The Atacama Cosmology Telescope: The Two-season ACTPol Sunyaev–Zel'dovich Effect Selected Cluster Catalog

A description of the ACTPol maps used in this work can be found in Naess et al. (2014) and Louis et al. (2017). ACTPol observed two deep fields on the celestial equator, referred to as D5 and D6, from 2013 September 11 to 2013 December 14 (Season 13), using a single 148 GHz detector array (PA1). Each of the D5 and D6 fields covers an area of roughly 70 deg². In Season 14 (2014 August 20–December 31), an additional 148 GHz detector array was added to the ACTPol receiver (PA2), and we obtained observations of a wider, approximately 700 deg² field, referred to as D56, in which the deeper D5 and D6 fields are embedded. We use only ACTPol night-time observations for this analysis, as the beam for this subset is well characterized and known to be stable. We made maps from the ACTPol data using similar methods to those applied to ACT MBAC data, as described in Dünner et al. (2013). Louis et al. (2017) give details of some changes and improvements in the data processing pipeline.

The ACTPol D56 field also overlaps with the previous ACT survey of the celestial equator, conducted using the MBAC receiver (Swetz et al. 2011) at a frequency of 148 GHz. These observations took place during 2009–2010 and covered the entire 270 deg² SDSS S82 optical survey region (Annis et al. 2014) to a white-noise level of 22 μK arcmin^–2 (when filtered on a 59 filter scale; Hasselfield et al. 2013, hereafter H13).

In this work, we combine the 148 GHz observations obtained by ACT using both the MBAC and ACTPol receivers, in order to maximize our sensitivity for cluster detection using the SZ effect. The resulting survey area, which we refer to as the E-D56 field, is shown in Figure 1, overplotted on the 2015 Planck 353 GHz map (Planck Collaboration et al. 2016a), which is sensitive to dust emission. As shown, this region has significant overlap with several large optical and IR public surveys. We combine a total of six maps, all now publicly available from LAMBDA,³⁴ inverse variance weighted by their white-noise level. Figure 2 shows the resulting variation of the white-noise level across the E-D56 survey region. The D5 and D6 regions, observed in 2013 with ACTPol, are easily identified by eye as the lowest noise regions. A common area of 296 deg² within the E-D56 field is covered by both ACT and ACTPol observations. The boundary of the E-D56 cluster search region itself is shown as the black polygon in Figure 1. The survey boundary was chosen to enclose the area with a maximum white-noise level of approximately 30 μK arcmin^–2.

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We masked the locations of point sources in the E-D56 map before searching for clusters, as high-pass filtering of the maps leads to negative rings around point sources, which can then be falsely flagged as cluster candidates. Although sources have already been subtracted from the ACT and ACTPol maps we used in this work, in some cases this is not perfect, and residuals left in the maps can also result in the detection of spurious cluster candidates after high-pass filtering (Section 2.2). We masked sources with fluxes in the ranges 0.015–0.1 Jy, 0.1–1 Jy, and >1 Jy with circles of radius 24, 36, and 72, respectively. We also masked the locations of three artifacts in the map, arising from the construction of the weighted-average map from the individual ACT and ACTPol maps, with circles of radius 36. The masking process reduced the available sky area by 1.3%, resulting in 987.5 deg² being available for the cluster search. The median white-noise level in the cluster search area is 16.8 μK arcmin^–2.

In previous ACT cluster searches (Marriage et al. 2011, H13), clusters were detected using a matched filter, applied in Fourier space, which amplifies the signal from cluster scales and in turn suppresses large-scale noise fluctuations in the map, whether due to the CMB or to the atmosphere. The use of only 148 GHz data in the previous and current analysis restricts us to using only spatial rather than spectral information for SZ cluster detection.

In this work, we take a slightly different approach to spatial filtering for cluster detection to H13. We begin by constructing a matched filter in Fourier space, using a small section of the E-D56 map, chosen to coincide with the D6 field at 02^h30^m R.A. (see Figure 2). The noise power spectrum used in the matched filter construction is that of the map itself; this is a good approximation, as the maps are dominated by the CMB on large scales, and white noise on small scales, rather than cluster signal. As in H13, throughout this work we use the universal pressure profile (UPP; Arnaud et al. 2010, hereafter A10) and associated mass scaling relation to model the SZ signal from galaxy clusters (Section 2.3). This is used as the signal template in the matched filter, after convolution with the ACT beam. To maximize the efficiency of detection of clusters at different scales, we create a family of 24 such matched filters, corresponding to M_500c = (1, 2, 4, 8) × 10¹⁴ M_☉ over the redshift range 0.2 ≤ z ≤ 1.2, in steps of Δz = 0.2. Note that there is some degeneracy between lower mass and higher redshift.

In H13, each matched filter was applied to the map as a multiplication in Fourier space. However, since the signal from clusters exists only at arcminute scales, it is feasible to construct a real-space filter kernel from the matched filter and apply it to the maps by convolution. One advantage of the latter approach is that it simplifies the analysis of maps with arbitrary boundaries and does not require the edges of the map to be tapered to avoid ringing in the Fourier transform. It also makes it straightforward to split a large map into sections that can be analyzed separately, using the exact same filter kernel. This is useful both for parallelizing cluster detection in very large maps, as will be provided by Advanced ACTPol (De Bernardis et al. 2016), and for computation of the survey selection function (Section 2.4). We therefore constructed real-space kernels from the family of matched filters, truncating them at 7' radius, which results in a kernel with a footprint of 28 × 28 pixels. Figure 3 shows an example one-dimensional kernel profile.

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Having truncated the filter profile, we need to apply an additional high-pass filter to the maps, in order to remove noise on scales larger than 7' and reduce contamination from erroneously classifying larger-scale noise features as cluster candidates. We do this by subtracting a Gaussian-smoothed version of the unfiltered map from itself, with the smoothing scale set according to the location of the minimum of the matched filter kernel. This is typically σ = 25, as in the example shown in Figure 3. After high-pass filtering the maps in this way, we convolve them with the real-space matched filter kernel, which is normalized such that it returns the cluster central decrement ΔT in each pixel in the filtered map.

To detect clusters, we construct an S/N map for each filtered map, and in turn we make a segmentation map that identifies peaks (cluster candidates) with S/N > 4. We estimate the noise in each filtered map by dividing it up into square 20' cells and measuring the 3σ-clipped standard deviation in each cell, taking into account masked regions. This accounts for the significant variations in depth seen across the map (Figure 2). Finally, we apply the survey mask shown in Figure 2 to reject the noisiest regions at the edges of the E-D56 map. Figure 4 shows a side-by-side comparison of a section of the unfiltered 148 GHz E-D56 map with the corresponding filtered map (in units of S/N), after application of the survey and point-source masks.

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To construct the catalog of cluster candidates, we first make catalogs of candidates at each filter scale, from each S/N map. We use a minimum detection threshold of a single pixel with S/N > 4 in any filtered map. We adopt the location of the center of mass of the S/N > 4 pixels in each detected object in the filtered map as the coordinates of the cluster candidate. We then create a final master candidate list by cross-matching the catalogs assembled at each cluster scale using a 14 matching radius. We adopt the maximum S/N across all filter scales for each candidate as the "optimal" S/N detection. However, as in H13, and discussed in Section 2.3, we also adopt a single reference filter scale (chosen to be θ_500c = 24) at which we also measure the S/N. Throughout this work we use S/N to refer to the "optimal" S/N (maximized over all filter scales), and S/N_2.4 for the S/N measured at the fixed 24 filter scale.

