The Massive and Distant Clusters of WISE Survey: SZ effect Verification with the Atacama Compact Array -- Localization and Cluster Analysis
Luca Di Mascolo, Tony Mroczkowski, Eugene Churazov, Emily Moravec, Mark Brodwin, Anthony Gonzalez, Bandon B. Decker, Peter R. M. Eisenhardt, Spencer A. Stanford, Daniel Stern, Rashid Sunyaev, Dominika Wylezalek
AAstronomy & Astrophysics manuscript no. madcows c (cid:13)
ESO 2020April 30, 2020
The Massive and Distant Clusters of
WISE
Survey
SZ effect of Verification with the Atacama Compact Array – Localization andCluster Analysis
Luca Di Mascolo , Tony Mroczkowski , Eugene Churazov , , Emily Moravec , , Mark Brodwin ,Anthony Gonzalez , Bandon B. Decker , Peter R. M. Eisenhardt , Spencer A. Stanford ,Daniel Stern , Rashid Sunyaev , , and Dominika Wylezalek Max-Planck-Institut für Astrophysik (MPA), Karl-Schwarzschild-Strasse 1, Garching 85741, Germanye-mail: [email protected] European Southern Observatory (ESO), Karl-Schwarzschild-Strasse 2, Garching 85748, Germany Space Research Institute, Profsoyuznaya 84 /
32, Moscow 117997, Russia Astronomical Institute of the Czech Academy of Sciences, Prague, Bˇocní II 1401 / Department of Astronomy, University of Florida, 211 Bryant Space Science Center, Gainesville, FL 32611, USA Department of Physics and Astronomy, University of Missouri, 5110 Rockhill Road, Kansas City, MO 64110, USA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA Department of Physics, University of California, Davis, One Shields Avenue, Davis, CA 95616, USAReceived 25 February 2020 / Accepted 15 April 2020
ABSTRACT
Context.
The Massive and Distant Clusters of WISE Survey (MaDCoWS) provides a catalog of high-redshift (0 . (cid:46) z (cid:46) .
5) infrared-selected galaxy clusters. However, the verification of the ionized intracluster medium, indicative of a collapsed and nearly virializedsystem, is made challenging by the high redshifts of the sample members.
Aims.
The main goal of this work is to test the capabilities of the Atacama Compact Array (ACA; also known as the Morita Array)Band 3 observations, centered at about 97.5 GHz, to provide robust validation of cluster detections via the thermal Sunyaev–Zeldovich(SZ) e ff ect. Methods.
Using a pilot sample that comprises ten MaDCoWS galaxy clusters, accessible to ACA and representative of the mediansample richness, we infer the masses of the selected galaxy clusters and respective detection significance by means of a Bayesiananalysis of the interferometric data.
Results.
Our test of the
Verification with the ACA – Localization and Cluster Analysis (VACA LoCA) program demonstrates thatthe ACA can robustly confirm the presence of the virialized intracluster medium in galaxy clusters previously identified in full-skysurveys. In particular, we obtain a significant detection of the SZ e ff ect for seven out of the ten VACA LoCA clusters. We note thatthis result is independent of the assumed pressure profile. However, the limited angular dynamic range of the ACA in Band 3 alone,short observational integration times, and possible contamination from unresolved sources limit the detailed characterization of thecluster properties and the inference of the cluster masses within scales appropriate for the robust calibration of mass–richness scalingrelations. Key words. galaxies: clusters — galaxies: clusters: intracluster medium — cosmic background radiation
1. Introduction
Galaxy cluster richness has long been demonstrated to providean observationally inexpensive proxy for cluster mass (see, e.g.,Ryko ff et al. 2012; Andreon 2015; Saro et al. 2015; Geach &Peacock 2017; Rettura et al. 2018; Gonzalez et al. 2019). Beingpractically independent of the specific dynamical state of galaxyclusters, properly calibrated mass–richness relations play a keyrole in obtaining mass estimates in lieu of data that could di-rectly probe the mass distribution of a cluster. For cluster can-didates discovered through optical and infrared selection criteriasuch as richness, it is essential to verify that the observed galaxyoverdensities cannot be ascribed to spurious e ff ects (e.g., line-of-sight projection of galaxies belonging to di ff erent haloes). Cen-tral to this aim is confirming the presence of a hot X-ray emit-ting intracluster medium (ICM) heated by gravitational infall andnearly in virial equilibrium. X-ray confirmation, which has been the traditional tool for probing the ICM, becomes exceedinglydi ffi cult and observationally challenging at high redshift due tocosmological dimming. We note, however, that at z (cid:38) ff ect (Sunyaev &Zeldovich 1972) o ff ers an alternative, redshift-independent wayto confirm the presence of the ICM. Here we provide a firsttest of the capabilities of the 7-meter Atacama Compact Array(ACA; Iguchi et al. 2009), or Morita Array, in providing an SZconfirmation of cluster candidates identified in wide-field sur-veys. In particular, we consider a first pilot sample of the obser-vational program, Verification with the ACA – Localization andCluster Analysis (VACA LoCA), aimed at providing cluster veri-fication and localization of the intracluster gas of galaxy clusters
Article number, page 1 of 19 a r X i v : . [ a s t r o - ph . C O ] A p r & A proofs: manuscript no. madcows selected from the Massive and Distant Clusters of WISE (Wrightet al. 2010) Survey (MaDCoWS; Gonzalez et al. 2019).The paper is structured as follows. An overview of the obser-vational details of the VACA LoCA cluster sample is provided inSect. 2. In Sect. 3 we briefly discuss the modeling technique em-ployed for inferring the cluster masses. The results of our analy-sis, comprising estimates of mass and detection significance forall the VACA LoCA clusters, are presented in Sect. 4. A sum-mary of the work is then given in Sect. 5.All results discussed in this paper were derived in the frame-work of a spatially flat Λ CDM cosmological model, with Ω m = . Ω Λ = .
70, and H = . − Mpc − . In this cosmol-ogy, 1 arcsecond corresponds to 8 .
01 kpc at the average redshift z (cid:39)
2. ACA observations
Gonzalez et al. (2019) reports a preliminary, low-scatter mass–richness scaling relation for the MaDCoWS cluster sample basedon the infrared richness estimates from observations with the In-frared Array Camera (IRAC; Fazio et al. 2004) on the
SpitzerSpace Telescope and masses derived from the SZ signal mea-sured by the Combined Array for Research in Millimeter-waveAstronomy (CARMA; see Brodwin et al. 2015; Gonzalez et al.2015; Decker et al. 2019). In order to improve the calibrationof the mass–richness correlation, the VACA LoCA observationswere devised to target a sample of ten MaDCoWS galaxy clus-ters observable by ACA and representative of the median samplerichness.The ACA observations of the selected MaDCoWS clusterswere carried out between May and October 2017 as part ofALMA Cycle 4 operations (project ID: 2016.2.00014.S, PI: M.Brodwin). In order to reach a target continuum sensitivity ofaround 80 µ Jy, the integration time on source for each of thepointings amounts to an average of 2 . . − . .
5, 92 .
5, 102 . . ff between prob-ing the SZ signal spectrum near its minimum (i.e., maximumamplitude of the negative spectral distortion) and probing thelargest scales accessible by ACA Band 3 data. The resulting dy-namic range of uv (Fourier space) distances in the ACA observa-tions of the MaDCoWS clusters span, on average, between 2 . .
23 k λ , corresponding respectively to angular scales from1 .
30 arcmin to 11 .
