A Measurement of the Kinetic Sunyaev-Zel'dovich Signal Toward MACS J0717.5+3745
Jack Sayers, Tony Mroczkowski, Michael Zemcov, Phil M. Korngut, James Bock, Esra Bulbul, Nicole G. Czakon, Eiichi Egami, Sunil R. Golwala, Patrick M. Koch, Kai-Yang Lin, Adam Mantz, Sandor M. Molnar, Leonidas Moustakas, Elena Pierpaoli, Tim D. Rawle, Erik D. Reese, Marie Rex, Jennifer A. Shitanishi, Seth Siegel, Keiichi Umetsu
DDraft version December 16, 2013
Preprint typeset using L A TEX style emulateapj v. 5/2/11
A MEASUREMENT OF THE KINETIC SUNYAEV-ZEL’DOVICH SIGNAL TOWARD MACS J0717.5+3745
J. Sayers , T. Mroczkowski , M. Zemcov , P. M. Korngut , J. Bock , E. Bulbul , N. G. Czakon ,E. Egami , S. R. Golwala , P. M. Koch , K.-Y. Lin , A. Mantz , S. M. Molnar , L. Moustakas , E. Pierpaoli ,T. D. Rawle , E. D. Reese , M. Rex , J. A. Shitanishi , S. Siegel , & K. Umetsu Draft version December 16, 2013
ABSTRACTWe report our analysis of MACS J0717.5+3745 using 140 and 268 GHz Bolocam data collected atthe Caltech Submillimeter Observatory. We detect extended Sunyaev-Zel’dovich (SZ) effect signal athigh significance in both Bolocam bands, and we employ
Herschel -SPIRE observations to subtract thesignal from dusty background galaxies in the 268 GHz data. We constrain the two-band SZ surfacebrightness toward two of the sub-clusters of MACS J0717.5+3745: the main sub-cluster (named C),and a sub-cluster identified in spectroscopic optical data to have a line-of-sight velocity of +3200 kms − (named B). We determine the surface brightness in two separate ways: via fits of parametric modelsand via direct integration of the images. For both sub-clusters, we find consistent surface brightnessesfrom both analysis methods. We constrain spectral templates consisting of relativistically correctedthermal and kinetic SZ signals, using a jointly-derived electron temperature from Chandra and
XMM-Newton under the assumption that each sub-cluster is isothermal. The data show no evidence fora kinetic SZ signal toward sub-cluster C, but they do indicate a significant kinetic SZ signal towardsub-cluster B. The model-derived surface brightnesses for sub-cluster B yield a best-fit line-of-sightvelocity of v z = +3450 ±
900 km s − , with (1 − Prob[ v z ≥ . × − (4 . σ away from 0 fora Gaussian distribution). The directly integrated sub-cluster B SZ surface brightnesses provide abest-fit v z = +2550 ± − , with (1 − Prob[ v z ≥ . × − (2 . σ ). Subject headings: galaxies: clusters: intracluster medium — galaxies: clusters: individual: (MACSJ0717.5+3745) INTRODUCTION
Measurements of large-scale peculiar velocities providea direct probe of cosmological models and can be usedto place constraints on parameters that are highly de-generate and/or unconstrained via other cosmologicalprobes, such as measurements of primary CMB fluctu-ations (Bennett et al. 2012; Hinshaw et al. 2012; PlanckCollaboration et al. 2013b,c) and supernovae distancemeasurements (Conley et al. 2011; Suzuki et al. 2012).Specifically, these peculiar velocities depend on the prop-erties and distributions of large-scale structure, alongwith the characteristics of dark energy and the behav-ior of gravity on the corresponding length scales. Con- Division of Physics, Math, and Astronomy, California Insti-tute of Technology, 1200 East California Blvd, Pasadena, CA91125 Norris Foundation CCAT Postdoctoral Fellow Jet Propulsion Laboratory, 4800 Oak Grove Drive,Pasadena, CA 91109 NASA Einstein Postdoctoral Fellow Harvard-Smithsonian Center for Astrophysics, 60 GardenStreet, Cambridge, MA 02138 Steward Observatory, University of Arizona, 933 NorthCherry Avenue, Tucson, AZ 85721 Institute of Astronomy and Astrophysics, Academia Sinica,P.O. Box 23-141, Taipei 10617, Taiwan Kavli Institute for Cosmological Physics, University ofChicago, 5640 South Ellis Avenue, Chicago, IL 60637 LeCosPA Center, National Taiwan University, Taipei 10617,Taiwan Department of Physics and Astronomy, University of South-ern California, 3620 McClintock Avenue, Los Angeles, CA 90089 Department of Physics and Astronomy, University of Penn-sylvania, 209 South 33rd Street, Philadelphia, PA 19104 [email protected] sequently, peculiar velocity measurements for large num-bers of objects can probe the redshift evolution of theproperties of dark energy (Bhattacharya & Kosowsky2008) and also distinguish between dark energy and mod-ified gravity models (Kosowsky & Bhattacharya 2009).In addition, measurements of an extremely large peculiarvelocity for a single object (e.g., 1E0657-56, also knownas the bullet cluster) can be used to directly test the va-lidity of standard cosmological models (Hayashi & White2006; Lee & Komatsu 2010; Thompson & Nagamine2012).In the local universe, line-of-sight peculiar velocitiescan be measured using a combination of spectroscopyand distance measurements via the extragalactic distanceladder, generally using the relation described by Tully& Fisher (1977). Such measurements have been usedto constrain cosmological parameters like the total mat-ter density Ω m and the normalization of density fluctu-ations σ , generally finding good agreement with othercosmological probes (e.g., Feldman et al. 2010; Nusser& Davis 2011; Ma et al. 2012). Unfortunately, uncer-tainties in the extragalactic distance ladder are propor-tional to distance, therefore preventing the applicationof these methods outside the local universe. In contrast,the kinetic Sunyaev-Zel’dovich (SZ) effect provides a di-rect measurement of the line-of-sight peculiar velocity ofthe distribution of hot electrons within galaxy clusters(Sunyaev & Zel’dovich 1972, See Section 2). In addi-tion, the surface brightness of the kinetic SZ signal isindependent of redshift, depending only on the electronoptical depth and line-of-sight peculiar velocity. Conse-quently, many groups have performed detailed studies of a r X i v : . [ a s t r o - ph . C O ] D ec the cosmological constraints that would be possible withlarge-scale peculiar velocity surveys using the kinetic SZsignal (e.g., Bhattacharya & Kosowsky 2008; Kosowsky& Bhattacharya 2009; Mak et al. 2011).Despite the great promise of kinetic SZ surveys, mea-surements of the kinetic SZ signal have proven to be asignificant observational challenge. Over the past twodecades, several attempts have been made to detect thekinetic SZ signal toward a variety of individual massiveclusters. These observational efforts have used a rangeof instrumentation, including: the dedicated multi-bandphotometer SuZIE and its successors (Holzapfel et al.1997; Benson et al. 2003), multi-band data collected froma range of facilities (Kitayama et al. 2004), the mod-erate resolution spectroscopic receiver Z-Spec (Zemcovet al. 2012), and the two-band photometric imaging cam-era Bolocam (Mauskopf et al. 2012; Mroczkowski et al.2012). None of these observations have made a high-significance detection of the kinetic SZ signal, and thederived uncertainties on the line-of-sight peculiar veloc-ities have not improved significantly from the first mea-surements with SuZIE, at least in part because none ofthe subsequent measurements have used instrumentationspecifically designed to detect the kinetic SZ signal.Recently, data from the WMAP and
Planck satelliteshave been used to place upper limits on bulk flows andrms variations in peculiar velocities via the kinetic SZsignal (Osborne et al. 2011; Planck Collaboration et al.2013d). In addition, Hand et al. (2012) used a com-bination of Atacama Cosmology Telescope (ACT) andSloan Digital Sky Survey III data to constrain the meanpairwise momentum of clusters using a kinetic SZ signa-ture that is inconsistent with noise at a confidence levelof 99.8%. Furthermore, upper limits on the kinetic SZpower spectrum measured by the South Pole Telescope(SPT) have been used to inform cosmological simulationsand to place constraints on the reionization history of theuniverse (Reichardt et al. 2012; Zahn et al. 2012).One of the strongest hints of a kinetic SZ detection waspresented in Mroczkowski et al. (2012, hereafter M12)toward the massive cluster MACS J0717.5+3745 usingBolocam measurements at 140 and 268 GHz. Motivatedby this result, we have collected a significant amountof additional 268 GHz Bolocam data toward this clus-ter. The results we obtain using this additional, deeperdata are presented in this manuscript, which is orga-nized as follows. In Section 2 we present the SZ effectand in Section 3 we describe previous analyses of MACSJ0717.5+3745. In Section 4 we provide the details of ourdata reduction. We describe our model of the SZ signaltoward MACS J0717.5+3745 in Section 5 and providethe corresponding constraints on the two-band SZ sur-face brightnesses of the cluster in Sections 6 and 7. InSection 8 we give the line-of-sight peculiar velocity con-straints derived from these surface brightnesses, in Sec-tion 9 we put these results in a broader context, and inSection 10 we briefly summarize our analysis. We alsoinclude an Appendix which fully details our treatmentof the cosmic infrared background (CIB) in the 268 GHzdata. THE SZ EFFECT
When a massive galaxy cluster is moving with respectto the rest frame of the CMB, the Doppler-induced spec- tral distortion of the CMB due to the bulk motion of theelectrons in the intra-cluster medium (ICM) is describedby the kinetic SZ effect (e.g., Sunyaev & Zel’dovich 1972;Birkinshaw 1999; Carlstrom et al. 2002). The change inCMB temperature due to the kinetic SZ effect is givenby ∆ T CMB T CMB = − v z c τ e , (1)where v z is the ICM peculiar velocity along the line-of-sight, c is the speed of light, and τ e is the total electronoptical depth τ e = (cid:90) n e σ T dl, (2)for an electron density n e integrated along the line ofsight dl ( σ T is the Thompson cross section). We note thata positive peculiar velocity results in a negative temper-ature change, under the convention that a Doppler shifttoward higher redshift corresponds to a positive value of v z . In addition, we note that there are small relativisticcorrections to the kinetic SZ signal (e.g., Nozawa et al.1998a; Sazonov & Sunyaev 1998; Nozawa et al. 2006;Chluba et al. 2012).There is also a thermal SZ effect, which describes theCompton scattering of CMB photons off of high energyelectrons in the ICM of massive clusters (e.g., Sunyaev &Zel’dovich 1972; Rephaeli 1995a; Birkinshaw 1999; Carl-strom et al. 2002). Specifically, the change in CMB tem-perature due to the thermal SZ effect is given by∆ T CMB T CMB = f ( ν, T e ) y, (3)where f ( ν, T e ) encodes the frequency ν dependence, in-cluding relativistic corrections that depend on the elec-tron temperature T e (e.g., Rephaeli 1995b; Itoh et al.1998; Nozawa et al. 1998b; Itoh & Nozawa 2004; Chlubaet al. 2012) and y = (cid:90) n e σ T k B T e m e c dl (4)( k B is Boltzmann’s constant and m e is the electronmass). In the limit of an isothermal distribution, y isdirectly and linearly proportional to the total electronoptical depth τ e . PREVIOUS ANALYSES OF MACS J0717.5+3745
MACS J0717.5+3745, located at z = 0 .
