THE ATACAMA COSMOLOGY TELESCOPE: THE LABOCA/ACT SURVEY OF CLUSTERS AT ALL REDSHIFTS

Galaxy clusters produce a spectral distortion in the cosmic microwave background (CMB) known as the Sunyaev–Zel'dovich effect (SZE; Zel'dovich & Sunyaev 1969; Sunyaev & Zel'dovich 1970a). The thermal Sunyaev–Zel'dovich effect (tSZ) signal is quantified by ${{Y}_{{\rm tSZ}}}\equiv \int y\;d{\Omega }$ in terms of the Compton parameter

$$\begin{eqnarray}&&y=\int {{\sigma }_{T}}\;{{n}_{e}}\frac{{{k}_{{\rm B}}}{{T}_{e}}}{{{m}_{e}}{{c}^{2}}}dl,\end{eqnarray} \tag{ 1 }$$

the Thomson cross section ${{\sigma }_{T}}$, Boltzmann's constant ${{k}_{{\rm B}}}$, the electron density n_e, the electron temperature T_e, and the line of sight (LOS) path length dl. The Compton parameter is insensitive to cluster redshift, allowing for the unbiased detection of massive clusters out to large distances. This selection is complementary to that of surveys using optical richness or X-ray flux, which generally yield lower-redshift cluster samples (for a review of the SZE in clusters, see, e.g., Carlstrom et al. 2002). The mass function of SZE-selected galaxy clusters has been used to constrain the properties of dark energy, as well as the mean matter density ${{{\Omega }}_{m}}$ and amplitude of fluctuations ${{\sigma }_{8}}$ (e.g., Sehgal et al. 2011; Benson et al. 2013; Hasselfield et al. 2013b; Planck Collaboration et al. 2014b).

The number of known SZE-selected clusters is rising rapidly. The first surveys produced samples of ∼20 blind SZE-detected clusters (Menanteau et al. 2010; Vanderlinde et al. 2010; Marriage et al. 2011). A sample of 68 SZE-selected clusters from the equatorial footprint of the Atacama Cosmology Telescope (ACT) survey has recently been presented by Menanteau et al. (2013) and Hasselfield et al. (2013b); 158 were detected in the first 720 deg² of the South Pole Telescope (SPT) SZ survey (Reichardt et al. 2013); 677 were detected in the full 2500 deg² SPT–SZ survey (Bleem et al. 2014); and ∼1200 more all-sky SZE cluster candidates have been catalogued by the Planck Collaboration et al. (2014c). Yet with samples ranging from 9 (Sehgal et al. 2011) to 18 (Vanderlinde et al. 2010; Benson et al. 2013) clusters, the first analyses found that the statistical errors on w and ${{\sigma }_{8}}$ are already smaller than systematic errors due to uncertainties in the ${{Y}_{{\rm SZ}}}$-to-mass scaling relation. Hasselfield et al. (2013b) confirm this limitation by finding that the improvements in cosmological parameters from their sample of 68 SZE-selected clusters are mainly due to the inclusion of dynamical mass information, not to an increased sample size. Therefore, to further improve constraints from SZE-cluster cosmology using these larger samples, we need a better understanding of the scaling between integrated SZE signal and cluster mass in individual systems. For example, Sifón et al. (2013) have measured the dynamical masses of 16 massive SZE-selected clusters (nine of which are in our sample) and found that disturbed or merging systems could be biasing the derived ${{Y}_{{\rm SZ}}}$-to-mass scaling relations.

A number of physical processes are known to cause deviations from equilibrium scaling relations. Cluster mergers are predicted to cause departures from hydrostatic equilibrium, and can produce transient pressure enhancements that boost the SZE signal (e.g., Poole et al. 2006, 2007; Wik et al. 2008). Such pressure enhancements are invisible in X-ray observations of the massive cluster RXJ1347-1145, for example, but have been revealed through high-resolution SZE-imaging to contribute ∼10% of the bulk signal (Komatsu et al. 2001; Kitayama et al. 2004; Mason et al. 2010). Kinetic Sunyaev–Zel'dovich (kSZ) signals due to clusters' peculiar velocities can also introduce additional scatter to ${{Y}_{{\rm SZ}}}$ measurements. Hand et al. (2012) recently achieved a statistical detection of the pairwise kSZ signal from an ACT sample, but the peculiar velocity distribution of clusters remains unconstrained. Mroczkowski et al. (2012) find some evidence for large kSZ distortions in the triple merger system MACS J0717.5+3745, perhaps indicating that high-velocity substructures in merging clusters introduce additional deviations to ${{Y}_{{\rm SZ}}}$. Ruan et al. (2013) predict these deviations could bias ${{Y}_{{\rm SZ}}}$ results by ∼10%. The emission from bright galaxies near the clusters (in projection) can further bias the SZE signal. Synchrotron emission from star-forming galaxies and active galactic nuclei may "fill in" SZE decrements. Reese et al. (2012) estimate contamination from synchrotron sources to be $\lesssim 20\%$ in the 90 GHz SZE decrement based on high-resolution imaging of two ACT clusters, and Sayers et al. (2013) estimate that radio sources contaminate the 140 GHz SZE decrement by ∼1–20%. SZE increments, on the other hand, can be artificially enhanced by the strong infrared emission from dusty, high-redshift star-forming submillimeter galaxies (SMGs; for a review, see Blain et al. 2002). Gravitational lensing by the clusters' potentials may increase contamination by lensed SMGs (e.g., Knudsen et al. 2008; Jain & Lima 2011; Johansson et al. 2011) or introduce deficits in surface brightness at the location of the cluster (Zemcov et al. 2013), and disturbed or merging systems may be more susceptible to lensing effects due to their greater lensing efficiency (e.g., Meneghetti et al. 2007; Zitrin et al. 2013b). Benson et al. (2003) conclude that direct measurements of cluster peculiar velocities in maps with angular resolution $\gtrsim 1\;{\rm arcmin}$ will be limited by SMG contamination.

The number counts of the most massive clusters have the potential to constrain cosmological parameters. Unfortunately, these systems also tend to be most affected by the effects described above. Massive systems will produce the greatest gravitational lensing shear, and in our hierarchical universe, they are also commonly disrupted by recent merging activity. In this work, we aim to better understand how these considerations affect the observed SZE signals using high-resolution submillimeter and radio imaging of a representative sample of SZE-selected clusters.We present new observations at 345 GHz (19 2 resolution) with the Large APEX Bolometer Camera (LABOCA; Siringo et al. 2009) on the Atacama Pathfinder EXperiment (APEX; Güsten et al. 2006) telescope²⁵ and at 2.1 GHz (5'' resolution) with the Australia Telescope Compact Array (ATCA) of a sample of massive SZE-selected galaxy clusters. We call the project "LASCAR," the LABOCA/ACT Survey of Clusters at All Redshifts, in honor of the Lascar volcano near the ACT site in northern Chile. We use these data to measure the properties of the clusters' spatially resolved SZE increment signals, and quantify the degree of background and foreground radio and infrared galaxy contamination. Section 2 describes our cluster sample. Section 3 presents observations and data reduction techniques. Section 4 assesses the SZE contamination by point sources. Section 5 uses the point-source subtracted multi-wavelength SZE maps to place constraints on cluster peculiar velocities. In Section 6 we discuss our results in the context of previous work, and in Section 7, we conclude. In our calculations, we assume a flat ΛらむだCDM cosmology with ${{H}_{0}}=70\;{\rm km}\;{{{\rm s}}^{-1}}\;{\rm Mp}{{{\rm c}}^{-1}}$, ${{{\Omega }}_{M}}=0.27$, and ${{{\Omega }}_{{\Lambda }}}=0.73$ (Komatsu et al. 2011).

Our sample consists of eleven clusters with 148 GHz decrement signal-to-noise ratio (S/N) $\gt \;4.7$ from the ACT (Fowler et al. 2007; Swetz et al. 2011) southern survey (Menanteau et al. 2010; Marriage et al. 2011). Our sample is selected from the 15 highest S/N ACT southern clusters, and includes 9 of 10 clusters not known before ACT or SPT; it only excludes one cluster with $z\lt 0.15$ and three clusters that had been previously mapped with AzTEC (D. Hughes 2015, private communication). The properties are listed in Table 1. The systems span a large redshift range, z = 0.3–1.1, and have masses ${{M}_{500c}}\geqslant 3\times {{10}^{14}}\;{{M}_{\odot }}$ (Menanteau et al. 2010; Sifón et al. 2013), where ${{M}_{500c}}=500(4\pi /3){{\rho }_{c}}r_{500c}^{3}$, and r_500c is the radius enclosing a mass density equal to 500× the critical density of the universe at the redshift of the cluster. We define the angular radius ${{\theta }_{500c}}={{r}_{500c}}/{{D}_{A}}$, and use the typical scaling relation ${{M}_{200c}}\sim 1.6\;{{M}_{500c}}$ (Duffy et al. 2008) to convert from the dynamical masses of Sifón et al. (2013). Each SZE detection has been confirmed to be a rich optical cluster through follow-up imaging by Menanteau et al. (2010). Included in the sample are the notable cluster mergers ACT J0102-4915, also known as "El Gordo" (Menanteau et al. 2012), and 1E0657-56 (ACT J0658-5557), the original "Bullet" cluster (Markevitch et al. 2002).

