THE ATACAMA COSMOLOGY TELESCOPE: PHYSICAL PROPERTIES AND PURITY OF A GALAXY CLUSTER SAMPLE SELECTED VIA THE SUNYAEV–ZEL'DOVICH EFFECT

ACT is a dedicated arcminute resolution CMB experiment consisting of a 6 m off-axis Gregorian telescope located at 5190 m on Cerro Toco, near the Chajnantor Plateau, in the Atacama Desert in northern Chile (see Fowler et al. 2007, 2010; Hincks et al. 2009; Swetz et al. 2010, for a complete description). The SZE cluster selection for this work is based on 148 GHz data from the ACT 2008 southern survey using the Millimeter Bolometer Array Camera (MBAC; Niemack et al. 2008) on the ACT focal plane and with band centers at 148 GHz, 218 GHz, and 277 GHz. The 2008 southern survey area is 9° wide, centered on declination −535, and extends from right ascension 19^h to 24^h and 00^h to 07^h30^m. A total of 850 hr of data with an average of 680 working detectors at 148 GHz (yielding a data volume of 3200 GB) are used to make the microwave sky map. Relative detector pointings are established through observations of Saturn which has a high enough signal-to-noise ratio to allow a pointing fit for each detector. Absolute pointings for the survey are iteratively solved by comparing ACT radio source detections. The resulting rms uncertainty in the reported positions is 5'' (Fowler et al. 2010).

The data are calibrated with 6% precision to Uranus by extrapolating the lower frequency WMAP7 Uranus calibration (Weiland et al. 2010). A highly parallelized preconditioned conjugate gradient code is used to simultaneously solve for the maximum likelihood millimeter-wave map and correlated noise (e.g., from large-scale atmospheric emission).

Cluster candidates were detected in a 148 GHz, 455 deg² submap from the ACT 2008 observing season. The submap lies between right ascensions 00^h12^m and 07^h08^m and declinations −56°11'' and −49°00''. The median noise level in this submap in terms of the decrement amplitude is 31μK. After masking bright sources from the ACT 148 GHz source catalog, the map is match-filtered in the Fourier domain using the isothermal β-model (β = 2/3) convolved with the ACT 148 GHz beam and models for the ACT noise, primary CMB fluctuations, and undetected sources. The form of the filter (Melin et al. 2006; Haehnelt & Tegmark 1996) is

$$\begin{equation} \Phi (\vec{k}) = \frac{ \tilde{B_{\theta _{\rm c}}}^*(\vec{k}) \mid \widetilde{T}_{\rm other}(\vec{k}) \mid ^{-2}}{ \int \!\tilde{B_{\theta _{\rm c}}}^*(\vec{k^{\prime }}) \mid \widetilde{T}_{\rm other}(\vec{k^{\prime }}) \mid ^{-2} \tilde{B_{\theta _{\rm c}}}(\vec{k^{\prime }}) {\rm d}\vec{k^{\prime }}}, \end{equation} \tag{ 1 }$$

where $\tilde{B_{\theta _{\rm c}}}(\vec{k^{\prime }})$ is the Fourier transform of the beam-convolved β-model with critical radius θ_c, and $\widetilde{T}_{\rm other}(\vec{k^{\prime }})$ is the transform of the noise obtained from a combination of ACT difference maps, the WMAP5 primary CMB signal, and the undetected sources (and clusters) based on the amplitudes of Fowler et al. (2010). The map is filtered using β-models with critical radii from 025 to 40 in 025 steps. For a given filter, the signal-to-noise ratio (S/R) of a cluster detection is defined as the ratio of decrement amplitude to total rms. The reported significance of a cluster detection corresponds to the filter which maximizes this S/R. Furthermore, any detection that was not detected at greater than S/R > 3.5 in at least four conjoined pixels was discarded.

During 2009B the ACT data reduction pipeline and cluster extraction algorithms evolved such that everything from pointing to data selection to the matched filter for the final candidate list changed from one observing run to the next. Thus we observed more SZE candidates than used in the purity study (although we report all confirmed cluster detections regardless of its origin). Despite this inefficiency the optical study completely vetted an S/R-ordered list of candidates selected in the manner described above. A final caveat is that after the optical observing season ended, the ACT pipeline continued to evolve such that the finalized candidate list tested here is not identical to the list presented in Marriage et al. (2010). While the S/R of the high significance candidates remains similar between this study and Marriage et al. (2010), the fainter candidates differ in S/R with some of the faintest candidates falling below the S/R threshold of the Marriage et al. list. This is expected: different map-making configurations weight the data in different ways, and a faint candidate which is decrement boosted by noise in one realization of map may not be boosted in the next.

