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Galaxy cluster cosmology with the Atacama Cosmology Telescope Hasselfield, Matthew 2013

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Galaxy Cluster Cosmology with the Atacama CosmologyTelescopebyMatthew HasselfieldBSc, University of Manitoba, 2003MSc, University of British Columbia, 2006a thesis submitted in partial fulfillmentof the requirements for the degree ofDoctor of Philosophyinthe faculty of graduate and postdoctoral studies(Physics)The University Of British Columbia(Vancouver)December 2013c? Matthew Hasselfield, 2013AbstractObservations of the Cosmic Microwave Background (CMB) are crucial components of ourunderstanding of cosmology. Modern high resolution, ground-based CMB survey instru-ments provide important information about the mass and energy content of our presentUniverse and the high-energy physics of the Big Bang.In this work we present several aspects of our work on the Atacama Cosmology Tele-scope (ACT), a 6m telescope in Northern Chile that observed the CMB in three millimetrewavelength bands from 2007?2010. We begin with a description of the Multi-Channel Elec-tronics readout system, an important component of the data acquisition systems for ACTand several other CMB observatories. The system provides room-temperature electronicsand software for controlling and reading out arrays of Transition Edge Sensor bolometersvia a cryogenic time-domain multiplexing system.We next present our measurement of the ACT point spread function, or beam, usingobservations of Solar System planets. An accurate understanding of the beam and itscovariant error is essential for interpretation of astrophysical and cosmological signal in theACT data. We then use our understanding of the beam and the instrument calibrationto measure the brightness temperatures of Uranus and Saturn at millimetre wavelengths.Precise measurements of planetary brightnesses provide convenient calibration sources forother observatories at these wavelengths.Finally we present a sample of galaxy clusters detected in the ACT maps. We develop anew approach for the analysis of Sunyaev-Zeldovich signal that incorporates a model for thetypical cluster pressure to better understand selection effects and evaluate cluster masses.Addressing the current level of systematic uncertainty in the overall mass calibration ofclusters, we explore the cosmological constraints obtained when calibrating the mass relationbased on pressure profile measurements from X-ray data and from models that take differentapproaches to the cluster physics. Ultimately we use dynamical mass estimates based onoptical velocity dispersion measurements to obtain constraints on the amplitude of scalarfluctuations, the matter density, the Dark Energy equation of state parameter, and the sumof the neutrino mass species.iiPrefaceThroughout my doctoral studies I have been involved in the Atacama Cosmology Tele-scope (ACT) collaboration. The present work does not describe all of my contributions toACT, nor have any of the results here been developed in isolation from other collaborationmembers.The work presented in Chapter 2 relates to specialized telescope instrumentation devel-oped at the University of British Columbia. While not involved in the original design ofthe instrument, I contributed significant improvements over several years to system soft-ware, optimization algorithms, the implementation of new features, and assisted with theintegration and use of the system in several observatories. For completeness, the text inChapter 2 does include descriptions of certain features of the instrument with which I amfamiliar, but to which my contributions were marginal.The majority of the text in Chapters 3 and 4 has been extracted from the manuscriptM. Hasselfield et al., ?The Atacama Cosmology Telescope: Beam Measurements and theMicrowave Brightness Temperatures of Uranus and Saturn,? which has been accepted forpublication in the Astrophysical Journal Supplement Series. I conducted the bulk of thedata reduction with my primary co-author, extending previous approaches as described inthe text. The techniques for Fourier space treatment of the planetary signal are my owninventions. The modeling and fitting of the Saturn ring model was primarily the work of aco-author. I wrote the paper, with advice from various co-authors.The text in Chapters 5 and 6 has been published as M. Hasselfield et al., ?The AtacamaCosmology Telescope: Sunyaev-Zeldovich selected galaxy clusters at 148 GHz from threeseasons of data,? Journal of Cosmology and Astroparticle Physics, 7:008, July 2013. Thiswork is presented here with only minor modifications. I performed the data analysis de-scribed in these chapters, starting from the ACT survey maps. The galaxy cluster detectionand confirmation program was already underway when I began work on this project, butthe analysis techniques are my own innovations. In particular, the Profile Based AmplitudeAnalysis and the approach to the cosmological likelihood formalism were my own ideas,developed as solutions to the challenges of understanding these data. I wrote the majorityof this paper, with contributions from my two primary co-authors, and under the guidanceof the rest of the ACT collaboration.