THE MASSIVE AND DISTANT CLUSTERS OF WISE SURVEY. III. SUNYAEV–ZEL'DOVICH MASSES OF GALAXY CLUSTERS AT z ∼ 1

CARMA is an interferometer that consists of six 10.4 m, nine 6.1 m, and eight 3.5 m telescopes, providing fields of view of FWHM 38, 66, and 114 at 30 GHz, respectively. All 23 telescopes have 30 and 90 GHz receivers, while the 10.4 and 6.1 m telescopes have an additional 230 GHz receiver. CARMA is equipped with two correlators: an eight-station correlator with 7.5 GHz of bandwidth per baseline (the "wideband correlator") and a more flexible correlator that can be configured to correlate 23 stations with 2 GHz bandwidth per baseline at 30 GHz ("spectral line correlator"). To maximize sensitivity, both correlators can be used simultaneously.

Clusters MOO J0012+1602, MOO J0319–0025, and MOO J1014+0038 were observed when the 10.4 and 6.1 m telescopes were in E configuration, the 3.5 m telescopes were in SL configuration, and the signals were processed by both correlators ("E+SL"). MOO J1155+3901 was observed using the wideband correlator and the eight 3.5 m telescopes in the SH configuration. MOO J1514+1346 was observed twice, first using the eight 3.5 m telescopes in the SL configuration with the wideband correlator and later with all 23 telescopes in the E+SL configuration using only the spectral line correlator. All observations were centered around 31 GHz.

With the exception of MOO J1514+1346, cluster observations in the E+SL configuration used the wideband correlator to process the intermediate frequency signal from eight of the 6.1 m telescopes. The synthesized beam formed by the $6.1\times 6.1\;{\rm m}$ baselines is approximately 1', a resolution well matched to the angular size of the SZ signal from these distant clusters. The wideband correlator provides most of the sensitivity to the cluster signal in these observations. The 23 element observations of MOO J1514+1346 lacked the wideband correlator due to a hardware problem and were primarily useful for confirming a point source that was not well detected by the SL data alone. For the standard E+SL observations, the spectral line correlations sample baselines from 0.35 to 12.0 kλ, while the wideband correlations sample baselines from 0.65 to 4.0 kλ.

The CARMA observations, summarized in Table 1, used the WISE centroid positions as the pointing and phase centers. The data were reduced with a pipeline using MIRIAD (Sault et al. 1995) similar in function to the one described in Muchovej et al. (2007). After filtering for bad weather and instrumentation problems, the data were gain-calibrated using observations of bright, unresolved quasars interleaved every 15 minutes between the cluster observations. Flux densities are calibrated against observations of Mars using the model presented in Rudy et al. (1987). The pipeline produces a set of flux-calibrated visibilities of the cluster field. The CARMA images in Figure 1 are created by combining naturally weighted uv data from both correlators. They are in signal-to-noise ratio (S/N) units and a 2 kλ cutoff is applied to the data to highlight the cluster-sensitive baselines in the images. Models fit to emissive sources are removed (see Section 3.1). The residual maps are CLEANed inside a square box 3' on a side, centered on the position of the map with the largest absolute value in S/N units. CLEAN is allowed to proceed until the largest peak in the map is 1.5 times the map rms value.

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All but one of these clusters (MOO J1014+0038) were observed with the Gemini Multi-Object Spectrograph (GMOS) on Gemini North. Exposure times of 15 minutes were obtained in the r and z bands to produce color–magnitude diagrams (CMDs) from which red-sequence members could be selected for follow-up spectroscopic observations. These images are combined with IRAC 3.6 μm or WISE 3.4 μm images to make the color images for four of the five clusters shown in Figure 1.

These images were used to construct several of the masks, for both Gemini/GMOS-N and Keck/DEIMOS, with which we spectroscopically confirmed 20 MaDCoWS clusters to date, including four of the five in the present work. Stanford et al. (2014) provide a full description of the MaDCoWS spectroscopy.

Cluster MOO J1014+0038 was observed on UT 2014 January 22 with the Inamori Magellan Areal Camera and Spectrograph (IMACS; Dressler et al. 2006) in the g, r and z bands for 2, 12, and 12 minutes, respectively. These data were reduced with the SPT optical pipeline, as described in Song et al. (2012), and the r and z images are combined with IRAC 3.6 μm to make the color image of this cluster shown in Figure 1.