97 arcsec (we refer to Table 1 for further ob-servational details).We perform the calibration of all the data in the CommonAstronomy Software Application (
CASA ; McMullin et al. 2007)package version 4.7.2 using the standard calibration pipelinesprovided at data delivery. A direct inspection of the reduced datasets did not highlight any significant issue with the calibration.We hence adopt the nominal value of 5% for the fiducial uncer-tainty on the ACA absolute calibration .All the interferometric images presented in this work aregenerated using the tclean task in CASA version 5.6.1. To bet-ter highlight the SZ features in the maps, we do not correct for http: // https: // almascience.nrao.edu / documents-and-tools / cycle4 / alma-technical-handbook . . . . . F r ac ti ono f v i s i b iliti e s [ % ] . . . . . . . u v distance [ k λ ] N o i s e R M S [ m J y ]
45 30 15Angular scale [arcsec]
Fig. 1.
Fraction of visibility points for a given bin of uv distances (top)and corresponding cumulative noise root mean square (RMS; bottom).The blue lines correspond to the individual fields, while the red shadedregion to their average. The clear flattening of the cumulative noisecurve for uv distance larger than around 10 k λ suggests the sensitivitybudget is overall dominated by short baselines (i.e., large-scale modes). the primary beam attenuation. The fields are cut o ff at the stan-dard 0.2 gain level of the ACA antenna pattern. As our study isentirely performed on the raw interferometric data, we note thatthe ACA maps are included for display purposes only. No de-convolution is performed to reduce the e ff ects of sidelobes onthe reconstructed “dirty” maps.
3. Analysis technique
Spatial filtering due to the incomplete sampling of the Fouriermodes of the observed sky may represent a severe challengein the analysis of radio-interferometric measurements of galaxyclusters. The issue is in fact twofold: first, the sparse coverageof the Fourier plane results in poor constraints for some angu-lar scales within the range probed by the interferometer; second,the shortest baseline achievable is essentially determined by theshadowing limit, when one antenna is in front of another as seenfrom the source. This sets a hard upper limit on the maximumrecoverable scale (MRS) of the observation. This high-pass fil-tering e ff ect is evident in the case of astrophysical objects cover-ing large angular scales such as galaxy clusters, whose SZ signaloften extends well beyond the field of view of current millime-ter and submillimeter facilities that provide subarcminute reso-lution (see, e.g., Basu et al. 2016 and Di Mascolo et al. 2019b,or Mroczkowski et al. 2019 for a broader review). To provide asense of the net e ff ects of ACA filtering on the SZ signal from agalaxy cluster, in Fig. 2 we compare the model and filtered SZprofiles for a cluster with a mass of 2 . · M (cid:12) at a redshift z = . Article number, page 2 of 19. Di Mascolo et al.: MaDCoWS SZ-VACA LoCA
Table 1.
Summary of the observational properties of the VACA LoCA sample of MaDCoWS clusters. The reported noise RMS is the averagenoise level as measured from naturally weighted dirty images. The corresponding dirty beam is reported in the table as the nominal data resolution.The maximum recoverable scale (MRS) is instead derived from the minimum projected baseline in the full-bandwidth measurements.
Cluster ID Obs. date On-source time Noise RMS uv range Resolution MRS(hours) (mJy) (k λ ) (arcsec) (arcmin)MOO J0129 − .
78 0 .
061 1 . − .
20 17 . × . . − .
15 0 .
055 1 . − .
03 18 . × . . + .
05 0 .
087 1 . − .
69 17 . × . . − .
08 0 .
069 2 . − .
51 19 . × . . − .
14 0 .
081 2 . − .
22 19 . × . . + .
07 0 .
061 2 . − .
67 16 . × . . − .
46 0 .
071 1 . − .
19 17 . × . . + .
09 0 .
066 1 . − .
30 17 . × . . − .
37 0 .
101 1 . − .
41 19 . × . . + .
61 0 .
062 1 . − .
98 18 . × . . − C o m p t ony [ − ] − − − −
200 0 200 400 600 800
Physical distance [kpc] − R a ti o -1.50 -0.75 0.00 0.75 1.50Angular distance [arcmin] Fig. 2.
Simulated SZ profile for a cluster with mass of 2 . · M (cid:12) and redshift z = .
00, analogous to the MaDCoWS targets previouslyreported in Gonzalez et al. (2019). The top panel shows a comparisonof the input SZ model (i.e., the true profile; dotted blue line), and thecorresponding profiles after application of the interferometric transferfunction (i.e., the filtered, observed profiles; red lines). These clearlyshow how the fraction of missing flux is significant already well withinthe r of the simulated cluster (see Sect. 3.1 for a definition; verticallines). The two filtered profiles are measured along directions at con-stant right ascension or declination (respectively dashed and solid lines).Their di ff erence reflects the asymmetry in the uv coverage. The lowerpanel reports the ratio of the filtered and raw profiles. The line style isthe same as the upper panel, corresponding to the ratio of the filtered(observed) profiles to the unfiltered (true) profile. The blue dotted lineindicates unity (i.e., no filtering). scopes). However, these large-scale observations should havesensitivities comparable to the corresponding interferometricmeasurements, a condition that is di ffi cult to realize in the caseof SZ data.In order to circumvent any of the above challenges, we per-form a Bayesian forward-modeling analysis directly on the vis-ibilities of the ACA MaDCoWS sample. This allows us to inferthe cluster masses from the raw interferometric data, account-ing for the exact sampling function of the visibility plane, andproviding a strong leverage on possible contamination from un-resolved (point-like) sources. An extensive discussion of the modeling methodology andthe implementation is provided in Di Mascolo et al. (2019a,b). Hydrodynamic simulations (Nagai et al. 2007) have shown thatthe pressure distribution of the electrons within the ICM can bereasonably described as P e ( ξ ) = P × p ( ξ ) , (1)where the scaled pressure profile p ( ξ ) is defined by a generalizedNavarro-Frenk-White (gNFW) profile, p ( ξ ) = P ξ − c (cid:2) (1 + ξ a ) (cid:3) ( c − b ) / a . (2)Here, P acts as a simple normalization factor. The parameters a , b , and c are respectively the radial slopes at intermediate, large,and small scales with respect to a scale radius r s , while ξ = r / r s is the radial distance r from the pressure centroid in units of r s .Following Arnaud et al. (2010), the scaling parameter P isdefined as P ( M , z ) = . · − E ( z ) / (cid:34) M · M (cid:12) (cid:35) / + a p ( ξ ) keV cm − , (3)where E ( z ) is the ratio of the Hubble constant at redshift z to itspresent value H , and M is the mass enclosed within the ra-dius r at which the average cluster density is 500 × the criticaldensity ρ c ( z ) of the Universe at the redshift of the cluster. Un-der the assumption of spherical symmetry, the radius r can beeasily expressed as a function of a given mass M and redshift z as r ( M , z ) = (cid:34) π M ρ c ( z ) (cid:35) / . (4)This can then be related to the scale radius r s of the normalizedgNFW profile in Eq. (2) by adding a concentration parameter c as r s = r / c . Finally, the running slope a p ( ξ ) is intro-duced to account for any departure from self-similarity in theinnermost regions of galaxy clusters, a p ( ξ ) = a / [1 + ξ ] (5) Article number, page 3 of 19 & A proofs: manuscript no. madcows
Table 2.
Best-fit parameters of the gNFW pressure models from Arnaudet al. (2010), Planck Collaboration et al. (2013), and McDonald et al.(2014, referred to here as MD14). universal cool core disturbed
Planck
MD14 P .
40 3 .
25 3 .
20 6 .
41 3 . + . − . c .
18 1 .
13 1 .
08 1 .
81 2 . + . − . a .
05 1 .
22 1 .
41 1 .
33 2 . + . − . b .
49 5 .
49 5 .