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xviii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Cosmological Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 The Cosmic Microwave Background . . . . . . . . . . . . . . . . . . . . . . 41.3 Cosmology from Galaxy Cluster Surveys . . . . . . . . . . . . . . . . . . . . 71.4 Galaxy Cluster Observations . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4.1 Optical Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4.2 X-ray Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.4.3 Microwave Observations . . . . . . . . . . . . . . . . . . . . . . . . . 121.5 The Atacama Cosmology Telescope (ACT) . . . . . . . . . . . . . . . . . . 162 Bolometer Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . 192.1 Readout System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.1.1 Cold Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.1.2 Warm Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.1.3 Control Computer and Low-Level Software . . . . . . . . . . . . . . 242.2 Multiplexing Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3 SQUID Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3.1 Setting up the Series Array . . . . . . . . . . . . . . . . . . . . . . . 272.3.2 Setting up the First and Second Stage SQUID . . . . . . . . . . . . 282.3.3 Finalizing the Lock Point . . . . . . . . . . . . . . . . . . . . . . . . 30iv2.4 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.4.1 Servo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.4.2 Readout Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.4.3 Flux Jumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.4.4 High Speed Readout . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.4.5 Raw Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.4.6 Internal Commanding . . . . . . . . . . . . . . . . . . . . . . . . . . 353 Beams and Window Functions . . . . . . . . . . . . . . . . . . . . . . . . . 363.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2 Observations and Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2.1 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2.2 Planet Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.2.3 Map Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.3 Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.3.1 Radial Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.3.2 Harmonic Transforms and Window Functions . . . . . . . . . . . . . 443.3.3 Beam and Calibration Covariance . . . . . . . . . . . . . . . . . . . 453.3.4 Correction for Systematics . . . . . . . . . . . . . . . . . . . . . . . . 483.3.5 Mean Instantaneous vs. Effective Beam . . . . . . . . . . . . . . . . 483.4 Planet Brightness Measurements . . . . . . . . . . . . . . . . . . . . . . . . 503.4.1 Planet Amplitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.4.2 Calibration Parameters from Uranus Observations . . . . . . . . . . 533.4.3 Relation to WMAP -Based Calibration . . . . . . . . . . . . . . . . . 554 Planet Temperature Measurements . . . . . . . . . . . . . . . . . . . . . . 584.1 Uranus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.1.1 Temperature Measurement . . . . . . . . . . . . . . . . . . . . . . . 594.1.2 Comparison to Previous Measurements and Models . . . . . . . . . . 594.1.3 Empirical Model for Uranus Temperature . . . . . . . . . . . . . . . 614.2 Saturn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.2.1 Ring Model and Temperature Constraints . . . . . . . . . . . . . . . 614.2.2 Comparison to Previous Measurements . . . . . . . . . . . . . . . . 625 The ACT Equatorial Galaxy Cluster Sample . . . . . . . . . . . . . . . . 665.1 Maps and Cluster Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.1.1 Equatorial Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.1.2 Gas Pressure Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.1.3 Galaxy Cluster Detection . . . . . . . . . . . . . . . . . . . . . . . . 705.1.4 Galaxy Cluster Confirmation . . . . . . . . . . . . . . . . . . . . . . 74v5.2 Recovered Cluster Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 765.2.1 Profile Based Amplitude Analysis . . . . . . . . . . . . . . . . . . . . 765.2.2 Cluster Mass and SZ Quantity Estimates . . . . . . . . . . . . . . . 815.2.3 The Planck Pressure Profile . . . . . . . . . . . . . . . . . . . . . . . 835.2.4 Scaling Relation Calibration from SZ Models . . . . . . . . . . . . . 845.2.5 Scaling Relation Calibration from Dynamical Masses . . . . . . . . . 875.2.6 Completeness Estimate . . . . . . . . . . . . . . . . . . . . . . . . . 895.2.7 Redshift distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.3 Comparison with Other Catalogues . . . . . . . . . . . . . . . . . . . . . . . 935.3.1 Comparison to Planck Early SZ Sample . . . . . . . . . . . . . . . . 935.3.2 Comparison to Weak Lensing Masses . . . . . . . . . . . . . . . . . . 965.3.3 Comparison to SZA Measurements . . . . . . . . . . . . . . . . . . . 965.3.4 Optical Cluster Catalogues . . . . . . . . . . . . . . . . . . . . . . . 975.3.5 X-ray Cluster Catalogues . . . . . . . . . . . . . . . . . . . . . . . . 985.3.6 Radio Point Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . 995.4 Revisiting the ACT Southern Clusters . . . . . . . . . . . . . . . . . . . . . 