Table 1.  Cluster Sample

	R.A.a	Decl.a		${{\theta }_{500c}}$	M500c		${{t}_{{\rm obs}}}$ b	rmsc
Name	(h:m:s)	($\circ :^{\prime} :^{\prime\prime}$)	z	(')	(${{10}^{14}}\;{{M}_{\odot }}$)	Project ID (P.I.)	(hr)	(${\rm mJy}\;{\rm b}{{{\rm m}}^{-1}}$)
ACT-CL J0102-4915	01:02:53	−49:15:19	0.870d	2.50e	10.2 ± 2.4e	M-087.F-0037-2011 (A. Baker)	11.3	2.4
ACT-CL J0215-5212	02:15:18	−52:12:30	0.480e	3.16e	6.0 ± 1.7e	C-088.F-1772A-2011 (L. Infante)	17.6	2.0
ACT-CL J0232-5257	02:32:45	−52:57:08	0.556e	2.42e	3.7 ± 1.4e	O-086.F-9302A-2010 (A. Baker)	17.0	1.7
ACT-CL J0235-5121	02:35:52	−51:21:16	0.278e	5.18e	7.4 ± 2.1e	O-087.F-9300A-2011 (A. Baker)	12.2	2.1
ACT-CL J0245-5302	02:45:33	−53:02:04	0.300f	3.08g	$\simeq 3.1$ g	M-088.F-0003-2011 (A. Weiß)	11.6	2.0
ACT-CL J0330-5227	03:30:54	−52:28:04	0.442e	4.08e	10.7 ± 2.5e	E-086.A-0972A-2010 (A. Baker)	8.1	1.9
ACT-CL J0438-5419	04:38:19	−54:19:05	0.421e	4.53e	13.2 ± 3.1e	E-086.A-0972A-2010 (A. Baker)	18.3	1.6
ACT-CL J0546-5345	05:46:37	−53:45:32	1.066e	1.75e	5.1 ± 2.6e	C-086.F-0668A-2011 (L. Infante)	16.3	1.6
ACT-CL J0559-5249	05:59:43	−52:49:13	0.609e	3.08e	9.3 ± 2.7e	C-087.F-0012A-2011 (L. Infante)	13.3	2.8
ACT-CL J0616-5227	06:16:36	−52:28:04	0.684e	2.60e	7.0 ± 3.1e	O-088.F-9300A-2011 (A. Baker)	14.8	2.1
ACT-CL J0658-5557	06:58:30	−55:57:04	0.296h	3.44i	11.0 ± 6.8i	E-380-A-3036A-2007 (M. Birkinshaw)	16.5	2.2
						O-079.F-9304A-2007 (D. Johansson)

Notes.

^aSZE decrement centroid from Marriage et al. (2011). ^bTotal un-flagged, on-target integration time. ^crms in the beam-smoothed maps, which have an effective resolution of 28''. ^dMenanteau et al. (2012). ^eSifón et al. (2013). ^fEdge et al. (1994). ^gr_500c for ACT-CL J0245-5302 was estimated using its velocity dispersion $\sigma \simeq 900\;{\rm km}\;{{{\rm s}}^{-1}}$ (Edge et al. 1994), giving ${{M}_{200c}}\sim 5\times {{10}^{14}}\;{{M}_{\odot }}$ and ${{r}_{200c}}=1260\;{\rm kpc}$. ^hTucker et al. (1998). ⁱr_500c from Zhang et al. (2006).

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3.1. 345 GHz APEX/LABOCA

We obtained new LABOCA 345 GHz imaging of 10 clusters in 2010–2011 (see Table 1). The LABOCA data for an 11th cluster that is also detected by ACT (ACT-CL J0658-5557) are from the European Southern Observatory (ESO) archive. The following subsections describe the algorithms used to reduce the LABOCA data and extract SZE signals for our full sample of eleven clusters.

3.1.1. LABOCA Observations

Observations were taken using the standard raster spiral mode, in which the telescope traces out one spiral every 35 s at each of four raster points defining a square with 27'' sides. In polar coordinates (r, ϕ), the spiral track has an initial radius ${{r}_{0}}=18^{\prime\prime}$, a constant radial speed $\dot{r}=2\buildrel{\prime\prime}\over{.} 2\;{{{\rm s}}^{-1}}$, and a constant angular rate $|\dot{\phi }|=\pi /2\;{\rm rad}\;{{{\rm s}}^{-1}}$. The 345 GHz zenith opacity is interpolated between skydip measurements that punctuate observing sessions, and is used to correct for LOS atmospheric absorption. Flux calibration is determined by observing a planet or secondary calibrator²⁶ before each observing session, and the telescope pointing is monitored throughout the observations with periodic scans of bright quasi-stellar objects (QSOs). Scans that either had abnormally high rms noise or were taken during rapidly changing atmospheric conditions were removed from the analysis. The total on-target integration time for the sample is 140 hr, as shown in Table 1.

The LABOCA main beam has a Gaussian profile with FWHM of 192. The full beam²⁶ includes broader, low-level wings and has total Ωおめが = 12.17 ± 0.43 nsr. We use the full beam when computing integrated flux densities of extended sources, and we use the Gaussian main lobe when fitting PSF profiles to point sources.

3.1.2. LABOCA Data Reduction

We reduced the LABOCA data using the Python-based Bolometer Array Analysis Software (BoA²⁷ ) package. The data time-stream $T(c,t)$, a function of channel c and time t, is first flux calibrated and corrected for atmospheric absorption. Next, median filtering at each time step is applied to all channels, then to each of twelve subgroups of channels that share readout cabling, then to each of four subgroups that share amplifier boxes. Despiking is performed between stages of median filtering, before a linear baseline is subtracted from each channel; channels with rms noise greater than 4× the median value are flagged. Low-frequency "1/f " noise is removed using BoA's noise-whitening algorithm flattenFreq, which sets the magnitudes of Fourier modes with frequencies less than some cutoff frequency $f\lt {{f}_{c}}$ to the average magnitude of those in the range ${{f}_{c}}\lt f\lt 1.2\times {{f}_{c}}$. Because the celestial scanning velocity increases as a function of time during each scan as $v(t)\simeq ({{r}_{0}}+\dot{r}t)|\dot{\phi }|$, flattenFreq filters out emission on angular scales larger than the cutoff scale s_c(t) given by²⁸

$$\begin{eqnarray}&&{{s}_{c}}(t)=v(t)/{{f}_{c}}=\left( 28+3.5\times t \right)\;f_{c}^{-1}\ ({\rm arcsec}),\end{eqnarray} \tag{ 2 }$$

with t in seconds and f_c in Hz. The data are then gridded onto an equatorial 03 × 03 image with 36 pixels (oversampling the beam by a factor of 5 in each direction). The resulting rms sensitivities within 4' of the centers of the beam-smoothed maps are presented in Table 1.

The above reduction steps, represented by $\mathcal{R}$, operate on time-stream data and return a gridded map, i.e., $I(\alpha ,\delta )=\mathcal{R}[T(c,t),l]$, where the parameter l represents the largest source size to which the entire scan remains responsive. The corresponding f_c is found from Equation (2) by setting s_c at t = 0 (where it achieves its minimum value) equal to l convolved with the LABOCA beam FWHM ${{\theta }_{{\rm beam}}}$:

$$\begin{eqnarray}&&{{f}_{c}}(l)=\frac{28}{\sqrt{{{l}^{2}}+\theta _{{\rm beam}}^{2}}}({\rm Hz}),\end{eqnarray} \tag{ 3 }$$

for l and ${{\theta }_{{\rm beam}}}$ in arcseconds . For $l=0^{\prime\prime}$ and $l=120^{\prime\prime}$, ${{f}_{c}}(l)=1.47$ and 0.23 Hzへるつ, respectively.

3.1.3. Iterative Multi-scale Algorithm

The filtering steps described above, primarily median filtering on cabling subgroups and noise whitening (Section 3.1.2), can remove the desired astrophysical emission from the data along with atmospheric noise. To recover this lost signal, we have developed an iterative, multi-scale pipeline. Our approach is inspired by techniques used by Enoch et al. (2006) and Nord et al. (2009). One important difference is that we maximize our sensitivity to low-level extended emission by using a series of matched filters to search for signal at multiple cluster-sized spatial scales, similar in nature to adaptive filtering algorithms (e.g., Scoville et al. 2007).