We assess the fraction of false-positive detections above a given S/N_2.4 cut by running the cluster detection algorithm over sky simulations that are free of cluster signal. We generate 100 random realizations of the CMB sky using a CAMB (Lewis et al. 2000) power spectrum model with parameters consistent with Planck 2015 results (Planck Collaboration et al. 2016b). To these we add white noise, varying across the E-D56 field according to the ACT scan strategy, and scaled to match the noise level seen in the real data. We apply the same survey boundary and point-source mask to these simulations as were applied to the real data, in order to match the real survey area. Figure 5 shows the result after averaging over 100 simulated sky maps: at S/N_2.4 > 4.0, the false-positive rate is 52%, which falls to 30% for S/N_2.4 > 4.5, 8% for S/N_2.4 > 5.0, and 0.7% for S/N_2.4 > 5.6. The fraction of cluster candidates that have been optically confirmed as clusters in the final catalog (see Section 5) shows that Figure 5 gives a reasonable estimate of the false-positive rate.

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Figure 6 presents postage stamp images of the 15 highest-S/N candidates detected in the E-D56 field, which cover the range 9.6 < S/N < 23.5. None of them are new cluster discoveries. Ten of these were previously detected by ACT (three of which were entirely new systems: ACT-CL J0059.1−0049, ACT-CL J0022.2−0036, and ACT-CL J0206.2−0114), and the remainder were known before the era of modern SZ surveys. For comparison, only 2/68 objects in the H13 equatorial ACT survey were detected with S/N higher than the lowest-S/N cluster shown in Figure 6, which reflects the greater depth and larger area coverage of the ACTPol maps.

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The final candidate list contains a total of 517 cluster candidates detected with S/N > 4 (110 candidates with S/N > 5). As described in Sections 3 and 4, 182/517 candidates have been optically confirmed as clusters and have redshift measurements at the time of writing. We discuss the redshift completeness and purity of the sample in Section 5. Table 1 presents the SZ properties of the 182 candidates detected with S/N > 4 that are optically confirmed as clusters.

Although we select cluster candidates using a suite of matched filters in order to maximize the cluster yield, we follow H13 by choosing to characterize the cluster signal and its relation to mass using a single fixed filter scale. This approach is called Profile Based Amplitude Analysis (PBAA) and has the advantage that it avoids the complication of interfilter noise bias (see the discussion in H13, where this method was introduced) and in turn simplifies the survey selection function (see Section 2.4). However, we note that the cluster finder still maximizes S/N over location in the sky, which results in a small positive bias in the recovered S/N values (at most ≈7% at S/N_2.4 = 4.0; see, e.g., Vanderlinde et al. 2010).

We use the UPP to model the cluster signal, and we relate mass to the SZ signal using the A10 scaling relation, applying the methods described in H13. For a map filtered at a fixed scale, the cluster central Compton parameter ${\tilde{y}}_{0}$ is related to mass through

$$\begin{eqnarray}&&{\tilde{y}}_{0}={10}^{{A}_{0}}E{(z)}^{2}{\left(\displaystyle \frac{{M}_{500{\rm{c}}}}{{M}_{\mathrm{pivot}}}\right)}^{1+{B}_{0}}Q({M}_{500{\rm{c}}},z){f}_{\mathrm{rel}}({M}_{500{\rm{c}}},z),\end{eqnarray} \tag{ 1 }$$

where ${10}^{{A}_{0}}=4.95\times {10}^{-5}$ is the normalization, B₀ = 0.08, and M_pivot = 3 × 10¹⁴ M_☉ (these values are equivalent to the A10 scaling relation; see H13). We describe the cluster–filter scale mismatch function, Q (M_500c, z), and the relativistic correction, f_rel, below.

The function Q(M_500c, z), shown in Figure 7, accounts for the mismatch between the size of a cluster with a different mass and redshift to the reference model used to define the matched filter (including the effect of the beam) and in turn ${\tilde{y}}_{0}$ (see Section 3.1 of H13). In this work, we use a UPP model cluster with M_500c = 2 × 10¹⁴ M_☉ at z = 0.4 to define the reference filter scale. This has an angular scale of θ_500c = 24, which is smaller than the θ_500c = 59 scale adopted in H13; this is motivated by the fact that this scale is better matched to the majority of the clusters in our sample and results in higher-S/N ${\tilde{y}}_{0}$ measurements than would be achieved by filtering on a larger scale. Our cluster observable ${\tilde{y}}_{0}$ is therefore extracted from the map filtered at the θ_500c = 24 scale at each detected cluster position. We also define an equivalent S/N at this fixed filter scale, which we will refer to as S/N_2.4.

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The relativistic correction f_rel in Equation (1) is implemented in the same way as in H13, i.e., we use the Arnaud et al. (2005) mass–temperature relation in order to convert M_500c to temperature at a given cluster redshift, and then we apply the formulae of Itoh et al. (1998) to calculate f_rel. These corrections are at the <10% level for the ACTPol sample.

For cosmological applications, the quantity of interest in Equation (1) is M_500c, but to extract a mass for each cluster in the sample, we must also take into account the intrinsic scatter in the SZ signal–mass scaling relation, as well as the fact that the average recovered mass will be biased high owing to the steepness of the cluster mass function. To extract a mass estimate for each cluster with a redshift measurement, we calculate the posterior probability

$$\begin{eqnarray}&&P({M}_{500{\rm{c}}}| {\tilde{y}}_{0},z)\propto P({\tilde{y}}_{0}| {M}_{500{\rm{c}}},z)P({M}_{500{\rm{c}}}| z),\end{eqnarray} \tag{ 2 }$$

assuming that there is intrinsic lognormal scatter σ_int in ${\tilde{y}}_{0}$ about the mean relation defined in Equation (1), in addition to the effect of the measurement error on ${\tilde{y}}_{0}$. Following H13, we take σ_int = 0.2 throughout this work. H13 showed that this level of scatter is seen in both numerical simulations (taken from Bode et al. 2012) and dynamical mass measurements of ACT clusters (taken from Sifón et al. 2013). Here, $P({M}_{500{\rm{c}}}| z)$ is the halo mass function at redshift z, for which we use the results of the calculation by Tinker et al. (2008), as implemented in the hmf³⁵ python package (Murray et al. 2013). We assume σ₈ = 0.80 for such calculations throughout this work. Where we use photometric redshifts, we also marginalize over the redshift uncertainty. We adopt the maximum of the $P({M}_{500{\rm{c}}}| {\tilde{y}}_{0},z)$ distribution as the cluster M_500c estimate, and the uncertainties quoted on these masses are 1σ error bars that do not take into account any uncertainty on the scaling relation parameters. The mass estimates obtained through Equations (1) and (2) are referred to as ${M}_{500{\rm{c}}}^{\mathrm{UPP}}$ throughout this work.

It is the inclusion of the $P({M}_{500{\rm{c}}}| z)$ term that corrects the derived cluster masses for the effect of the steep halo mass function on cluster selection. For the ACT UPP-based masses, and assuming the Tinker et al. (2008) mass function, this leads to an ≈16% correction (Battaglia et al. 2016). For some comparisons to other samples, and for the calculation of mass limits based on the survey selection function (Section 2.4), it is necessary to omit this correction. We list such "uncorrected" mass estimates as ${M}_{500{\rm{c}}}^{\mathrm{Unc}}$ in Table 3.