55, was dis-covered as part of the Massive Cluster Survey (MACS,Ebeling et al. 2001, 2007), and is extremely massive anddynamically disturbed. As such, it has been the fo-cus of many studies at a range of wavelengths, and ithas been chosen as part of the six-cluster Hubble SpaceTelescope Frontier Fields program. Radio observationshave shown that MACS J0717.5+3745 hosts the mostpowerful radio halo known (Edge et al. 2003; van Weerenet al. 2009; Bonafede et al. 2009), and strong lensing datahave shown that MACS J0717.5+3745 has the largestknown Einstein radius (Zitrin et al. 2009; Meneghettiet al. 2011; Waizmann et al. 2012). From both the galaxydistribution (Ebeling et al. 2004), and weak lensing stud-ies (Jauzac et al. 2012; Medezinski et al. 2013), MACS AC D B
HST F814WChandraLimousin et al
Fig. 1.—
False-color composite image of MACS J0717.5+3745with the lensing results of Limousin et al. (2012) in blue, the HubbleSpace Telescope image using the F814W filter in green, and the
Chandra
X-ray image in red. The blue contours show the Limousinet al. (2012) result on a linear scale, and clearly indicate the foursub-clusters labeled A through D, with white Xs marking the sub-cluster positions determined by Ma et al. (2009) from the galaxydistribution.
J0717.5+3745 also appears to be part of a large, extendedfilamentary structure. In addition, it has the highest X-ray temperature among all of the clusters in the MACScatalog (Ebeling et al. 2007).Ma et al. (2009) performed a joint analysis using X-raydata, along with the measured galaxy positions and red-shifts, and identified four distinct sub-clusters in MACSJ0717.5+3745, from N to S labeled as A, B, C, and D(see Figure 1). An independent strong lensing analysisdescribed in Limousin et al. (2012) also identified foursub-clusters, with similar positions to the ones given inMa et al. (2009). Both analyses found sub-cluster C tobe the most massive system, and Ma et al. (2009) de-termined that sub-cluster C is probably the highly dis-turbed core of the main system. Sub-clusters B and Dare assumed to be relatively intact cores of systems thatare merging along a direction close to the line-of-sight.In particular, sub-cluster B is coincident with an X-raytemperature that is colder than the surrounding regions,indicating that its core has not been highly disruptedby the merger. From the spectroscopic data, Ma et al.(2009) found that sub-cluster B has a line-of-sight veloc-ity that differs from the other components by approxi-mately 3000 km s − . Further indications of this largeline-of-sight velocity for sub-cluster B were presented inM12, who found a similar best-fit velocity by using X-rayand SZ measurements to constrain the kinetic SZ signaltoward that sub-cluster, although the statistical signif-icance of their kinetic SZ constraint on the velocity ismodest ( (cid:39) σ ). This wide range of observational datatoward MACS J0717.5+3745 is therefore converging towhat appears to be a coherent picture of this complexsystem. DATA REDUCTION
Bolocam
We observed MACS J0717.5+3745 with Bolocam fromthe Caltech Submillimeter Observatory (CSO) for a totalof 12.5 hours at 140 GHz and for a total of 27.3 hours at268 GHz, where the effective band centers are quoted fora CMB spectrum. Compared to the previous Bolocamanalysis presented in M12, this represents an additional19.3 hours of data collected at 268 GHz in 2012 Decem-ber. In contrast to the original 8.0 hours of 268 GHzintegration used in M12, much of which was collected inpoor observing conditions with a 225 GHz optical depth τ > .
10, most of the additional 19.3 hours of 268 GHzintegration was obtained with τ (cid:39) .
05. This ad-ditional data was therefore collected during the lowestopacity conditions generally available from the CSO.The Bolocam instrument has an 8 (cid:48) diameter circularfield of view (FOV), and point-spread functions (PSFs)that are approximately Gaussian with full-widths athalf-maximums (FWHMs) equal to 58 (cid:48)(cid:48) and 31 (cid:48)(cid:48) at 140and 268 GHz, respectively (Glenn et al. 2002; Haiget al. 2004). All of our Bolocam observations of MACSJ0717.5+3745 involved scanning the CSO in a Lissajouspattern with an RMS velocity of approximately 4 (cid:48) /sec.The details of our data reduction are given elsewhere(Sayers et al. 2011, M12), and we briefly summarize ourprocedure below.First, we obtain pointing corrections accurate to 5 (cid:48)(cid:48) us-ing frequent observations of nearby quasars, and we ob-tain an absolute flux calibration accurate to 5% and 10%at 140 and 268 GHz, respectively, using observations ofUranus and Neptune (Griffin & Orton 1993; Sayers et al.2012). We note that Hasselfield et al. (2013) recentlydetermined the brightness temperature of Uranus to be106 . ± . WMAP satellite. Also, Planck Collaboration et al.(2013a) recently determined the brightness temperatureof Uranus to be 108 . ± . Planck data. Our calibration model assumes a brightness tem-perature of 106 . ± . WMAP
94 GHz brightness measurementspresented in Weiland et al. (2011) using the model ofGriffin & Orton (1993). This model predicts the bright-ness temperature of Uranus to increase with decreasingfrequency. As a result, the ACT and
Planck measure-ments imply a best-fit 140 GHz brightness temperaturethat is approximately 2.5 K higher than our assumedvalue of 106.6 K. However, this difference is comparableto the ACT and
Planck measurement uncertainties, andit is well below our estimated 5% flux calibration uncer-tainty at 140 GHz. We therefore have not updated ourcalibration model. Furthermore, we note that the accu-racy of the ACT and
Planck
Uranus brightness temper-atures is 2 − Planck would thus nothave a significant effect on our overall calibration uncer-tainty, which itself is already sub-dominant to measure-ment uncertainties (see Table 2). Finally, we note thatour 10% flux calibration at 268 GHz is limited largely byatmospheric fluctuations, and therefore a more accurateUranus brightness temperature at that frequency wouldhave no effect on our overall calibration uncertainty.To remove atmospheric fluctuations from the data, wefirst subtract a template of the common mode signal overthe FOV, and we then high-pass filter (HPF) the time-stream data at 250 and 500 mHz at 140 and 268 GHz, re-spectively. The large amplitude of the atmospheric fluc-tuations in the 268 GHz data necessitates this more ag-gressive HPF, and this filtering represents a slight changefrom the M12 analysis, which used a 250 mHz HPF forboth datasets. We used a scan speed of (cid:39) (cid:48) /sec for ourobservations, and the HPFs at 250 or 500 mHz thereforecorrespond to angular scales of 16 (cid:48) and 8 (cid:48) , respectively.Consequently, the maximum angular scale preserved byour filtering is largely set by the common mode sub-traction over Bolocam’s 8 (cid:48) FOV. Because our processingremoves astronomical signals with angular sizes largerthan the 8 (cid:48)
FOV, we determine the map-space transferfunction at each wavelength by reverse-mapping and pro-cessing an image template through the entire reductionpipeline. We estimate the instrumental and atmosphericnoise in our images by forming 1000 separate jackkniferealizations of the data, where a randomly selected sub-set of half the single observations is multiplied by − (cid:48) × (cid:48) , to constrain parametric models of the as-tronomical signals (see Section 5). This analysis involvesconvolving the model with the signal transfer functionof the data processing and the Bolocam PSF. To de-termine best-fit parameters for a given model, we usethe generalized least squares fitting algorithm MPFIT-FUN (Markwardt 2009) under the simplifying assump-tion that the map noise covariance matrix is diagonal.We have demonstrated that this fitting method producesunbiased estimates of the best-fit parameter values (Say-ers et al. 2011), although in some cases it does producea slightly biased estimate of the uncertainties on thesebest-fit parameters. Therefore, to fully account for all ofthe subtleties of our noise, we derive all of the parameter uncertainties via the spread of best-fit values we obtainfrom applying the same fitting algorithm to a sample of1000 noise plus signal realizations. Each noise plus signalrealization is generated by adding a noise realization tothe best-fit model found for the real data.We also deconvolve the transfer function of the dataprocessing to obtain unbiased images after first reduc-ing the image to a maximum size of 10 (cid:48) × (cid:48) to preventsignificant amplification of the noise on the largest angu-lar scales. One subtlety in this process is the fact thatthe signal transfer function is equal to 0 at an angularwavenumber of 0 (i.e., the DC signal level of the im-age is unconstrained). We therefore use the parametricmodel fits to constrain the DC signal level, as describedin Section 6.1. As a result, the deconvolved images havesome model dependence. Consequently, to ensure thatthe uncertainties on the model accurately represent theunderlying uncertainties on the data, both for the modelfits alone and for the results derived from the deconvolvedimages, the model must provide an acceptable fit quality.By requiring a model with an acceptable fit quality, wealso ensure that the results derived from model fits willbe consistent with those derived from the deconvolvedimages. To estimate the noise in the deconvolved im-ages, we also deconvolve the transfer function from eachof the 1000 noise realizations. Chandra
Our analysis of the
Chandra
X-ray exposures of MACSJ0717.5+3745 is nearly identical to the analysis describedin M12, and we briefly summarize the main aspects be-low. As in M12, we utilize both
Chandra
ACIS-I X-rayobservations of MACS J0717.5+3745 (Obs IDs 1655 and4200), for a total exposure time of 81 ksec (see Reeseet al. (2010) for the reduction details). From these X-raydata we compute pseudo-pressure P e = n e k B T e (cid:39) (cid:115) π (1 + z ) S X l Λ ee ( T e , Z ) k B T e , (5)where S X is the X-ray surface brightness S X = 14 π (1 + z ) (cid:90) n e Λ ee ( T e , Z ) dl, (6) l is the effective line-of-sight extent of the ICM, andΛ ee ( T e , Z ) is the X-ray emissivity as a function of T e andmetallicity Z . To generate pseudo-pressure maps fromthe Chandra images, we first bin the data using contbin (Sanders 2006). We construct the pseudo-pressure mapsfrom T e maps generated by computing T e within each binand n e maps computed from the X-ray surface brightness(see Equation 5). To rescale the pseudo-pressure mapsto units of Compton- y , we need to determine the valueof l (which in M12 was done using 31 GHz SZA data,but in practice is left as a free parameter in all of ourfits). This X-ray template for the thermal SZ signal,which is simply a rescaling of the X-ray pseudo-pressuremap, is called a “pseudo Compton- y map” throughoutthis manuscript. For consistency with M12, we employthe same pseudo Compton- y map that was generated forthat analysis. We note that this map was generated us-ing CIAO version 4.3 and calibration database (CALDB)version 4.4.5 (Fruscione et al. 2006). Fig. 2.—
Thumbnails of the pseudo Compton- y maps we derive from the Chandra
X-ray data. From left to right, the thumbnails show thebest-fit map and two realizations based on the X-ray measurement uncertainties. The top row shows the maps at 140 GHz, and the bottomrow shows the maps at 268 GHz. In both cases, the maps are convolved with the Bolocam PSF at the respective frequency. The whitecontours are spaced by 0.10 MJy sr − , with solid representing positive values and dashed representing negative values. The 1 (cid:48) diameterapertures centered on sub-cluster C (lower left) and sub-cluster B (upper right) are shown in green. Note that the approximate conversionfactor from MJy sr − to y is − × − at 140 GHz and +1 × − at 268 GHz. New for this analysis compared to M12, we also gen-erate 20 realizations of the pseudo Compton- y map thatare fluctuated by the X-ray measurement uncertaintieson T e , which dominate the uncertainty of the pseudo-pressure maps (see Figure 2). We note that, in addi-tion to measurement uncertainties, the pseudo Compton- y maps are also subject to possible systematic errors dueto gas clumping within the ICM. Clumping is defined as C = (cid:104) n e (cid:105)(cid:104) n e (cid:105) , (7)and from the equations listed above, we see that thepseudo-Compton- y maps are sensitive to √ C . Typicalclumping factors of C (cid:39) . − . R are ex-pected from simulations (e.g., Zhuravleva et al. 2013).Assuming clumping is uncorrelated with temperaturevariations, clumping is sub-dominant to the variations in-cluded in the input temperature maps, and we thereforedo not include any additional uncertainty from clumpingin our 20 realizations of the pseudo Compton- y maps.In addition, we note that the average systematic trendfor X-ray surface brightness to be boosted by clumping ismitigated by the fact that the amplitude of the Compton- y maps is constrained by the SZ data via the factor of l . We also use the Chandra data to constrain the electrontemperature T e within two 1 (cid:48) diameter regions centeredon sub-clusters B and C (these temperatures are appliedto our analysis in Section 8). In contrast to the pseudoCompton- y maps, which we obtain via the same reduc-tion that was used in M12, we constrain these valuesof T e using maps generated with CIAO version 4.5 and calibration database (CALDB) version 4.5.6 (Fruscioneet al. 2006). We fit the temperatures and metallicities ofthe regions in XSPEC (Dorman & Arnaud 2001) usingthe Astrophysical Plasma Emission Code (APEC) model(Smith et al. 2001). We find T e = 13 . +1 . − . keV for sub-cluster B and T e = 24 . +7 . − . keV for sub-cluster C, usingthe extended C-statistic to determine the temperaturelikelihoods. XMM-Newton
