma et al. 2010) or optical cluster studies (Lin & Mohr 2004; Popesso et al. 2007; Brough et al. 2008), and smaller studies extending to higher redshifts (z < 1) by Whiley et al. (2008). The derived stellar mass is also consistent with other studies of BCGs from X-ray samples at similar cluster masses and redshifts (Stott et al. 2010). The derived ages from the BC03 model fits listed in Table 2 suggest that the stellar mass of these brightest galaxies had formed by the time of the observed epoch was probably complete by redshift 2 or 3, or perhaps earlier, also consistent with previous studies of stellar ages of cluster galaxies at high redshift (Collins et al. 2009; Henry et al. 2010). However, this does not rule out the scenario of "dry merging" hierarchical build up of these galaxies between redshift 1.3 and 3.

As a further check on the cluster galaxy properties, we measure the observed [3.6] (roughly rest H band) luminosity function of galaxies with [3.6]–[4.5] colors consistent with the BC03 model from our initial redshift estimate. Galaxies selected as cluster members are within 1 Mpc (physical distance) of the SZ-derived center and have [3.6]–[4.5] colors within 2σ (based on each galaxy's photometric uncertainty) of the BC03 model. We then measure the number density in 0.4 mag bins from the BCG to 1 mag brighter than the measured 10σ magnitude limit (to reduce any systematic errors due to incompleteness in the catalog). Field galaxy contamination was corrected by measuring the same quantity outside of the 1 Mpc aperture and subtracting. We used the Schechter luminosity function

$$\begin{equation} \Phi (m)=0.4\ln (10)\Phi ^*10^{-0.4\mu (\alpha +1)}{\rm exp}(-10^{-0.4\mu }), \end{equation} \tag{ 1 }$$

where μ = m − m* and allowed Φ*, α, and m* to vary. The final derived parameters and uncertainties are from the least-squares fit to the data and bootstrapping the whole procedure thousands of times from the catalog selection stage. We found the [3.6] best-fit parameters are Φ* = 2.73 ± 0.31 arcsec⁻², α = −1.02 ± 0.11 and m* = 16.58 ± 0.29 (Vega), which are roughly consistent with our previous model assumptions of α = −1.0 and m* = 17.09 at this redshift, calculated from the evolving stellar population BC03 models, normalized to the Coma cluster luminosity function (see H10 for a discussion). Recent measurements of the luminosity function in evolved z > 1 clusters find a similarly flat faint-end slope, α (Mancone et al. 2012). In contrast, less-evolved high-redshift clusters have a paucity of faint galaxies, indicated by a shallower faint-end slope (e.g., Rudnick et al. 2012; Lemaux et al. 2012).

This best-fit luminosity function also corresponds to a richness measurement of N_gal = 47 ± 4 using the H10 procedure (integrating the luminosity function down to m*+1 within a 1 Mpc physical radius of the BCG) and is consistent with the H10 sample of SPT-SZ clusters which are drawn from the same SPT-SZ significance although sampled at a different wavelength (observed i band).

We use an SZ mass estimate as described in R12 and Benson et al. (2011), which is calculated from the Markov chain Monte Carlo method using available CMB, BAO, SNe, and SPT_CL (from the R12 cluster sample) data. The masses reported are posterior estimates based on the probability density function using the ξ and redshift for SPT-CL J0205−5829, marginalized over uncertainties in the SZ and X-ray (Y_X) observable- mass scaling relations and cosmology. In Table 3, we quote mass estimates with and without a Bayesian prior assumption on the underlying population of clusters. The expected bias on the flat-prior mass estimate is related to Eddington bias and affects the SPT-CL J0205−5829 mass estimate at the ∼10% level. This bias is due to the steeply falling mass function which makes it more likely for SPT-CL J0205−5829 to be a lower mass cluster that scattered up than a higher mass cluster scattering down. The total uncertainty in mass (∼20%) is dominated a combination of the intrinsic scatter and the uncertainty in the normalization of the SZ–mass scaling relation. In Table 3, the mass estimates are given as M₅₀₀, defined as the mass within a radius in which the cluster has a density 500 times the critical density of the universe. We can convert between this M₅₀₀ and M₂₀₀ with respect to ρ_mean, defined as the mass within a radius in which the cluster has a density 200 times the mean density of the universe, by assuming a Navarro–Frenk–White profile (Navarro et al. 1997) and the mass–concentration relation by Duffy et al. (2008). Using this conversion, the M₂₀₀ masses are a factor of ∼1.8 times larger, such that the unbiased SZ mass estimate is M₂₀₀ = (8.7 ± 1.8)× 10¹⁴h⁻¹₇₀ M_☉.