Since we are using a different filtering and cluster-finding scheme from that used in H13, and we have 296 deg² of sky area in common between the H13 ACT equatorial survey and the ACTPol observations, we performed an end-to-end check of SZ signal measurement and mass recovery by using the ACT and ACTPol data independently. These are disjoint data sets with independent detector noise. For this test, we applied the θ_500c = 24 filtering scheme described in Section 2.2 to ACTPol data alone and cross-matched the detected cluster candidates with the H13 cluster catalog using a 25 matching radius, finding 25 such clusters (the ACTPol observations only overlap with part of the H13 map, and some low-S/N objects reported in H13 are not included in the ACTPol sample; see the discussion in Section 5). After estimating their masses using Equations (1) and (2), we compare them with the UPP masses listed in the H13 cluster catalog (shown as ${M}_{500{\rm{c}}}^{\mathrm{UPP}}\,[{\rm{H}}13]$ in this work). Figure 8 shows the result. Although the uncertainties on individual masses are large, the ${M}_{500{\rm{c}}}^{\mathrm{UPP}}$ measurements inferred from the ACTPol data are unbiased with respect to the H13 masses, with an unweighted mean ratio of $\langle {M}_{500{\rm{c}}}^{\mathrm{UPP}}/{M}_{500{\rm{c}}}^{\mathrm{UPP}}\,[{\rm{H}}13]\rangle =1.03\pm 0.04$ (where the quoted uncertainty is the standard error on the mean, i.e., $\sigma /\sqrt{N}$, where N = 25). Moreover, the results of a two-sample Kolmogorov–Smirnov (K-S) test are consistent with the null hypothesis that both samples are drawn from the same mass distribution (D = 0.12, p-value = 0.99).

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Table 3 presents SZ mass estimates derived from ${\tilde{y}}_{0}$ measurements in the E-D56 map for all optically confirmed clusters detected with ACTPol.

We assess the completeness of the ACTPol cluster search by inserting UPP model clusters into the real ACTPol E-D56 map, after first inverting it to avoid any bias due to the presence of real clusters. Given the complications of interfilter bias, we characterize the survey completeness using only the θ_500c = 24 filter.

As can be seen from Figure 2, the white-noise level in the map varies considerably, and so we break up the map into tiles that are 20' on a side and check the recovery of model clusters in each tile separately. We insert into each tile a UPP model cluster with one of 20 linearly spaced M_500c values between (0.5 and 10) × 10¹⁴ M_☉ in turn. We repeat this for each of a set of 15 different redshifts in the range 0.05 < z < 2, and for 80 randomly chosen positions within each tile, taking into account the survey and point-source masks (Section 2.1). We then perform the same filtering operations on each tile that were applied to the map in the cluster search (i.e., using the θ_500c = 24 real-space matched filter kernel in combination with the σ = 25 high-pass filter), and we extract the S/N_2.4 and ${\tilde{y}}_{0}$ values at each of the 80 positions within each tile for each different cluster model. We take the median S/N_2.4 and ${\tilde{y}}_{0}$ over the different positions within each tile and use these to perform a linear fit for ${\tilde{y}}_{0}$ as a function of S/N_2.4, in order to determine the ${\tilde{y}}_{0}$ signal level corresponding to a chosen cut in S/N_2.4 in each tile. Figure 9 shows the resulting ${\tilde{y}}_{0}$-limit map corresponding to S/N_2.4 = 5, which captures not only the variation in the white-noise level due to the ACT/ACTPol scan strategy but also additional noise variation at the 20' scale, due to the CMB and galactic dust emission.

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In order to express the survey-averaged completeness in terms of a mass limit, we apply Equations (1) and (2) to the S/N_2.4 versus ${\tilde{y}}_{0}$ relation measured in each tile, over a grid of redshifts spanning the range 0.05 < z < 2, and weighting by fraction of the survey area. Figure 10 shows the resulting survey-averaged 90% completeness limit for a cut of S/N_2.4 > 5. As seen in H13, the ACTPol cluster sample is expected to be incomplete for all but the most massive clusters at z < 0.2. This limitation is due to using only a spatial filter to remove the CMB, resulting in confusion when the angular size of low-redshift clusters approaches that of CMB anisotropies. The SZ signal increases at fixed M_500c as redshift increases for our adopted scaling relation (Equation (1)), and so lower-mass clusters are relatively easier to detect at higher redshift. Averaged over the redshift range 0.2 < z < 1.0, we estimate that the survey-averaged 90% completeness limit is M_500c > 4.5 × 10¹⁴ M_☉ for S/N_2.4 > 5. This mass limit is approximately 10% lower than that found in H13 in the S82 survey region and reflects the lower average noise in the E-D56 map in comparison to the ACT maps used in that work. On this basis, we expect the ACTPol sample to contain roughly 4.8 times as many S/N_2.4 > 5 clusters as the H13 sample, after correcting for the differences in the depth and area between the two surveys (although the definitions of S/N are not exactly equivalent, as they are measured on different angular scales). A comparison of the two cluster catalogs shows that this is the case.

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We can similarly assess the variation in the mass limit across the survey area. Figure 11 shows the fraction of survey area as a function of the inferred 50% completeness mass limit for an S/N_2.4 > 5 cut, averaged over the redshift range 0.2 < z < 1. Over 75% of the map, the 50% completeness limit is ≈4.2 × 10¹⁴ M_☉. In roughly 15% of the map, corresponding to the ACTPol D5 and D6 fields, the 50% completeness limit is M_500c ≈ 3.0 × 10¹⁴ M_☉ for S/N_2.4 > 5.

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We now describe our algorithm, named zCluster,³⁶ for estimating cluster redshifts using multiband optical/IR photometry. In this paper it has been applied to SDSS (Albareti et al. 2017), S82 (Annis et al. 2014), and CFHTLS survey data (we use the photometric catalogs of the CFHTLenS project; Hildebrandt et al. 2012; Erben et al. 2013), in addition to our own follow-up observations (Section 4.1). The aim of zCluster is to use the full range of photometric information available and to make a minimal set of assumptions about the optical properties of clusters, since the algorithm is being used to measure the redshifts of clusters selected by other methods (in this case via the SZ effect). This is a different approach to that used by redMaPPer (Rykoff et al. 2014), for example, where the colors of cluster red-sequence galaxies are used both to find the clusters themselves and to estimate the redshift. The approach we describe here avoids modeling the evolution of the cluster red sequence but does require the choice of an appropriate set of spectral templates.

The first step in zCluster is to measure the redshift probability distribution p(z) of each galaxy in the direction of each cluster candidate using a template-fitting method, as used in codes like BPZ (Benéz 2000) and EAZY (Brammer et al. 2008). In fact, we use the default set of galaxy spectral energy distribution (SED) templates included with both of these codes.³⁷ For each template SED and filter transmission function (u, g, r, i, z in the case of SDSS, for which the filter curves are taken from BPZ), we calculate the AB magnitude that would be observed at each redshift z_i over the range 0 < z < 3, in steps of 0.01 in redshift. We then compare the observed broadband SED of each galaxy with each template SED at each z_i and construct the p(z) distribution for each galaxy from the minimum χ² value (over the template set) at each z_i. We apply a magnitude-based prior that sets p(z) = 0 at redshifts where the r-band absolute magnitude is brighter than −24 (i.e., 2.5 mag brighter than the characteristic magnitude of the cluster galaxy luminosity function, as measured by Popesso et al. 2005), since the probability of observing such galaxies in reality is extremely small. Note that the peak of the p(z) distribution gives the maximum likelihood galaxy redshift (see, e.g., Benéz 2000), although these are not what we use for estimating the cluster photometric redshift—we make use of the full p(z) distributions instead.

We estimate the cluster photometric redshift from the weighted sum of the individual galaxy p(z) distributions. For the case of SDSS DR13 data, we start with all galaxies within a 36' radius of each cluster position. The reason for this large initial choice of aperture is for calculating the contrast of each cluster above the local background (see Section 3.2 below). We define the weighted number of galaxies n(z) as

$$\begin{eqnarray}&&n(z)=P\displaystyle \sum _{k=0}^{N}{p}_{k}(z){w}_{k}(z){s}_{k},\end{eqnarray} \tag{ 3 }$$

where z represents the array of z_i values; p_k(z) is the p(z) distribution of the kth galaxy of N galaxies in the catalog; w_k(z) is a weight that depends on the projected radial distance r of the kth galaxy from the cluster center, as determined by the SZ cluster detection algorithm, and calculated at z_i; s_k is an overall "selection weight" (with value 1 or 0) for the kth galaxy; and P is a prior distribution for the cluster redshift, which depends on the depth of the optical/IR survey.