In the technique described below, a single "reduction" refers to one application of the standard pipeline described in Section 3.1.2. Our iterative pipeline is built "on top" of the standard pipeline by chaining together standard reductions using different values of f_c. The first step of the pipeline is reducing the data with aggressive filtering by setting the angular scale of fully preserved emission to $l=0^{\prime\prime}$. This first image, $I_{1}^{l={{0}^{\prime\prime }}}$, is minimally affected by $1/f$ noise, although it has complete responsiveness only to point sources. High-significance structures in this first image are located by producing a ${\rm S}/{\rm N}$ image $S(\alpha ,\delta )$ using a spatial matched filter (e.g., Serjeant et al. 2003)

$$\begin{eqnarray}&&S=\frac{I\;\otimes \;k}{\sqrt{W\;\otimes \;{{k}^{2}}}},\end{eqnarray} \tag{ 4 }$$

where k is a 2D Gaussian kernel with ${\rm FWHM}=\sqrt{{{l}^{2}}+\theta _{{\rm beam}}^{2}}$, and $W(\alpha ,\delta )$ is a weight map defined by the inverse variance of time-stream data within each pixel. Pixels where $S(\alpha ,\delta )\lt {{S}_{{\rm thresh}}}$ are set to zero in $I_{1}^{l={{0}^{\prime\prime }}}$. The significance level ${{S}_{{\rm thresh}}}$ is chosen so that we would expect $\leqslant 0.3$ spurious sources in the S/N map due to noise fluctuations (assuming a Gaussian noise distribution), and therefore depends on l and the image size. This clipped image is then smoothed to the angular scale of interest by convolving it with a normalized 2D Gaussian with ${\rm FWHM}=l$ to produce a model image $M_{1}^{l={{0}^{\prime\prime }}}$. For the case of $l=0^{\prime\prime}$, a small amount of smoothing, ${\rm FWHM}=7^{\prime\prime}$, is still applied to help reduce sharp discontinuities in the model image. If the model image $M_{1}^{l={{0}^{\prime\prime }}}$ is not empty, iteration proceeds and $M_{1}^{l={{0}^{\prime\prime }}}$ is transformed into time-stream data $\mathcal{T}[M_{1}^{l={{0}^{\prime\prime }}}]$ and subtracted from the original time-stream. This residual time-stream $T-\mathcal{T}[M_{1}^{l={{0}^{\prime\prime }}}]$ is then reduced using the procedure from Section 3.1.2, and the resulting residual image is added to $M_{1}^{l={{0}^{\prime\prime }}}$ to produce the next image, ${{I}_{2}}=\mathcal{R}[T-\mathcal{T}[{{M}_{1}}]]+{{M}_{1}}$. This process is carried out until the signal in the map converges, $({\Sigma }({{I}_{n}}-{{I}_{n-1}})\simeq 0)$, and we are left with a final image I_N and model M_N. Ten iterations are sufficient for the model image to converge.

Now we begin to search for larger spatial scale emission. $M_{N}^{l={{0}^{\prime\prime }}}$ (the final, converged model image with $l=0^{\prime\prime}$ filtering) is subtracted from the original time streams, and the residual time-stream is reduced with a relaxed filtering, initially $l=30^{\prime\prime} .$ If high-significance 30'' scale emission is located using a matched filter, iteration begins again. This process is carried out for $l=0^{\prime\prime} ,30^{\prime\prime} ,60^{\prime\prime} ,$ and 120''; the final image is the sum of all converged models, plus any residual low-level signal and the remaining noise:

$$\begin{eqnarray}&&{{I}_{{\rm final}}}={{M}_{f}}+\mathcal{R}(T-\mathcal{T}[{{M}_{f}}]),\end{eqnarray} \tag{ 5 }$$

where M_f is the sum of all scales' converged model images ${{M}_{f}}={{{\Sigma }}_{l}}M_{N}^{l}$. The array loses sensitivity quickly for angular scales that are larger than the typical size of contiguous subsets of channels that share cabling (i.e., $\gtrsim 6\buildrel{\,\prime}\over{.} 7$); therefore, the pipeline is limited to $l\leqslant 120^{\prime\prime}$, which allows for recovery of emission on scales up to $\left\langle {{s}_{c}}(t,l=120^{\prime\prime} ) \right\rangle \leqslant 6\buildrel{\,\prime}\over{.} 5$.

We detect bright SMGs in all clusters and strong SZE increment signals (S/N $\gt 3.5$) in six clusters (see Table 2). The final, converged, iteratively reduced 345 GHz images of all eleven clusters after point-source subtraction and smoothing are shown in Figure 1.

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Table 2.  SZE Properties

	Te	θしーた'a		vpb	$S_{345}^{{\rm SZE}}(\lt {{\theta }^{\prime }})$	$Y_{{\rm SZ}}^{\prime }$ b,c
Name	(keV)	(arcmin)	SPIRE?b	$({\rm km}\;{{{\rm s}}^{-1}})$	(mJy)	(${{10}^{-10}}{\rm sr}$)	S/Nd
${\rm S}/{\rm N}\geqslant 5$
ACT-CL J0102-4915	14.5 ± 1.0e	2.2	✓	$-1100_{-2200}^{+1300}$ ($-2800_{-3100}^{+1700}$)	276 ± 28	$1.8_{-0.3}^{+0.3}$ ($1.4_{-0.3}^{+0.2}$)	9.7
ACT-CL J0215-5212	5.9 ± 1.3f	1.9	⋯	$-1100_{-600}^{+400}$	171 ± 21	$0.8_{-0.1}^{+0.1}$	8.2
ACT-CL J0438-5419	11.9 ± 1.2f	1.9	✓	$900_{-1000}^{+1000}$ ($600_{-1200}^{+1000}$)	127 ± 15	$0.9_{-0.1}^{+0.1}$ ($0.8_{-0.1}^{+0.1}$)	8.7
ACT-CL J0546-5345	$8.54_{-1.05}^{+1.38}$ g	1.9	✓	$-300_{-700}^{+700}$ ($-300_{-700}^{+700}$)	162 ± 20	$1.0_{-0.1}^{+0.1}$ ($0.9_{-0.1}^{+0.1}$)	8.2
ACT-CL J0616-5227	6.6 ± 0.8f	1.9	⋯	$-300_{-600}^{+600}$	160 ± 21	$0.9_{-0.1}^{+0.1}$	7.7
ACT-CL J0658-5557	10.8 ± 0.9h	1.6	⋯	$2500_{-1000}^{+1000}$	121 ± 22	$1.1_{-0.2}^{+0.1}$	5.4
${\rm S}/{\rm N}\lt 5$
ACT-CL J0232-5257	9.1 ± 2.1f	1.8	⋯	$-1200_{-1900}^{+1200}$	67 ± 16	$0.4_{-0.1}^{+0.1}$	4.3
ACT-CL J0235-5121	5.0c	1.7	✓	$-1500_{-2800}^{+1800}$ ($-1500_{-2800}^{+1800}$)	36 ± 16	$0.2_{-0.1}^{+0.1}$ ($0.2_{-0.0}^{+0.1}$)	2.2
ACT-CL J0245-5302	5.0c	1.9	✓	$500_{-600}^{+1200}$ ($500_{-600}^{+1200}$)	53 ± 18	$0.4_{-0.1}^{+0.1}$ ($0.4_{-0.1}^{+0.1}$)	2.9
ACT-CL J0330-5227	$4.32_{-0.19}^{+0.21}$ g	1.9	✓	$100_{-1000}^{+1000}$ ($100_{-800}^{+1000}$)	70 ± 34	$0.5_{-0.2}^{+0.2}$ ($0.5_{-0.2}^{+0.1}$)	2.1
ACT-CL J0559-5249	8.09 ± 0.75g	1.5	⋯	$3100_{-1000}^{+1900}$	41 ± 23	$0.4_{-0.1}^{+0.1}$	1.8

^aAperture radius used in computing $Y_{{\rm SZ}}^{\prime }$. ^bHerschel SPIRE data obtained through proposal OT2_abaker01_2. Results that include SPIRE data are shown in parentheses. ^cFor clusters with unknown T_e, $Y_{{\rm SZ}}^{\prime }$ is computed assuming ${{T}_{e}}=5.0\;{\rm keV}$. ^dS/N based on integrated S₃₄₅ inside $Y_{{\rm SZ}}^{\prime }$ apertures using the point-source subtracted, iteratively reduced maps. ^eMenanteau et al. (2012). ^fJ. P. Hughes et al. (2015, in preparation) ^gMenanteau et al. (2010). ^hMass-weighted temperature from Halverson et al. (2009).