During the 2009B semester we were awarded a total of 10 dark nights for this project in three observing runs on 4 m class telescopes obtained through different Telescope Allocation Committees (TACs). Unfortunately, our first run (two nights), which occurred during the Chilean winter, was completely lost due to snow and no data were obtained (09B-1007, PI: Infante). The next two observing runs had optimal conditions and enabled the successful completion of our program. In Table 1, we summarize the telescopes, instruments, dates, number of good (photometric) nights, and the TACs that awarded the time.

In the run during 2009 October 22–26, we used the ESO Faint Object Spectrograph and Camera (EFOSC) on the 3.6 m NTT on La Silla (084.A-0619, PI: Barrientos) and observed SZE candidates using the Gunn gri filter, with exposure times of 270 s (3 × 90 s), 360 s (3 × 120 s), and 1100 s (4 × 275 s) in g, r, and i, respectively. EFOSC consists of a 2048 × 2048 pixel thinned, AR coated CCD#40 detector projecting a 41 × 41 field of view at 02408 pixel⁻¹ (2 × 2 binning) on the sky. For the three first nights of this run atmospheric conditions were photometric with seeing 07–1''. The last and fourth night of the run was lost due to clouds and no data were taken. Throughout the run we also observed photometric standards from the Southern Hemisphere Standards Stars Catalog (Smith et al. 2007) to calibrate our data.

For our final run, we used the SOAR Optical Imager (SOI) on the 4.1 m SOAR Telescope on Cerro Pachón (09B-0355, PI: Menanteau) for four nights from 2009 December 9–12. SOI is a bent-Cassegrain mounted optical imager using a mini-mosaic of two E2V 2048 × 4096 pixel CCDs to cover a 526 × 526 field of view at a scale of 0154 pixel⁻¹ (2 × 2 binning). For our cluster search we used the same exposure times as in the NTT using the SDSS gri filter set. For three cluster candidates presumed to be at high redshift we obtained observations twice as long as the nominal exposure times and additional deep 2200 s (8 × 275 s) z-band observations. The run conditions were optimal and all four nights were photometric, with seeing in the range 05–1''. We observed photometric standard stars using the same set and method as we did for the earlier NTT run.

For the optical analysis we take advantage of an existing imaging data pipeline that takes us from raw data to galaxy catalogs. We use a modified version of the Python-based Rutgers Southern Cosmology image pipeline (Menanteau et al. 2009, 2010) to process the data from the NTT and SOAR runs. The initial standard CCD processing steps are performed using IRAF²⁵/ccdproc tasks via the STScI/PyRAF²⁶ interface. The fast read-out time of the CCDs allowed us to accommodate multiple dithered exposures for each targeted cluster candidate. In our cluster observations we followed a 10'' off-center 3-, 3-, and 4-point dither pattern in the g, r, and i bands, respectively, which helped to avoid saturated stars, remove chip defects and artifacts, and cover the 10'' gap between CCDs in the SOI camera. Individual science frames were astrometrically recalibrated before stacking by matching sources with stars from the US Naval Observatory Catalog. Observed fields with photometric standard stars from the Smith et al. (2007) catalog were processed in the same fashion and we obtained a photometric zero-point solution in AB magnitudes for each observing night. For each targeted cluster we associated all science frames in all filters and aligned and median combined them into a common pixel reference frame using SWarp (Bertin 2006) to a plate scale of 02408 pixel⁻¹ for the NTT and 01533 pixel⁻¹ for SOAR. Source detection and photometry for the science catalogs were performed using SExtractor (Bertin & Arnouts 1996) in dual-image mode in which sources were identified on the i-band images using a 1.5σ detection threshold, while magnitudes were extracted at matching locations from all other bands. The computed magnitudes in our catalogs were corrected for Galactic dust absorption in each observed band utilizing the infrared maps and C routines provided by Schlegel et al. (1998). This step is particularly important for obtaining unbiased colors, required for accurate photometric redshifts, as significant variations occur over the large area covered by the ACT 2008 survey region.