Photometric redshifts based on the cluster red-sequence were measured from both optical and IRAC color–magnitude relations, shown in Figure 2. The best-fit photometric redshift in both cases is consistent with ${{z}_{{\rm ph}}}=1.27\pm 0.08$. We have used this value in converting the observed SZ decrement to a total mass.

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Compact radio sources are a potential source of uncertainty in SZ cluster mass measurements. Since these synchrotron sources are often variable, it is important to identify and remove their contribution contemporaneously with the SZ measurement. The long baselines of our CARMA observations (up to 12 kλ) can identify compact emission sources at high sensitivity. We identify contaminating sources by visual inspection of the long-baseline data and checking the 1.4 GHz catalogs from the NRAO VLA Sky Survey (NVSS, Condon et al. 1998) and the VLA Faint Images of the Radio Sky at Twenty-Centimeters (FIRST, Becker et al. 1995). A radio source is jointly modeled with the cluster signal if its flux is detected in the CARMA data at 3σ or greater, or if there is a source in the NVSS or FIRST catalog. In the case that the source is only marginally detected in the CARMA data and present in a VLA catalog, its position is fixed and only the flux is allowed to vary. The simultaneous fit mitigates the contamination of our significance and mass fits due to variable emissive sources, as described below.

In MOO J1155+3901, which has a centrally located source of emission detected at ∼2.5σ in the CARMA data, there exists a slight positive correlation between the measured Y parameter for the cluster and the point source flux. In the remaining four clusters, there is no sign of covariance between the cluster parameters and other source parameters. The coordinates and beam-corrected fluxes of compact radio sources identified toward each cluster are given in Table 2.

To determine the significances of the observed SZ decrements, we measure the difference in ${{\chi }^{2}}$ between a model of our observations that contains no cluster with models (described in Section 3.3) that do include a cluster. In the cases where there is contaminating radio emission, models for these point sources are fitted in both the cluster and no-cluster models. The models are fit to the data in the uv-plane using a Markov Chain Monte Carlo routine, which correctly accounts for the noise in our data from the heterogeneous CARMA array (see, e.g., Plagge et al. 2013).

The resulting ${{\chi }^{2}}$ values are converted to significances in terms of Gaussian standard deviations. They range from 2.7σ to 9.5σ and are listed in Table 3. In fitting the SZ cluster centroids, a uniform 15 radius prior centered on the IR position is used. For low significance decrements, negative noise spikes can formally bias the S/N to higher values. However, given the strong prior of an IR-selected, confirmed cluster at the targeted position, and the small number of independent beams ($\lt 10$) over which the SZ centroid is allowed to vary, we expect all of these decrements to be robust. Using an approximate analytical calculation of the noise properties in our CARMA maps we conservatively estimate the probability of false detection for the two least significant clusters to be ∼8%–10%. The higher significance clusters have no significant probability of false detection.

Table 3.  SZ Properties of MaDCoWS Clusters

ID	Redshift	Significance	r500	Y500	M500	M200a	${\Delta }{{C}_{{\rm IR}-{\rm SZ}}}$ b
		(σ)	(Mpc)	(10−6 Mpc2)	(1014 ${{M}_{\odot }}$)	(1014 ${{M}_{\odot }}$)	(Mpc)
MOO J0012+1602	0.944	2.7	0.56 ± 0.07	7.6 ± 4.6	1.4 ± 0.5	2.2 ± 0.8	0.270
MOO J0319–0025	1.194	6.6	0.65 ± 0.03	30.0 ± 5.9	3.1 ± 0.4	5.1 ± 0.6	0.194
MOO J1014+0038	1.27 ± 0.08c	9.5	0.66 ± 0.02	37.0 ± 7.1	3.4 ± 0.4	5.6 ± 0.6	0.142
MOO J1155+3901	1.009	2.8	0.69 ± 0.06	26 ± 11	2.9 ± 0.7	4.7 ± 1.2	0.099
MOO J1514+1346	1.059	3.2	0.61 ± 0.05	16.0 ± 6.9	2.2 ± 0.6	3.5 ± 0.9	0.282

^aM₂₀₀ masses were extrapolated from the measured M₅₀₀ masses using the Duffy et al. (2008) mass–concentration relation. ^b ${\Delta }{{C}_{{\rm IR}-{\rm SZ}}}$ is the offset between the IR and SZ positional centroids. ^cThe fit for this cluster assumed a Gaussian redshift prior with σ_z = 0.08 centered on the photometric redshift of z = 1.27. Due to the flat angular diameter distance, the redshift independence of the SZ and the narrow evolutionary window, no scatter is imposed by the redshift uncertainty at the significance presented.