For the radial weights, w_k(z), we assume that clusters follow a projected 2D Navarro–Frenk–White profile (NFW; Navarro et al. 1997), as in Koester et al. (2007) following Bartelmann (1996). We adopt a scale radius of r_s = R₂₀₀/c = 150 kpc (c is the concentration parameter). We define w_k(z) such that w_k(z) = 1 for a galaxy located at the cluster center (r = 0), and we set w_k(z) = 0 for galaxies with r > 1 Mpc. Note that because of the way w_k(z) is defined, different galaxies contribute to n(z) at different redshifts.

For some galaxies, the p(z) distribution can be relatively flat. In these cases, the photometric redshift of the galaxy itself is not well constrained, and including such objects only adds noise to n(z). To mitigate this, we use an "odds" parameter p_Δz (as introduced by Benéz 2000 for BPZ, and also implemented in EAZY), where we define p_Δz as the fraction of p(z) found within Δz = ±0.2 of the maximum likelihood redshift of the galaxy. We set the selection weight s_k = 1 for galaxies with p_Δz > 0.5 and s_k = 0 otherwise to disregard such galaxies.

The redshift distribution of clusters that we expect to find in a given survey depends on its depth. For SDSS, for example, very few clusters can be detected in the optical data at z > 0.5 (as seen by the lack of such objects in optical cluster catalogs based on these data; e.g., Rykoff et al. 2014). We encode this information in the prior P, which for simplicity we take to have a uniform distribution. We adopt (minimum z, maximum z) priors of (0.05. 0.8) in SDSS DR13, (0.2, 1.5) in S82, (0.05, 1.5) in CFHTLenS, and (0.5, 2.0) for our own APO/SOAR photometry (Section 4.1). The maximum z limits used for this prior are quite generous, because in practice the magnitude-based prior prevents most contamination in the form of spurious high-redshift estimates of individual galaxy photometric redshifts.

In principle, the cluster redshift can be estimated from the location of the peak of the n(z) distribution. In practice, we have seen that, in a small number of cases, the maximum of n(z) is identified with a sharp, thin peak that contains only a small fraction of the integrated n(z) distribution. Hence, we define n_Δz(z), which is the integral of n(z) between Δz = ±0.2 calculated at each z_i (this is similar to the definition of p_Δz, except n_Δz(z) is evaluated over the whole redshift range). This procedure makes n_Δz(z) a smoothed version of n(z). Given the choice of Δz, this also changes the minimum and maximum possible cluster redshifts that can be obtained from a given survey by 0.1 compared to the redshift prior cuts. Figure 12 shows a comparison of n_Δz(z) and n(z) (normalized so that the integral of each is equal to 1) for a few example clusters to illustrate the difference. However, for six clusters, we still found it necessary to adjust the minimum redshift of the prior to avoid the algorithm selecting a spuriously low redshift. We adopt the peak of n_Δz(z) as the cluster redshift z_c. We estimate the uncertainty of z_c through comparison with the subset of clusters that also have spectroscopic redshift measurements (see Section 3.3.2 below).

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To confirm the detected SZ candidates as bona fide clusters and check the assignment of cluster redshifts, we used a combination of visual inspection of the available optical imaging and more objective statistical criteria. For the latter, we define an optical density contrast statistic δ (e.g., Muldrew et al. 2012), which is evaluated for clusters with zCluster photometric redshifts,

$$\begin{eqnarray}&&\delta ({z}_{{\rm{c}}})=\displaystyle \frac{{n}_{0.5\mathrm{Mpc}}({z}_{{\rm{c}}})}{{{An}}_{3-4\mathrm{Mpc}}({z}_{{\rm{c}}})}-1.\end{eqnarray} \tag{ 4 }$$

Here, ${n}_{0.5\mathrm{Mpc}}({z}_{{\rm{c}}})$ is calculated using Equation (3) with uniform radial weights (i.e., w_k(z_c) = 1 for galaxies within the specified projected distance of 0.5 Mpc given in the subscript, and w_k(z_c) = 0 otherwise). Similarly, ${n}_{3-4\mathrm{Mpc}}({z}_{{\rm{c}}})$ is the weighted number of galaxies at z_c in a circular annulus 3–4 Mpc from the cluster position (taken to be the local background number of galaxies), and A is a factor that accounts for the difference in area between these two count measurements. The primary use of δ in this work is to flag unreliable photometric redshifts (see Section 3.3.2 below).

During the visual inspection stage, we checked that each SZ detection is associated with an optically identified cluster. We inspected all SZ cluster candidates with S/N > 5. For candidates with 4 < S/N < 5, we only inspected those with δ > 2 (as measured by zCluster), with a spectroscopic redshift (see below), or with a possible match to a known cluster in another catalog. We used a simple 25 matching radius to search for possible cluster counterparts to ACTPol detections in the NASA Extragalactic Database (NED³⁸ ), redMaPPer (v5.10 in SDSS, and v6.3 in DES; Rykoff et al. 2014, 2016), CAMIRA (Oguri et al. 2017), ACT (Hasselfield et al. 2013), and various X-ray cluster surveys (Piffaretti et al. 2011; Mehrtens et al. 2012; Liu et al. 2015; Pacaud et al. 2016). The positions of SZ clusters detected by Planck are more uncertain, and so we use a 10' matching radius when matching to Planck catalogs (Planck Collaboration et al. 2014b, 2016d).

For many objects, spectroscopic redshifts are available from large public surveys. We cross-matched the ACTPol cluster candidate list with SDSS DR13 and the VIMOS Public Extragalactic Redshift Survey (VIPERS Public Data Release 2; Scodeggio et al. 2018). We assign a redshift to each candidate using an iterative procedure. We first measure the cluster redshift, from all galaxy redshifts found within 15 of the SZ candidate position, using the biweight location estimator (Beers et al. 1990), which is robust to outliers. We then iterate, performing a cut of ±3000 km s⁻¹ around the redshift estimate before remeasuring the cluster redshift using the biweight location estimate of the remaining galaxies that are located within 1 Mpc projected distance. For candidates with redshifts available from NED only, we checked the literature to ensure that the redshift was indeed spectroscopic before adopting it. We assigned spectroscopic redshifts to 142 clusters from publicly available data or the literature (103 from SDSS DR13, 1 from VIPERS PDR2, 38 from other literature sources) by this process. We obtained an additional five spectroscopic redshifts for clusters using our own Southern African Large Telescope (SALT) observations (Section 4.2).

At this stage, we also identified the brightest cluster galaxy (BCG) in each cluster, using a combination of visual inspection and the i, r − i color–magnitude diagram, where available. This was done using the best data available for each object (e.g., SDSS, S82, or our own follow-up observations; Section 4.1 below). For one cluster, ACT-CL J0220.9−0333 (z = 1.03; first discovered as RCS J0220.9−0333; see Jee et al. 2011), we could not identify the BCG. Hubble Space Telescope observations of this cluster suggest that the BCG may be hidden behind a foreground spiral galaxy (Lidman et al. 2013).

Figure 13 presents some example optical images of ACTPol clusters confirmed in SDSS using the process described above. Table 2 lists the cluster redshifts, δ measurements, and adopted BCG positions.

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We performed validation checks to test the performance of zCluster both in confirming clusters (using the δ statistic) and in photometric redshift accuracy.