The final step in our pipeline involves computing the photometric redshift and redshift probability distributions, p_BPZ(z), for each object using the spectral energy distribution (SED) based BPZ code (Benítez 2000) with a flat prior. We compute photometric redshifts using the dust-corrected g, r, i isophotal magnitudes, as defined by the i-band detection and the BPZ set of template spectra described in Benítez et al. (2004), which is based on the templates from Coleman et al. (1980) and Kinney et al. (1996). This set consists of El, Sbc, Scd, Im, SB3, and SB2 and represents the typical SEDs of elliptical, early/intermediate type spiral, late-type spiral, irregular, and two types of starburst galaxies, respectively.

The exposure times for our observations were designed to confidently detect sub-L* early-type galaxies up to z ≈ 0.8 and BCGs at z>1.0 in order to confirm the presence of a galaxy cluster. In order to assess the depth reached by the observations as well as the differences between telescopes, we performed Monte Carlo simulations to estimate the recovery fraction of early-type galaxies as a function of magnitude in each of our observing runs. We used the IRAF/artdata package to create simulated data sets for the NTT and SOAR observations, which were subsequently processed through our pipeline using the same detection and extraction procedures as for the science images. Within artdata we used the mkobjects task to draw artificial elliptical galaxies on science fields as de Vaucouleurs profiles with the same noise properties as the real data. We scaled the surface brightness of the galaxy profiles according to their magnitude for a range of assumed sizes (1–7 kpc, but converging to the typical image seeing at the faint limits). Using this procedure we generated 20 and 25 artificial elliptical galaxies for the NTT and SOAR data sets respectively over a wide range of magnitudes (19 < i < 27) sampled at small (Δ_mag = 0.1) steps. We repeated this 10 times for each data set at each step. At each magnitude step we matched the recovered galaxies in the simulations with the input positions from the artificial catalogs. In Figure 2, we show the recovered fraction of galaxies as a function of the input i-band magnitude for the NTT and SOAR data set, as well as the 80% and 50% levels for reference. From this exercise we conclude that we reach 80% completeness at i = 23.5 and i = 24.3 for elliptical galaxies for the NTT and SOAR data sets, respectively. We emphasize that we followed the same observing strategy (i.e., same filter set, dithering pattern, and exposure times) for both runs and therefore the relatively large difference (0.8 mag) in the completeness limit is likely due to a combination of telescope size (3.6 m versus 4.1 m), CCD sensitivity, and telescope throughput. The re-aluminization of the SOAR primary mirror in 2009 November, just before our run, might have played a role in the higher sensitivity of the SOAR imaging.

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We can use the completeness limits estimated from our simulations to determine how far in redshift we can "see" massive clusters. For this, we compare the completeness limits of our observations to the expected and observed (i.e., known) apparent magnitudes of galaxies in clusters as a function of redshift. We estimated the expected apparent galaxy i-band magnitude as a function of redshift using L* as defined for the population of red galaxies by Blanton et al. (2003) at z = 0.1 and allowing passive evolution according to a solar metallicity (Bruzual & Charlot 2003) τ = 1.0 Gyr burst model formed at z_f = 5. We show this in Figure 3 for a range of luminosities (0.4 L*, L*, and 4 L*) aimed at representing the cluster members from the faint ones to the BCG. We also show as different gray levels the 80% completeness as determined by the simulations for the NTT and SOAR run, which provides evidence that we can reach typical L* galaxies to z ≈ 0.8 for both data sets (and z ≈ 1 for the SOAR data). We also compare the depth of our imaging campaign to the observed i-band apparent magnitudes of galaxies in three massive high-redshift (z>1.2) clusters for which we could find suitable data in the literature for comparison. In Figure 3, we plot the observed magnitude of the three brightest galaxies for the clusters RDCS 1252.9−2927 (Blakeslee et al. 2003; Rosati et al. 2004) at z = 1.237, XMMU J2235.3−2557 (Mullis et al. 2005; Rosati et al. 2009) at z = 1.393, and XMMXCS J2215.9−1738 (Stanford et al. 2006; Hilton et al. 2009) at z = 1.457. We conclude that, with the possible exception of the cluster-like XMMXCS J2215.9−1738 observed during the NTT run, we comfortably detect luminous galaxies in clusters at high redshift. This provides further evidence that our observation's integration times allow us to confidently identify real SZE clusters up to z ≈ 1.2–1.4, below this redshift according to the ΛCDM model >99% of all clusters more massive 8 × 10¹⁴ M_☉ should reside. In Section 4.7, we further discuss the possibility of missing z>1.2 massive clusters in our observations.