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The mass estimates are produced following the method described in recent CARMA papers (e.g., Brodwin et al. 2012). Briefly, we parameterize the SZ signal as a pressure profile that we integrate to measure the integrated Compton Y parameter. We use a generalized NFW pressure profile as presented in Nagai et al. (2007),

$$\begin{eqnarray}&&P(x)=\frac{{{P}_{0}}}{{{x}^{\gamma }}{{(1+{{x}^{\alpha }})}^{(\beta -\gamma )/\alpha }}},\end{eqnarray} \tag{ 1 }$$

where P₀ is the normalization, $x\equiv r/{{r}_{s}}$ is a dimensionless radial variable, and P₀ and r_s are allowed to vary. The power-law exponents are fixed to the "universal" values (i.e., α = 1.0510, β = 5.4905, and γ = 0.3091) of Arnaud et al. (2010). The cluster centroid and the positions and fluxes of any coincident emissive sources are allowed to vary as well. There is a strong degeneracy between P₀ and r_s in the data, however the resulting Y parameter, as defined below, is well-constrained.

We integrate the derived pressure profile to a cutoff radius to calculate the integrated Y parameter,

$$\begin{eqnarray}&&{{Y}_{{\Delta }}}=\frac{1}{D_{A}^{2}}\frac{{{\sigma }_{T}}}{{{m}_{e}}{{c}^{2}}}\int _{0}^{{{r}_{{\Delta }}}}P(r/{{r}_{s}})dV.\end{eqnarray} \tag{ 2 }$$

To determine the cutoff radius, we enforce consistency with the ${{Y}_{SZ,500}}-{{M}_{500}}$ scaling relation derived in Andersson et al. (2011) by requiring that the chosen integration radius (and thus, mass) and resulting Y lie on the mean relation. We determine the final integration radius iteratively, and the value of Y typically converges in roughly five iterations. The ${{M}_{500}}$ values in Table 3 correspond to the derived values of ${{r}_{500}}$ in our cosmology.

The SZ and IR galaxy density centroids trace different physical probes of the potential, namely the integrated pressure of the ICM and the distribution of massive galaxies, respectively. For individual clusters these need not be coincident. Indeed, recent work has suggested that even X-ray and SZ centroids may be offset from each other during a major merger (Zhang et al. 2014).

In Figure 3 we plot the angular offsets of the CARMA SZ cluster centroids from the WISE IR cluster positions, taken as the peaks in the wavelet detection map. The SZ–IR offset is less than 300 kpc for all the clusters in this sample. The error bars represent the quadrature sum of the uncertainties in the CARMA and WISE centroids. The CARMA positional errors, ${{\sigma }_{{\rm CARMA}}}$, determined in the fit described in Section 3.3, are jointly fit with the positions and fluxes of the emissive radio sources. The WISE centroiding precision is limited by finite gridding (15''/pixel) in the WISE cluster search, and to a lesser extent, to confusion caused by the relatively large WISE beam (∼6''). However, the metric offsets caused by these technical factors should be small (${{\sigma }_{WISE}}$ ≲ 50 kpc) for these high-S/N cluster detections.

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The larger offsets seen here are likely due to real differences between IR galaxy density and SZ ICM centroids. We estimate the average residual positional offset, ${{\sigma }_{{\rm IR}-{\rm SZ}}}$, by setting the reduced chi-squared statistic equal to unity:

$$\begin{eqnarray}&&\chi _{\nu }^{2}=\frac{1}{\nu }\mathop{\sum }\limits_{{\rm clusters}}{{\left( \frac{{\rm Offset}}{\sqrt{\sigma _{{\rm CARMA}}^{2}+\sigma _{WISE}^{2}+\sigma _{{\rm IR}-{\rm SZ}}^{2}}} \right)}^{2}}=1,\end{eqnarray} \tag{ 3 }$$

where ν is the number of degrees of freedom. We find ${{\sigma }_{{\rm IR}-{\rm SZ}}}$ = 188.6 kpc, shown as the filled circular region at the center of the plot. A similar result is obtained using IR centers defined by the BCGs identified in follow-up IRAC imaging, confirming the IR–SZ offset is not due to an unknown systematic in the WISE centering.