3.3.1. Null Test

The δ statistic (Section 3.1) measures the density contrast at a given (R.A., decl.) position, by comparison with a local background estimate. To be useful as an automated method of confirming SZ candidates as clusters, we would expect such a measurement to give a low value of δ at a position on the sky that is not associated with a galaxy cluster. Hence, we performed a null test, running the zCluster algorithm on 1000 random positions in the SDSS DR12 survey region. Note that in building the catalog of null test random positions, we rejected those that were located within 5' of known clusters in NED or the redMaPPer catalog. Figure 14 shows the results. Interpreting the number of null test positions for which δ is greater than some chosen threshold as the false detection rate, 2% of objects with δ > 3 are expected to be spurious. For δ > 5, the false detection rate falls to 0.6%, and to zero for δ > 7. Therefore, in the full list of 517 ACTPol cluster candidates with S/N > 4, we would expect 11 of the objects with δ > 3 to be spurious. Based on visual inspection, we find only five candidates that are not clusters but have δ > 3 as measured in SDSS photometry, in agreement with the null test.

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3.3.2. Photometric Redshift Accuracy

We used the 147 ACTPol clusters with spectroscopic redshifts to characterize the photometric redshift accuracy of the zCluster algorithm. Figure 15 shows the comparison between z_c, as measured using SDSS or S82 data, and spectroscopic redshift z_s. Clusters with δ > 3 are highlighted.

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Using SDSS photometry, we found that the zCluster redshift estimates are unbiased, with small scatter. The typical scatter σ_z in the photometric redshift residuals (${z}_{{\rm{s}}}-{z}_{{}_{{\rm{c}}}})/(1+{z}_{{\rm{s}}}$) is σ_z = 0.015, for objects with δ > 3. We adopt this σ_z as the measurement of the redshift uncertainty for the 11 clusters in the final catalog that are assigned zCluster SDSS redshifts, as no spectroscopic redshift is available for them (Section 5). As can be seen in Figure 15, some clusters with z_s > 0.5 (beyond the reach of SDSS) are assigned erroneous redshifts by zCluster, but these are easily identified and rejected because they have low δ values.

We see similarly small scatter in the comparison of zCluster redshifts measured in S82 with the spectroscopic redshifts, with σ_z = 0.011 for objects with δ > 3 over the full redshift range. We adopt this as the redshift uncertainty for the nine clusters assigned zCluster S82 redshifts in the final cluster catalog. However, as Figure 15 shows, on average the zCluster S82 photometric redshifts are underestimated by Δz/(1 + z) = 0.013. We therefore correct the redshifts recorded for these nine clusters in the final catalog to account for this bias.

Using CFHTLenS photometry, we see no evidence that the zCluster redshifts are biased, although the comparison sample is small, with only five objects with spectroscopic redshifts having δ > 3. We adopt the measured scatter of σ_z = 0.07 as the photometric redshift error. Only one object in the final catalog is assigned a zCluster CFHTLenS redshift.

4.1.1. SOAR Observations

4.1.2. ARC 3.5 m Observations

4.1.3. Photometric Redshifts from APO/SOAR Observations

We performed matched aperture photometry on all available rizK_s imaging using SExtractor v2.19.5 (Bertin & Arnouts 1996). We used SWARP to first rebin all images for a given field onto a common coordinate grid, so that the images are aligned at the pixel level. We used SExtractor in dual-image mode, using the reddest available band (z or K_s) as the detection image. We adopt MAG_AUTO as the magnitude measurement that we use in computing photometric redshifts, after first correcting for Galactic extinction using the maps and software of Schlegel et al. (1998).

We estimated photometric redshifts by applying the zCluster algorithm described in Section 3.1. Given the small field of view for both the APO and SOAR imaging, we were not able to define a background galaxy sample within an annulus for the measurement of δ (Equation (4)). Instead, we created a separate background galaxy sample from observations of eight candidates that were found not to contain clusters. The total area covered by this background galaxy sample is 0.238 deg². We visually inspected the APO/SOAR images and confirmed the presence of high-redshift clusters for 10/12 candidates, with 9/10 of these having δ > 2.5, and the remaining cluster being spectroscopically confirmed with SALT (Section 4.2). Figure 16 shows some examples. These objects have photometric redshifts in the range 0.70–1.12 (median z_c = 0.94). We have obtained spectroscopic redshifts for only three of these clusters and find that they are all within $| {z}_{{\rm{s}}}-{z}_{{}_{c}}| \lt 0.05$ of the photometric redshift estimates. We adopt this as the photometric redshift uncertainty.

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We obtained spectroscopic redshifts for five clusters with the SALT, using the Robert Stobie Spectrograph (RSS) in its multi-object spectroscopy (MOS) mode. The observations were obtained in programs 2015-2-MLT-003 and 2016-1-MLT-008. The design of SALT limits the maximum observing time for our targets to blocks of less than 1 hr duration, and so targets were visited several times during each observing semester to build up the integration time, taking advantage of queue scheduling. The total integration times varied between 1950 and 5850 s, depending on the number of blocks observed. The observations were conducted in dark time, with a maximum seeing constraint of 2''. For all observations, we used the PG0900 grating with the PC04600 order blocking filter and 2 × 2 binning of the RSS detectors, giving a dispersion of 0.96 Å per binned pixel.

The MOS mode of SALT uses custom-designed slit masks. Target galaxies were selected using color–magnitude cuts applied to photometric catalogs, either from public surveys (S82, CFHTLenS) or from our own APO/SOAR observations (Section 4.1). In every cluster, the BCG was selected, with the remaining slits being placed on galaxies fainter than the BCG and with r − i > 1.0, using the same automated algorithm for target selection as in Kirk et al. (2015). Each slit was 15 wide and 10'' long. We observed 17–26 target galaxies per slit mask, observing one slit mask per target.

The data were reduced using a pipeline that operates on the basic data products delivered from SALT. The initial processing is carried out using the PySALT package (Crawford et al. 2010), which prepares the image headers, applies CCD amplifier gain and cross-talk corrections, and performs bias subtraction. The PySALT data products are then passed into a fully automated pipeline⁴⁰ that performs flat-field corrections, wavelength calibration, and extraction and stacking of one-dimensional spectra.

Redshifts were measured using the XCSAO task of the RVSAO IRAF package (Kurtz & Mink 1998) and verified by visual inspection. We consider redshifts measured from spectra in which two or more strongly detected features were identified (for example, the H and K lines due to Ca ii) to be secure. We successfully measured secure redshifts for two to seven member galaxies, including the BCG, in each cluster. We adopt the biweight location of the member redshifts as the final spectroscopic redshift for each cluster (listed in Table 2). Figure 17 shows some examples of SALT spectra for members identified in one of the observed clusters.

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Throughout this work we have modeled the SZ signal using the UPP and have related this to mass using the A10 scaling relation (Section 2.3). However, several works have noted that this mass scaling relation typically underestimates cluster masses inferred from weak-lensing measurements by ≈30% (e.g., von der Linden et al. 2014; Hoekstra et al. 2015; Planck Collaboration et al. 2016c; Penna-Lima et al. 2017), while other studies, based on either weak-lensing measurements or dynamical mass estimates, have not found evidence of a significant bias, although the uncertainties are quite large (≈10%–30%; Battaglia et al. 2016; Sifón et al. 2016; Rines et al. 2016). It is possible that the bias depends on the dynamical states of clusters (e.g., the fraction of cool-core versus non-cool-core clusters in a sample; Andrade-Santos et al. 2017) or is redshift dependent; for an analysis restricted to z < 0.3, Smith et al. (2016) found no evidence for a bias, at the 5% level, between weak-lensing masses and Planck SZ masses.