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A number of the SZE cluster candidates were associated with previously known clusters at lower redshifts. For a few of these we obtained new NTT/SOAR gri observations in order to calibrate our photometric redshift and to test our identification procedure; however, for the most part these were avoided and we relied on public archival imaging and on data from other existing programs to compare with the SZE sources.

AS0295 and AS0592 are included among the low-redshift SZE clusters reported by Hincks et al. (2009) and are the focus of a separate observing program by our group (09B-0389, PI: Hughes) aimed at obtaining weak lensing masses using deep V and R observations. These were obtained using the MOSAIC camera on the Blanco 4 m telescope on 2010 January 9 under photometric conditions.

1E0657−56 (the Bullet Cluster) has been extensively observed at different wavelengths. Here we show the optical observations of the cluster central region taken with the Advanced Camera for Surveys aboard the Hubble Space Telescope (HST; GO:10200, PI: Jones; GO:10863, PI: Gonzalez) using the F606W (V), F814W (I), and F850LP (z) filters which were taken from the HST archive.²⁷

For RXCJ0217.2−5244 we used our own pipeline to process raw V (720s) and R (1200 s) images obtained from the ESO archive²⁸ (70.A-0074-A, PI: Edge) utilizing the SUSI camera on the NTT on 2002 October 7 and 12.

A fraction of the area covered by ACT overlaps with the 41 deg²griz imaging from the CTIO 4 m telescope MOSAIC camera on the 05 hr field from the Southern Cosmology Survey (Menanteau et al. 2010). We used these data to search for optical identification of SZE cluster candidates in the region to avoid re-targeting with the NTT and SOAR telescopes.

Our analysis has resulted in a sample of 23 optically confirmed SZE clusters selected from 455 deg² of ACT data between 0.1 < z < 1.1. Nine of these clusters, such as 1E0657−56 (the Bullet Cluster), AS0592, and A3404, are well known and appear at low redshift (z < 0.4); four systems in our sample have been reported as SZE-selected clusters by SPT in their area overlapping with the ACT coverage. Three of these systems (ACT-CL J0509−5341, ACT-CL J0528−5259, and ACT-CL J0546−5345) were originally reported as SZE-selected clusters by Staniszewski et al. (2009), with optical and X-ray properties subsequently studied by us (Menanteau & Hughes 2009), and ACT J0559−5249 has been recently reported by High et al. (2010). About two-thirds of the clusters we present here (14), however, are new SZE-discovered systems (four of which overlap with the SPT cluster sample of High et al. 2010) previously unrecognized in the optical or X-ray bands; ten of these are entirely new discoveries by ACT, with photometric redshifts ranging from z = 0.4 to z = 0.8. All of the new clusters are optically quite rich and a number show strong lensing arcs (see Section 4.2). We present the full list of clusters, positions, and redshifts (photometric in some cases) in Table 2. In Figures 4–10, we show the composite color optical images of all clusters in our sample with the ACT 148 GHz contours (six equally spaced between the minimum and maximum levels in μK shown between brackets) overlaid on the images.

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In the following sections, we provide detailed information on individual clusters in the sample in increasing redshift order.

4.1.1. ACT-CL J0145−5301 (A2941)

4.1.2. ACT-CL J0641−4949 (A3402)

4.1.3. ACT-CL J0645−5413 (A3404)

4.1.4. ACT-CL J0638−5358 (AS0592)

4.1.5. ACT-CL J0516−5430 (AS0520)

4.1.6. ACT-CL J0245−5302 (AS0295)

4.1.7. ACT-CL J0217−5245 (RXC J0217.2−5244)

4.1.8. ACT-CL J0330−5227 (A3128 North-East)

4.1.9. ACT-CL J0658−5557 (1ES0657−558)

4.1.10. Overlap with the SPT Sample

A number of clusters in our sample show gravitational lensing features, indicative of massive systems. The excellent seeing conditions of the 2009B runs used for this study enable us to unambiguously determine that 6 of the 23 clusters show strong lensing arcs. Three of these have already been reported in the literature: ACT-CL J0658−5557 (1E0657-56/Bullet), ACT-CL J0245−5302 (AS0295), and ACT-CL J0546−5345. Arcs in the other three are reported here for the first time: ACT-CL J0330−5227 (A3128-NE), ACT-CL J0509-5341, and ACT-CL J0304−4921. In Figure 11, we show close-up monochromatic images of the clusters with newly identified strong-lensing arcs in the sample.