49 4 .
13 3 . + . − . c .
31 0 .
77 0 .
38 0 .
31 0 . + . − . a .
22 0 .
22 0 .
22 0 .
00 0 . a ,the pressure normalization P , the concentration parameter c ,and the gNFW slopes a , b , and c are kept fixed. The parameters a , P , and c are degenerate with the mass parameter M ,and unconstrained fittings would significantly a ff ect the recoveryof the cluster masses. On the other hand, test fittings with freegNFW slopes have shown that all three parameters a , b , and c would remain entirely unconstrained, and would undergo strongdegeneracies with any of the other gNFW parameters and mass M . This is a direct consequence of the limited dynamic rangeof angular scales probed by ACA which, in combination withthe modest sensitivity of the VACA LoCA observations, limitsthe information available for reconstructing pressure profiles forthe individual fields.Hence, we set the above gNFW parameters alternatively tothe best-fit values reported in Arnaud et al. (2010) for the uni-versal pressure profile, or for the subsamples of cool-core andmorphologically disturbed clusters. For a comparison, we addi-tionally consider gNFW parameters derived in Planck Collabo-ration et al. (2013) from the joint fit of the XMM-Newton - and
Planck -selected sample of galaxy clusters, as well as the high-redshift
Chandra gNFW model by McDonald et al. (2014). Thedi ff erent set of parameters adopted in our analysis is summarizedin Table 2.At each iteration of the posterior sampling, we then computethe expected thermal SZ signal by integrating the pressure modeldefined in Eq. (1) for a given value of M and redshift z . Theresulting variation in the CMB surface brightness in a direction x on the plane of the sky and at a frequency ν is (Sunyaev &Zeldovich 1972) δ i t sz ( x , ν ) ∝ g t sz ( ν ) (cid:82) P e ( x , (cid:96) ) d (cid:96). (6)The integral along the line-of-sight coordinate (cid:96) is computedfrom 0 up to the fiducial value of 5 r (Arnaud et al. 2010).The factor g t sz ( ν, T e ) represents the frequency scaling of the non-relativistic thermal SZ e ff ect (Sunyaev & Zeldovich 1972). Forsimplicity, we neglect any temperature-dependent correctionsarising from the fully relativistic treatment of the thermal SZe ff ect. The ACA observations cover a frequency band that is notbroad enough, or deep enough, to constrain any relativistic con-tribution to the SZ spectrum, and hence to get direct constraintson the average temperature of the electron populations within theobserved clusters (Challinor & Lasenby 1998; Itoh et al. 1998;Sazonov & Sunyaev 1998). Further, the correction to the non-relativistic thermal signal for the ACA MaDCoWS clusters isexpected to be on average less than ∼ The average relativistic correction reported in the text is computedemploying the formulation by Itoh & Nozawa (2004). The average elec- bias the reconstructed masses systematically to lower values, thee ff ect will be at most on the same order as the flux uncertain-ties discussed in Sect. 2, and well within the modeling statisticaluncertainties (see Sect. 4 below).Similarly, the ACA frequency coverage is not wide enoughto retrieve any information about the bulk velocities of the ob-served clusters (or parts of them). Therefore, we assume anycontributions from a possible kinetic SZ component (Sunyaev &Zeldovich 1980) to be subdominant with respect to the thermale ff ect, and we neglect it in our analysis. Contamination from point-like radio sources may limit and sig-nificantly a ff ect the reconstruction of a cluster model from SZobservations (Gobat et al. 2019; Mroczkowski et al. 2019). Inorder to assess the level at which the unresolved flux might havecontributed to the estimates of the masses of VACA LoCA clus-ters, we perform blind searches of point-like components overthe entire fields of view of the ACA observations and simulta-neously with the SZ analysis. We assume the unresolved com-ponents to be described by a Dirac- δ model with flat spectrumover the entire ACA band. The long-baseline data range, mostsensitive to the signal from compact sources, is the least denselyparsed region of the visibility plane (see Fig. 1). This results inhigh noise on the smaller angular scales, hence limiting the pos-sibility of constraining the spectral properties of the unresolvedsources in the observed fields. The point-like model thus simpli-fies to (Di Mascolo et al. 2019a) V ( u , ν ) = i ps e π j u · x ps , (7)given a set of interferometric data with visibility coordinates u .The position x ps and the source flux i ps are left free to vary.Due to the limited information provided by the ACA dataabout the population of unresolved sources in the VACA LoCAfields, here we consider them as nuisance model components andgenerally marginalize over them. A future analysis with higherresolution, multi-frequency observations will be key for theirproper characterization. The comparison of cluster positions identified through the MaD-CoWS search and the galaxy distribution centroids measured by
Spitzer are found to deviate by σ RA = . σ Dec =
15 arcsec in declination (Gonzalez et al. 2019).We thus assume normal priors with standard deviations of σ ra and σ Dec on the right ascension and declination coordinates ofthe cluster centroids, respectively.The mass parameter M and the redshift z are heavily de-generate as they both enter in the determination of the pressuremodel through the pressure normalization P and the scale ra-dius r . In order to alleviate the degeneracy, we adopt split-normal priors (Wallis 2014) on the redshifts z based on the pho-tometric constraints on the cluster members from Spitzer (Gon-zalez et al. 2019). When fitting the gNFW profile from McDon-ald et al. (2014), the gNFW parameters were also assigned split- tron temperature is inferred from the core-excised temperature-redshift-mass scaling relation in Bulbul et al. (2019). To keep a conservative up-per limit, we consider an extreme case of a galaxy cluster with the samemass as the most massive object identified in the MaDCoWS survey(Ruppin et al. 2020) at a redshift equal to the highest value in the ACAsample.Article number, page 4 of 19. Di Mascolo et al.: MaDCoWS SZ-VACA LoCA normal priors, with standard deviations given by the respectiveparameter uncertainties in Table 2.To account for the ACA flux uncertainties in the recoveredmasses (Sect. 2), we introduce a normalization hyperparameter,as detailed in Di Mascolo et al. (2019a). In particular, we con-sider a scaling parameter characterized by a normal prior distri-bution with unitary mean value and standard deviation equal tothe inherent calibration uncertainty.Finally, we assume wide uninformative priors on all the pointsource parameters apart from the position. For the blind search,this is bound to vary uniformly within the region defined by thefirst null of the ACA primary beam. Data-free runs for each ofthe analyzed data sets (Di Mascolo et al. 2019a,b) have shownno biases in the parameter inference related to choice in the priordistributions.
4. Results and discussion
A summary of the masses of the VACA LoCA pilot sample ispresented in Table 3. The results presented in previous MaD-CoWS papers (Brodwin et al. 2015; Decker et al. 2019; Gonza-lez et al. 2019) were derived adopting the universal profile byArnaud et al. (2010) to describe the electron pressure distribu-tion. For consistency, we report here only the masses estimatedunder the same assumption. A discussion of the impact of modelchoice on the inferred masses is presented in Sect. 4.4.We quantify the detection significance of the SZ signal inthe VACA LoCA observations by comparing the log-evidence ofthe full modeling runs Z with those considering only the pointsource model component Z by means of the Je ff reys scale (Je ff reys 1961). To get a more immediate handle on the signifi-cance of each detection, we report in Table 3 the number of e ff ec-tive standard deviations σ e ff between the model with and withoutan SZ component. This can be computed as σ e ff (cid:39) (cid:112) ∆ log Z given a log-Bayes factor ∆ log Z = log ( Z / Z ) (Trotta 2008).This di ff ers from the approach taken in the CARMA SZ follow-up papers (Brodwin et al. 2015; Gonzalez et al. 2015; Deckeret al. 2019) in that it is more statistically robust, as it properlyaccounts for the change between di ff erent models in the numberof parameters and respective priors. We note that σ e ff is to be in-terpreted in a merely heuristic manner, as we are not accountingfor the di ff erent degrees of freedom or prior volumes between themodels. According to the Je ff reys criterion, introduced above, avalue of σ e ff (cid:38) ff ect towardseven out of the ten clusters of the VACA LoCA sample,while the presence of SZ signal is only weakly favored forMOO J1223 + + ff reys criterion, the detec-tion significance of MOO J1223 + ff reys1961; Trotta 2008). For the single case of MOO J0903 + uv -space.Along with the advantages discussed in Sect. 3, this providesan approach to cluster detection in interferometric SZ data that As a reference, we consider a cluster to be significantly detected ifthe corresponding model has a Bayes factor Z / Z higher than 100. h m s s s − ◦ RA (J2000) D ec ( J )
150 kpc − . − . . . . S u rf ace b r i gh t n e ss [ m J yb ea m − ] Fig. 3.