1046 Cosmological Constraints from the ACT Equatorial Galaxy ClusterSample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136.1 Likelihood Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136.2 Parameter Constraints for Fixed Scaling Relations . . . . . . . . . . . . . . 1196.3 Parameter Constraints from Dynamical Mass Data . . . . . . . . . . . . . . 1246.3.1 Neutrino Mass Constraints . . . . . . . . . . . . . . . . . . . . . . . 1276.3.2 wCDM Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.3.3 Scaling Relation Constraints . . . . . . . . . . . . . . . . . . . . . . 1316.4 Comparison to Other Cluster-Based Constraints . . . . . . . . . . . . . . . 1326.4.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138viList of TablesTable 3.1 Number of Saturn and Uranus observations selected for cal-ibration purposes for each season and array. . . . . . . . . . . 38Table 3.2 Summary of beam parameters by array and season. . . . . . . . 43Table 3.3 Pointing variance and beam correction parameters. . . . . . . 51Table 3.4 Properties of planetary data and calibration model fit pa-rameters by season and array. . . . . . . . . . . . . . . . . . . . . 56Table 4.1 RJ temperature measurements of Uranus and Saturn. . . . . 62Table 5.1 Scaling relation parameters . . . . . . . . . . . . . . . . . . . . . . 86Table 5.2 Comparison of Planck and ACT cluster measurements . . . . . . 94Table 5.3 Confirmed galaxy clusters in the ACT Equatorial region. . . 101Table 5.4 SZ-derived mass estimates for ACT clusters. . . . . . . . . . . . 105Table 5.5 Uncorrected central Compton parameters for the clustersfrom Marriage et al. (2011). . . . . . . . . . . . . . . . . . . . . . . 110Table 5.6 SZ-derived mass estimates for the ACT Southern cluster sam-ple of Marriage et al. (2011). . . . . . . . . . . . . . . . . . . . . . 112Table 6.1 Cosmological parameter constraints for the ?CDM model. . 121Table 6.2 Cosmological parameter constraints for the flat wCDM model.123Table 6.3 Cosmological parameter constraints for ?CDM, extended withone additional parameter for non-zero neutrino density. . . . 128Table 6.4 Cosmological parameter constraints for the flat wCDM model,for various combinations of WMAP7, ACT cluster data (withscaling relation constrained using dynamical mass data), andType Ia Supernovae results. . . . . . . . . . . . . . . . . . . . . . . 130viiList of FiguresFigure 1.1 All-sky map of the CMB temperature variations from the WMAP satel-lite 9-year results, from Bennett et al. (2013). Reproduced by permissionof the AAS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Figure 1.2 Angular power spectrum measurements from WMAP , ACT, and SouthPole Telescope (SPT), highlighting the acoustic peaks originating in theprimordial plasma. From Das et al. (2013). . . . . . . . . . . . . . . . . 6Figure 1.3 Angular power spectrummeasurements from ACT in 148GHz and 218GHzbands. Secondary anisotropies dominate the power beginning at ? ? 1800in the 218GHz, and at somewhat larger ? at 148GHz. Grey points arefrom WMAP 7-year results (Larson et al., 2010). From Das et al. (2013). 7Figure 1.4 An analytic form for the mass function (solid lines) fit to cluster abun-dances from several different cosmological simulations (data points). Thethree data sets and best fit lines correspond to masses defined at over-densities of, from top to bottom, ? = 200, 800, and 3200 with respectto the mean matter density. From Tinker et al. (2008). Reproduced bypermission of the AAS. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Figure 1.5 Composite image of galaxy cluster Abell 383 in X-ray (purple) and opticalwavelengths (white). X-ray: NASA/CXC/Caltech/A. Newman et al./TelAviv/A. Morandi & M. Limousin; Optical: NASA/STScI, ESO/VLT,SDSS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 1.6 The intensity of the SZ signal as a function of frequency for constantCompton y parameter. This is computed from the product of the CMBintensity and the SZ spectrum f(?). Coloured regions indicate the ACTobserving bands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Figure 1.7 Cross-sections of the Compton y parameter through the centres of clus-ters of several masses, from integration of the electron pressure profilein Arnaud et al. (2010), in a standard ?CDM cosmology. The clustermasses, from top to bottom in each panel, are M500c = 1015, 3 ? 1014,and 1014 M?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14viiiFigure 1.8 SZ signal at 150GHz based on simulations (from Springel et al., 2001)with typical CMB anisotropies. Images are one degree square and grayscaleis CMB temperature in ?K. Republished with permission of Annual Re-views, from Carlstrom et al. (2002); permission conveyed through Copy-right Clearance Center, Inc. . . . . . . . . . . . . . . . . . . . . . . . . . 15Figure 1.9 Left : Atacama Cosmology Telescope during installation, with partiallycompleted ground shield. Photo credit: Michele Limon. Right : Viewshowing primary mirror. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Figure 2.1 Bolometer count in recent ground-based (square), balloon-based (circle)and space-based (star) observatories. Filled symbols identify experimentsthat use MCE for readout. . . . . . . . . . . . . . . . . . . . . . . . . . 19Figure 2.2 Left : Current-voltage characteristic curve of a TES detector (solid line),measured during ACT observations in 2008. As the device voltage de-creases (from right to left), the device transitions from ohmic behaviour(dashed line), to a regime where the device dissipates a constant powerIV ? 