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Ten systems in our sample of ACT SZE clusters are completely new systems, for which the only optical data available are from our NTT and SOAR imaging collected during 2009B. The main objective of our observations was to confirm SZE clusters via optical identification as real systems, and in the case that observations were carried under photometric conditions—which was true for both NTT and SOAR runs—to compute crude photometric redshift estimates using the gri (and z in some cases) imaging for the observed clusters. Therefore we can provide only photometric redshift estimates for these new systems (see Table 2). A small subsample of the targeted clusters (9) has spectroscopic information available, which we can use to perform some basic comparison between the photometric and spectroscopic redshifts. Unfortunately, the imaging of this subsample is quite heterogeneous and comes from different data sets (four from CTIO 4 m, three from NTT, and two from SOAR) making it difficult to characterize the photometric redshift errors for the sample. In Figure 12, we show the comparison between spectroscopic and photometric redshift for the mean cluster value (top panel) and the BCG (bottom panel) for the subsample of nine clusters. We calculate the mean photometric redshift for each cluster, z_cluster, with a procedure similar to that used in Menanteau et al. (2010). This consists of iteratively selecting cluster member galaxies using a 3σ median sigma-clipping algorithm within a local color–magnitude relation (using all available colors) defined by galaxies that (1) were photometrically classified as E or E/S0s according to their BPZ-fitted SED type, (2) are within a projected radius of 500 kpc from the BCG, and (3) are within the redshift interval |z − z_cluster| = |Δz| = 0.05. The uncertainty on this redshift estimate was taken to be the weighted rms of the individual galaxies chosen as members. The uncertainties associated with the BCG photometric redshifts were estimated from the BCG p_BPZ(z) function. These probability functions are non-Gaussian as revealed by the asymmetric error bars in Figure 12 (lower panel).

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In Table 3, we provide the mean cluster and BCG photometric redshift estimates and associated 68% C.L. uncertainties. Despite the relatively large errors on the photometric redshifts (driven by the limited number of bands used) they are still useful for providing cosmological constraints (see Sehgal et al. 2010).

We expect fewer than 0.010 false positives based on targeting 49 regions of the sky and assuming an expected cluster number density of 0.06 deg⁻² and a positional offset between the BCG and the SZ target centroid of 2'. This assumes a random association with a cluster at or above the mass threshold of our sample. We would expect to find one random association for a cluster density of 5.96 deg⁻², which corresponds to a mass threshold of 1.7 × 10¹⁴ M_☉ assuming a distribution of massive halos using the Tinker et al. (2008) mass function. A3402 might be in this situation, which would explain the large positional offset between its BCG and peak SZ decrement and its lack of significant X-ray emission.

The extraction methodology of SZE cluster candidates evolved during the 2009B season and as a result the candidates observed in the first run (at the NTT) came from a list of targets that was later revised once the selection method was more stable (see Section 3.1). The revised sample for our second run (at SOAR) in 2009 December contained all of the high signal detections observed on the NTT run. This later list, from which we targeted 49 systems, is therefore the most uniformly observed as a function of signal to noise and the one best suited to estimate the purity of SZE candidates. We utilized the Blanco archival data in the 05 hr field to supplement our NTT and SOAR imaging, although no new clusters were found (beyond those previously found by SPT). By purity here we mean the ratio of optically confirmed clusters to SZE detections. In Figure 13, we show the purity from the sample of 49 targeted systems as a function of signal to noise as the thick and thin solid line types (these correspond to different event binning). Since we did not observe every cluster candidate at signal-to-noise ratios below 5, for reference we also show, using dashed lines, the fraction of candidates greater than a given signal to noise that were actually imaged in this program.