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As an instructive check of our approach to data processing, we can compare our map of ACT J0658-5557 to the 345 GHz map made by Johansson et al. (2010) from the same LABOCA data using different reduction software (CRUSH²⁹ ), and to the 1' resolution 150 GHz map of the cluster made with the APEX-SZ instrument. Johansson et al. (2010) deliberately filter the LABOCA data to suppress extended structure, including SZE increment signal. However, the flux densities they measure for the three most significantly detected SMGs in their Gaussian-matched-filtered map (48.6 ± 1.3, 15.1 ± 1.0, and 6.9 ± 0.9 mJy) agree well with those we have extracted from our own version of the map (48 ± 2, 13 ± 2, and 7 ± 2 mJy: P. Aguirre et al. 2015, in preparation). Halverson et al. (2009) fit an isothermal elliptical βべーた model to their SZE decrement observations and determine a projected core radius of 142 ± 18 arcsec that is well-matched to the size of the (rather asymmetric) structure we see in our 345 GHz map. Broadly speaking, our mapping algorithm porduces resutls that are consistent with previous work that focuses on eitehr point sources or extended emission.

3.1.4. Systematic Uncertainties of the Iterative Pipeline

In Figure 2, we show the results when a noise-free³⁰ image of an ideal cluster model is transformed to time-stream data and passed through the full iterative pipeline. We use an isothermal beta profile with βべーた = 0.86 and core radius ${{r}_{{\rm rc}}}=1^{\prime}$, typical parameters for SZE clusters in Marriage et al. (2011). Foreground and background SMGs are modeled by injecting 15 point sources with flux densities ranging between 5 and 20 mJy at random locations in the map. We define the transfer function efficiency (TFE) as the ratio of flux densities of structures in the final map divided by their "true" flux densities in the input model image. Point-source flux densities are measured using a least-squares fit to a circular Gaussian profile with a floating constant offset, and the integrated SZE signal is measured as the integrated flux density within a circular aperture of radius 15 (the typical radius used to extract SZE photometry in Section 5) after subtraction of point sources. For a single-pass reduction, the TFEs of point sources and the extended SZE signal are 0.50 and 0.10, and increase to 0.97 and 0.54 after running the full iterative pipeline. The spatially extended SZE signal is not fully recovered because of the pipeline's inability to faithfully recover signals on scales larger than 120''. Figure 2 displays the initial model, a single (non-iterative) reduction, and the final iterated image for our simulated cluster, and Figure 3 displays the input and output flux densities of individual point sources before and after iteration.

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For extended SZE signals, the TFE will range between 0.10 and 0.54 depending on whether the SZE signal was strong enough to trigger the iterative filter. The TFE for extended emission is ignored in the following sections because identical filtering and aperture photometry is used in all SZE wavebands, and we only require relative photometry to derive peculiar velocities. For SMGs, the flux that remains lost after iteration is much lower than the typical statistical uncertainty of our measurements and can be ignored.

3.2. 148 and 218 GHz ACT

3.3. 2.1 GHz ATCA

3.3.1. ATCA Observations

We acquired 2.1 GHz ATCA observations of the ten clusters in our sample with new LABOCA observations. We used the 16 cm-band receiver with the Compact Array Broadband Backend (CABB) giving 2049 one MHz wide channels spanning 1.1–3.1 GHz. Observations were made in 2011 January (PI: Baker), 2011 December (PI: Baker), and 2012 April (PI: Lindner). All clusters have been observed with the 6A antenna configuration (baseline range B = 628–5939 m), and ACT J0102-4915 has additional data in the 1.5B configuration (B = 31–4301 m). For flux and bandpass calibration we used PKS 1934-638 (Reynolds 1994). The Australia Telescope National Facility (ATNF) online calibrator database³¹ was used to choose one or more suitably bright, nearby, and compact phase calibrators for each cluster; these are listed in Table 3.

Table 3.  ATCA 2.1 GHz Observations

			tobsb
Month	Target	Phase Cal	(hr)	Configuration
2011 Jan	ACT-CL J0232-5257	J0214-522	19.8	6A
	ACT-CL J0546-5345	J0539-530	21.0	6A
2011 Dec	ACT-CL J0102-4915	J0047-579	12.1	6A
	ACT-CL J0215-5212	J0214-522	8.6	6A
	ACT-CL J0235-5121	J0214-522	8.5	6A
	ACT-CL J0245-5302	J0214-522	10.3	6A
	ACT-CL J0330-5227	J0334-546	8.8	6A
	ACT-CL J0438-5419	J0522-611	8.1	6A
	ACT-CL J0559-5249	J0539-530	8.9	6A
	ACT-CL J0616-5227a	J0539-530	7.8	6A
	⋯	J0522-611	⋯	6A
	⋯	J0647-475	⋯	6A
2012 Apr	ACT-CL J0102-4915	J0047-579	6.8	1.5B

^aObservations used three phase calibrators. ^bTotal un-flagged, on-source integration time.

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The software package MIRIAD (Sault et al. 1995) was used to calibrate, flag, invert, and clean the visibility data. Radio frequency interference (RFI) that affected all channels at a given time or a certain channel at all times was removed manually using pgflag and blflag. Transient RFI was removed using the automated flagging algorithm mirflag (Middelberg 2006). Baseline 1–2 in the 2012 April data contained powerful broad-spectrum RFI and was entirely flagged. First-order multi-frequency synthesis images with robust parameter robust = 0 were made using invert and mfclean. Two rounds of self-calibration were then carried out, one solving for phase only, and one for both phase and amplitude together. The final rms sensitivities at phase center vary over the range 6.9–12 μみゅーJy beam⁻¹ (see Table 4).

Table 4.  ATCA Map Properties

	$\left\langle \nu \right\rangle$ a	θしーたmajorb	θしーたminorc	P.A.d	Map rmse
Target	(GHz)	('')	('')	$\left( \circ \right)$	(μみゅーJy beam−1)
ACT-CL J0102-4915	2.15	6.13	3.09	−1.9	7.5
ACT-CL J0215-5212	2.16	4.66	2.93	−21.0	11.0
ACT-CL J0232-5257	2.13	4.80	3.06	6.0	8.1
ACT-CL J0235-5121	2.17	5.26	2.71	−10.0	10.9
ACT-CL J0245-5302	2.16	4.44	2.97	4.3	10.5
ACT-CL J0330-5227	2.17	5.06	2.73	17.7	11.7
ACT-CL J0438-5419	2.15	5.30	2.80	−19.6	11.9
ACT-CL J0546-5345	2.13	4.66	3.21	−3.1	6.9
ACT-CL J0559-5249	2.15	5.35	2.86	−13.1	9.6
ACT-CL J0616-5227	2.15	4.99	2.98	26.2	12.0

Notes.

^aEffective frequency (different for different clusters due to RFI flagging). ^bSynthesized beam major axis. ^cSynthesized beam minor axis. ^dSynthesized beam position angle. ^erms noise at the phase center.

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3.4. Herschel Observations

3.5. Foreground Galactic Dust Subtraction

3.6. The Sunyaev–Zel'dovich Effect

The deflection in CMB intensity due to the thermal SZE for a single-temperature gas is (Zel'dovich & Sunyaev 1969; Sunyaev & Zel'dovich 1970b)

$$\begin{eqnarray}&&{\Delta }{{I}_{{\rm tSZ}}}=y\;{{I}_{0}}\;g(x,{{T}_{e}}),\end{eqnarray} \tag{ 6 }$$

in terms of the scaled frequency $x\equiv h\nu /{{k}_{{\rm B}}}{{T}_{{\rm CMB}}}$, ${{I}_{0}}=2{{({{k}_{{\rm B}}}{{T}_{{\rm CMB}}})}^{3}}/{{(hc)}^{2}}=22.87\;{\rm Jy}\;{\rm arcmi}{{{\rm n}}^{-2}}$, the electron temperature T_e, and the Compton parameter y (see Equation (1)). The function $g\left( x,{{T}_{e}} \right)$ is the derivative of the Planck function ($d{{B}_{\nu }}/dT$) multiplied by the SZE spectrum,

$$\begin{eqnarray}&&g(x,{{T}_{e}})=\frac{{{x}^{4}}{{e}^{x}}}{{{\left( {{e}^{x}}-1 \right)}^{2}}}\left( x\frac{{{e}^{x}}+1}{{{e}^{x}}-1}-4 \right)\left[ 1+{{\delta }_{{\rm tSZ}}}\left( x,{{T}_{e}} \right) \right],\end{eqnarray} \tag{ 7 }$$

where ${{\delta }_{{\rm tSZ}}}$ represents relativistic corrections that become important at high electron temperatures, especially when $x\gg 1$.

The change in CMB intensity due to the kSZ effect is given by (Sunyaev & Zel'dovich 1972)

$$\begin{eqnarray}\begin{array}{rcl} {\Delta }{{I}_{{\rm kSZ}}} & = & -{{\tau }_{e}}\;{{I}_{0}}\left( \frac{{{v}_{p}}}{c} \right)\frac{d{{B}_{\nu }}}{dT} \\ {} & = & -{{\tau }_{e}}{{I}_{0}}\left( \frac{{{v}_{p}}}{c} \right)\frac{{{x}^{4}}{{e}^{x}}}{{{\left( {{e}^{x}}-1 \right)}^{2}}}\left[ 1+{{\delta }_{{\rm kSZ}}}\left( x,{{T}_{e}} \right) \right], \\ \end{array}\end{eqnarray} \tag{ 8 }$$

where v_p is the cluster LOS peculiar velocity with respect to the CMB in the cluster rest frame, the optical depth to electron scattering ${{\tau }_{e}}=\int {{\sigma }_{{\rm T}}}{{n}_{e}}\;dl$, and ${{\delta }_{{\rm kSZ}}}$ represents higher-order relativistic corrections.