The ratio of SZ mass to weak-lensing mass, i.e., the mass bias $\langle {M}_{500{\rm{c}}}^{\mathrm{SZ}}\rangle /\langle {M}_{500{\rm{c}}}^{\mathrm{WL}}\rangle$, is often parameterized as (1−b), where b is the fraction by which the "true" mass (typically taken as corresponding with the weak-lensing mass) is underestimated (Planck Collaboration et al. 2014a). Hydrodynamical simulations have shown that X-ray analyses, which assume hydrostatic equilibrium and on which the A10 scaling relation is based, underestimate the "true" mass in the simulations by ≈10%–20% (e.g., Biffi et al. 2016; Henson et al. 2017), and so if this were the only source of bias, b = 0.1–0.2 would be expected. Instrument calibration issues affecting X-ray telescopes (e.g., Mahdavi et al. 2013; Israel et al. 2015; Madsen et al. 2017) are another potential source of bias. Given the location of the E-D56 field on the sky and its large size, there are a number of published weak-lensing masses and weak-lensing calibrated cluster mass measurements with which we can compare our UPP/A10-scaling-relation-based SZ masses. Here, we compare against the CoMaLit (Sereno 2015) public compilation of weak-lensing mass measurements and the Simet et al. (2017) optical richness (λ)–mass relation, which was measured via a stacked weak-lensing analysis of redMaPPer (Rykoff et al. 2014) clusters detected in the SDSS.

Figure 23 shows the ACTPol–CoMaLit comparison, including previous stacked weak-lensing masses of ACT clusters reported in Battaglia et al. (2016), labeled as CS82-ACT. Here we used the LC²–single catalog from CoMaLit, which consists of objects modeled using a single halo. Inspection of Figure 23 shows that the majority of the weak-lensing masses are larger than the SZ masses. One of the most significant outliers, with a very high weak-lensing mass, is Abell 370 (ACT-CL J0239.8−0134). We note that this cluster has been observed with the Hubble Space Telescope as part of the Frontier Fields initiative, and initial results show that a complicated, multicomponent lensing model is required to describe the mass distribution in this cluster (Lagattuta et al. 2017). Given the heterogeneous nature of the CoMaLit catalog, we limit this comparison to a qualitative one, since modeling the selection function between ACTPol clusters and pointed weak-lensing observations of individual clusters analyzed by several groups is nontrivial.

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In Figure 24, we compare our SZ-based masses with the redMaPPer richness-based masses that were calibrated with stacked weak-lensing measurements by Simet et al. (2017). Although the analysis of Simet et al. (2017) is restricted to z < 0.3, we applied this relation to the full subsample of ACTPol clusters with redMaPPer richness measurements (using an extended version of the Rykoff et al. (2014) redMaPPer v5.10 catalog, which contains objects down to λ = 5), since a similar study using deeper DES data found no evidence that the λ–mass relation evolves with redshift (Melchior et al. 2017). Note that as masses from the Simet et al. (2017) scaling relation are defined within a radius R_200m (within which the average density is 200 times the mean density of the universe at the cluster redshift), we apply the concentration–mass relation of Bhattacharya et al. (2013) to scale them to measurements within R_500c. We label these richness-based weak-lensing masses as ${M}_{500{\rm{c}}}^{\lambda \mathrm{WL}}$. Within z < 0.6, there are 101 ACTPol clusters that have redMaPPer counterparts with λ > 5 and four that do not. Out of the four ACTPol clusters in the common ACTPol/redMaPPer survey area without a redMaPPer match, two of them were probably masked in the redMaPPer optical cluster search, as they are within a few arcminutes of a bright star and a low-redshift dwarf galaxy, and another object (ACT-CL J2342.4+0406 at z = 0.57) does have a match in v6.3 of the redMaPPer catalog, but not in v5.10. We discard these objects.

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To quantify the mass bias, we compute the ratio of the average SZ mass to the average richness-based, weak-lensing calibrated mass $\langle {M}_{500{\rm{c}}}^{\mathrm{UPP}}\rangle /\langle {M}_{500{\rm{c}}}^{\lambda \mathrm{WL}}\rangle$, following the methodology and reasoning presented in Sifón et al. (2016). Computing the ratio of the averages, with uniform weighting of each measurement, has the advantage that many of the uncertainties related to the selection of these clusters and the underlying mass function are removed (see the Appendix in Sifón et al. 2016). This ratio is then used to calibrate the normalization of the Arnaud et al. (2010) relation we use to infer SZ masses.

Using the subsample of S/N > 5.6 ACTPol clusters that is both 100% pure and complete for z < 0.6, we find $\langle {M}_{500{\rm{c}}}^{\mathrm{UPP}}\rangle =(4.88\,\pm 0.21)\times {10}^{14}\,{M}_{\odot }$ and $\langle {M}_{500{\rm{c}}}^{\lambda \mathrm{WL}}\rangle =(7.13\pm 1.05)\times {10}^{14}\,{M}_{\odot }$, and their ratio is $\langle {M}_{500{\rm{c}}}^{\mathrm{UPP}}\rangle /\langle {M}_{500{\rm{c}}}^{\lambda \mathrm{WL}}\rangle =0.68\pm 0.11$. The uncertainty quoted on each average mass is the standard error on the mean, to which we have added the 7% systematic uncertainty in the richness-based weak-lensing masses (Simet et al. 2017). As Figure 24 shows, there is clearly intrinsic scatter between ${M}_{500{\rm{c}}}^{\mathrm{UPP}}$ and ${M}_{500{\rm{c}}}^{\lambda \mathrm{WL}}$, in addition to the scatter caused by the measurement uncertainties. We stress that the purpose of this exercise is to obtain an overall rescaling factor for application to the cluster population as a whole, and not to examine the scatter between the different mass estimates for any individual cluster. The intrinsic scatter should not in principle affect our measurement of the ratio of the average masses. We obtain consistent results (well within the uncertainties) if we repeat this analysis using the entire sample, using a higher cut in S/N (>8), or splitting into two ${M}_{500{\rm{c}}}^{\mathrm{UPP}}$ bins. If we split the sample at z = 0.3 into two redshift bins, we again find consistent results within 1σ, although we note that the lower redshift bin favors a mass ratio that is closer to unity ($\langle {M}_{500{\rm{c}}}^{\mathrm{UPP}}\rangle /\langle {M}_{500{\rm{c}}}^{\lambda \mathrm{WL}}\rangle =0.88\pm 0.18$ using 28 z < 0.3 clusters, and $\langle {M}_{500{\rm{c}}}^{\mathrm{UPP}}\rangle /\langle {M}_{500{\rm{c}}}^{\lambda \mathrm{WL}}\rangle =0.66\pm 0.10$ using 73 z > 0.3 clusters). A larger sample is needed to test for significant redshift evolution.

The mass bias that we measure is consistent with the value of $\langle {M}_{500{\rm{c}}}^{\mathrm{UPP}}\rangle /\langle {M}_{500{\rm{c}}}^{\mathrm{WL}}\rangle =0.97\pm 0.26$ measured by Battaglia et al. (2016) using a stacked weak-lensing analysis of ACT clusters in the CS82 survey region, although the uncertainties are large. We also plot the measured mass bias in Figure 23, for comparison with the CoMaLit sample, which is an independent data set.

We use our $\langle {M}_{500{\rm{c}}}^{\mathrm{UPP}}\rangle /\langle {M}_{500{\rm{c}}}^{\lambda \mathrm{WL}}\rangle$ measurement to rescale the ACTPol UPP/A10-scaling-relation-based SZ-derived masses and record these as ${M}_{500{\rm{c}}}^{\mathrm{Cal}}$ in Table 3.