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We achieve 100% purity for signal-to-noise ratios greater than 5.7 where there are 10 clusters. This drops to a purity value of 80% for an S/R of 5.1. We targeted all of the SZ candidates down to a signal to noise of 4.8 and for this sample the purity is 71% (17/24). Below this S/R value the purity of the SZ candidates drops sharply. Only 6 clusters were optically confirmed out of 25 candidates targeted (24% purity) over the S/R range 4.2–4.8. However, as we were unable to target all of the SZ candidates in this S/R range, assigning a precise estimation of the purity is not possible. Another estimate for the purity comes from conservatively assuming that none of the untargeted SZE candidates is a real system, in which case the overall purity would be ≃9% in the signal-to-noise ratio range between 4.2 and 4.8.

An important conclusion of this analysis is that within our high S/R sample (>5.7), which was fully observed, we report no clusters above a redshift of 1.1. As we show next, this distribution is fully consistent with expectations of ΛCDM which are based on Gaussian fluctuations in the primordial matter density distribution. Deviations from Gaussianity can perturb the expected number of massive clusters at high redshift. Thus, the large area surveyed by ACT and the well-established redshift distribution of the sample can be used to put important constraints on the level of non-Gaussianity, defined by the dimensionless coupling parameter, f_NL (see Komatsu & Spergel 2001; Lo Verde et al. 2008). This will be the focus of a future study.

Here we describe how we estimate the approximate mass limit of the observed sample. We binned the number of clusters as a function of redshift in bins of Δz = 0.2 and fitted to the redshift distribution of massive halos using the Tinker et al. (2008) mass function and cosmological parameters from Komatsu et al. (2009), assuming that all (no) clusters above (below) the threshold were detected. The number counts were assumed to be Poisson distributed in each bin and the appropriate likelihood function was calculated and used as the figure-of-merit function for the fits. In Figure 14, we show the cumulative number distribution of optically confirmed ACT SZ clusters (the histograms) per square degree as a function of redshift. We make two assumptions here: (1) that the area surveyed is 455 deg² even though all of this was not covered to the same depth, and (2) that the sample is complete out to a redshift of 1.2. The upper histogram is for the entire sample of clusters from Table 2, while the bottom histogram is for the subset of clusters above an S/R of 5.7 which has 100% purity. We overplot curves that give the expected distribution for different mass thresholds based on structure formation in an ΛCDM model (Tinker et al. 2008). The full sample of 23 is well characterized by a mass threshold of 8 × 10¹⁴ M_☉ and the 10 highest significance clusters, where all ACT SZ candidate clusters were optically confirmed, are consistent with a mass threshold of 1 × 10¹⁵ M_☉. These mass thresholds are in agreement with their X-ray luminosities (Figure 15) and with simulations given the current ACT survey noise (Sehgal et al. 2010). Thus there is consistency between the SZ, optical, and X-ray observations with the model. Note that if the actual area were significantly smaller than 455 deg² or clusters were missed, the mass thresholds would decrease. Therefore, the mass threshold values quoted here can be considered strong upper limits.

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Beyond the reported sample of 23 clusters (Table 2), there are in addition three SZE cluster candidates (not reported) at relatively high S/R (>5.1) for which we do not find an optical counterpart using the procedure described above. One of these we observed at the NTT and then again for twice as long at SOAR, where we also included the z-band. Although there are potential BCGs in the field of view (based on our low accuracy photometric redshifts), none is accompanied by a red sequence containing more than ≃ 15 galaxies within a projected radius of 500 kpc. This value is consistent with the average surface density of galaxies at z ≃ 1 and additionally is far below the typical observed richness of the confirmed clusters (≃ 60 members) in the optical. Thus we can confidently conclude that these three candidates are not optical clusters in the redshift range z ≲ 1.2 with optical properties like those of the confirmed sample (Table 2). An obvious possibility is that these are high-redshift clusters, beyond the reach of our observational program. However, for the Tinker et al. (2008) distribution of massive halos in the ΛCDM cosmology, we expect only 0.6 or 0.1 clusters (for M = 6 and 8 × 10¹⁴ M_☉, respectively) beyond a redshift of 1.2 over the area surveyed. Future near-IR or warm phase Spitzer Infrared Array Camera imaging is required to determine whether these are high-redshift massive clusters.