To better constrain the electron temperatures of sub-clusters B and C, we make use of (cid:39)
200 ksec of
XMM-Newton
X-ray data toward MACS J0717.5+3745.These data became public in 2012 October (Obs Ids;0672420101, 0672420301, 0672420301), and thereforewere not included in M12. We perform the
XMM
MOSdata processing and background modeling with the
XMM
Extended Source Analysis Software (
ESAS ) using themethods reported in Kuntz & Snowden (2008) and Snow-den et al. (2008). The details of our
XMM analysis aredescribed fully in Bulbul et al. (2012), and we provide asummary and discuss important differences here.Our
XMM-Newton data analysis includes productionof the calibrated event files, filtering for the high inten-sity soft proton flares, and determination of the back- Our uncertainties on the
Chandra -derived temperature ofsub-cluster B are significantly lower than the values reported inTable 3 of M12. This is due to the fact that our current analysisuses a 1 (cid:48) diameter region, while the M12 analysis used a 40 (cid:48)(cid:48) diam-eter region (both analyses use a 1 (cid:48) diameter region for sub-clusterC). There are additional <
5% differences due to the updated cal-ibration we use for our current analysis. ground intensity in each observation. The net exposuretime after filtering the event files for good time inter-vals is 155 ksec. Given the superior spatial resolutionof
Chandra , we use both
Chandra and
XMM to identifyregions contaminated by extragalactic X-ray sources notassociated with the cluster gas. Excluding these regions,we extract spectra using 1 (cid:48) diameter regions centered onsub-clusters B and C, identical to the regions we use forthe
Chandra analysis. The temperature gradient is notlarge, and so contamination by adjacent regions (e.g.,other sub-clusters) due to the wider PSF of
XMM shouldnot affect the extracted temperature for each region.For each extracted spectrum, we model a superposi-tion of four main background components: quiescent par-ticle background, soft X-ray background emission (in-cluding solar wind charge exchange, Galactic halo, lo-cal hot bubble, and extragalactic unresolved sources),and residual contamination from soft protons (Kuntz &Snowden 2008). As in Snowden et al. (2008), we modelthe contamination due to unresolved point sources usingan absorbed power law component with spectral index α = 1 .
46 and normalization = 8 . × photons keV − cm − s − at 1 keV.We simultaneously fit all of the EPIC-MOS spectra us-ing the energy range 0 . − . Chandra spectral analysis, we use the absorbed APEC model to fitthe cluster emission, employing the extended C-statisticfor our likelihood analysis within each sub-cluster region.From the
XMM data, we find T e = 10 . +0 . − . keV forsub-cluster B and T e = 18 . +1 . − . keV for sub-cluster C.We note that these values are (cid:39)
25% lower than theelectron temperatures we derive from the
Chandra data.This systematic difference at high temperature is con-sistent with previous comparisons between
XMM and
Chandra (e.g., Nevalainen et al. 2010; Li et al. 2012;Mahdavi et al. 2013), although we note that, in our case,the statistical significance of the difference is relativelysmall ( (cid:46) σ ). We consequently choose to combine thetemperature measurements from the two X-ray observa-tories, and we obtain maximum likelihood values of T e =11 . +0 . − . keV for sub-cluster B and T e = 19 . +1 . − . keV forsub-cluster C. We explore the impact of using this jointtemperature constraint, rather than the constraint fromeither XMM or Chandra individually, in Section 9.2. MODEL OF THE SZ SIGNAL
In order to model the SZ signals from the ICM ofMACS J0717.5+3745, we employ the pseudo Compton- y map to describe the overall shape of the thermal SZsignal. The X-ray data we use to create the pseudoCompton- y map depend negligibly on the line-of-sightvelocity of the ICM, and the map therefore provides aspatial template for the thermal SZ signal that is freefrom contamination from the kinetic SZ signal. We thenconvert this map to units of surface brightness in eachBolocam observing band according to the thermal SZequations (Sunyaev & Zel’dovich 1972), including rel-ativistic corrections (Itoh et al. 1998; Nozawa et al.1998b,a; Itoh & Nozawa 2004). For this conversionwe compute the responsivity-weighted average bandpassover all the Bolocam detectors, and from this spectrumwe determine the effective band center for a thermal SZspectrum. Due to relativistic corrections, this effective band center depends on the ICM temperature. For the140 GHz band, both the thermal and kinetic SZ bandcenters are (cid:39)
140 GHz, while the 268 GHz thermal SZband center is (cid:39)
275 GHz and the kinetic SZ band centeris (cid:39)
268 GHz. Then, for each Bolocam band, we con-volve the pseudo Compton- y map with both the BolocamPSF and the transfer function of the data processing.We first constrain the normalization of the pseudoCompton- y map via a simultaneous fit to both the 140and 268 GHz Bolocam data. Physically, this correspondsto a constraint on the effective line-of-sight extent of theICM l , under the assumption of zero kinetic SZ signal.For this fit, we use only the data within a 4 (cid:48) × (cid:48) squareregion approximately centered on the peak of the SZ sig-nal at 140 GHz. We choose this region because it is largeenough to contain the bulk of the SZ signal and it is smallenough to mitigate the effects of the large-angular-scaleatmospheric noise in the 268 GHz data. The quality ofthis fit is very poor, with a χ = 853 . y mapalone is inadequate to describe our Bolocam SZ data (seeFigure 3).Motivated by this poor fit, along with the significantdifferences in the line-of-sight velocities measured by Maet al. (2009) for the four identified sub-clusters in MACSJ0717.5+3745, and the results from M12, we consideradditional components to our model of the ICM. To de-termine which, if any, additional model components arerequired in order to describe the data, we perform a simu-lated F-test according to the procedure described in Cza-kon (2013). To perform this test we first insert the base-line model into each of our 1000 noise realizations (inthis case the baseline model is the pseudo Compton- y map with our best-fit single normalization). We then fittwo models to each of these realizations, one consistingof only the baseline model, and one with an extensionto the baseline model. We compute the value of ∆ χ from these two separate fits for each of the 1000 realiza-tions, and the resulting values provide a measurement ofthe distribution of ∆ χ for the null hypothesis that themodel extension is not required by the data.There are several possible model extensions to con-sider, and we therefore proceed according to the follow-ing decision tree: 1) determine the value of ∆ χ sepa-rately for each possible model extension; 2) perform thesimulated F-test to determine which extension is mostpreferred by the data; 3) if the most preferred model ex-tension is preferred at a high enough significance, whichwe quantify based on a probability to exceed (PTE) fromthe simulated F-test, then the model extension is addedto the baseline model. These steps are repeated untilnone of the possible model extensions have a simulatedF-test PTE below our threshold, which we have chosento be equal to 0.02. As a first possible model extension, we consider asmooth template of the SZ signal centered on one of the As we describe below, we consider 5 independent potentialmodel extensions, and consequently a possible total of 2 = 32model permutations. Our PTE threshold, which is necessarilysomewhat arbitrary, is therefore small enough to ensure that arandom fluctuation among this set of 32 permutations is unlikelyto produce a PTE small enough for us to include an extension thatis not justified by the data. We explore the sensitivity of our resultsto this PTE threshold in detail in Section 6.2. Th e r m a l S Z - on l y m od e l Th e r m a l + K i n e t i c S Z m od e l Th e r m a l S Z - on l y m od e l Th e r m a l + K i n e t i c S Z m od e l Fig. 3.—
Bolocam thumbnails showing the processed data within the 4 (cid:48) × (cid:48) region we use to constrain our model of the SZ signal. Fromleft to right the thumbnails show the Bolocam data, the best-fit model, and the difference between the data and the best-fit model (i.e., theresidual map). The top block shows the 140 GHz data convolved with a 60 (cid:48)(cid:48) FWHM Gaussian, and the bottom block shows the 268 GHzdata convolved with a 30 (cid:48)(cid:48)
FWHM Gaussian. In the left plots, the contours are spaced by S/N = 2, with solid representing positive S/N,black representing 0, and dashed representing negative S/N. In the right plots the contours are spaced by S/N = 1, and the color stretchis reduced by a factor of 2.5 to better highlight the residuals between the data and the model. For each wavelength, the top row assumesa model composed of only the pseudo Compton- y map with a single normalization (a purely thermal SZ signal). This model is not a goodfit to the data, and there is a clear dipole residual from ESE to WNW, at a significance of (cid:39) σ at 140 GHz and (cid:39) σ at 268 GHz. Thebottom row for each wavelength assumes our nominal model of the pseudo Compton- y map with a single normalization plus an SZ templatecentered on sub-cluster B with different normalizations at 140 and 268 GHz (a thermal plus kinetic SZ signal). This model does providea good fit to the data, and the residual maps are consistent with noise. The green circles are centered on sub-cluster C (lower left) andsub-cluster B (upper right), with diameters of 60 (cid:48)(cid:48) . four sub-clusters according to the positions given by Maet al. (2009), allowing for different normalizations of thetemplate at 140 and 268 GHz. We construct the SZtemplate according to the average profile constrained byBolocam for a sample of 45 clusters (Sayers et al. 2013a),fixing the scale radius according to the estimated mass ofeach sub-cluster, which we obtain by using the ratios ofsub-cluster masses determined by Limousin et al. (2012),in combination with the whole-cluster value of M de- termined by Mantz et al. (2010). We note that thistemplate represents a more physically motivated modelthan the Gaussian profile assumed by M12. We performfour separate fits, in each case fitting a single normaliza-tion to the pseudo Compton- y map (i.e., assuming thatthe pseudo Compton- y map contains only thermal SZsignal), along with separate normalizations at 140 and268 GHz for an SZ template centered on one of the foursub-clusters (i.e., allowing the SZ template for that sub-cluster to be free to include any arbitrary mixture of ther-mal and kinetic SZ signal). We find values of ∆ χ equalto 48.3, 108.1, 9.5, and 26.3 when the model contains anadditional SZ template coincident with sub-clusters A, B,C, and D, respectively. These values of ∆ χ correspondto F-test PTEs of 0.001, 4 × − , 0.213, and 0.026. Wenote that the second value is extrapolated, due to thefact that we only have 1000 realizations of ∆ χ .As another possible extension to the baseline model ofa pseudo Compton- y map with a single normalization inboth Bolocam bands, we also explore the option of allow-ing for different normalizations of the pseudo Compton- y map at 140 and 268 GHz. Physically, this would repre-sent a single bulk velocity for the entire cluster, withthe cluster being isothermal so that the kinetic SZ sig-nal has a spatial profile identical to the spatial profileof the thermal SZ signal. This fit results in a value of∆ χ = 52 .