Dirty image of MOO J0129 − σ , 2 σ , 3 σ , and 4 σ signif-icance levels of the SZ signal, with σ = .
061 mJybeam − . Althoughthe integrated SZ decrement is detected at σ e ff = .
77 (Table 3), thepeak SZ amplitude has a significance only slightly higher than 4 σ whenmeasured in image space. avoids the drawbacks of image-space analysis, in particular thebiased reconstructions produced by the CLEAN algorithm. For acomparison, we show in Fig. 3 the dirty image of the most sig-nificant detection in our sample, MOO J0129 − − .
24 mJy beam − , cor-responding to a statistical significance of 4 . σ , which is lowerthan the cluster detection σ e ff = .
77 (Table 3). This is not sur-prising, as σ e ff is a measure of the significance of the total SZsignal. However, in addition to the resolved SZ signal, the rea-son for this discrepancy also resides in the fact that the inter-ferometric images are a ff ected by heavily correlated noise. As aconsequence, the resulting fluctuations may attenuate the mea-sured signal and limit the confidence of its detection. On theother hand, side lobes further contaminate interferometric im-ages. This is generally solved by applying CLEAN -like deconvo-lution techniques to the data (Högbom 1974; Thompson et al.1986). However, these techniques are specifically devised to re-duce the e ff ects of the incomplete sampling of the visibility planeon the overall quality of the reconstructed image, and would notprovide any serious improvement in the significance of the ob-served SZ signal. It is worth noting that any deconvolved imagewould still provide a heavily high-pass filtered view of the verycore of a galaxy cluster, as ACA does not measure the SZ signalon scales larger than the maximum recovered scale (Table 1).Another important remark is that the dirty map shown inFig. 3 is generated only after subtraction from the visibility dataof the most significant point-like sources detected by our mod-eling algorithm, allowing for a cleaner identification of the SZsignal in the cluster image. In fact, the presence of very brightcompact sources may completely hide any SZ e ff ect component,as either their signal would be superimposed on the one from thegalaxy cluster or the side lobes would be blended with the SZfeature. Figure 4 shows a comparison of the mass–richness scaling forthe VACA LoCA sample and the CARMA measurements previ-
Article number, page 5 of 19 & A proofs: manuscript no. madcows
Table 3.
Inferred quantities for the VACA LoCA sample clusters under the assumption of a universal pressure profile (Arnaud et al. 2010). SeeSect. 4 for more details about the e ff ective significance estimate σ e ff . The photometric redshift z phot and infrared richness λ are taken from Gonzalezet al. (2019). Cluster ID z phot λ r θ Y sph ( < r ) Y cyl ( < r ) M σ e ff – – (Mpc) (arcmin) 10 − Mpc − Mpc (10 M (cid:12) ) – Significant detection
MOO J0129 − . + . − . ± . + . − . . + . − . . + . − . . + . − . . + . − . . − . + . − . ± . + . − . . + . − . . + . − . . + . − . . + . − . . − a . + . − . ± . + . − . . + . − . . + . − . . + . − . . + . − . . . + . − . . + . − . . + . − . . + . − . . + . − . MOO J1139 − . + . − . ± . + . − . . + . − . . + . − . . + . − . . + . − . . − . + . − . ± . + . − . . + . − . . + . − . . + . − . . + . − . . + . + . − . ± . + . − . . + . − . . + . − . . + . − . . + . − . . − a . + . − . ± . + . − . . + . − . . + . − . . + . − . . + . − . . . + . − . . + . − . . + . − . . + . − . . + . − . Non-detection
MOO J0903 + . + . − . ± . + . . + . . + . . + . . + . –MOO J1223 + b . + . − . ± . + . − . . + . − . . + . − . . + . − . . + . − . . + . + . − . ± . + . − . . + . − . . + . − . . + . − . . + . − . . Notes. ( a ) The two mass values provided for MOO J0917 − − ( b ) The SZ signal from MOO J1223 + ously reported by Gonzalez et al. (2019). Although there is goodconsistency between our estimates and the MaDCoWS mass–richness scaling, the VACA LoCA mass–richness distribution issystematically below the expected correlation. We quantify theaverage scaling by fitting the VACA LoCA data points with alinear function, with the slope constrained to that of the mass–richness scaling in Gonzalez et al. (2019) but with a free normal-ization parameter (which translates to an o ff set in the logarith-mic relation). We find that the VACA LoCA cluster masses aredownscaled by a factor of 0 . + . − . with respect to the CARMA-derived mass–richness scaling when considering all the VACALoCA clusters. The resulting scatter of the ACA masses with re-spect to the reconstructed relation is σ aca log M | λ = . + . − . , broaderthan the scatter observed in the CARMA measurements. How-ever, if we exclude all the non-detections from the analysis,the scatter decreases to a value comparable with the CARMAmeasurement, σ aca log M | λ = . + . − . , while the relative normaliza-tion remains statistically consistent with the previous estimate(0 . + . − . ). This suggests that the non-detections are major ac-tors in the increase of the measured scatter, possibly representingoutliers from the mass–richness relation (either due to propertiesinherent to the clusters themselves or as a result of modeling is-sues). The observed deviation from the nominal mass–richnessrelation may imply an overall systematic in the cluster mass es-timates. On the other hand, a joint fit of the CARMA and VACALoCA samples provides an overall scatter of σ joint log M | λ = . + . − . .It may thus be possible that a scatter intrinsic to the mass–richness distribution or arising due to the limited size of stud-ied sample may dominate the calibration of the mass–richnessrelation. Further observations of the SZ footprint of galaxy clus-ters spanning a broader richness range will be key to improvingthe current constraints on the MaDCoWS mass–richness scalingrelation.The fact that ACA can only provide a high-pass filteredview of the SZ signal (coupled with possible deviations from the fiducial average pressure profile; see discussion below) maybe among the main causes of the slight discrepancy of the VACALoCA masses with respect to the scaling relation obtained usingSZ measurements from CARMA. In fact, CARMA probed theSZ signal out to scales larger the r values of the observed clus-ters, hence accessing spatial information crucial to mass deter-mination within a cosmologically relevant overdensity. In con-trast, though the ACA observations have improved sensitivityon subarcminute scales, the reconstructed masses are derived byextrapolating the assumed pressure profile from the very core re-gions of the clusters. In order to assess whether filtering e ff ectsplay a major role in biasing the cluster masses low, we re-runthe modeling by forcing the model mass M to be equal tothe value expected from the mass–richness relation by Gonzalezet al. (2019), and fit for the normalization P by assuming a wideuninformative prior. Once again, to be consistent with previousstudies, we only consider the universal profile case. If the mass–richness relation provides an unbiased estimate of the clustermasses for the measured richnesses, we should then expect therespective SZ model to describe the ACA uv data well, and theinferred estimates of P to be consistent with the nominal valuein Table 2. To facilitate interpretation, we limit the analysis hereto the clusters with a single SZ feature with a strong significance.As shown in Fig. 5, the results are in qualitative agreement withthe overall low-mass trend observed in the mass–richness dis-tribution of the VACA LoCA sample cluster. Nevertheless, it isnot possible to highlight any evident systematic e ff ect commonto all the data points. We thus conclude that the interferomet-ric filtering is unlikely to play a major role in biasing our massreconstruction to lower masses.This of course presumes that the universal pressure model byArnaud et al. (2010) can successfully describe the electron pres-sure distribution of such systems. However, departures from self-similarity, for example due to an actual evolution of the averagepressure profile with the cluster redshift (McDonald et al. 2014) Article number, page 6 of 19. Di Mascolo et al.: MaDCoWS SZ-VACA LoCA
40 60 80 100
Richness M [ M (cid:12) ] Fig. 4.