We searched for X-ray counterparts to the ACT clusters using the RASS data following the same procedure as in Menanteau & Hughes (2009). The raw X-ray photon event lists and exposure maps were downloaded from the MPE ROSAT Archive²⁹ and were queried with our own custom software. At the position of each cluster, RASS count rates in the 0.5–2 keV band (corresponding to PI channels 52–201) were extracted from within radii of 3' to 9' (chosen appropriately for each cluster) for the source emission and from within a surrounding annulus (12' to 30' inner and outer radii) for the background emission. Obvious point sources were excluded from both source and background regions. The background-subtracted count rates were converted to X-ray luminosity (in the 0.1–2.4 keV band) assuming a thermal spectrum (kT = 5 keV) and the Galactic column density of neutral hydrogen appropriate to the source position, using data from the Leiden/Argentine/H i Bonn survey (Kalberla et al. 2005). In Table 4, we show the X-ray fluxes and luminosities for all ACT clusters, regardless of the significance of the RASS detection.

All available archival Chandra data for clusters in our sample are used in this analysis. The combined exposure times of the observations for each cluster are shown in Table 5. Data are reduced using CIAO version 4.2 and calibration data base version 4.2.0. The data are processed starting with the level 1 events data, removing the cosmic ray afterglow correction, and generating a new bad pixel file that accounts for hot pixels and cosmic ray afterglows. Using the newly generated bad pixel file, the charge transfer inefficiency correction, time-dependent gain adjustment, and other standard corrections are applied to the data. The data are filtered for ASCA grades 0, 2, 3, 4, 6 and status = 0 events and the good time interval data provided with the observations are applied. Periods of high background count rate are excised using an iterative procedure involving creating light curves in background regions with 259 s bins (following the ACIS "Blank-Sky" Background File reduction), and excising time intervals that are in excess of 3σ (=rms) from the mean background count rate. This sigma clipping procedure is iterated until all remaining data lie within 3σ of the mean. All observations are in the ACIS-I configuration and background regions are chosen among the chips free from cluster emission, at approximately the same distance from the readout as the cluster. This is to account for a gradient in the front-illuminated chip response seen when investigating deep blank-sky exposures (Bonamente et al. 2004).

Images are created by binning the data by a factor of 4, resulting in a pixel size of 197. Exposure maps are constructed for each observation at an energy of 1 keV. Images and exposure maps are combined in cases where there are multiple observations of the same cluster. A wavelet-based source detector is used on the combined images and exposure maps to generate a list of potential point sources. The list is examined by eye, removing bogus or suspect detections, and then used as the basis for our point source mask.

Spectra are extracted in regions that are 3σ above the background level, where σ is the uncertainty in the background measurement. Surface brightness profiles are constructed using 5'' bins and are used to estimate the background surface brightness and the uncertainty in the background. The radius corresponding to 3σ above the background, θ_3σ, is computed and used for the spectral extraction, accounting for the point source mask. Spectra are extracted and responses calculated for each individual observation. All of the spectra for a given cluster are then fit simultaneously.

ACIS quiescent backgrounds are used to construct background spectra for each of the observations. Appropriate quiescent background files are reprojected to match each observation and background spectra are extracted in the same θ_3σ regions used for the cluster spectra. The background spectra are then normalized to match the count rate of the cluster spectra in the 9.5–12.0 keV range, where the Chandra response is negligible and the particle background dominates (e.g., Vikhlinin et al. 2005).

XSPEC (Arnaud 1996) is used to fit the X-ray spectrum assuming a thermal plasma emission model (using the so-called Mekal model; Mewe et al. 1985), multiplied by a Galactic absorption model, with solar abundances of Asplund et al. (2009) and cross sections of Balucinska-Church & McCammon (1992) including an updated He cross section (Yan et al. 1998). For the absorption component we fixed the column density of neutral hydrogen to the Galactic value toward the cluster position (obtained in the same way as for the RASS data). Spectra are grouped such that there are a minimum of 20 counts per bin and the χ² statistic is used for the fit. All spectra for a given cluster are fit simultaneously to the same plasma model, including linking the normalizations between data sets. The fit is limited to photons within the energy range 0.3–9.0 keV. To estimate fluxes in the 0.1–2.4 keV ROSAT band, the energy range is extended below Chandra's nominal energy range. Fluxes, F_X, and luminosities, L_X, in the 0.1–2.4 keV band are then computed from the best-fit model. Uncertainties in the fluxes and luminosities are estimated by varying the temperature, T_e, abundance, Z, and normalization of the model using the extremities of the 68% confidence regions for the parameters. The results are summarized in Table 5, which shows the redshift (z), total effective exposure time (t_exp), column density (N_H), the spectral extraction radius in angular (θ_3σ) and physical (R_3σ) units, spectral parameters from the fit (T_e and Z), and the resulting flux and luminosity (F_X and L_X) for each cluster.