1, which corresponds to a simulated F-testPTE of 3 × − , where we have again used an extrapo-lation due to our finite number of realizations. Therefore,according to our F-test decision tree, we assume a newbaseline model consisting of the pseudo Compton- y witha single normalization, along with a SZ template centeredon sub-cluster B, as this is the model extension with thesmallest simulated F-test PTE.To fully characterize the fit of this new baseline model,we insert the best-fit model into each of our 1000 noiserealizations, and then fit the same model to each of theserealizations. The best-fit model has an overall χ = 745 . χ is 23.9, 8.4, and 21.1, which correspondsto a simulated F-test PTE of 0.033, 0.260, and 0.046. Asbefore, we also perform a fit allowing the normalizationof the pseudo Compton- y map to be different at 140 and268 GHz, and we find a ∆ χ = 0 .
1, with an associatedsimulated F-test PTE of 0.963. All of these fits havePTEs larger than 0.02, and we therefore conclude thatnone of these additional degrees of freedom are requiredto describe our data. Consequently, our baseline modelof the SZ signal includes a pseudo Compton- y map with asingle normalization, along with an SZ template centeredon sub-cluster B with separate normalizations at 140 and268 GHz (see Figure 3).The data’s strong lack of a preference for separate nor-malizations of the pseudo Compton- y map at 140 and268 GHz justifies our choice of that model to describethe thermal component of the SZ signal. Furthermore,the best-fit normalization of the pseudo Compton- y mapis 1 . ± .
11. The pseudo Compton- y map was nor-malized based on the integrated SZ signal measured at31 GHz by the SZA as reported in M12. Compared tothe Bolocam observing bands, the kinetic SZ signal isa factor of (cid:39) y map foundby Bolocam and SZA further indicate that it provides a good description of the thermal SZ signal toward MACSJ0717.5+3745. As an additional cross-check, we also refitthe normalization of the pseudo Compton- y map usingthe Bolocam data, but excluding the data within a 1 (cid:48) diameter aperture centered on sub-cluster B. This fit,which did not include any additional SZ components, re-sults in a best-fit normalization of 1 . ± .
08 for thepseudo Compton- y map. The fit quality is good, with aPTE of 0.38, indicating that, outside sub-cluster B, theM12 pseudo Compton- y map, which was normalized toSZA, describes the Bolocam data well. Although theseresults serve as additional evidence that our model choiceis physically justified, we emphasize that our resultsdescribed below do not strictly depend on the pseudoCompton- y map being a good template for the thermalSZ signal, only that our model is physically motivatedand provides an adequate description of the data. MEASUREMENT OF THE SZ SPECTRUM TOWARDSUB-CLUSTER B
Two-Band SZ Photometry
Based on the requirement of an additional model com-ponent centered on sub-cluster B to describe our data,we compute the SZ brightness at both 140 and 268 GHztoward that sub-cluster. In order to eliminate as muchcontamination from other regions of the cluster as pos-sible, we use a circular aperture with a diameter of 1 (cid:48) ,which is slightly larger than the PSF FWHM at 140 GHz.We first compute the average surface brightnesses withinthis aperture using the best-fit model from Section 5,convolved with the Bolocam PSF to accurately repre-sent the resolution of the measurement. To include allof the subtle effects of the noise, such as the correlationsbetween pixels due to residual atmospheric noise and pri-mary CMB fluctuations, we also compute the averagesurface brightness within the same aperture using themodel fits to the 1000 noise realizations. Kolmogorov-Smirnov (KS) tests against Gaussians on the distribu-tions of 1000 values at 140 and 268 GHz yield PTEs of0.19 and 0.93, respectively, and therefore indicate thatour noise is Gaussian within our ability to measure it.Using these model fits, we estimate the surface bright-ness of sub-cluster B to be − . ± .
028 MJy sr − at140 GHz and 0 . ± .
029 MJy sr − at 268 GHz, wherethe errors represent only measurement uncertainties.In addition to the best-fit model, we also compute thesurface brightness toward sub-cluster B by directly in-tegrating our deconvolved images, which are shown inFigure 4. As described in Section 4.1, the deconvolvedimages have no sensitivity to the DC signal level. As aresult, we determine the DC signal level of the decon-volved images using the best-fit model. Specifically, weadd a signal offset to the deconvolved images so that theaverage signal level within the 4 (cid:48) × (cid:48) region we use toconstrain the model is equal to the average signal levelof the best-fit model within the same region. We ex-clude the 1 (cid:48) diameter aperture centered on sub-clusterB in this calculation to avoid any potential bias in thesurface brightness we derive within that aperture. Thisdirect integration yields average surface brightnesses of − . ± .
027 MJy sr − and 0 . ± .
049 MJy sr − , re-spectively, where we have again estimated the uncertain-ties using the 1000 noise realizations. As with the modelderived results, we used a KS test to determine if the Fig. 4.—
Thumbnails of the deconvolved Bolocam images at 140 and 268 GHz. We have scaled both images to units of Compton- y ,including positionally dependent relativistic corrections based on the X-ray-determined temperature map. The relativistic correctionsgenerally range from 8 −
15% at 140 GHz and from 20 −
40% at 268 GHz. The 140 GHz image is smoothed with a 60 (cid:48)(cid:48)
Gaussian, and the268 GHz image is smoothed with a 30 (cid:48)(cid:48)
Gaussian. The contours are spaced by 1 × − , with solid showing positive y and dashed showingnegative y . The green circles show the 1 (cid:48) diameter apertures centered on sub-cluster C (lower left) and sub-cluster B (upper right). Thetotal Compton- y signal toward sub-cluster C is nearly identical at the two wavelengths, while there is a clear difference toward sub-clusterB. distribution of 1000 values is consistent with Gaussian,and we find PTEs of 0.75 and 0.57 at 140 and 268 GHz,respectively. We note that these surface brightness val-ues are consistent with those derived from the best-fitmodel, although there is significantly more measurementuncertainty on the 268 GHz value. This additional un-certainty is a result of the significant large-angular-scaleatmospheric noise in those data, which is amplified bythe deconvolution of the signal transfer function. Systematic Uncertainties
First, we note that our flux calibration is accurate to5% at 140 GHz, and to 10% at 268 GHz (Sayers et al.2012). We have included these uncertainties in our sys-tematic error budget.To estimate the systematic errors due to the model-dependence of our results, we repeat our analysis ofcomputing model-based and directly integrated surfacebrightnesses toward sub-cluster B at both 140 and268 GHz using a range of different models, with a sum-mary of the results in Table 1. First, we replace thebaseline pseudo Compton- y map we use in our modelwith a set of 20 realizations of the pseudo Compton- y map that we generate according to the X-ray measure-ment uncertainties on the mean T e for each contbin region(see Section 4.2). Next, we constrain our baseline modelusing 3 (cid:48) × (cid:48) and 5 (cid:48) × (cid:48) regions of the Bolocam images in-stead of the nominal 4 (cid:48) × (cid:48) region we use in Section 5. Inaddition, we consider an SZ model that does not includethe pseudo Compton- y map, and instead only includesSZ templates centered on the sub-clusters. We repeatthe F-test decision tree described in Section 5 to deter-mine which of the sub-clusters require an SZ template forthis model. We find that, without the pseudo Compton- y map, the data require SZ templates centered on sub-clusters B, C, and D. This fit produces a PTE of 0.64,indicating that the data are adequately described by thismodel. Furthermore, we re-ran the F-test decision treewith the PTE threshold increased by a factor of two to The adequacy of this somewhat simple and ad-hoc model indescribing our data is likely due to Bolocam’s coarse angular res-olution, which largely blurs any sub-structures not well described y map with a single normalization,along with SZ templates centered on sub-clusters A andB (i.e., relative to the baseline model, an additional SZtemplate is required for sub-cluster A). Finally, we deter-mine the effects of varying the scale radius of the profileused as a template of the SZ signal toward sub-cluster B.We vary the scale radius over a range of 0 . − . . − . by the smooth SZ templates. However, we note that this modelrequires twice as many free parameters as our baseline model inorder to obtain an adequate fit according to our F-test decisiontree. TABLE 1Variations in Sub-Cluster B’s Surface Brightness due toPossible Changes in Our Analysis Method
Model-Derived Direct Integration140 GHz 268 GHz 140 GHz 268 GHzMJy sr − MJy sr − MJy sr − MJy sr − Nominal Values from Baseline Model − . ± .
028 0 . ± . − . ± .
027 0 . ± . y within X-ray uncertainties ± . ± . ± . ± . ± . σ ) ( ± . σ ) ( ± . σ ) ( ± . σ )vary region used for fit from 3 (cid:48) to 5 (cid:48) ≤ . ≤ . ≤ . ≤ . ≤ . σ ) ( ≤ . σ ) ( ≤ . σ ) ( ≤ . σ )model with no pseudo Compton- y ; templates at B, C, and D0.028 0.026 0.016 0.015(1 . σ ) (0 . σ ) (0 . σ ) (0 . σ )F-test decision tree with PTE threshold equal to 0.040.007 0.017 0.001 0.026(0 . σ ) (0 . σ ) (0 . σ ) (0 . σ )vary scale radius of B template by 0 .