We estimate the X-ray physical parameters of SPT-CL J0205−5829 using an iterative process over the cluster radius. We measure the core-excised X-ray temperature, T_X, within r₅₀₀, defined as the radius inside which the mass density is higher than 500 times the critical density of the universe. We iterate over values of r₅₀₀ so that the measured T_X maintains consistency with the M − T relation from Vikhlinin et al. (2009, V09).

For each value of r₅₀₀, we extract spectra and redistribution and ancillary response files. We excise all detected point sources from both the source and background regions as well as the central r ⩽ 0.15 r₅₀₀ cluster core region. Given the significant residual quiescent contamination (Section 2.4), we opt to use a local background model in the fitting procedure. For each camera, we subtract a background spectrum extracted from an annulus centered on the cluster between 160'' and 320'' in radius. These radii were selected based on the cumulative count rate profiles so that the annulus is not contaminated by cluster emission while still lying on the same MOS chips as the source. The total number of background-subtracted source counts is ∼5500 for all three cameras. We use Xspec v12.5 to fit the spectra with a MeKaL model (Mewe et al. 1985; Kaastra et al. 1992; Liedahl et al. 1995) using C-statistics on minimally binned spectra (i.e., binning only channels to obtain ⩾1 counts bin⁻¹). From this fit to the spectrum, we measure the X-ray temperature.

We then use the measured X-ray temperature and the redshift from optical spectroscopy to infer an M₅₀₀ mass from the V09 M − T relation, which we also convert to a corresponding r₅₀₀ value. Given this new value of r₅₀₀, we iterate on this process until two successive r₅₀₀ estimates differ by ⩽25 (equal to the bin size of our X-ray images). This criterion was reached in four iterations and we have verified that the final solution is independent of the initial r₅₀₀ value. The r₅₀₀ radius is 710 kpc (∼85'') and the excised core region (i.e., 0.15 r₅₀₀) has a radius of ∼13'' (roughly twice the point spread function (PSF) FWHM).

The final spectrum is displayed in Figure 5. The best-fit temperature is T_X  = 8.7^+1.0_−0.8keV. This corresponds to a mass of M₅₀₀ = (5.2 ± 1.3) × 10¹⁴h⁻¹₇₀ M_☉ using the relation from V09. There is no evidence that SPT-CL J0205−5829 is unrelaxed from the X-ray morphology or the galaxy distributions, either on the sky or in the velocities, therefore we use the standard M − T relation from V09 and make no corrections based on the dynamical state of the cluster. In the T_X-based mass estimate, we include the statistical uncertainty in the measurement of T_X, uncertainties in cosmology, and assume a 20% intrinsic scatter in the M − T relation, as noted by V09.

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We constrain the mean [Fe] abundance to Z = 0.26 ± 0.15 Z_☉ which is consistent with a typical mean metallicity for the ICM in a massive galaxy cluster (Z ∼ 0.3 Z_☉) at lower redshifts (e.g., Matsumoto et al. 2000; Tozzi et al. 2003; Maughan et al. 2008). The luminosity within r₅₀₀ is L_X(0.5–2.0 keV) = (3.91 ± 0.05) × 10⁴⁴ erg s⁻¹ in the rest frame.

We also note that we detect the Fe K line clearly in PN and MOS2 and more weakly in MOS1. If we allow the redshift to vary during fitting the best-fit value from the joint fit is z = 1.39 ± 0.02, which is ∼5% larger than the optical spectroscopic redshift of z = 1.322^+0.001_−0.002. The redshifts derived from individual cameras are 1σ consistent with the joint PN+MOS1+MOS2 fit (except MOS1 which gives a slightly lower redshift). This is one of the highest redshifts measured from X-ray spectra (cf. Lloyd-Davies et al. 2011).