We now compare the ACTPol E-D56 cluster sample against the most recent cluster catalogs from other blind SZ surveys: the Bleem et al. (2015) SPT catalog, and the PSZ2 catalog (Planck Collaboration et al. 2016d). Ideally, one would compare the distributions of the SZ cluster signals measured by the surveys; however, each project quantifies the SZ signal differently, and in a model-dependent way, and so it is just as straightforward to compare the mass distributions (in any case the quantity of interest for cosmological studies) derived from the SZ measurements. In order to do this, a scaling relation between the chosen SZ observable and mass must be assumed, and each survey has made different assumptions. Therefore, we first make a comparison of the SZ masses measured by each survey, to test whether any correction is necessary to place them on an equivalent mass scale to this work.

In the case of SPT, there is no overlap between the Bleem et al. (2015) catalog and the ACTPol E-D56 field. However, there is an overlapping sample of 18 clusters in common with the southern ACT survey (Marriage et al. 2011), for which H13 provided revised M_500c measurements using the same PBAA method we have used to estimate ${M}_{500{\rm{c}}}^{\mathrm{UPP}}$ in this work (Section 2.3). Moreover, we have shown (Figure 8) that the E-D56 ${M}_{500{\rm{c}}}^{\mathrm{UPP}}$ mass measurements are on the same mass scale as the UPP masses tabulated in H13. We therefore rescale the H13 UPP masses by the factor of 1/0.68 determined from comparing the ACTPol UPP masses with the richness-based weak-lensing masses (Section 6.1). Figure 25 plots the ratio ${M}_{500{\rm{c}}}^{\mathrm{Cal}}\,[{\rm{H}}13]/{M}_{500{\rm{c}}}\,[\mathrm{SPT}]$ versus ${M}_{500{\rm{c}}}^{\mathrm{Cal}}\,[{\rm{H}}13]$. We see that the mass ratio is constant over the mass range, and the unweighted mean ratio $\langle {M}_{500{\rm{c}}}^{\mathrm{Cal}}\,[{\rm{H}}13]/{M}_{500{\rm{c}}}\,[\mathrm{SPT}]\rangle =1.00\pm 0.04$ (where the quoted uncertainty is the standard error on the mean). Therefore, the SPT masses listed in the Bleem et al. (2015) catalog are consistent with the ${M}_{500{\rm{c}}}^{\mathrm{Cal}}$ mass scale, and the two samples can be directly compared. This agreement is remarkable, given that the mass calibration in each case has been arrived at from two very different directions. The scaling relation used to calculate the SPT masses as listed in Bleem et al. (2015) is derived from a Markov Chain Monte Carlo analysis of the Reichardt et al. (2013) cluster counts, with the cosmological parameters fixed to σ₈ = 0.80, Ω_m = 0.3, Ω_Λ = 0.7, and H₀ = 70 km s⁻¹ Mpc⁻¹. This contrasts with the richness-based weak-lensing mass calibration, using an independent external data set, that we have applied to the ACTPol sample. Bleem et al. (2015) also used the projected isothermal β-model (Cavaliere & Fusco-Femiano 1976), rather than the UPP, to describe the expected cluster signal.

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We perform a similar exercise with the PSZ2 Union catalog, this time using the 30 clusters in common with the ACTPol E-D56 catalog (Section 5). We compare the ACTPol SZ masses, after rescaling by the richness-based weak-lensing mass calibration factor (${M}_{500{\rm{c}}}^{\mathrm{Cal}}$), with the PSZ2 SZ masses as listed in Planck Collaboration et al. (2016d). The left panel of Figure 26 shows the result. The most striking feature of this plot is the mass-dependent trend, with the ACTPol masses becoming larger in comparison to PSZ2 with mass (although the uncertainties are large). Although we have plotted the comparison with ${M}_{500{\rm{c}}}^{\mathrm{Cal}}$ in Figure 26, the systematic trend is still present if comparing to the ACTPol ${M}_{500{\rm{c}}}^{\mathrm{UPP}}$ measurements, as the former results from changing only the normalization of the scaling relation, and not its slope. The mass-dependent bias is surprising, given that the UPP and the associated Arnaud et al. (2010) scaling relation are used in both the ACTPol and Planck analyses. This bias does not seem to depend on redshift, angular size (as inferred from the recorded PSZ2 mass), or the detection significance in the PSZ2 catalog.

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A mass-dependent trend is also seen in the comparison of the Bleem et al. (2015) SPT sample with PSZ2 (shown as the gray points in the left panel of Figure 26, where we plot ${M}_{500{\rm{c}}}\,[\mathrm{SPT}]/{M}_{500{\rm{c}}}\,[\mathrm{PSZ}2]$ vs. ${M}_{500{\rm{c}}}\,[\mathrm{SPT}]$). Despite the differences between the SPT and ACT analyses, including in the modeling of the SZ signal itself, we do not see a similar mass-dependent trend when comparing to SPT (Figure 25), nor do we see a mass-dependent trend when comparing ACTPol masses to weak-lensing measurements, although the cross-matched sample is small (Figure 23).

A mass-dependent trend between weak-lensing mass and Planck SZ-based masses has previously been noted in other studies (von der Linden et al. 2014; Hoekstra et al. 2015; Mantz et al. 2016), with Mantz et al. (2016) finding ${M}_{500{\rm{c}}}\,[\mathrm{PSZ}2]\,\propto {M}_{\mathrm{WL}}{}^{0.73\pm 0.02}$ (a similar mass-dependent trend is also seen by Schellenberger & Reiprich 2017) when comparing the Planck SZ-based masses with hydrostatic mass estimates derived from Chandra X-ray data). Using the Kelly (2007) regression method, we find a nonlinear slope, ${M}_{500{\rm{c}}}\,[\mathrm{PSZ}2]\,\propto {M}_{500{\rm{c}}}^{\mathrm{Cal}}{}^{0.55\pm 0.18}$. We caution that this result, which is significant at the 2.5σ level, does not account for selection effects. This is a concern because Figure 26 shows the intersection of the PSZ2 and ACTPol cluster samples, and therefore clusters that were detected in one survey, but not the other, could potentially drive the mass-dependent trend that we see.

To mitigate selection effects, we define a volume-limited sample of PSZ2 clusters, adopting limits of M_500c[PSZ2] > 5.5 × 10¹⁴ M_☉ and 0.2 < z < 0.35, where the low-redshift limit is set to avoid the underrepresentation of such clusters in the ACTPol sample (see Figure 10). The chosen mass limit is well above the apparent mass limit of the PSZ2 sample, as shown in the right panel of Figure 26, and all of the PSZ2 clusters within this volume-limited sample are detected by ACTPol. These objects are highlighted using black boxes in Figure 26 and, again, follow the same mass-dependent trend. We also considered the effect of clusters that were detected by ACT but are below the PSZ2 mass threshold. For the purposes of calculating the average ratio ${M}_{500{\rm{c}}}^{\mathrm{Cal}}/{M}_{500{\rm{c}}}\,[\mathrm{PSZ}2]$ in bins of ${M}_{500{\rm{c}}}^{\mathrm{Cal}}$, we assigned PSZ2 masses at the approximate 2σ detection threshold for the PSZ2 sample (estimated from the PSZ2 mass–redshift distribution shown in the right panel of Figure 26) to those clusters that were detected by ACT but not PSZ2. The corresponding upper limit is shown as the dotted line in the left panel of Figure 26. Similarly, we show the result of assigning PSZ2 masses at the estimated 5σ detection threshold for the PSZ2 sample as the dot-dashed line in the left panel of Figure 26. Again, these follow the mass-dependent trend seen for the clusters that were detected in both catalogs. Nevertheless, given the relatively simple nature of these tests and the relative complexity of the PSZ2 cluster selection compared to the method used in this work, we cannot completely rule out selection effects as the cause of the effect seen in Figure 26.