Mass vs. richness relation for all the MaDCoWS clusters withSZ-based mass estimates. The blue squares correspond to the CARMAMaDCoWS cluster sample from Gonzalez et al. (2019). In solid redare the clusters from this work that have been significantly detected,while open red points denote the clusters MOO J1223 + + + .
25 0 .
50 0 .
75 1 .
00 1 . P / P model0 MOO J0129 − − − − + Fig. 5.
Inferred pressure normalization P when assuming a clustermass derived using the mass–richness relation from Gonzalez et al.(2019) and a universal pressure profile (Arnaud et al. 2010). The ra-tios reported here are normalized by the nominal value for P given inTable 2. As discussed in Sect. 4.1, the observed scatter indicates a truediscrepancy, which could be due to deviations from the Gonzalez et al.(2019) mass–richness scaling or to deviations from the Arnaud et al.(2010) ensemble-average pressure profile. If ACA filtering were driv-ing the mass reconstruction, we would expect a uniformly low value forthe ratio, which is not observed. The error bars for each of the pointsincorporates both statistical uncertainties and scatter intrinsic to MaD-CoWS mass–richness scaling relation. h m s s s RA (J2000)150 kpc − . . . S u rf ace b r i gh t n e ss [ m J yb ea m − ] h m s s s − ◦ − ◦ RA (J2000) D ec ( J ) MOO J0917 − h m s s s RA (J2000)150 kpc − . . . S u rf ace b r i gh t n e ss [ m J yb ea m − ] h m s s s − ◦ RA (J2000) D ec ( J ) MOO J2146 − Fig. 6.
Marginalized posterior for the cluster centroids and dirty im-ages (left and right panels, respectively) of the two VACA LoCA clus-ters characterized by multiple SZ features, MOO J0917 − − . σ ,1 σ , 1 . σ , and 2 σ statistical significance levels of the filtered model withrespect to the map noise RMS. To better highlight the SZ e ff ect, we sub-tract from the visibility data the most significant point-like sources, asin Fig. 3, and apply a 10 k λ taper to the data. or the disturbed state of any of the studied clusters, may signif-icantly a ff ect the mass reconstruction (see Ruppin et al. 2019a,for a cosmological application). The marginalized posterior distribution for the centroids of thegalaxy clusters MOO J0917 − − /
1E 2215.7-0404; Akamatsu et al. 2016). In such cases,however, the electron pressure distribution will deviate signifi-cantly from the average gNFW models adopted in our analysis(Wik et al. 2008; Sembolini et al. 2014; Yu et al. 2015; Ruppinet al. 2019b). In particular, we expect the resulting pressure dis-tribution to be shallower than for the case of a relaxed cluster,hence resulting in an SZ signal more a ff ected by the interfero-metric short-spacing filtering (see discussion in Sect. 3). Simi-larly, non-thermal e ff ects may play a central role in providingpressure support to the system (e.g., Battaglia et al. 2012; Shiet al. 2015; Bi ffi et al. 2016; Ansarifard et al. 2020). As a conse-quence, we might expect the reconstructed masses to be greatlybiased toward values lower than the true ones. Article number, page 7 of 19 & A proofs: manuscript no. madcows h m s s s s − ◦ − ◦ RA (J2000) D ec ( J ) MOO J0917-0700 152025303540455055 G a l a xyd e n s it y [ a r c m i n − ] h m s s s s − ◦ RA (J2000) D ec ( J ) MOO J2146-0320 152025303540455055 G a l a xyd e n s it y [ a r c m i n − ] Fig. 7.
Maps of the color-selected galaxy overdensities aroundMOO J0917 − − Spitzer / IRAC. Overplotted are the contours of the SZ models ofthe two clusters, as in Figure 6. In both cases the elongated morphologyof the galaxy density distribution may support the merger scenario. Thelight gray points denote the positions of the individual IRAC-selectedgalaxies. For display purposes, the galaxy overdensity maps have beenpreliminary smoothed by a Gaussian kernel with standard deviation of ∼
12 arcsec.
On the other hand, the elongation observed in the marginal-ized posterior probability for the cluster centroid may be a con-sequence of the combined e ff ect of an elliptical geometry of thecore region of the ICM and residual contributions from unre-solved sources (see discussion in Sect. 4.3 below). In any case,the non-regular electron pressure distribution would indicate thatthe clusters may be highly disturbed, again inducing a potentialbias in the reconstructed masses.Additional hints about the potential presence of merger activ-ity in the two clusters come from the analysis of the distributionof their member galaxies. In Figure 7, we show Spitzer / IRACcolor-selected galaxy overdensities (a description of the specificcolor-selection strategy employed here can be found in Gonza-lez et al. 2019, and is based on the works by Wylezalek et al.2013, 2014). For both clusters a significant elongation is ob-served in the galaxy density distribution. In the specific caseof MOO J0917 − ff -axiscollision at a large impact parameter with the main cluster (theeastern SZ component). The two mass components should thenbe interpreted as highlighting a disturbed and elongated clustermorphology, rather than the presence of separate subclusters. Onthe other hand, the agreement in both the orientation and positionof the SZ model and galaxy overdensity in MOO J2146 − As already briefly mentioned in the previous section, a possiblesystematic e ff ect that may prevent the proper estimation of thecluster masses from the modeling of ACA data is any residualcontamination from emissions that have not been accounted for.Along with radio synchrotron sources, we expect dusty galaxiesto contribute to the overall confusion noise (see discussion in DiMascolo et al. 2019a). However, although we were able to locateand constrain a number of unresolved components, the lack ofhigh-resolution data (e.g., from the main 12-meter array) mayin fact have limited the identification to the brightest end of thesource population contaminating the SZ signal.On the other hand, the poor resolution and sensitivity do notallow us to separate with reasonable confidence the SZ e ff ectfrom any possible di ff use radio components. Studies by Moravecet al. (2019, 2020) show that a large fraction of the sources be-longing to the population of radio-loud AGNs within the MaD-CoWS clusters exhibit extended morphologies. In this regard,external data may be key to complementing information aboutradio contaminants. Unfortunately, the available radio surveyso ff er only partial coverage of the VACA LoCA sample.In particular, we first checked the NRAO VLA Sky Survey(NVSS; Condon et al. 1998) for possible radio components. Theinspection of the NVSS images of the VACA LoCA fields, how-ever, does not highlight any significant radio sources, point-likeor di ff use.We further inspect the VLA Faint Images of the Radio Sky atTwenty-Centimeters (FIRST; Becker et al. 1995) survey, whichprovides coverage for only five sources from the VACA LoCApilot sample. One low-significance source is found in each of theMOO J0917 − + δ = −
40 in S Band (2-4 GHz),which o ff ers the advantage of sharing the same sky coverage asthe full MaDCoWS sample but at much higher resolution thanNVSS. The first epoch maps reach a depth of ≈ µ Jy RMSon average. Surprisingly, the only sources we were able to con-
Article number, page 8 of 19. Di Mascolo et al.: MaDCoWS SZ-VACA LoCA h m s s s s ◦ RA (J2000) D ec ( J ) . . . . . S u rf ace b r i gh t n e ss [ m J yb ea m − ] Fig. 8.