Equations (6) and (8) are shown to highlight the leading order terms in the thermal and kinetic SZE signal. In our analysis, we do not use the analytic expressions, but instead compute the SZE signal with numerical integration using the C++ package SZPACK (Chluba et al. 2012, 2013). SZpack allows for quick computations of the relativistic tSZ and kSZ signals, with 10⁻⁵ precision for temperatures up to ${{T}_{e}}\simeq 25\;{\rm keV}$ at frequencies up to and including the high-frequency Herschel SPIRE bands ($x\lesssim 20$) and peculiar velocities up to $|{{v}_{{\rm pec}}}|/c\simeq 0.1$ ($|{{v}_{{\rm pec}}}|\simeq 30\times {{10}^{3}}\;{\rm km}\;{{{\rm s}}^{-1}}$).

3.7. Isolating SZE Signal in SPIRE Maps

We isolate the SZE signal in the 350 and 500 μみゅーm SPIRE maps by using the 250 μみゅーm map (which contains a negligible contribution from SZE signals compared to the 350 and 500 μみゅーm bands) to derive a model for the confused SMG background. This approach was presented by Zemcov et al. (2010), but our implementation of it differs in several important respects. For a given cluster, we begin by producing a model of the background SMG confusion signal at 250 μみゅーm (${{\mathcal{B}}_{250}}$) by applying a median filter with kernel size 3 × FWHM₂₅₀ to the 250 μみゅーm image. We then smooth ${{\mathcal{B}}_{250}}$ to the angular resolution of the 350 μみゅーm image to produce an estimate of the confused background at 350 μみゅーm, ${{\mathcal{B}}_{350}}$.

We next locate bright sources that stand out from the confused 250 μみゅーm background by first subtracting ${{\mathcal{B}}_{250}}$ from the original 250 μみゅーm image, and then searching for point sources in the resulting background-subtracted image using a spatial matched filter (e.g., Serjeant et al. 2003). The matched filter identifies high S/N peaks, which are then individually fit to an ideal 250 μみゅーm PSF with positions and flux densities allowed to vary. Sources are extracted to an S/N level of 4.5σしぐま; we find 100–200 sources per cluster. The properties of the 250 μみゅーm point sources represent a starting point for modeling bright SMGs at 350 μみゅーm.

The 350 μみゅーm map is then fit to a $3N+2$ parameter model consisting of the confused background plus bright SMGs. The offset a and scaling b of the confused background template and the remaining $3N$ parameters representing the coordinates ${{\vec{x}}^{\prime }}$ and flux densities (S) of bright SMGs are combined into a parameter vector $\theta =(\{\vec{x}_{i}^{\prime },{{S}_{i}}\}_{n=1}^{N},a,b)$. The resulting model

$$\begin{eqnarray}&&\mathcal{M}(\vec{x};\theta )=a+b\;{{\mathcal{B}}_{350}}+\mathop{\sum }\limits_{n}^{N}{{S}_{n}}\;{{e}^{-{{\left| \vec{x}-\vec{x}_{n}^{\prime } \right|}^{2}}/2\sigma _{n}^{2}}},\end{eqnarray} \tag{ 9 }$$

is then fit to the 350 μみゅーm image using least-squares minimization. The optimization is carried out using Powell's method (Powell 1964), where in each iteration the parameters are minimized individually. Powell's method works well for this problem because each source affects only a small fraction of the data. This joint optimization naturally accommodates the increased blending that occurs in the longer wavelength images. A 350 μみゅーm source is considered an SMG and subtracted from the map if its final converged position is less than a distance 0.25 FWHM₃₅₀ from the location intially guessed for that source from the 250 μみゅー data. To avoid fitting the confusion model to the cluster signal itself, the above optimization is carried out once while masking in the central cluster region and allowing all parameters in θしーた to vary, then once more without the mask and holding a and b fixed at their previously fit values.

The process described above is repeated (independently, but in the same way) for the SPIRE 500 μみゅーm map. Emission that remains in the 350 and 500 μみゅーm maps after subtraction of the 250 μみゅーm-inspired SMG background model is due either to (a) SZE increment or (b) SMGs that were not detected in the 250 μみゅーm map at all, possibly because they lie at very high redshifts. After removing the SMG confusion noise, the 350 and 500 μみゅーm maps have mean rms sensitivities of 2.9 and $2.7\;{\rm mJy}\;{\rm bea}{{{\rm m}}^{-1}}$, respectively.

Figure 4 shows an example of the 500 μみゅーm SZE extraction process in ACT-CL J0102-4915. The upper panel shows the original SPIRE 500 μみゅーm image. The lower panel shows the image after removal of the confused SZ background using the technique described above (and after Fourier-filtering the image to simulate the LABOCA transfer function). Radial profiles of the resulting SZ signals for clusters with Herschel SPIRE coverage are shown in Figure 5.

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To test the reliability of our data reduction pipeline and source extraction algorithm, we compared our 250 μみゅーm integral number counts to those from the Herschel Multi-tiered Extragalactic Survey (HerMES; Oliver et al. 2010). Because our point-source removal technique breaks up 350 and 500 μみゅーm sources and divides their flux among multiple 250 μみゅーm counterparts, our number counts for 350 and 500 μみゅーm cannot be meaningfully compared to those of Oliver et al. (2010). We can, however, compute the number density of sources with ${{S}_{250}}\gt 100\;{\rm mJy}$ around all clusters with Herschel SPIRE data (except ACT-CL J0330-5227, which has significantly reduced sensitivity), also masking within 5' radii of the cluster centers to avoid the effects of gravitational lensing. At these bright flux densities where completeness corrections will be minimal, we find ${{N}_{\gt 100\,{\rm mJy}}}=8.0\;\pm \;4.0\;{{{\rm deg} }^{-2}}$, in agreement with the results from Oliver et al. (2010) who find ${{N}_{\gt 100\,{\rm mJy}}}=12.8\;\pm \;3.5\;{{{\rm deg} }^{-2}}$.

4.1. SMGs

In the iteratively reduced LABOCA images, we find bright SMGs superposed on the clusters' extended SZE emission. A complete analysis of the statistical properties of the detected SMGs and their multi-wavelength counterparts will be presented in a forthcoming paper (P. Aguirre et al. 2015, in preparation). Here we only consider the SMGs nearest to the clusters and study how their presence affects the measured SZE signals.

SMGs are extracted from the iterative multi-scale LABOCA map (Section 3.1.3) of a given cluster using the following process. First, SMG locations are found by using a spatial matched filter (Serjeant et al. 2003) to search for sources shaped like the ideal telescope PSF within an unsharp-masked version of the map. The unsharp mask uses a median filter with a kernel size of 3 × FWHM, and allows for point sources to be disentangled from the diffuse large spatial-scale SZE signals near the cluster centers. Next, we measure the flux density of each detected SMG by fitting the original (non-unsharp-masked) data at the source's location with an ideal PSF while holding the position fixed and varying the flux density and a non-negative background offset.

We detect a total of 36 ${\rm S}/{\rm N}\gt 4$ point sources within ${{\theta }_{500c}}$ of our 11 cluster centers, giving an estimated total flux density per cluster of $46_{-32}^{+24}\;{\rm mJy}$ in high-significance SMGs. Using the combined area of $0.10\;{{{\rm deg} }^{2}}$, this sample has cumulative number counts of $\gt 10\;{\rm mJy}$ SMGs of $N(\gt 10\;{\rm mJy})=223\;\pm \;49\;{{{\rm deg} }^{-2}}$, 6–10 times greater than those of sources with comparable brightness in blank fields (Weiß et al. 2009). Due to the negative k-corrections and high redshifts of SMGs, the number density enhancement is likely due to gravitational lensing by the clusters' potentials. Gravitational lensing does not alter the average integrated flux density of the projected SMG population, but it does increase the Poisson "shot noise" variance (e.g., Refregier & Loeb 1997), and could introduce a bias in flux-constrained (i.e., either a S/N threshold or upper limit) aperture photometry near versus away from clusters.

The 345 GHz flux density in bright SMGs inside the smaller apertures used in our analysis of the SZE (Section 5) is $26_{-26}^{+21}\;{\rm mJy}$, corresponding to $6\;\pm \;5\;{\rm mJy}$ at 218 GHz and $2\;\pm \;2\;{\rm mJy}$ at 148 GHz. The scaling to lower frequencies is done using a modified Planck function with parameters βべーた = 1.5 and ${{T}_{{\rm D}}}=37.4\;{\rm K}$, values for typical blank-field 345 GHz-selected SMGs (Wardlow et al. 2011). The contaminating SMG signal represents 18% of the SZE signal per cluster at 345 GHz, and 2% at 148 GHz, respectively. The contaminating SMGs are subtracted from the maps before further analysis of the SZE signals.