67 to 1 . ≤ . ≤ . ≤ . ≤ . ≤ . σ ) ( ≤ . σ ) ( ≤ . σ ) ( ≤ . σ )Variations due to Aperture Choiceaperture centered on Limousin et al. (2012) coords0.018 0.019 0.009 0.003(0 . σ ) (0 . σ ) (0 . σ ) (0 . σ )aperture centered on X-ray centroid0.019 0.034 0.010 0.048(0 . σ ) (1 . σ ) (0 . σ ) (1 . σ )vary aperture diameter from 0 . (cid:48) to 1 . (cid:48) ≤ . ≤ . ≤ . ≤ . ≤ . σ ) ( ≤ . σ ) ( ≤ . σ ) ( ≤ . σ ) Note . — Top block: best-fit surface brightnesses from the base-line model described in Section 5, and associated 1 σ uncertaintiesdue to measurement noise only. Next block: variations in the sur-face brightness of sub-cluster B based on our choice of model. Weconsider five different model fits to describe the SZ data. Thesemodels are explained in detail in the text, and we refer the readerthere for more details. From left to right, the columns give thechange in surface brightness at 140 and 268 GHz for the model-derived and direct integration surface brightnesses. The top rowsgive these values in MJy sr − , and the bottom rows give thesevalues relative to the measurement uncertainties in the top block.When noise variations to the models are considered, these valuesindicate the 1 σ range with a ± symbol, when a range of modelinputs are considered, these values show the magnitude of themaximum change with a ≤ symbol, and when a single alterna-tive model is considered these values show the magnitude of thechange with no symbol. Based on these results, we add a system-atic uncertainty equal to 1.0 times the measurement uncertainty forthe model-derived values and equal to 0.6 times the measurementuncertainty for the direct integration values. Bottom block: varia-tions in the surface brightness of sub-cluster B for different choicesof aperture. From top to bottom, the rows show the change rela-tive to our nominal 1 (cid:48) diameter aperture centered on the Ma et al.(2009) coordinates for 1) an aperture centered on the Limousinet al. (2012) coordinates, 2) an aperture centered on the X-raycentroid, and 3) varying the aperture diameter between 0 . (cid:48) and1 . (cid:48) for the aperture centered on the Ma et al. (2009) coordinates.All of these differences are consistent with the expected measure-ment noise fluctuations for the different aperture choices. Limousin et al. (2012) based on the matter distribution(7:17:30.2, +37:45:15), and 3) the location of the X-raybrightness centroid (7:17:31.4, +37:45:29). Our nominalanalysis uses the Ma et al. (2009) coordinates, and wegive the changes in surface brightness when we use theother two possible apertures in Table 1. Compared tothe measurement uncertainties given in Section 6.1, thesurface brightnesses we measure in these new aperturesdiffer by less than ≤ . σ with a median of (cid:39) . σ . Thethree sets of coordinates are separated from each otherby (cid:39) (cid:48)(cid:48) , which is a significant fraction of the aper-ture radius of 30 (cid:48)(cid:48) , and means that less than 50% of thearea enclosed by one aperture is also enclosed by an-other aperture. Consequently, completely uncorrelatedmeasurement noise between any given pair of apertureswill produce surface brightnesses that differ by (cid:39) σ .Therefore, the differences in surface brightness that wemeasure between these aperture locations are consistentwith the expectation due to noise fluctuations.We also examine the effects of varying the diameter ofthe aperture from 0 . (cid:48) to 1 . (cid:48) (compared to the nomi-nal diameter of 1 (cid:48) ), and again find results that are con-sistent within 1 σ . As with the different aperture loca-tions, this is consistent with the variations that we ex-pect due to uncorrelated measurement noise between theaperture choices, and indicates that variations in the lo-cation, or diameter, of the aperture we use to measurethe SZ surface brightness result in differences consistentwith measurement noise. We therefore conclude that ourresults are not sensitive to the exact choice of aperture,and we do not include any additional systematic error inour overall noise budget. We note that in all cases theapertures are comparable in size to the Bolocam PSF,and there is consequently some signal leakage from out-side to inside the apertures and vice versa. Furthermore,the separation between the apertures centered on sub-clusters B and C is also comparable to the size of theBolocam PSF, and so there is some signal leakage be-tween apertures. Although we are not able to accountfor this signal leakage in our analysis, the consistency ofour results using various aperture positions and diame-ters indicates that the leakage is below our measurementuncertainties. Comparison to Previous Results
We note that the 140 GHz surface brightnesses we findfor sub-cluster B are slightly different compared to thevalues reported in M12, although identical Bolocam datais used for both analyses. Our model-derived surfacebrightness of − . ± .
028 MJy sr − is more than 1 σ lower than the M12 value of − . ± .
030 MJy sr − . More than half of this difference is due to a minor errorin the analysis presented in M12. The total flux densitiesgiven in Table 3 of M12 were mistakenly computed fromthe average surface brightness within a 1 . (cid:48) aperture,rather than the 1 (cid:48) aperture claimed in the text of M12and also used in our present analysis. The remaining dif-ference between our current surface brightness values andthe ones presented in M12 is due to minor changes in ourassumed model of the SZ signal. First, M12 constrained Table 3 of M12 lists a total flux density of − . ± . − . ± .
030 MJysr − . TABLE 2SZ Surface Brightness
Frequency Best Fit Measurement Err. Flux Err. Modeling Err. Total Err.GHz MJy sr − MJy sr − MJy sr − MJy sr − MJy sr − Sub-Cluster B
Model Fits140 -0.344 0.028 0.017 0.028 0.043268 0.052 0.029 0.005 0.029 0.041Direct Integration140 -0.341 0.027 0.017 0.016 0.036268 0.095 0.049 0.010 0.029 0.058
Sub-Cluster C
Model Fits140 -0.262 0.026 0.013 0.028 0.040268 0.217 0.039 0.022 0.029 0.053Direct Integration140 -0.270 0.026 0.014 0.016 0.034268 0.220 0.059 0.022 0.029 0.069
Note . — The average surface brightness within a 1 (cid:48) diameter aperture centered on sub-clusters B and C. From left to right the columns give the observing frequency, the best-fitaverage surface brightness, the measurement uncertainty on this value, the uncertaintyon this value due to flux calibration, the uncertainty on this value due to the range ofmodels we could have chosen to describe the data, and the total combined uncertaintywhich is the quadrature sum of the previous three columns. For each sub-cluster, the toprows give the values we derive from the best-fit model of the SZ signal, and the bottomrows give values we derive from direct integration of the deconvolved images. the normalization of the pseudo Compton- y map sepa-rately at 140 and 268 GHz, compared to the joint con-straint we use in our present analysis. In addition, M12assumed that the SZ template centered on sub-cluster Bhad a Gaussian profile, compared to the more physicallymotivated profile we use in this analysis, with a shape de-scribed by the best-fit profile to a sample of 45 clustersobserved with Bolocam (Sayers et al. 2013a).Furthermore, we note that, in our current analysis, themodel-derived surface brightness agrees quite well withthe surface brightness we obtain from a direct integrationof the deconvolved image. This result is in contrast tothe measurements presented in M12, where the two val-ues differed by slightly more than 1 σ . This change is dueto differences in how the DC signal offset of the decon-volved images is computed. M12 computed the DC sig-nal offset based on a fit of the average profile determinedby Arnaud et al. (2010) to the full 140 GHz Bolocamdataset. Although the fit quality of this single profile isnot particularly poor, with a PTE of 0.07, the adequacyof using a single profile to describe a complex mergingsystem like MACS J0717.5+3745 is questionable. There-fore, as described above, for this analysis we choose toconstrain the DC signal offset of the 140 GHz decon-volved image using our nominal model of the SZ signal(a pseudo Compton- y map with an additional SZ com-ponent centered on sub-cluster B). Not surprisingly, thischange in our estimate of the DC signal level results in abetter agreement between the model-derived and directlyintegrated surface brightnesses. MEASUREMENT OF THE SZ SPECTRUM TOWARDSUB-CLUSTER C
M12 computed the SZ surface brightness toward bothsub-cluster B and sub-cluster C. The latter measurementwas motivated primarily by the fact that Ma et al. (2009)identified sub-cluster C as the most massive componentof MACS J0717.5+3745, along with the fact that sub-cluster C is coincident with the highest surface brightnessin the 268 GHz Bolocam image. Therefore, although ourF-test decision tree indicates that our data do not re-quire a component in addition to the thermal SZ tem-plate toward sub-cluster C, we again measure its SZ sur-face brightness. For these measurements we add an SZtemplate centered on sub-cluster C to our model, to en-sure that the model has enough freedom to describe anypossible deviations from a purely thermal SZ spectrum.We again estimate the SZ surface brightness using a 1 (cid:48) diameter aperture centered on the coordinates from Maet al. (2009), with the results given in Table 2. As withsub-cluster B, we estimate the uncertainties on these sur-face brightnesses using our 1000 noise realizations, andwe again find that the distribution of values is consis-tent with Gaussian noise. In addition, we estimate thesystematic uncertainty due to our choice of model usingthe same formalism described for sub-cluster B in Sec-tion 6.2. We find systematic errors consistent with thosethat we find for sub-cluster B, and we therefore adoptidentical values for sub-cluster C. Finally, we note thatthe 140 GHz brightness values differ from those derivedin M12 by roughly the same amounts as for sub-clusterB, with the differences due to the same reasons describedin detail in Section 6.3.We do not attempt to constrain the SZ brightness to-ward either sub-cluster A or sub-cluster D. We do notconsider sub-cluster A due to the fact that it is notstrongly detected in either Bolocam dataset. We do2not consider sub-cluster D due to the fact that it is notseparately resolved from sub-cluster C due to Bolocam’scoarse angular resolution, and therefore any estimate ofsub-cluster D’s SZ brightness would be highly correlatedwith our estimate of sub-cluster C’s SZ brightness. PECULIAR VELOCITY CONSTRAINTS
Using our two-band measurements of the SZ surfacebrightness toward sub-clusters B and C, we are able toplace constraints on the properties of the ICM of eachsub-cluster. Based on the equations presented in Sec-tion 2, the total SZ brightness depends on four quanti-ties related to the cluster ICM: f ( ν, T e ), y , τ e , and v z .Our two-band SZ surface brightness measurements areinsufficient to constrain all of these quantities, and sowe therefore make the assumption that the ICM withineach sub-cluster is isothermal and equal to the X-rayspectroscopic temperature determined within the same1 (cid:48) diameter apertures that we use to measure the SZ sur-face brightness. As a result, f ( ν, T e ) is fully constrainedby the Chandra -and-
XMM -measured T e , and from Equa-tions 4 and 2 we have y = τ e k B T e m − e c − , meaning that y and τ e are not independent. Therefore, we are leftwith two free parameters to constrain using the two-bandBolocam surface brightnesses, either τ e and v z or y and v z (in practice we constrain Y int and v z , where Y int = y ∆Ω,and ∆Ω is equal to the solid angle of our 1 (cid:48) aperture). Inall of the fits, we compute the band-averaged values of f ( ν, T e ) for a given T e using the full Bolocam bandpassesrather than a single effective band center.Using our X-ray measured T e , along with our SZ sur-face brightnesses, we then perform a grid search to con-strain the values of v z and Y int for sub-clusters B andC. For these constraints, we use the best-fit SZ surfacebrightness values from Table 2, along with the total un-certainties in the far-right column of that table. There-fore, we fully include not only measurement uncertain-ties, but also flux calibration uncertainties, and possiblesystematic uncertainties due to our choice of model to de-scribe the SZ signal. Because the noise in our SZ surfacebrightness measurements is indistinguishable from Gaus-sian, we compute likelihoods based on a Gaussian distri-bution. When fitting the SZ spectra, we marginalize overthe range of T e values allowed by the X-ray data, relyingon the C statistic to give a likelihood for each tempera-ture in the range 2 −