VLASS map of the radio structure in MOO J1223 + − ). The white crosses denote the position of the most signifi-cant point sources and respective uncertainties from the 68% credibilityinterval around each posterior peak. Regardless of the accuracy in thedetermination of the position of any point-like sources, the low resolu-tion of ACA does not resolve the possible di ff erent contributions fromthe jets and the central galaxy. firm at > σ significance are those also seen in the FIRST dataon MOO J1414 + + + + + + ν aca = . α = − .
85, appropriate for thisredshift range (see van Velzen et al. 2015), and account for boththe VLASS and ACA broadband spectral coverage. The fluxesintegrated over the eastern and western lobes in the VLASS dataare respectively i vlass = .
35 mJy and i vlass = .
11 mJy, corre-sponding to i aca = .
32 mJy and i aca = .
31 mJy at the centralfrequency of our ACA observations. As indicated by the con-tours in Fig. 8, the ACA observations do not resolve the in-dividual radio lobes, and these will manifest in the interfero-metric image of MOO J1223 + .
60 mJy. On the other hand, the peakof the SZ signal expected in the case that the cluster mass ex- actly follows the MaDCoWS mass–richness relation would bearound − .
45 mJy beam − . Furthermore, the sum of the extrapo-lated lobe flux and the SZ signal is consistent with the amplitudeof the point source component identified by the blind search, i ps = . + . − . mJy. Under the assumption of a spatial corre-spondence of the radio source and the SZ centroid, this impliesthat most of the SZ signal from the cluster core could be en-tirely dominated by the emission of the radio lobes and, in turn,dim the measured flux from the radio source. Since the ACA iscapable of probing the SZ signal from only the innermost radiiof MOO J1223 + + As already mentioned in Sect. 3.1, we further test the mass re-construction against di ff erent versions of the gNFW pressureprofiles. In Fig. 9, we provide a direct comparison of the massesand respective e ff ective significance levels for the VACA LoCAclusters with significant detections. The full list with the esti-mates of the cluster masses for all the profiles considered in Ta-ble 2 can be found in Table A.1.Not unexpectedly, the specific value for the cluster mass ishighly dependent on the specific profile assumed to describe thepressure distribution. As shown in the uv radial profile of Fig. 10,most of the SZ flux is not probed by ACA, making it sensitiveonly to the pressure distribution within the inner region of galaxyclusters. This can also be inferred by comparing the values forthe MRS in each observation to 2 × θ using Tables 1 and 3,respectively. This e ff ect couples with the primary beam attenu-ation of the edges of the ACA fields, which drives the charac-teristic radius of the gNFW profile to be on the same of orderof the antenna pattern half width half maximum, and thus a ff ect-ing the mass reconstruction. As a result, the model based on thegNFW parameterization from McDonald et al. (2014) and forthe morphologically disturbed sample in Arnaud et al. (2010)present masses systematically higher than the other profiles, as adirect consequence of their flatter radial trend at small radii. Con-versely, the strongly peaked cool-core profile by Arnaud et al.(2010) allows us to easily fit low-mass (and, then, very compact)cluster models to the observed SZ signal. Nevertheless, as wewere not able to infer any of the parameters defining the gNFWpressure profile in Eq. (2), the small scatter in the e ff ective sig-nificance for each of the di ff erent pressure models does not allowus to select or rule out any of the mass estimates.The impossibility of discriminating between di ff erent gNFWscenarios is an immediate consequence of the limited sensitiv-ity of the ACA observations we are analyzing, along with thelack of information on large angular scales. Figure 10 showsthe uv radial plot for the di ff erent gNFW best-fit models forthe most significantly detected cluster of the VACA LoCA sam-ple, MOO J0129 − Article number, page 9 of 19 & A proofs: manuscript no. madcows − . . . MOO J0129 − . . . . − . . . MOO J0345 − − . . . MOO J1139 − . . . . − MOO J1342 − − . . MOO J1414 + Planck M [ M (cid:12) ] σ e ff − < σ e ff > Fig. 9.
Deviations from average significance levels for the best-detectedgalaxy clusters of the VACA LoCA pilot sample. The points correspondto the mass estimates obtained by assuming di ff erent versions of thegNFW pressure profile. The variations in σ e ff are always less than 3(see Sect. 4), which, according to the Je ff reys model selection criterion,implies that no pressure model is strongly favored over the others forany of the VACA LoCA clusters. The large uncertainties on the massesderived assuming the profile by McDonald et al. (2014) are due to thelarge uncertainties on the respective best-fit gNFW parameters. Perrott et al. (2019), the joint analysis of interferometric mea-surements and lower-resolution, single-dish observations pro-vides a straightforward solution for improving the reconstruc-tion of models of the SZ signal from galaxy clusters. Cosmicmicrowave background experiments designed to detect clustersat arcminute resolution, such as the Atacama Cosmology Tele-scope (ACT; see, e.g., Hilton et al. 2018) or the South Pole Tele-scope (SPT; see, e.g., Bleem et al. 2015, 2020) could fulfill theneeds of complementary large-scale data, and the VACA LoCAclusters are comparable in mass to some of the high-redshift sys-tems detected by those surveys (see Fig. 11). However, the pub-licly available data do not cover the portion of the sky compris-ing the VACA LoCA fields.Additionally, Gonzalez et al. (2019) compares the
Planck mass-redshift relation to the masses inferred for the entire MaD- − − − − R e ( V )[ m J y ] Arnaud et al. 2010, universalArnaud et al. 2010, cool coreArnaud et al. 2010, disturbed
Planck u v distance [ k λ ]− I m ( V )[ m J y ] Fig. 10.
Comparison of the real (top) and imaginary (bottom)parts of ACA point source-subtracted visibilities V = V ( u , v ) forMOO J0129 − uv radial pro-files for the di ff erent flavors of gNFW (Table 2). The data are binned sothat each bin contains the same number of visibilities (here set to 2500for plotting purposes). Before averaging, we shifted the phase center tothe position of the cluster centroid to minimize the ringing e ff ect dueto non-zero phases. As a result, the imaginary part of the visibilities areoverall consistent with zero. Any significant deviations would be symp-tomatic of residual o ff -center point-like sources or asymmetries in thecluster SZ signal that are unaccounted for in the analysis, for example. CoWS sample, and finds that they predominantly lie below themass selection function of
Planck . For the VACA LoCA sam-ple of MaDCoWS clusters, we find that no useful constraint onthe integrated Compton parameter Y can be obtained from the Planck maps, due to beam dilution and limited sensitivity. In allbut the most extreme case the integrated SZ signal for each clus-ters would fall within a single 10 (cid:48) resolution element of
Planck .Extrapolating the fits to the VACA LoCA sample, each membershould have an average Compton Y value (cid:104) Y (cid:105) (cid:46) . × − overan area of 100 square arcminutes, while the RMS noise level inthe Planck maps is ≈ . × − on average (Planck Collabo-ration et al. 2016b). This indicates that the most massive clus-ters in VACA LoCA may be on the order of 1 σ significance inthe Planck maps, while the rest are well below that, and even astacked measurement using the ten members of the pilot samplewould be marginal.It is worth noting that the small range of inferred σ e ff impliesthat ACA is able to provide robust detections of the SZ signalfrom the VACA LoCA sample clusters independent of assump-tions about the underlying pressure electron distribution.