4.1.1. El Gordo and "La Flaca"

El Gordo (ACT-CL J0102-4915) has two bright point sources projected at small clustercentric radii; the brighter of the two (${{S}_{\nu }}=36\pm 2\;{\rm mJy}$) we refer to as "La Flaca." We briefy describe La Flaca's properties here because it is exceptionally bright (the next brightest SMG within our sample has a flux density of ∼27 mJy and is located in ACT-CL J0438-5419), second in brightness only to the lensed SMG (e.g., Wilson et al. 2008; Johansson et al. 2010) behind the Bullet cluster (ACT-CL J0658-5557). La Flaca is located at $\alpha =15\buildrel{\circ}\over{.} 732207$ δでるた = −49252415 and has an extremely faint radio counterpart with ${{S}_{2.1}}=24\pm 7\;\mu {\rm Jy}$. To test the possibility that La Flaca is a local SZE enhancement, we compare the spectral fits of the source's LABOCA+SPIRE photometry using a modified blackbody spectrum and thermal SZE spectrum. Figure 6 shows the best-fit curves for each model. We find that the SZE spectral shape is incompatible with the data; thus, La Flaca is more likely to be a high-redshift dusty star-forming galaxy than a compact SZE enhancement.

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The best-fit modified Planck function parameters are z = 4.1 and ${{L}_{{\rm IR}}}=3.2\times {{10}^{12}}\;{{L}_{\odot }}$, assuming the median observed ${{T}_{{\rm D}}}=37.4\;K$ and βべーた = 1.5 from the LABOCA Extended-CDFS SMG survey (LESS; Wardlow et al. 2011). Using the 610 MHz Giant Metre-wave Radio Telescope (GMRT) data (Lindner et al. 2014), we derive a radio spectral index of αあるふぁ ∼ −1.3, giving a redshift estimate of z = 4.0 based on the radio-to-far-IR spectral index (Carilli & Yun 1999), in agreement with that of the spectral fit and further supporting the conclusion that La Flaca is a high-redshift SMG.

There are two faint Hubble Space Telescope sources within 1'' of La Flaca's 345 GHz centroid. The brighter source has a magnitude of ${{m}_{775}}=23.8$ and resembles a spiral galaxy, and the fainter source has a magnitude of ${{m}_{775}}=26.8$ and is unresolved. La Flaca is also only a few arcseconds away from the positions of gravitational lensing critical curves for background galaxies between z = 4–9 (Zitrin et al. 2013a).

4.2. Radio Sources

Radio and IR-bright sources can potentially "fill in" SZE decrement signals and artificially enhance SZE increment signals in the 15 resolution SZE maps typically used to detect clusters. With our high-resolution 2.1 and 345 GHz imaging, we can disentangle the signals of point sources from those of the true SZE signal, allowing us to derive more robust measurements of the thermal and kinetic SZE signals. In this section, we quantify the degrees of radio and submillimeter contamination of the SZE signal.

4.2.1. 2.1 GHz Number Counts

We use the Common Astronomy Software Applications (CASA; McMullin et al. 2007) task findsources to fit elliptical Gaussian profiles to all bright sources in the ATCA maps down to a significance of 4σしぐま and out to the 10% primary beam power radius (22'). We adopt a primary beam profile based on the effective mean frequency of each observation (see Table 4). To minimize radial selection bias, we only consider sources that have primary beam-corrected flux densities above the detection threshold at all radii, i.e., $\gt 4\sigma /0.1=400\;\mu {\rm Jy}$. Additionally, only compact sources that have major and minor FWHMs, a and b, satisfying $a\lt 3\times {\rm FWHM}_{{\rm maj}}^{{\rm beam}}$, $b\gt 0.5\times {\rm FWHM}_{{\rm min} }^{{\rm beam}}$, and $a/b\lt 1.5$ $\times \;{\rm FWHM}_{{\rm maj}}^{{\rm beam}}/{\rm FWHM}_{{\rm min} }^{{\rm beam}}$ are kept. We consider only compact sources because extended radio sources like jets and lobes from active galactic nuclei have steep radio spectral indices and will therefore contribute negligibly in the frequency range νにゅー ≥ 148 GHz. These criteria result in a total for all clusters of 1934 radio sources with flux densities between $28\;\mu {\rm Jy}$ and $1.65\;{\rm Jy}$.

Fainter sources have an increased chance of having their flux densities scattered below the detection threshold by noise, thus lowering their completeness. Because the noise in the 2.1 GHz maps is nearly Gaussian, we correct for completeness using an analytic correction in the following way. The completeness probability, C, that a source with true flux density ${{S}_{\nu }}$ will be detected above a threshold of Nσしぐま is given by

$$\begin{eqnarray}&&C=1-{\Phi }\left( \frac{N\sigma -{{S}_{\nu }}}{\sigma } \right),\end{eqnarray} \tag{ 10 }$$

where Φふぁい(x) is the cumulative normal distribution function. The completeness correction is then implemented by computing number counts using a weighted histogram with weights ${{w}_{i}}=C_{i}^{-1}$.

Figure 7 (upper panel) shows combined and individual 2.1 GHz number counts in nine log-spaced flux density bins. The power-law index of the counts δでるた, where $dN/dS\propto {{S}^{-\delta }}$, is $\delta \simeq 1.7$. We next compute the number counts in three disjoint regions defined relative to the clusters' physical radii, and find that the counts in the $\theta \lt {{\theta }_{2500c}}$ region are elevated (especially at high flux densities) compared to the more distant regions (Figure 7, lower panel), in agreement with a previous radio survey of southern X-ray-selected clusters (Slee et al. 2008). This enhanced source density in cluster interiors is likely due to the presence of both radio-loud cluster member galaxies and (possibly at a lower level) gravitationally lensed background AGNs and star-forming galaxies. We have also checked for variation in the counts for the top, bottom, left, and right halves of the radio images and find no significant differences.

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4.2.2. Radio Contamination Extrapolated to 148 GHz

We use our 610 MHz GMRT image of ACT-CL J0102-4915 (Lindner et al. 2014) to compute the radio spectral index $\alpha _{610}^{2.1}$ distribution of 2.1 GHz sources, which allows us to extrapolate their flux densities to the higher frequencies of the SZE decrement. We find 28 2.1 GHz/610 MHz pairs of sources with $\lt 1^{\prime\prime}$ (7.8 kpc) separation and $\gt 4\sigma$ significance out to a 6' radius relative to the SZE decrement centroid, and compute their spectral indices as

$$\begin{eqnarray}&&\alpha _{610}^{2.1}=-{\rm log} ({{S}_{2.1}}/{{S}_{610}})/{\rm log} (2.1/0.610).\end{eqnarray} \tag{ 11 }$$

The distribution $\alpha _{610}^{2.1}$ is shown in Figure 8. We find a median spectral index $\alpha _{610\,{\rm median}}^{2.1}=0.56$ with interquartile range 0.37–0.69. Only 4.9% of $\gt 4\sigma$ ATCA radio sources have optically selected cluster member counterparts (for the clusters that overlap between the two samples) from Sifón et al. (2013). The disjoint source catalogs, along with the fact that our spectral index distribution is similar to that of Owen et al. (2009), indicates that radio source contamination in our clusters is due mostly to foreground and background galaxies, allowing us to use the spectral index distribution measured in the field of ACT-CL J0102-4915 to predict the 148 GHz contamination in our full cluster sample. The recent study by Gralla et al. (2014) of the average submillimeter emission associated with 1.4 GHz-selected AGN finds that a low-frequency estimate of average AGN spectral index remains valid when extrapolating all the way to 218 GHz, validating our extrapolation of 2.1 GHz emission up to the ACT bands at 148 and 218 GHz.

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Because we only measure the spectral indices of sources that are detected at both 610 MHz and 2.1 GHz, we check for sources with flat/inverted spectral indices that may not be detected at 610 MHz but could be bright at 2.1 GHz and higher frequencies by searching for 20 GHz counterparts to our ATCA and GMRT detections using the Australia Telescope 20 GHz survey (AT20G; Murphy et al. 2010). There is one match between the AT20G catalog (Murphy et al. 2010) and our ATCA and GMRT sources. The source lies 15' away from the center of cluster ACT-CL J0215-5212 and has ${{S}_{20}}=0.11\pm 0.01\;{\rm Jy}$ and ${{S}_{2.1}}=0.011867\pm 0.001726\;{\rm Jy}$, giving an inverted spectral index of αあるふぁ = 1.0. This source is only 10'' away from a much brighter ATCA source with ${{S}_{2.1}}=0.897\pm 0.001\;{\rm Jy}$.