40 keV. A summary of our resultsfor both sub-clusters is given in Table 3 and Figures 5and 6, and we highlight some of these results below.For sub-cluster B we find a best-fit v z = +3450 kms − using the SZ surface brightnesses we determine fromthe model fit to our data and a best-fit v z = +2550 kms − using the SZ surface brightnesses we determine fromdirect integration of our deconvolved images. Both ofthese values are consistent with the value of +3238 kms − determined by Ma et al. (2009) based on optical spec-troscopy under the assumption that the peculiar veloc-ity of the entire cluster is 0 along the line-of-sight (seeFigure 5). The 1 σ uncertainties about these best-fit ve-locities are similar for both the model-derived and directintegration results, and are (cid:46) − . We alsocompute the probability of v z ≥
0, and we obtain valuesof (1 − Prob[ v z ≥ . × − and 2 . × − for themodel-derived and direct integration SZ surface bright-nesses, respectively (see the bottom panels of Figure 5). For a Gaussian distribution, these one-sided probabili-ties correspond to a difference from v z = 0 of 4.2 σ and2.9 σ , respectively. For sub-cluster C we find a best-fit v z of (cid:39) −
500 km s − from both the model fit and directintegration of the deconvolved image, which is fully con-sistent with both the value of −
733 km s − determinedby Ma et al. (2009) and with zero velocity. We note thatthe uncertainties on the value of v z for sub-cluster C are (cid:39)
50% larger compared to sub-cluster B. This increase isdue entirely to the higher temperature of sub-cluster C.This higher temperature produces a smaller value of τ e for a fixed value of Y int and therefore a correspondinglylower kinetic SZ signal for a fixed value of v z .We note that the difference between our best-fit v z and the best fit v z from Ma et al. (2009) is quite smallfor both sub-clusters (0 . σ and 0 . σ for the model-derived results for sub-clusters B and C, and 0 . σ and0 . σ for the direct-integration results for sub-clusters Band C). The random probability of obtaining such resultsfrom two independent measurements of two independentparameters is 2% for our model-derived results and 6%for our direct-integration results. These probabilities aresmall, but they are not small enough to cause significantconcern. In addition, our intentionally conservative esti-mates of the uncertainties due to our choice of SZ modelhave likely resulted in over-estimated errors on the SZbrightness, thus rendering the good agreement betweenour results and those of Ma et al. (2009) more likely. DISCUSSION
Differences Compared to the Results in M12
Compared to the results presented in M12, ourbest-fit values of v z for sub-cluster B are somewhatlower (+3450 km s − and +2550 km s − compared to+4640 km s − and +3600 km s − for the model-derivedand direct integration surface brightnesses, respectively).This is mainly due to an increase in the best-fit sur-face brightness at 268 GHz as a result of the additionaldata we use in our present analysis. In contrast, ourbest-fit values of v z for sub-cluster C are smaller in mag-nitude compared to M12 ( −
550 km s − and −
500 kms − compared to − − and − − forthe model-derived and direct integration surface bright-nesses, respectively). These differences are again drivenby the additional 268 GHz data we use in our currentanalysis, which indicates that sub-cluster C is dimmercompared to the analysis of M12. However, we empha-size that all of our measured values of v z are consistentto within 1 σ of the values presented in M12, and thereis no tension between the two results.Our uncertainties on the value of v z for sub-cluster Bare a factor of (cid:39) (cid:39) . T e found in our present analysis, whichfor a fixed Y int corresponds to a larger τ e and thereforea larger kinetic SZ signal for a fixed v z . In contrast, ouruncertainties on v z for sub-cluster C have only decreasedby a factor of (cid:39) TABLE 3Peculiar Velocity Constraints T e optical SZ model fit SZ direct integrationkeV km s − km s − km s − sub-cluster B 11 . +0 . − . +3238 +252 − +3450 +900 − (1 − Prob[ v z ≥
0] = 1 . × − ) +2550 +1050 − (1 − Prob[ v z ≥
0] = 2 . × − )sub-cluster C 19 . +1 . − . − +486 − − +1350 − (1 − Prob[ v z ≤
0] = 3 . × − ) − +1600 − (1 − Prob[ v z ≤
0] = 4 . × − ) Note . — Line-of-sight velocity constraints from our analysis. From left to right the columns give the the X-ray-derived temperaturefrom
Chandra and
XMM , the line-of-sight velocity derived by Ma et al. (2009) based on optical spectroscopy, and the line-of-sightvelocity from our kinetic SZ constraints using the best-fit model and a direct integration of the deconvolved image. The top row showsthe constraints for sub-cluster B, and the bottom row shows the constraints for sub-cluster C. For the fits we have used the best-fit SZbrightnesses given in Table 2, with the total uncertainties listed in the far-right column of that table. Next to the kinetic SZ velocityconstraints, we give the probability that the line-of-sight velocity is greater than 0 for sub-cluster B, and the probability that theline-of-sight velocity is less than 0 for sub-cluster C. int ( × −11 ) v z ( × k m / s ) Constraints on Sub−Cluster B 1 1.5 2 2.5−505 Y int ( × −11 ) v z ( × k m / s ) Constraints on Sub−Cluster C0 2 4 6 800.51 v z ( × L i k e li hood Sub−Cluster B Velocity −5 0 500.51 v z ( × L i k e li hood Sub−Cluster C Velocity
Fig. 5.—
Our SZ-derived constraints on the ICM toward sub-cluster B (left) and sub-cluster C (right). The top row shows two-dimensionalconfidence regions for the values of Y int and v z , with contours drawn at 1 σ , 2 σ , and 3 σ for a two-parameter likelihood (e.g., 1 σ correspondsto a ∆ χ = 2 . v z , with vertical lines drawn at ± σ (correspondingto ∆ χ = 1). In all cases blue corresponds to the constraints from the model-derived SZ surface brightnesses, and yellow corresponds to theconstraints from the SZ surface brightnesses we derive from direct integration of the deconvolved images. The solid black line representsthe best-fit velocity derived by Ma et al. (2009) based on optical spectroscopy, and the dashed lines show the corresponding 1 σ confidenceregion around their best-fit. certainties. This difference relative to sub-cluster B isdriven by our best-fit value of v z , which is significantlylarger (less negative) than the results in M12. As a re-sult, the best-fit value of Y int is smaller, and thereforethe best-fit value of τ e is smaller. Consequently, for agiven change in v z , the corresponding change in the kSZsurface brightness is also smaller, resulting in less con-straining power on the value of v z .In contrast to the analysis presented in M12, note thatwe include additional systematic uncertainties in our de-rived SZ surface brightnesses due to differences based on the range of models we could have chosen to describethe SZ signal. These systematic uncertainties increasethe total error estimate on the model-derived and di-rectly integrated SZ surface brightnesses by (cid:39)
40% and (cid:39) v z without in-cluding this additional systematic error, and verify thatthe fractional improvement in our constraints matchesthese values. Therefore, the model-dependence of ourSZ data results in a non-negligible degradation of ourconstraining power on v z .4
100 200 300 400−0.4−0.200.20.4 ν (GHz) I S Z ( M Jy / s t e r) Sub−cluster B (Model) 100 200 300 400−0.4−0.200.20.4 ν (GHz) I S Z ( M Jy / s t e r) Sub−cluster B (Direct)100 200 300 400−0.4−0.200.20.4 ν (GHz) I S Z ( M Jy / s t e r) Sub−cluster C (Model) 100 200 300 400−0.4−0.200.20.4 ν (GHz) I S Z ( M Jy / s t e r) Sub−cluster C (Direct)
Fig. 6.—
Our best-fit SZ spectra. The top row shows the fits to sub-cluster B, and the bottom row shows the fits to sub-cluster C. Theleft column shows the SZ surface brightnesses we determine from the model fit, and the right column shows the SZ surface brightnesses wedetermine via direct integration of the deconvolved images. The best-fit thermal-SZ-only spectrum is shown in red, the best-fit kinetic SZspectrum is shown in green, and the best-fit thermal plus kinetic SZ spectrum is shown in blue, with the widths showing the 1 σ confidenceregion of the fits. We include relativistic corrections in all of the spectra. Limitations to Our Kinetic SZ Constraints
Given the range of multi-wavelength data that we useto place constraints on v z , we also estimate how eachof these datasets contribute to our overall uncertainties.First, as noted in Section 4.3, previous results have in-dicated that there is a systematic difference in temper-atures derived from Chandra and
XMM , and the tem-peratures we measure are in general agreement with thissystematic difference. At this point, the cause of thisdifference has not been conclusively demonstrated. Dueto this lack of a conclusive understanding of the differ-ence, combined with the fact that the difference betweenthe X-ray temperatures we derive from the two observa-tories is of modest statistical significance, we choose toconstrain the electron temperatures via the joint likeli-hood from the
Chandra and
XMM data. If we insteadadopt the
XMM -only values of T e , then we find best-fitvalues of v z equal to +3300 km s − and +2450 km s − forthe model fit and direct integration of sub-cluster B and −
450 km s − and −
400 km s − for the model fit and di-rect integration of sub-cluster C. If we instead adopt the Chandra -only values of T e , then we find best-fit values v z equal to +4000 km s − and +2900 km s − for the modelfit and direct integration of sub-cluster B and −
550 kms − and −
450 km s − for the model fit and direct inte-gration of sub-cluster C. For sub-cluster B, the Chandra -only temperatures yield line-of-sight velocities that differby (cid:39) . σ , but all of the other values are statistically in-distinguishable from our results in Table 3. Therefore, we conclude that X-ray calibration uncertainties do notstrongly affect our constraints on v z . We further notethat the significance of our kinetic SZ measurement from v z = 0 is nearly independent of the exact value of T e andthe slight differences in v z for the different temperaturesare due to the inverse relationship between T e and τ e fora fixed y , coupled with the inverse relationship between v z and τ e for a fixed kinetic SZ surface brightness.To assess the impact of the X-ray uncertainties on T e ,we also rerun all of our fits with vanishing uncertaintieson the X-ray derived T e . Even in the case of sub-clusterC, when using the Chandra -only measurement with un-certainties of T e +7 . − . keV, the derived uncertainties on v z increase by only (cid:39)
10% when using the measured un-certainties instead of assuming that the uncertainty on T e is equal to 0. Therefore, the X-ray uncertainties arenot significant in our overall error budget on v z .To determine the effect of the CIB on our measure-ment of v z , we also compute the SZ brightness underthe assumption that the CIB is completely and noise-lessly subtracted from the data. Specifically, comparedto our default noise realizations, we remove the noisefrom the undetected CIB, along with our uncertaintieson the subtracted CIB (see the Appendix). This resultsin a negligible change in the 140 GHz surface brightnessuncertainties, and a (cid:39) −
20% reduction in the 268 GHzsurface brightness uncertainties. There is a correspond-ing (cid:39) −
20% reduction in our derived uncertaintieson v z . In addition, we estimate the potential bias that5would result from not subtracting any of the Bolocamor SPIRE-detected galaxies from our 268 GHz data. Wefind that our best-fit 268 GHz surface brightness valueschange by (cid:39) (cid:39) v z . Therefore, noise from primary CMB fluctuationshas an effect on our kinetic SZ measurements that issmaller than, but comparable to, noise from CIB fluctua-tions. This mild sensitivity to primary CMB fluctuationsis due to the relative shallowness of our 140 GHz data,which have an rms of (cid:39) µ K CMB -arcmin (see Table 1of Sayers et al. 2013a).Examining the error budget in Table 2, the dominantuncertainties are associated with SZ measurement noiseand the exact choice of model used to describe the SZdata, although we note that uncertainties due to abso-lute flux calibration are only a factor of (cid:39)