One possible explanation of the mass-dependent bias seen in the comparison between Planck and weak-lensing mass measurements (e.g., Mantz et al. 2016) is unknown systematics in the weak-lensing analyses. However, this cannot explain Figure 26, where we are comparing SZ-based masses from two experiments that have made similar assumptions in modeling the SZ signal and mass scaling relation. The most obvious difference between the two experiments is angular resolution, with ACT having 14 resolution compared to ≈7' for Planck. Perhaps the key difference in terms of the analysis is the handling of the SZ signal–size degeneracy. Following H13, we do not attempt to measure R_500c from the ACTPol data, and we assume the combination of the UPP and the A10 scaling relation to model how the cluster signal changes with mass (and size), for a map filtered at a single reference angular scale. In contrast, in the Planck analysis, R_500c and in turn the integrated SZ signal Y_500c are inferred from the filtered map that optimizes the detection S/N. If the underlying average cluster profile is the UPP, as assumed in both analyses, then this should yield consistent results. However, the difference in angular resolution between the experiments means that Planck is more sensitive to emission at the outskirts of clusters, while the SZ signal measured by ACT is dominated by emission from within R_500c. In fact, for the ACTPol clusters that are cross-matched with PSZ2, their PSZ2 masses imply 2.7 < θ_500c(arcmin) < 7.4, and so they are not resolved by Planck. Therefore, one possible explanation of the trend seen in Figure 26 is that the true SZ signal in the outskirts of clusters differs from that implied by the UPP and varies with mass. Simulations have shown that this could result from the effects of nongravitational physics on the ICM, such as the level of active galactic nucleus feedback (e.g., Le Brun et al. 2015). Alternatively, it could be the case that the signal from within R_500c is on average higher than expected compared to the UPP, perhaps as a result of shocks from cluster mergers. This could bias the SZ masses measured by ACT high in comparison to the PSZ2 masses, although it is not obvious why such a scenario would depend on cluster mass, and the lifetimes of such merger boosts to the SZ signal are short (e.g., Poole et al. 2007; Wik et al. 2008; Yang et al. 2010; Nelson et al. 2012). We are investigating this by measuring the stacked profiles of ACT clusters beyond R_500c, and the results of this work will appear in a future publication. Alternatively, high-resolution measurements of the SZ pressure profile, as will be provided by MUSTANG-2 (Mason et al. 2016) and NIKA2 (Mayet et al. 2017), could resolve this issue.

Figure 27 shows a comparison of the ACTPol E-D56, SPT, and PSZ2 cluster samples in the (mass, redshift) plane. For ACTPol, we plot the masses after rescaling by the richness-based weak-lensing mass calibration (${M}_{500{\rm{c}}}^{\mathrm{Cal}}$). We do not apply any rescaling to the Bleem et al. (2015) SPT masses or the PSZ2 masses. Figure 27 shows the complementary nature of the ACT and SPT samples to PSZ2, with the former detecting clusters at lower mass and at higher redshift, with only a weak dependence of the mass threshold with redshift. PSZ2, on the other hand, is not biased against the detection of larger angular size, lower-redshift clusters, owing to its extensive multifrequency coverage and the absence of atmospheric noise in the Planck sky maps.

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Figure 27 also suggests that SPT detects a greater number of lower-mass clusters than ACTPol, while having an otherwise similar selection function. We investigate this by directly comparing the mass distributions of the two samples. This is shown in the left panel of Figure 28. We see that the number of clusters in the ACTPol sample begins to fall for ${M}_{500{\rm{c}}}^{\mathrm{Cal}}\,\lt 4\times {10}^{14}\,{M}_{\odot }$, indicating that below this mass limit the sample is largely incomplete. In contrast, the SPT sample contains a larger fraction of clusters below this mass limit. This is expected, as the average white-noise level of the E-D56 field is 18 μK arcmin^–2 (Louis et al. 2017), compared to 15.5 μK arcmin^–2 for SPT (Bleem et al. 2015) at the same frequency. In addition, the SPT cluster search benefits from the use of multifrequency (95, 220 GHz) data and SPT's smaller beam size (11 at 150 GHz). However, we do expect both ACTPol and SPT to detect similar numbers of clusters above a mass threshold where neither survey is incomplete. We tested this by applying a mass cut of ${M}_{500{\rm{c}}}^{\mathrm{Cal}}\gt 4\times {10}^{14}\,{M}_{\odot }$ to both samples; the right panel of Figure 28 shows the result. Both cluster samples are consistent with being drawn from the same population after applying this cut. This is confirmed by a two-sample K-S test, which is not able to reject the null hypothesis that both samples are drawn from the same parent distribution (D = 0.10, p-value = 0.49).

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In this section we comment on a few notable clusters in the E-D56 field, including pairs of clusters and very high redshift (z > 1.5) clusters that were detected at other wavelengths but are not currently detected via the SZ by ACTPol.

6.3.1. ACT-CL J0012.1−0046

6.3.2. ACT-CL J0207.7+0024

This cluster, detected at S/N = 5.3 by ACTPol, was previously identified as an extended X-ray source, detected at S/N = 9.7, in the Swift X-ray Clusters Survey (SWXCS; Tundo et al. 2012; Liu et al. 2015). However, no optical confirmation or redshift has previously been reported for this object. Liu et al. (2015) measured the (0.5–2.0 keV) X-ray flux of J0207.7+0024 to be F_X = (4.5 ± 0.5) × 10⁻¹⁴ erg cm⁻² s⁻¹ within an effective radius of 766, using data with an effective exposure time of 84 ks. For our photometric redshift estimate of z = 1.10, this implies that the cluster has (0.5–2.0 keV) luminosity L_X = (2.3 ± 0.3) × 10⁴⁴ erg s⁻¹ (assuming temperature T = 5 keV for the purpose of calculating the k-correction, and neglecting the uncertainty on the photometric redshift). Based on the cluster's SZ signal, we estimate ${M}_{500{\rm{c}}}^{\mathrm{UPP}}=({2.1}_{-0.3}^{+0.4})\times {10}^{14}\,{M}_{\odot }$ for this object. Figure 29 shows the S82 optical image of the cluster, with the Swift X-ray contours overlaid.

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6.3.3. ACT-CL J0248.1+0238

This z = 0.556 cluster has previously been identified in optical surveys by Lopes et al. (2004) and Rykoff et al. (2014). Our SZ observations indicate that this is a massive object (${M}_{500{\rm{c}}}^{\mathrm{UPP}}=({5.5}_{-0.9}^{+1.0})\times {10}^{14}\,{M}_{\odot }$), although it is not found in the PSZ2 sample or ROSAT X-ray-selected cluster catalogs. We have obtained Chandra observations of this object, and an X-ray spectral analysis confirms that this is a massive object, particularly given its redshift, with X-ray temperature $T={8.4}_{-1.0}^{+1.4}\,\mathrm{keV}$ (more details will be presented in a future publication). Figure 30 shows an optical image with overlaid X-ray contours; clearly, the cluster is somewhat morphologically disturbed.

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6.3.4. ACT-CL J2015.3−0126

This is a newly discovered, massive (${M}_{500{\rm{c}}}^{\mathrm{UPP}}\approx 5\times {10}^{14}\,{M}_{\odot }$) cluster at low Galactic latitude (b = −193), detected at S/N = 7.4. Since it lies outside of the SDSS footprint, we visually confirmed this object through Pan-STARRS imaging (Figure 31) and photometry (PS1; Chambers et al. 2016; Flewelling et al. 2016). We estimated the redshift (z = 0.39) of this cluster using the zCluster algorithm (Section 3.1), but since we have not yet fully tested zCluster using the PS1 photometry, which was released only recently, we adopt a conservative error of ±0.1 on the cluster redshift for now.

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6.3.5. Cluster Pairs

6.3.6. Nondetected z > 1.5 Clusters