5. Conclusions
In this work, we analyze a pilot sample of ACA observationsof ten high-redshift galaxy clusters representative of the typicalrichness of the MaDCoWS catalog. This has been mainly aimedat directly testing the capability of the ACA in ALMA Band 3for measurements of the SZ signal from high-redshift systems.In summary, our main findings are the following:
Article number, page 10 of 19. Di Mascolo et al.: MaDCoWS SZ-VACA LoCA . . . . z M [ M (cid:12) ] Planck
ACT SPTMaDCoWS VACA LoCA
Fig. 11.
Mass vs. redshift distribution of galaxy clusters in the VACALoCA pilot sample (red circles). The red points denote the VACALoCA clusters with significant detections. For comparison, we includethe mass estimates of previously reported MaDCoWS clusters (bluesquares; Gonzalez et al. 2019) and the samples from the SZ surveys of
Planck (green crosses; Planck Collaboration et al. 2016a), ACT (greentriangles; Marriage et al. 2011; Hasselfield et al. 2013; Hilton et al.2018), and SPT (green diamonds; Bocquet et al. 2019; Huang et al.2020; Bleem et al. 2020). All the MaDCoWS clusters with SZ data arefound to be comparable in mass with the clusters detected by these sur-veys over the same range of redshifts. – The ACA can provide robust and relatively straightforwardvalidation of galaxy cluster identifications through thedetection of the SZ signal from the intracluster gas. We notethat the on-source integration times are typically (cid:46) ff ected by the specific choice of pressure distribution model. – The limited sensitivity and angular dynamic range probedby the observations limit the accuracy of the mass estimates.The mass estimates within r are strongly dependent onthe specific choice of pressure model, as the maximumrecoverable scale in the observations is smaller than thetypical radius within which one would like to probe theintegrated SZ signal, θ (see Tables 1 and 3, respectively). – Related to the point above, a thorough characterization ofthe cluster dynamical state cannot be achieved, as the ACAangular resolution and limited sensitivity do not constrainsmall-scale features in the ICM within the observed galaxyclusters. However, the analysis does reveal two potentiallyexciting merging cluster candidates that merit more detailedfollow-up. – The uv -space analysis of ACA data is crucial for separat-ing the SZ signal from unresolved sources of contamina-tion. However, the reconstruction of a proper and exhaustivemodel is limited by the above-mentioned sensitivity, resolu-tion, and maximum recoverable scale.Data at higher angular resolution than ACA (e.g., from theALMA 12-meter array) would provide a dramatic improvement in the identification and characterization of point-like sourcespopulating the cluster fields. Furthermore, multi-frequency cov-erage of the cluster fields would provide fundamental insightinto, and better constraints on, the spectral properties of any con-taminant source, and thus better disentangle its signal from theunderlying SZ e ff ect.On the other hand, as discussed in Sect. 4.4, the possibil-ity of complementing interferometric observations with single-dish measurements of the same targets will be key to gaininga better description of the electron pressure distribution out tolarge scales, and hence a more accurate reconstruction of thecluster masses. However, the scales recoverable with current SZsurvey instruments are limited to greater than 1 arcminute at90 GHz, leaving a gap with little to no overlap in Fourier modesprobed in such joint analyses (see discussion in Di Mascolo et al.2019a). An exciting advance could be obtained using a futurelarge single-dish telescope with at least three times the size ofthe ACA and ALMA primary mirrors and a wide ( > ◦ ) field ofview, such as the Atacama Large Aperture Submillimeter Tele-scope (AtLAST; Klaassen et al. 2019).Finally, ALMA Bands 1 (35-51 GHz; Di Francesco et al.2013; Huang et al. 2016) and 2 (67-116 GHz; Yagoubov et al.2020) will further increase the maximum recoverable scale overthe next few years, and thus the sensitivity of ALMA and theACA to di ff use, low surface brightness signals on arcminutescales. Acknowledgments
We thank the anonymous referee for the thoughtful sug-gestions and comments that helped improving this work.This paper makes use of the following ALMA data:ADS / JAO.ALMA / NRAO and NAOJ. EC and RS acknowledge partialsupport by the Russian Science Foundation grant 19-12-00369.The work of PRME and DS was carried out at the Jet PropulsionLaboratory, California Institute of Technology, under a contractwith NASA.
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Appendix A: Mass estimates
Table A.1 reports the inferred cluster masses when employingthe di ff erent gNFW models proposed in Arnaud et al. (2010),Planck Collaboration et al. (2013), and McDonald et al. (2014).A summary of the profile parameters is provided in Table 2. Appendix B: uv plots and dirty images We provide here the uv radial plots of the data and respectivegNFW models for all the VACA LoCA clusters (Fig. C.1). Asdiscussed in Sect. 4, all the model profiles show a fairly goodagreement with data over the range of probed angular scales,while being a ff ected by a large scatter at short baselines dueto the lack of large-scale information. MOO J0345 − − uv scales, while the data points for MOO J2146 − ff set with respect to the models. These may arise dueto o ff -center SZ components unaccounted for by the model, ordue to extended (positive) emission. However, in the case ofMOO J0345 − σ . Onthe other hand, the SZ signal from both MOO J0917 − − ff erences between the modeland residual dirty images generated with di ff erent gNFW mod-els, we consider here only the case of a universal pressure profile(Arnaud et al. 2010). We again note that all the images reportedhere are for illustrative purposes only, and were not used in ouranalysis. Appendix C:
Spitzer /IRAC galaxy overdensities
For comparison, we show in Fig. C.3 the SZ model con-tours for all the VACA LoCA clusters with either a firm or amarginal detection of their SZ signature overlaid on the maps oftheir respective color-selected galaxy density distributions from
Spitzer / IRAC (see Sect. 4.2 and Figure 7). For the sake of clar-ity, we do not plot the secondary negative lobes arising due tothe non-Gaussian pattern of the interferometric beam.
Article number, page 13 of 19 & A proofs: manuscript no. madcows C l u s t e rI D z pho t λ M σ e ff M σ e ff M σ e ff M σ e ff M σ e ff –– ( M (cid:12) ) – ( M (cid:12) ) – ( M (cid:12) ) – ( M (cid:12) ) – ( M (cid:12) ) – un i v e r s a l c oo l - c o r e d i s t u r b e d P l an ck M c D on a l d e t a l . S i gn i fi c an t d e t ec ti on M OO J − . + . − . ± . + . − . . . + . − . . . + . − . . . + . − . . . + . − . . M OO J − . + . − . ± . + . − . . . + . − . . . + . − . . . + . − . . . + . − . . M OO J − . + . − . ± . + . − . . . + . − . . . + . − . . . + . − . . . + . − . .
41 2 . + . − . . + . − . . + . − . . + . − . . + . − . M OO J − . + . − . ± . + . − . . . + . − . . . + . − . . . + . − . . . + . − . . M OO J − . + . − . ± . + . − . . . + . − . . . + . − . . . + . − . . . + . − . . M OO J + . + . − . ± . + . − . . . + . − . . . + . − . . . + . − . . . + . − . . M OO J − . + . − . ± . + . − . . . + . − . . . + . − . . . + . − . . . + . − . .