Additional Potential Sources of Bias
Our analysis constrains the line-of-sight peculiar veloc-ities of two of the sub-clusters of MACS J0717.5+3745via a measurement of the SZ surface brightnesses withinsmall apertures centered on these sub-clusters. Due tothe complex dynamics in MACS J0717.5+3745, the SZsignal within these apertures may not be sourced by gasbound to a single sub-cluster with a single coherent bulkvelocity. However, as described in Section 3, the X-raydata show that sub-cluster B does appear to have a rel-atively intact core region. Therefore, at least for sub-cluster B, the assumption of a single bound ICM appearsto be justified. Sub-cluster C seems to be more disturbed,and this assumption may not be valid for that region.In addition to possible merger-induced gas inhomo-geneities, there are also likely to be line-of-sight projec-tion effects that cause the SZ signal within a single aper-ture to be sourced by the ICMs of multiple sub-clusters. In part to answer this question, Ruan et al. (2013) stud-ied the SZ signal from a simulated triple-merger systemin detail. Their simulated cluster is similar to MACSJ0717.5+3745, and contains one sub-cluster with a veloc-ity of 2500 km s − . They used kinetic SZ measurementsat 90 and 268 GHz to constrain the line-of-sight velocitiesof sub-clusters within the merger and found best-fit ve-locities that are consistent with the true velocities of thesub-clusters to within (cid:39) Cosmological Implications
Our kinetic SZ measurements are in good agreementwith the spectroscopic measurements of Ma et al. (2009)and indicate that sub-cluster B is moving with a line-of-sight velocity of (cid:39) − compared to the cen-ter of mass of the system. Ma et al. (2009) note thatthis value is close to the maximum expected velocitydue to infall from infinity. For example, if sub-clusterB starts from rest at infinity, and if the main cluster hasa mass of 1 . × M (cid:12) , then sub-cluster B would needto be within (cid:39) . − . This is in fairly goodagreement with N-body simulations, which indicate thata relative velocity of (cid:39) − is possible for aMACS J0717.5+3745-like cluster within the frameworkof the standard cosmological model. For example, Lee& Komatsu (2010) showed that mergers with main clus-ter masses above 1 × M (cid:12) at z = 0 . − when the sub-cluster is within the virial ra-dius of the main cluster. In addition, the cluster studiedby Ruan et al. (2013, see Section 9.3) was selected from acosmological simulation of a 400 h − Mpc cube, and oneof its sub-clusters has a line-of-sight velocity of 2500 kms − . Therefore, we conclude that while the velocity ofsub-cluster B is large, it is not in any tension with thestandard cosmological models. SUMMARY
We detect an extended SZ signal toward MACSJ0717.5+3745 at high significance in two observing bandswith Bolocam (140 and 268 GHz). The 268 GHz dataalso contain significant emission from dusty star form-ing galaxies. We subtract all of the galaxies brighterthan (cid:39)
Herschel -SPIREand Bolocam data, although both this subtraction, andthe un-subtracted population of dimmer galaxies, pro-duce a non-negligible amount of noise in our measure-ment of the SZ signal (see Section 9.2). Using a rig-orous decision tree based on application of the F-test,we find that a physically-motivated model composed ofa
Chandra -derived pseudo Compton- y map to describe6the thermal SZ signal, plus an additional template cen-tered on sub-cluster B with different normalizations at140 and 268 GHz, is the minimum model that is ade-quate to describe our data. We note that sub-clusterB has a measured spectroscopic line-of-sight velocity of+3200 km s − (Ma et al. 2009).From this best-fit model, we compute the two-bandSZ surface brightness toward sub-cluster B, along withthe most massive sub-cluster, C. We also compute theSZ surface brightness by directly integrating the Bolo-cam images, although the best-fit model is required toconstrain the DC signal level of these images, which isfiltered away by our data processing. For both the model-derived and directly integrated SZ surface brightnesses,we include uncertainties due to measurement noise andabsolute flux calibration. In addition, we include an un-certainty due to the variations in derived surface bright-nesses for a range of physically motivated models thatwe could have chosen to describe our data, and we findthat this uncertainty is similar to our measurement un-certainty.Using our measured SZ surface brightnesses towardsub-clusters B and C, along with our X-ray-derived elec-tron temperatures for each sub-cluster, we constrain aspectral model consisting of thermal and kinetic SZ com-ponents (see Figure 6). For these fits, we assume that theICM is isothermal within small apertures centered oneach sub-cluster, and we include corrections for relativis-tic effects. We find that a thermal SZ signal is adequateto describe the SZ surface brightnesses of sub-cluster C,but that an additional kinetic SZ signal is required forsub-cluster B. From our model-derived SZ surface bright-nesses, this kinetic SZ signal implies a line-of-sight veloc-ity of v z = +3450 km s − , while the directly integratedSZ surface brightnesses imply a line-of-sight velocity of v z = +2550 km s − , both of which are in good agree-ment with the spectroscopic measurement of Ma et al.(2009, See Figure 5). From the model fit we find that(1 − Prob[ v z ≥ . × − , which corresponds tobeing 4 . σ from 0 for a Gaussian distribution. Similarly,from the direct integration of the SZ surface brightness,we find that (1 − Prob[ v z ≥ . × − , which corre-sponds to being 2 . σ from 0 for a Gaussian distribution.We consider potential biases in our derived values of v z due to possible systematics in the X-ray derived T e ,and due to merger and projection effects as a result ofthe complex dynamics of this cluster, and we find thatneither bias is likely to be significant compared to ourmeasurement uncertainties. We find that raw SZ mea- surement sensitivity limits our constraints on v z , and un-certainties from the X-ray data, the CIB, the CMB, andflux calibration are sub-dominant, although deeper SZmeasurements will likely be limited by some combina-tion of these factors. Our data, combined with the re-sults from Ma et al. (2009), indicate that sub-cluster B ismoving with a line-of-sight velocity of (cid:39) +3000 km s − ,a value that is high, but not in tension with standardcosmological models. ACKNOWLEDGMENTS
We acknowledge the assistance of: the day crew andHilo staff of the Caltech Submillimeter Observatory, whoprovided invaluable assistance during data-taking forthis data set; Kathy Deniston, Barbara Wertz, and Di-ana Bisel, who provided effective administrative sup-port at Caltech and in Hilo; the Bolocam observa-tions were partially supported by the Gordon and BettyMoore Foundation. JS was supported by NSF/AST-0838261, NASA/NNX11AB07G, and the Norris Foun-dation CCAT Postdoctoral Fellowship; support for TMwas provided by NASA through Einstein Fellowship Pro-gram grant number PF0-110077 awarded by the
Chan-dra
X-ray Center, which is operated by the Smithso-nian Astrophysical Observatory for NASA under con-tract NAS8-03060; PMK was supported by a NASAPostdoctoral Program Fellowship; NC was partially sup-ported by a NASA Graduate Student Research Fel-lowship; AM was partially supported by NSF/AST-0838187 and NSF/AST-1140019; EP and JAS were par-tially supported by NASA/NNX07AH59G; SS was sup-ported by NASA Earth and Space Science FellowshipNASA/NNX12AL62H; KU acknowledges partial sup-port from the National Science Council of Taiwan grantNSC100-2112-M-001-008-MY3 and from the AcademiaSinica Career Development Award. A portion of thisresearch was carried out at the Jet Propulsion Labo-ratory, California Institute of Technology, under a con-tract with the National Aeronautics and Space Admin-istration. This research made use of the Caltech Sub-millimeter Observatory, which was operated at the timeby the California Institute of Technology under coop-erative agreement with the National Science Founda-tion (NSF/AST-0838261). This work is based in parton observations made with
Herschel , a European SpaceAgency Cornerstone Mission with a significant participa-tion by NASA. Partial support for this work was providedby NASA through an award issued by JPL/Caltech.
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There is a significant amount of signal from unresolved dusty star-forming galaxies (e.g., Blain et al. 2002) in our268 GHz Bolocam map, and we describe our treatment of these galaxies in this Appendix. Unlike the resolved SZ signalwe seek to measure, all of the dusty star-forming galaxies in our Bolocam image are unresolved. Therefore, to maximizeour sensitivity to these unresolved sources, we process the 268 GHz data using an adaptive principal component analysis(PCA) algorithm in place of the common-mode subtraction we use for our SZ analysis. For brevity, we refer to the8maps generated by these reductions as the adaptive-PCA map and the common-mode-subtraction map. The detailsof the adaptive-PCA algorithm we use for this analysis are given in Wu et al. (2012). This processing results in anadaptive-PCA map with a noise rms of 0.7 mJy/beam, which is approximately equal to the confusion noise fromunresolved star-forming galaxies. We then subtract a template of the extended SZ signal from the adaptive-PCA mapby fitting a gNFW profile to the common-mode-subtraction map, processing the gNFW model through the adaptive-PCA reduction, and subtracting the processed model from the adaptive-PCA map (see Figure 7). The resultingextended-SZ-subtracted adaptive-PCA map contains a total of 8 unresolved galaxy candidates with a S/N >
4, and wemeasure the best-fit flux density for each of these candidates after accounting for the filtering effects of the adaptive-PCA reduction (see Table 4). Using these best-fit flux densities and positions, we then process these 8 candidatesthrough the common-mode reduction and subtract them from the common-mode-subtraction map used for our SZanalysis. In addition, we generate 1000 random realizations of each of the 8 candidates based on the measurementuncertainties on the best-fit flux densities, and we add one realization of the uncertainty for each candidate to each ofthe 1000 noise realizations described in Section 4.1.In addition to our Bolocam data, we also search for dusty star-forming galaxies in three-band (250, 350, and 500 µ m)observations obtained with the SPIRE photometer. All of the SPIRE images are dominated by confusion noise fromunresolved galaxies (Nguyen et al. 2010), and the effective rms is 7.2, 5.3, and 5.8 mJy/beam at 250, 350, and 500 µ m.The SPIRE data are reduced using the Herschel
Interactive Processing Environment HIPE (Ott et al. 2006; Ott 2010),along with the HerMES SMAP package (Levenson et al. 2010; Viero et al. 2013). Source catalogs are then compiledusing the SCAT procedure (Smith et al. 2012), and we identify a total of 200 source candidates within the 14 (cid:48) × (cid:48) Bolocam coverage with S/N > S ( ν ) = A × ν . × B ( ν, T ) , (1)where B ( ν, T ) is the Planck blackbody equation and the normalization A and temperature T are free parameters. Inperforming these fits, we make the assumption that this greybody parameterization describes the emission within theSPIRE PSF regardless of whether the emission is sourced by a single galaxy or many galaxies. Consequently, we do notinclude the effects of confusion noise in these fits. Using the greybody fits to the SPIRE data, we estimate the 268 GHzflux density centered on each of the 200 SPIRE candidates. We note that, probably due to the fact that multiplesources above the SPIRE measurement noise RMS are likely to be present within the extent of the SPIRE PSF, thissimple greybody model does not provide an adequate fit to all of the SPIRE source candidates. Specifically, 1/3 ofcandidates produce a fit PTE < .