We detect 346 2.1 GHz sources with ${{S}_{2.1}}\gt 4\sigma$ within ${{\theta }_{500c}}$ of our ten clusters with ATCA imaging, corresponding to a mean 2.1 GHz flux density within ${{\theta }_{500c}}$ per cluster of $39_{-6}^{+6}\;{\rm mJy}$. After scaling the flux density to the 148 GHz SZE decrement using $\alpha _{610\,{\rm median}}^{2.1}=0.56$ and including an additional uncertainty based on the variation in the spectral index between the extremes of the interquartile range, the typical contaminating radio signal from 2.1 GHz-detected synchrotron radio sources is estimated to lie between 2.1 and 8.1 mJy in the 148 GHz SZE decrement.

Inside the photometric apertures used to constrain the clusters' peculiar velocities (Section 5), radio sources contribute $28\;\pm \;8\;{\rm mJy}$, corresponding to $3\;\pm \;1\;{\rm mJy}$ at 148 GHz, which is $3\%$ of the typical decrement signal in our sample.

In addition to its Hubble-flow velocity, a galaxy cluster can have a velocity offset with respect to its local CMB rest-frame, known as its peculiar velocity v_p. As well as being interesting in its own right as a statistical cosmological probe of large-scale structure (e.g., Doré et al. 2003), v_p introduces a frequency-independent temperature fluctuation known as the kinetic SZ (kSZ; Equation (8)), in contrast to the frequency-dependent SZ signal due to thermal motion of the electrons in the cluster (tSZ; Equation (6)). This kSZ contribution can therefore affect the scaling between thermal ${{Y}_{{\rm SZ}}}$ and cluster mass.

Mroczkowski et al. (2012) report that their 268 GHz data for the triple-merger cluster MACS J0717.5+3745 adequately fit their SZE model only if they allow for a strong kSZ distortion from a high-velocity subcomponent. It is unclear whether strong kSZ distortions like those seen by Mroczkowski et al. (2012) are common in merging clusters. Recent results from Planck Collaboration et al. (2014d) only constrain the rms fluctuations in v_p to be $\leqslant 800\;{\rm km}\;{{{\rm s}}^{-1}}$ (95% confidence) for a sample from the Meta Catalogue X-ray Detected Clusters (Piffaretti et al. 2011). If transient kSZ distortions are common in merging cluster systems, then the ${{Y}_{{\rm SZ}}}$–mass relation in SZE clusters may be significantly affected. As a cautionary indicator here, Sifón et al. (2013) find at least one indication of dynamical activity in $81_{-22}^{+19}\%$ (13/16) of a representative sample of ACT clusters (nine of which overlap with this paper's sample).

We use our point source-subtracted multi-band data to constrain the peculiar velocities of our targets by parametrizing the observed SZE signal with v_p and the integrated SZE signal $Y_{{\rm SZ}}^{\prime }$. The iterative pipeline (Section 3.1.2) faithfully recovers extended emission only up to angular scales of ∼2', while ${{\theta }_{500c}}$ values can be much larger. Therefore, to strengthen constraints while fitting for v_p, we choose circular apertures for each cluster (typically 1.5–2' radii) that contain the observed scale of emission in the 345 GHz images. $Y_{{\rm SZ}}^{\prime }$ is therefore the effective integrated SZ signal within each of these apertures, and a lower limit on ${{Y}_{{\rm SZ}}}(\theta \leqslant {{\theta }_{500c}})$. We have recently obtained Chandra imaging (PI: Hughes) for many clusters in our sample and use these data to independently measure T_e in these systems (J. P. Hughes et al. 2015 in preparation). The systematic errors due to the different weighting between the X-ray-derived electron temperatures ($\propto n_{e}^{2}$) and the optical depth-weighted electron temperatures used in the calculations of the SZ effect are expected to be only 10–$20\;{\rm km}\;{{{\rm s}}^{-1}}$ (Sehgal et al. 2005). For the current analysis, we set ${{k}_{{\rm B}}}{{T}_{e}}=5{\rm keV}$ (see Table 2) for clusters with unknown gas temperatures.

For each integrated flux density measurement ${{S}_{{\rm SZ},{\rm i}}}$ at ${{x}_{i}}=h\;{{\nu }_{i}}/{{k}_{{\rm B}}}{{T}_{e}}$, we compute the expected SZE signal $S_{{\rm SZ}}^{{\rm model}}(Y_{{\rm SZ}}^{\prime },{{x}_{i}},{{v}_{p}},{{T}_{e}})$. We fit the data to the multi-band model using a grid-based search. The noise in all images is nearly Gaussian, and therefore the conditional probability density of obtaining measurements ${{S}_{{\rm SZ},i}}$, given the model parameters $\theta =(Y_{{\rm SZ}}^{\prime },{{v}_{{\rm pec}}})$ is

$$\begin{eqnarray}&&{{p}_{i}}({{x}_{i}};\theta )\propto {{e}^{-{{({{S}_{{\rm SZ},i}}-S_{{\rm SZ},i}^{{\rm model}})}^{2}}/2\sigma _{i}^{2}}}.\end{eqnarray} \tag{ 12 }$$

The joint probability density of obtaining all measurements is then given by $P(x;\theta )\propto {{{\Pi }}_{i}}{{p}_{i}}$. We take as the best-fit parameters those that maximize the likelihood function, and the final quoted 1σしぐま uncertainties in v_p and $Y_{{\rm SZ}}^{\prime }$ are found by marginalizing over the 2D likelihood parameter space and integrating the resulting 1D probability functions within iso-contours to contain ±68% probability. The best-fit peculiar velocities and corresponding 68.2% confidence intervals are presented in Table 2.

At 148 and 345 GHz, the SZE signal is much brighter than the background confusion noise. The situation is reversed for 350 and 500 μみゅーm, where great efforts must be made to extract the SZE signal from the strong SMG background (i.e., see Section 3.7). Recent work by Zemcov et al. (2013) has shown that by subtracting bright submillimeter point sources near massive clusters, one will produce a deficit in the surface brightness of the local cosmic infrared background compared to an off-cluster sky region. By subtracting point sources at a level comparable to that used in Section 3.7, Zemcov et al. (2013) find a typical intensity deficit of ∼0.5 MJy sr⁻¹ in the cores of four massive clusters. This may be related to why our SPIRE 500 μみゅーm photometry is systematically low compared to the other bands (see Figure 9). Because of this extra uncertainty in the SPIRE photometry, we present peculiar velocity fits for individual clusters both including and excluding the SPIRE data points (Table 2); other sample-wide properties are computed with only ACT+LABOCA photometry. Figure 9 shows the best-fit SZE spectra for all clusters, with the χかい² per degree of freedom (χかい²/νにゅー) and p values indicated in the panels.

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The mean peculiar velocity of the sample is $\langle {{v}_{p}}\rangle =153\pm 383\;{\rm km}\;{{{\rm s}}^{-1}}$, consistent with the limit of 72 ± 60 km s⁻¹ found by Planck Collaboration et al. (2014d) using the variance of the CMB toward X-ray detected clusters. The measured peculiar velocity dispersion of the clusters in our sample is $1449\;{\rm km}\;{{{\rm s}}^{-1}}$, and represents an upper limit to the intrinsic peculiar velocity dispersion. Halverson et al. (2009) find that the mass-weighted SZE-derived temperature measured for the Bullet cluster (10.8 ± 0.9 keV; Halverson et al. 2009) is significantly lower than that derived from the X-ray observations (13.9 keV; Govoni et al. 2004). This difference is caused by the different sampling functions for X-ray-derived temperatures ($\propto \int {{n}^{2}}$) and SZE-derived temperatures ($\propto \int n$). We adopt the SZE-based temperature for the Bullet cluster from Halverson et al. (2009) and derive a large peculiar velocity of $3100_{-1500}^{+1900}\;{\rm km}\;{{{\rm s}}^{-1}}$. This signal is unlikely to be caused by contamination of sources fainter than ${{S}_{345}}\lt 10\;{\rm mJy}$, because positive signal contamination acts to push ${{v}_{{\rm pec}}}$ to more negative values. In the Bullet cluster, Markevitch (2006) finds a central "bullet" collision velocity of $4700\;{\rm km}\;{{{\rm s}}^{-1}}$. Our signal may be due to a kSZ distortion related to this high-velocity subcomponent, similar to the findings of Mroczkowski et al. (2012) for MACS J0717.5+3745.

5.1. Impact of v_pec on Y_SZ−M Scaling Relations

5.2. Comparison to Simulations

To understand the intrinsic scatter and systematic uncertainties in our derived values for ${{v}_{{\rm pec}}}$, we applied our technique of extracting ${{v}_{{\rm pec}}}$ (Section 5) to the realistic simulated cluster images from the all-sky maps of Sehgal et al. (2010). We use the "Full SZ"³³ images at 148, 219, and 350 GHz, which contain thermal and kinetic SZ signals from clusters, groups, and the intracluster medium. The large scale mass distribution is created using a dark matter N-body simulation with a comoving box size of $L=1000\;{{{\rm h}}^{-1}}\;{\rm Mpc}$ (for details, see Sehgal et al. 2007, 2010). We cut out 03 × 03 images around 100 simulated clusters that were randomly chosen among those with $z\gt 0.3$ and ${{M}_{{\rm vir}}}\gt 3\times {{10}^{14}}\;{{M}_{\odot }}$. For each cluster image, we applied the Fourier-based LABOCA filtering, extracted the total flux densities at 148, 219, and 350 GHz within a 15 aperture centered on the central halo position, and performed the maximum likelihood fit from Section 5.