94 2 . + . − . . + . − . . + . − . . + . − . . + . − . N on - d e t ec ti on M OO J + . + . − . ± . + . –0 . + . − . . . + . − . . . + . − . . . + . – M OO J + . + . − . ± . + . − . . . + . − . . . + . − . . . + . − . . . + . − . . M OO J + . + . − . ± . + . − . . . + . − . . . + . − . . . + . − . . . + . − . . T a b l e A . . E s ti m a t e d m a ss e s o f t h e VA C A L o C A s a m p l ec l u s t e r s . S ee S ec t . f o r m o r e d e t a il s a bou tt h ee ff ec ti v e s i gn i fi ca n cee s ti m a t e σ e ff . T h e t w o m a ss v a l u e s p r ov i d e d f o r M OO J − a nd M OO J − c o rr e s pond t o t h e m a ss e s o f eac ho f t h e i nd i v i du a l S Z c o m pon e n t s d e t ec t e d . Article number, page 14 of 19. Di Mascolo et al.: MaDCoWS SZ-VACA LoCA MOO J0129 MOO J0903 + MOO J1139 + MOO J1342 + MOO J2146 + u v distance [ k ] A m p lit ud e o f c o m p l e xv i s i b iliti e s [ m J y ] u v distance [ k ] A m p lit ud e o f c o m p l e xv i s i b iliti e s [ m J y ] Arnaud et al. 2010, universalArnaud et al. 2010, cool coreArnaud et al. 2010, disturbed
Planck u v distance [ k ] A m p lit ud e o f c o m p l e xv i s i b iliti e s [ m J y ] Arnaud et al. 2010, universalArnaud et al. 2010, cool coreArnaud et al. 2010, disturbed
Planck u v distance [ k ] A m p lit ud e o f c o m p l e xv i s i b iliti e s [ m J y ] Arnaud et al. 2010, universalArnaud et al. 2010, cool coreArnaud et al. 2010, disturbed
Planck u v distance [ k ] A m p lit ud e o f c o m p l e xv i s i b iliti e s [ m J y ] Arnaud et al. 2010, universalArnaud et al. 2010, cool coreArnaud et al. 2010, disturbed
Planck MOO J0129 MOO J0903 + MOO J1139 + MOO J1342 + MOO J2146 + u v distance [ k ] A m p lit ud e o f c o m p l e xv i s i b iliti e s [ m J y ] Fig. C.1.
Comparison of the uv profiles of all the gNFW flavors adopted in our work. The data are binned so that each bin contains the same numberof visibilities (here set to 2500 for plotting purposes). Before being averaged, the phase center was shifted to the position of cluster centroid tominimize the ringing e ff ect due to non-zero phases. A model profile was not plotted for MOO J0903 + & A proofs: manuscript no. madcows h m s s s − ◦ RA (J2000) D ec ( J ) MOO J0129 − h m s s s RA (J2000) h m s s s RA (J2000) − . − . . . . S u rf ace b r i gh t n e ss [ m J yb ea m − ] h m s s s s s RA (J2000) D ec ( J ) MOO J0345 h m s s s s s RA (J2000) h m s s s s s RA (J2000) . . . . . S u rf ace b r i gh t n e ss [ m J yb ea m ] h m s s s s s RA (J2000) D ec ( J ) MOO J0345 h m s s s s s RA (J2000) h m s s s s s RA (J2000) . . . . . S u rf ace b r i gh t n e ss [ m J yb ea m ] h m s s s s s RA (J2000) D ec ( J ) MOO J0345 h m s s s s s RA (J2000) h m s s s s s RA (J2000) . . . . . S u rf ace b r i gh t n e ss [ m J yb ea m ] h m s s s s s RA (J2000) D ec ( J ) MOO J0345 h m s s s s s RA (J2000) h m s s s s s RA (J2000) . . . . . S u rf ace b r i gh t n e ss [ m J yb ea m ] h m s s s s − ◦ − ◦ RA (J2000) D ec ( J ) MOO J0917 − h m s s s s RA (J2000) h m s s s s RA (J2000) − . − . . . . S u rf ace b r i gh t n e ss [ m J yb ea m − ] Fig. C.2.
Dirty images of the raw (left), model (center), and residual (right) data of VACA LoCA observations. All the images are generatedby applying a multi-frequency naturally weighted, imaging scheme, and extend out to where the ACA primary beam reaches 20% of its peakamplitude. To better highlight the SZ features in each field a 10 k λ taper is applied, but without correction for the primary beam attenuation.Furthermore, as in Fig. 3, the most significant point-like sources from the raw interferometric data are removed.Article number, page 16 of 19. Di Mascolo et al.: MaDCoWS SZ-VACA LoCA h m s s s s − ◦ RA (J2000) D ec ( J ) MOO J1139 − h m s s s s RA (J2000) h m s s s s RA (J2000) − . − . . . . S u rf ace b r i gh t n e ss [ m J yb ea m − ] h m s m s s s ◦ RA (J2000) D ec ( J ) MOO J1223 + h m s m s s s RA (J2000) h m s m s s s RA (J2000) − . − . . . . S u rf ace b r i gh t n e ss [ m J yb ea m − ] h m s s s s − ◦ RA (J2000) D ec ( J ) MOO J1342 − h m s s s s RA (J2000) h m s s s s RA (J2000) − . − . . . . S u rf ace b r i gh t n e ss [ m J yb ea m − ] (continued from Fig. C.2) Article number, page 17 of 19 & A proofs: manuscript no. madcows h m s s s s ◦ RA (J2000) D ec ( J ) MOO J1414 + h m s s s s RA (J2000) h m s s s s RA (J2000) − . − . . . . S u rf ace b r i gh t n e ss [ m J yb ea m − ] h m s s s s − ◦ RA (J2000) D ec ( J ) MOO J2146 − h m s s s s RA (J2000) h m s s s s RA (J2000) − . − . . . . S u rf ace b r i gh t n e ss [ m J yb ea m − ] h m s s s ◦ RA (J2000) D ec ( J ) MOO J2147 + h m s s s RA (J2000) h m s s s RA (J2000) − . − . . . . S u rf ace b r i gh t n e ss [ m J yb ea m − ] (continued from Fig. C.2) Article number, page 18 of 19. Di Mascolo et al.: MaDCoWS SZ-VACA LoCA h m s s s s s − ◦ RA (J2000) D ec ( J ) MOO J0129-1641 152025303540455055 G a l a xyd e n s it y [ a r c m i n − ] h m s s s s s − ◦ RA (J2000) D ec ( J ) MOO J0345-2913 152025303540455055 G a l a xyd e n s it y [ a r c m i n − ] h m s s s s − ◦ − ◦ RA (J2000) D ec ( J ) MOO J0917-0700 152025303540455055 G a l a xyd e n s it y [ a r c m i n − ] h m s s s s − ◦ RA (J2000) D ec ( J ) MOO J1139-1706 152025303540455055 G a l a xyd e n s it y [ a r c m i n − ] h m s m s s s ◦ RA (J2000) D ec ( J ) MOO J1223+2420 152025303540455055 G a l a xyd e n s it y [ a r c m i n − ] h m s s s s − ◦ RA (J2000) D ec ( J ) MOO J1342-1913 152025303540455055 G a l a xyd e n s it y [ a r c m i n − ] h m s s s s ◦ RA (J2000) D ec ( J ) MOO J1414+0227 152025303540455055 G a l a xyd e n s it y [ a r c m i n − ] h m s s s s − ◦ RA (J2000) D ec ( J ) MOO J2146-0320 152025303540455055 G a l a xyd e n s it y [ a r c m i n − ] h m s s s s s ◦ RA (J2000) D ec ( J ) MOO J2147+1314 152025303540455055 G a l a xyd e n s it y [ a r c m i n − ] Fig. C.3.
Spitzer //