For the XMM-Newton observations we started with the pipeline-processed data supplied as part of the standard processing. A combined background-subtracted and exposure-corrected image was created for each cluster in the 0.5–2 keV band by merging data from the three EPIC cameras: PN, MOS1, and MOS2. These were used to define the optimal radii for spectral extraction, initially taken as the radius where the estimated cluster emission fell below the background level. These source regions were further refined by increasing the extraction radii by factors of 10% until the extracted flux values converged to an accuracy of a few percent. The regions, in nearly all cases, were elliptical. Background spectra came from a surrounding annular region with sufficient area to obtain good photon statistics. Event lists were filtered to remove time periods of high count rate background flares and to include only good event patterns (⩽ 12 for MOS and ⩽4 for the PN). Other standard filters to remove bad pixels and chip edges, for example, were applied. We used standard XMM-Newton software tools to calculate the instrumental response functions for each cluster (treating the data from each camera independently). The cluster image itself was used for the weighting to generate the response functions. The same absorbed thermal plasma model as described above was used to fit the PN, MOS1, and MOS2 data, again using XSPEC. The individual spectral data sets were fitted separately with linked parameters. X-ray fluxes and luminosities were determined using the best-fitted spectrum. The uncertainties on these include the 1σ range on temperature and overall normalization. Results are given in Table 6.

The soft X-ray fluxes as a function of redshift are shown in Figure 15. We plot all data sets: RASS in gray, Chandra in red, and XMM-Newton in blue. We indicate the region (at the high-end flux) that approximately corresponds to the flux limit of the RASS bright source catalog (Voges et al. 1999). In cases of multiple X-ray data sets the agreement among the observed fluxes is good, with the possible exception of ACT-CL-J0330-5227, where the emission from the foreground cluster contaminates the RASS flux estimate.

For reference we show curves of the expected (observed-frame) X-ray fluxes for clusters with assumed masses of M₂₀₀ = 4 × 10¹⁴M_☉ (dashed) and 1 × 10¹⁵M_☉ (solid) using the X-ray luminosity versus mass scaling relation in Vikhlinin et al. (2009). We use their Equation (22), which includes an empirically determined redshift evolution. We convert their X-ray band (emitted: 0.5–2 keV band) to ours (observed: 0.1–2.4 keV) assuming a thermal spectrum at the estimated cluster temperature determined using the mass–temperature relation also from Vikhlinin et al. (2009). This too has a redshift dependence, so the estimated temperatures vary in the ranges 2.9–5.0 keV and 5.2–9.0 keV over 0.0 < z < 1.1 for the two mass values we plot. We use conversion factors assuming the redshift-averaged temperatures of 4 keV and 7 keV, since the difference in conversion factor over the temperature ranges is only a few percent, negligible on the scale of Figure 15. The mass values in Vikhlinin et al. (2009) are defined with respect to an overdensity of 500 times the critical density of the universe at the cluster redshift, while in this paper we define cluster masses with respect to an overdensity of 200 times the average density at the cluster redshift. We calculate the conversion factor assuming a Navarro–Frenk–White halo mass profile with the power-law relation between concentration and mass determined by Duffy et al. (2008) from large cosmological N-body simulations. This mass conversion factor is approximately 1.8 averaged over redshift, varies from 2.2 to 1.7 over 0.0 < z < 1.1, and depends only weakly on the cluster mass (few percent) for the two values plotted here.

The X-ray fluxes of the ACT SZE-selected clusters scatter about the 1 × 10¹⁵ M_☉ curve, validating the mass threshold we estimated above from the cluster number counts. The most extreme outlier (on the low flux side) is A3402, indicating a considerably lower mass for this system, assuming (as we have) that the SZE candidate is at the redshift of A3402. For those clusters with archival Chandra or XMM-Newton data our measured temperatures are typically high kT>5 keV and in good agreement with results from the recent SPT cluster X-ray analysis (Andersson et al. 2010). The masses inferred from the X-ray temperatures are consistent with the mass curves shown in Figure 15.