05, indicating that a greybody fit does not describe the emission detected within theSPIRE PSF for those candidates. In addition, even if we discard these 1/3 of the candidates, the distribution of PTEvalues for the remaining 2/3 of the candidates is still marginally inconsistent with a uniform distribution, quantified bya KS test PTE of 0.03. This implies that a greybody fit is inadequate to describe a significant fraction of the SPIREcandidates. Unfortunately, it is not practical to fit a more complicated model to the 3-band SPIRE data alone due tothe lack of spectral information, and so there is no clear model extension to obtain a better fit quality for the SPIREcandidates that are not adequately described using a greybody model. We discuss the implications of this modelinglimitation in more detail below.We find a total of 14 of these SPIRE candidates are located within 30 (cid:48)(cid:48) of the 8 Bolocam candidates, indicatingthat they are possible counterparts. To compare the Bolocam and SPIRE measurements, we first estimate the best-fitnoise-de-boosted flux density for the 8 candidates detected by Bolocam according to the AzTEC de-boosting algorithmpresented in Austermann et al. (2009) by interpolating the tabulated values presented in Downes et al. (2012). Asshown in Figure 8 and Table 4, we in general find good agreement between the de-boosted Bolocam flux densities andthe sum of the extrapolated SPIRE flux densities for all of the likely counterparts. Therefore, the Bolocam candidatesare robust detections.Discarding the 14 SPIRE candidates that are likely counterparts of the Bolocam candidates because they have alreadybeen subtracted from the common-mode-subtraction map, along with 24 SPIRE candidates that have an extrapolated268 GHz S/N <
2, we then generate an image from the remaining 162 SPIRE candidates using the extrapolated268 GHz SPIRE flux densities convolved with the Bolocam PSF. This image is then processed through the adaptive-PCA reduction, and we subtract it from the corresponding extended-SZ-and-Bolocam-candidate-subtracted adaptive-PCA map (see Figure 7). Removal of this SPIRE template, which we generate independently from our Bolocam data,results in a significant reduction in the rms of the Bolocam image, with a ∆ χ = 166. To put this value in context, thetotal χ of the SPIRE template is 240, and therefore a perfect correlation between the SPIRE extrapolations and theBolocam data would have resulted in a ∆ χ = 240. As a further quality check, we compute the normalization of theSPIRE template that best fits our 268 GHz Bolocam extended-SZ-and-Bolocam-candidate-subtracted adaptive-PCAmap and find a value of 0 . ± .
09 including flux calibration uncertainties. The consistency of this value with unityindicates that the SPIRE template is a good description of the CIB in the 268 GHz Bolocam data.To subtract these 162 SPIRE-detected sources from our common-mode-subtraction map, we process the SPIREtemplate through the common-mode reduction and subtract the resulting map from the corresponding common-mode-subtraction map we use for SZ analysis. We also generate 1000 map realizations with flux densities for each source9
Fig. 7.—
Bolocam 268 GHz images we obtain from the adaptive-PCA reduction. Clockwise from upper left: nominal image, image aftersubtracting the best-fit extended-SZ template, image after also subtracting the 8 unresolved sources detected by Bolocam, and image afteralso subtracting the 162 sources detected by SPIRE and extrapolated to Bolocam’s band using a greybody fit. The blue contours showS/N, starting at 4 and separated by 1. There are no contours around the bright regions in the corners of the images, due to the highernoise in these regions as a result of reduced integration time relative to the central region. Note that even in this heavily filtered image,an extended SZ signal is detected at high significance. The crosses show: Bolocam detections (red), likely SPIRE counterparts to thosedetections (cyan), and all other SPIRE detections with an extrapolated S/N > (cid:48) diameter aperturescentered on sub-cluster C (lower left) and sub-cluster B (upper right). TABLE 4Unresolved Sources Detected by Bolocam at 268 GHz
RA (J2000) dec (J2000) flux density (mJy) de-boosted (mJy) SPIRE extrapolated (mJy) SPIRE distance ( (cid:48)(cid:48) )7:17:19.4 37:46:41 7 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . Note . — Unresolved sources that we detect with a S/N ≥ Fig. 8.—
Two of the eight candidate galaxies detected by Bolocam. In each plot the de-boosted Bolocam flux density is shown as a blackdiamond, and the SPIRE flux densities are shown as colored diamonds with a different color for each possible counterpart. The lines showgreybody SED fits to the SPIRE data only, with a separate fit for each possible counterpart. randomly distributed according to the uncertainty on the extrapolation and add one such realization to each of the1000 noise realizations. As described above, the likely Bolocam counterparts are not included in this SPIRE-sourcetemplate to avoid potential double subtractions, and the S/N < (cid:38) (cid:39)
100 galaxies with lower flux densities, significantlyreducing the contamination from these sources on our measurement of the SZ signal (see Figure 9, left).Due to the fact that the SPIRE candidates are in general not well described by the greybody model, the derived un-certainty on the extrapolation is likely to be underestimated. Therefore, to determine the effect that this underestimatemight have on our SZ results, we artificially increase the uncertainties on the SPIRE photometry for each candidateuntil the reduced χ of the greybody fit is equal to 1. For candidates with a reduced χ <
1, the uncertainties are leftunchanged. Although this procedure is unphysical, it does provide a reasonable basis for estimating the uncertainty onthe extrapolation for these sources. We find that the difference between the estimated uncertainties on the 268 GHzSZ brightnesses for sub-clusters B and C with and without including this artificial increase on the extrapolation un-certainty is < × − MJy sr − , or (cid:46)
1% of the nominal uncertainties. Therefore, we have not accounted for thepotentially underestimated uncertainties on the SPIRE candidates that are poorly fit by the greybody model.In addition, we also estimate the uncertainty on the extrapolation due to our particular choice of greybody model.Specifically, we fixed the spectral index of the greybody to 1.7, while the measured spectral indices from large sourcecatalogs vary between (cid:39) − σ bounds determined by Roseboom et al. (2013). Using the templates determined from these spectral indices,the 268 GHz SZ brightnesses toward sub-clusters B and C change by 0 . − .
005 MJy sr − , or by as much as 10% oftheir nominal uncertainties. When added in quadrature with our overall uncertainties this amount is negligible, andwe therefore have not included it in our uncertainty estimates.Furthermore, we note that the best-fit amplitude of our nominal CIB template using Bolocam data is 0 . ± . (cid:46) .
001 MJy sr − compared to those foundwith the default normalization of the template, or by approximately 2% of our nominal uncertainties. Therefore, thebias associated with a potential over-estimate of the CIB template is negligible, and we have not attempted to accountfor such a bias in our analysis.Bolocam and SPIRE do not individually detect the faint galaxies that comprise most of the CIB. Consequently, weuse the CIB model determined by B´ethermin et al. (2011) to account for the noise fluctuations from these undetectedgalaxies, as it provides a reasonable estimate for the behavior of the component of the CIB below the SPIRE detectionlimit. We model the undetected CIB using a number counts distribution obtained by subtracting the number countsalready detected by SPIRE and Bolocam from the B´ethermin et al. (2011) number counts model. We then generate1000 random sky realizations of the sources in this population, process each such realization through the common-modereduction, and add one realization of this faint CIB model to each of our 1000 noise realizations.We note that the B´ethermin et al. (2011) model was calibrated using observations of blank sky and therefore isnot necessarily an accurate description of the CIB toward a massive cluster like MACS J0717.5+3745. Although theemission from cluster-member galaxies at 268 GHz is likely to be negligible compared to the background CIB, the For example, see the arguments presented in Section 4 ofSayers et al. (2013b) based on the results presented in Geach et al. (2006); Bai et al. (2007); Marcillac et al. (2007); Finn et al. (2010);Rawle et al. (2012). Fig. 9.—
Left: number of galaxies above a given 268 GHz flux density within the 14 (cid:48) × (cid:48) Bolocam image. The solid black line denotesthe B´ethermin et al. (2011) model prediction, green denotes the Bolocam detections, red denotes the extrapolated SPIRE detectionsafter removing possible counterparts to the Bolocam detections along with S/N < significant magnification of the background due to gravitational lensing can distort the number counts. In particular,lensing preserves the total surface brightness of the CIB, but causes a significant and spatially dependent change in thenumber counts (Zemcov et al. 2013). Our data show hints of this change as an excess of sources at bright flux densities,which is consistent with measurements toward massive clusters using AzTEC at the same wavelength (Wardlow et al.2010; Downes 2009). It is therefore not clear how well the unlensed B´ethermin et al. (2011) model describes the faintpopulation of dusty star-forming galaxies toward MACS J0717.5+3745.To test the validity of the B´ethermin et al. (2011) model in describing our MACS J0717.5+3745 data, we add arandom sky realization to each jackknife realization of the adaptive-PCA map, where the sky realizations are based onthe aforementioned difference between the B´ethermin et al. (2011) model and our detected number counts. We findthat adding these random sky realizations increases the noise rms by 12.3%. We then fit a Gaussian to the distributionsof pixel S/N values for the adaptive-PCA map jackknife realizations, and to the actual data after subtraction of theextended-SZ template, the Bolocam detections, and the extrapolated SPIRE detections (see Figure 9, right). We findthat the Gaussian standard deviations returned by the fits differ by 11 . ± . µ m, contains a non-negligible amount of diffuse SZ signal. This signal would also be correlatedacross the multiple bands, and therefore such an analysis could subtract SZ signal from the Bolocam data in addition toCIB signal. Furthermore, the effective reddening of the CIB due to the SZ signal in the SPIRE data could potentiallycause a significant over-estimate of the signal when extrapolated to the Bolocam bands. Consequently, to mitigate theseeffects, we have chosen to subtract only the unresolved bright galaxies individually detected by SPIRE, which shouldnot be significantly contaminated by the diffuse SZ signal. Although beyond the scope of this work, an optimal analysiswould jointly constrain a model of the SZ and CIB signals via a simultaneous fit to both the SPIRE and Bolocamdata. However, given the relative dimness of the SZ signal in the SPIRE bands, along with the relative dimness ofthe CIB signal in the Bolocam bands, the improvement from such a joint fit is likely to be minimal compared to ouranalysis procedure.We note that the fluctuations from the CIB are accounted for in our 140 GHz data by adding noise realizationsgenerated according to the power spectrum measurements from SPT (Hall et al. 2010). We do not attempt to subtractany individual galaxies due to the large, and consequently potentially untrustworthy, spectral extrapolation that wouldbe required from the SPIRE measurements. In addition, as noted above, there are very few galaxies detected within theextended region containing bright SZ signal, and none of those galaxies are particularly bright. We note that this is ingeneral true for massive clusters, as shown in Zemcov et al. (2013). However, to verify that the CIB is sufficiently dimthat we can neglect subtracting it at 140 GHz, we extrapolated the SPIRE detections to 140 GHz and removed themfrom the Bolocam data. Even if this large extrapolation is potentially untrustworthy, it should provide a reasonableestimate of the potential brightness of the CIB at 140 GHz. When we subtract this extrapolated CIB, we find that2the best-fit 140 GHz SZ brightnesses toward both sub-cluster B and sub-cluster C changes by (cid:39) × − MJy sr −1