We follow Foley et al. (2011) and calculate a joint estimate using the SZ mass and X-ray mass estimates of SPT-CL J0205−5829. We assume the uncertainties are uncorrelated between the two masses. This allows for a more straightforward evaluation of the posterior probability distribution function (PDF),

$$\begin{equation} P(M|\xi,T_X) \propto P(M) P(\xi |M) P(T_X|M), \end{equation} \tag{ 2 }$$

where P(M) is the Tinker halo mass function (Tinker et al. 2008), P(ξ|M) is the flat-prior SZ mass estimate PDF, and P(T_X|M) is the flat-prior T_X mass estimate PDF. As calculated in Sections 3.5 and 3.6, we use the X-ray and SZ mass estimates derived from the observables T_X and ξ, respectively, which were marginalized over uncertainties in their scaling relations and cosmology. We find a combined, unbiased, mass estimate to be M₅₀₀ = (4.8 ± 0.8) × 10¹⁴h⁻¹₇₀ M_☉. Converting to M₂₀₀ as above gives M₂₀₀ = (8.8 ± 1.4) × 10¹⁴h⁻¹₇₀ M_☉.

Although SPT-CL J0205−5829 was included in the sample used in R12 for cosmological analysis, we did not assign a goodness of fit to the model, so it is interesting to quantify the probability of having found this cluster in the full 2500 deg² SPT-SZ survey. We use the full 2500 deg² SPT-SZ survey area in order to avoid a posteriori selection of the area in which SPT-CL J0205−5829 was found, which could artificially boost the apparent rarity. We follow Foley et al. (2011) and compute the probability of finding a cluster at higher mass and higher redshift than SPT-CL J0205−5829. We do so by sampling the cosmological and scaling relation constraints of the CMB+BBN+BAO+HST+SN+SPT_CL chain from R12 and producing a posterior statistical mass estimate P(M|ξ, z) at each step in the chain. We then compute the expected number of clusters at higher mass and higher redshift

$$\begin{eqnarray} &&\tilde{x}_{>z>M} = \int _{0}^\infty \int _z^\infty \frac{dN}{dM^{\prime } dz^{\prime }} \int _{0}^{M^{\prime }} P(M^{\prime \prime }|\xi, z) dM^{\prime \prime } dz^{\prime } dM^{\prime }, \nonumber\\ \end{eqnarray} \tag{ 3 }$$

where dN/dMdz is the mass function as calculated following Tinker et al. (2008). The median point in cosmological and scaling relation parameter space predicts $\tilde{x}_{>z>M} = 0.07$ clusters at higher mass and higher redshift than SPT-CL J0205−5829 in 2500 deg².

However, as noted by Hotchkiss (2011), Hoyle et al. (2012), and Waizmann et al. (2012a, 2012b), this statistic has a small expectation value due to the fact that it requires a cluster of simultaneously higher mass and higher redshift than a particular object. This statistic does not consider the fact that many similarly rare clusters could exist with a slightly higher mass and lower redshift or lower mass and higher redshift. Instead, we follow the treatment of Hotchkiss (2011) and compute the probability of finding the particular value of $\tilde{x}_{>z>M} = 0.07$, corresponding to SPT-CL J0205−5829 for an ensemble of simulated 2500 deg² surveys. We then create a normalized histogram of the resulting values of $\tilde{x}_{>z>M}$ for the rarest cluster in each catalog and integrate the area under the curve from 0 to the value of $\tilde{x}_{>z>M}$ for the particular cluster in question. This statistic, unlike $\tilde{x}_{>z>M}$ itself, has an expectation value of 0.5. We note that it depends only very weakly on the details of the simulation or the point in cosmological or scaling relation space at which the simulations are performed. This metric suggests that this cluster is not at all surprising with a probability of 0.69 of finding at least one cluster as rare as SPT-CL J0205−5829 in 2500 deg².

As a comparison to other more rare clusters in the SPT-SZ survey, using the same statistic we find 0.21 for SPT-CL J2106−5844, which was considered in Foley et al. (2011) and 0.05 for SPT-CL J0102−4915 (ACT-CL 0102-4915), currently the rarest cluster in 2500 deg² SPT-SZ survey.