We find an intrinsic scatter in output ${{v}_{{\rm pec}}}$ of ${{\sigma }_{{{v}_{{\rm pec}}}}}=213\;{\rm km}\;{{{\rm s}}^{-1}}$, and a bias of ($\langle {{v}_{{\rm pec},{\rm out}}}/{{v}_{{\rm pec},{\rm in}}}\rangle -1$) of 0.36. For 025 apertures, the scatter is $137\;{\rm km}\;{{{\rm s}}^{-1}}$ and the median bias is 0.15. Given that the smaller apertures reduce the bias and scatter, we attribute both effects to the aperture-dependent irreducible error from assuming a single temperature and velocity throughout the volume of a cluster.

To investigate the source of the scatter and bias in more detail, we next performed an experiment exactly the same as above, except that we computed the photometry for each system while varying the relation between the gas temperature assumed in the maximum likelihood fit ${{T}_{{\rm fit}}}$, and the true gas temperature of the cluster ${{T}_{{\rm true}}}$. When ${{T}_{{\rm fit}}}={{T}_{{\rm true}}}$, we find negligible scatter and bias, but for ${{T}_{{\rm true}}}=0.8\;\times {{T}_{{\rm fit}}}$, we find a median bias in the recovered peculiar velocity of 0.2. This induced temperature-related bias can explain the bias we see in the extracted ${{v}_{{\rm pec}}}$ of the simulated clusters above: in the simulations, ${{T}_{{\rm true}}}$ is measured in the 3D centers of the clusters, and larger apertures will include more cool gas at larger cluster-centric radii. This effect is also likely operating in the real observations since the X-ray-derived gas temperatures are weighted by n_e² and preferentially sample the dense interiors of clusters. This might explain, for example, the 22% difference found by Halverson et al. (2009) in SZE- and X-ray-derived temperatures quoted above. Figure 10 shows the input and output peculiar velocities for each of the three numerical experiments above.

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Figure 11 shows the combined absolute and relative contamination levels from radio sources and SMGs in our sample. Our results are in general agreement with previous predictions and measurements of radio and infrared source contamination at 148 GHz. For example, based on simulations of the microwave sky, Sehgal et al. (2010) predicted that $\lt 20\%$ of clusters with ${{M}_{200c}}\gt {{10}^{14}}\;{{M}_{\odot }}$ and $z\lt 0.8$ should have their decrements filled in by $\gt 50\%$. In our sample of clusters, we find a mean individual contamination fraction of $\left\langle {\Delta }S/S \right\rangle =8\%$, and none with contamination $\gt 50\%$.

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Lima et al. (2010) presented analytic predictions of the Poisson variance in SZ flux density due to lensed background SMG populations. At 148 GHz, Lima et al. (2010) predict ${{\sigma }_{{\rm lensed}\,{\rm SMG}}}\;\sim$ 2–3 mJy within r_2500c. Within our 1–2' radius apertures (similar to r_2500c for our cluster sample), we estimate the rms intensity of 148 GHz fluctuations due only to the significantly detected LABOCA point sources to be 2 mJy.

Using 1.4, 30, and 140 GHz observations of 45 massive clusters, Sayers et al. (2013) estimate the fractional contamination due to radio sources to be ≃20% on average, with only 1/4 of clusters showing contamination greater than 1%. The mean individual contamination ($\langle {\Delta }S/S\rangle$) by radio sources in our sample is 6%.

Benson et al. (2003) constrained the peculiar velocities of six clusters using the Sunyaev–Zel'dovich Infrared Experiment in three frequency bands between 150 and 350 GHz, and placed a constraint on the intermediate universe bulk flow velocity of $\lt 1420\;{\rm km}\;{{{\rm s}}^{-1}}$ (95% confidence), consistent with ours.

We present high-resolution 345 GHz LABOCA, 2.1 GHz ATCA (10 of 11) and Herschel SPIRE (6 of 11) imaging of 11 massive SZE-selected clusters from the ACT southern survey (Menanteau et al. 2010; Marriage et al. 2011). We use these data to constrain the levels of radio source and SMG contamination of the SZE signals of the clusters, and also to constrain the cluster peculiar velocities using the kSZ effect.

We find that the contamination by 2.1 GHz radio sources of the 148 GHz SZE decrement is $3\;\pm \;1\;{\rm mJy}$ per cluster, or ∼$3\%$ of the SZE decrement signal in our analysis. We measure the 2.1 GHz number counts in three disjoint regions around the clusters, $\theta \lt {{\theta }_{2500c}}$, ${{\theta }_{2500c}}\lt \theta \lt {{\theta }_{500c}}$, and ${{\theta }_{500c}}\lt \theta \lt 5\;{{\theta }_{500c}}$, and find an enhancement in the counts for $\theta \lt {{\theta }_{2500c}}$.

The typical contamination from bright, unresolved SMGs is $26_{-26}^{+21}\;{\rm mJy}$(18%) per cluster at 345 GHz, scaling to a 2% effect on the 148 GHz decrement. The number counts of bright ${{S}_{345}}\gt 10\;{\rm mJy}$ SMGs are ∼10× greater than blank field measurements, likely due to gravitational lensing by the clusters' potentials (as seen in, e.g., Knudsen et al. 2008; Johansson et al. 2011). The combined contamination by SMGs and radio sources (∼5% of the 148 GHz decrement signal on average) may contribute to, but still remains less than, the scatter found in the ${{Y}_{{\rm SZ}}}$-to-mass scaling relation of SZE clusters.

After subtraction of the bright SMGs, we use our multi-band data to constrain the peculiar velocities of the clusters. For clusters with high-significance SZE detections, the typical uncertainty in ${{v}_{{\rm pec}}}$ is ±1000 km s⁻¹, and for the full sample we find a mean peculiar velocity of $\langle {{v}_{p}}\rangle =153\pm 383\;{\rm km}\;{{{\rm s}}^{-1}}$. By comparing the best-fit $Y_{{\rm SZ}}^{\prime }$ values with and without fitting for ${{v}_{{\rm pec}}}$, we estimate that peculiar velocities introduce a scatter to the SZ-estimated mass of clusters at the level of $\langle {\Delta }M/M\rangle =3.5\pm 0.8\%$.

Future observations with higher angular resolution and support for multiple instantaneous millimeter/submillimeter bandpasses can help reduce the uncertainties on ${{v}_{{\rm pec}}}$. Higher angular resolution can resolve a larger fraction of the CIB into point sources, and therefore reduce the magnitude of the remaining confused SMG background. The capability to observe multiple wavebands spanning the SZE decrement to the increment would allow the wavebands to be analyzed homogeneously, reducing the complexity of data reduction and related systematic uncertainties. These capabilities can be provided by wide-format multi-band bolometer cameras on telescopes like the Large Millimeter Telescope and the upcoming Cerro Chajnantor Atacama Telescope.

R.R.L. and A.J.B. acknowledge significant support for this work from the U.S. National Science Foundation through grant AST-0955810. J.P.H. acknowledges support from the National Aeronautics and Space Administration (NASA) through Chandra Awards numbered GO1-12008X and GO2-13156X issued to Rutgers University by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060, and through an award issued by JPL/Caltech in association with Herschel, which is a European Space Agency Cornerstone Mission with significant participation by NASA. ACT operates in the Parque Astronómico Atacama in northern Chile under the auspices of the Programa de Astronomía de la Comisión Nacional de Investigación Científica y Tecnológica de Chile (CONICYT). This work was supported by the U.S. National Science Foundation through awards AST-0408698 and AST-0965625 for the ACT project, and PHY-0855887, PHY-1214379, AST-0707731, and PIRE-0507768 (award No. OISE-0530095). Funding was also provided by Princeton University, the University of Pennsylvania, and a Canada Foundation for Innovation (CFI) award to UBC. Computations were performed on the GPC supercomputer at the SciNet HPC Consortium. SciNet is funded by the CFI under the auspices of Compute Canada, the Government of Ontario, the Ontario Research Fund—Research Excellence, and the University of Toronto. We acknowledge support from the FONDAP Center for Astrophysics 15010003, BASAL CATA Center for Astrophysics and Associated Technologies. The authors thank the APEX staff for their help in carrying out the observations presented here, as well as Phil Edwards, Robin Wark, and Shane O'Sullivan for their assistance with the ATCA observations. We thank the anonymous referee for helpful feedback that has improved this manuscript. APEX is operated by the Max-Planck-Institut für Radioastronomie, the European Southern Observatory, and the Onsala Space Observatory.