5.0 pW (dotted line). Right : The resistance of the device as afunction of dissipated power. . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 2.3 Left : Diagram of First Stage SQUID operation. Current ITES from thedetector is inductively coupled to the SQUID loop (center), as is the cur-rent IFB from a feedback line controlled by external, room-temperatureelectronics. The room-temperature electronics also control the SQUIDbias current IS1. The SQUID voltage VS1 is a periodic function of thetotal flux, ?TES ? ?FB, and is fed into the next stage of the amplifierchain. The principle of operation of the S2 and SA stages is essentiallythe same as presented here for the S1. Right : Measured response from aFirst Stage SQUID, acquired by ramping the IFB at constant ITES. AllSQUID response curves shown in this work were acquired on the ACT148GHz array during regular ACT observations between 2008 and 2010. 22Figure 2.4 Schematic of SQUID multiplexing scheme for reading out TES signal.Figure Courtesy of R. Doriese. . . . . . . . . . . . . . . . . . . . . . . . 23Figure 2.5 Block diagram showing MCE component connections and electrical con-nections to control computer, Sync Box, and cryostat. . . . . . . . . . . 24Figure 2.6 SQUID tuning plot for the ?SA Ramp? stage. This curve is taken inopen loop by ramping the SA feedback. A locking region (shaded) isfound between two values of the feedback (dashed lines) that lie on asingle slope of the V?? curve, and the midpoint of this region is used todetermine the ERROR value at which subsequent servos will be set tolock. Note that the SA feedback is not fixed as a result of this analysis. 28ixFigure 2.7 V?? curves acquired for the SA at several different bias values. Thealgorithm selects the bias that yields the largest peak-to-peak response(shown in bold). The flat response regions are associated with the lowestbias values, and are an indication that the Josephson junctions are stillsuperconducting. The y-axis offsets of the curves are an artifact of thefull readout circuit configuration. . . . . . . . . . . . . . . . . . . . . . 29Figure 2.8 SQUID tuning plot for the ?S2 Servo? stage. This curve is taken in closedloop while ramping the S2 feedback, and servoing with the SA feedbackto keep the error signal at 0. The analysis is similar to the SA Rampcurve; here we fix the value of the SA FB such that it corresponds to themean flux over a single edge of the S2 V?? curve. . . . . . . . . . . . . . 30Figure 2.9 SQUID tuning plot for the ?S1 Servo? stage. An S2 feedback is chosenas the result of this operation. . . . . . . . . . . . . . . . . . . . . . . . 30Figure 2.10 SQUID tuning plot for the ?S1 Ramp? stage. This curve is taken in openloop by ramping the S1 feedback. The response here is the final open loopresponse of the SQUID chain. The dashed line is chosen to lie half waybetween the maximum and minimum of the V?? curve. The resultingvalue is used to set the ADC offset (Eoffset) so that the ERROR signalreturns 0 through the center of the open loop response. . . . . . . . . . 31Figure 3.1 Beam maps for each season and array, formed from the average of se-lected Saturn maps. Gray scale is logarithmic. Each panel is 12? by 12?.Each contributing Saturn map incorporates all live detectors in the array.The well-resolved Airy rings indicates that the relative detector offsetsare accurately known. The frequency labels correspond to the effectivefrequencies for CMB spectrum radiation (Swetz et al., 2011). . . . . . . 40Figure 3.2 Wing model fitted to binned radial profile data. Points shown, and thebest-fit model (solid line), are from a typical individual Saturn observa-tion for each array. A baseline is fit simultaneously and has been removedfrom the data points. The shaded area represents the standard deviationof all individual best-fits to wing models for the 2010 season. . . . . . . 42xFigure 3.3 Upper panels: Beam transforms B? for each array. Beams shown are forthe 2008 season. The total beam is the sum of the contribution fromthe core of the beam, and the extrapolated wing. Lower panels: Diag-onal error from the covariance matrix for the renormalized beam. Thebeam normalization has been fixed at calibration ? = 700 (1500) for the148GHz (218GHz and 277GHz) array(s), as described in Section 3.3.3.Note that these curves show uncertainty, not systematic trends, and theydo not include additional uncertainty from the empirical corrections ofSection 3.3.5. The full covariance matrix shows an anti-correlation be-tween the beam error at angular scales above the calibration ? and beamerror below the calibration ?. The window function is B2? and thus itsfractional error is 2?B?/B?. . . . . . . . . . . . . . . . . . . . . . . . . . 46Figure 3.4 Variation of planet amplitude measurements with angular scale. Eachpanel shows mean fractional deviation of ??? relative to ?? (solid line)and the standard deviation of all individual ???/?? curves (grey band) fora particular season, array, and planet. See Section 3.4.1 for definitionsof ??? and ??. We show results from 148GHz 2008 (left panels), wherethere is a high degree of consistency between the planet observations andthe season mean beam. We also show results for 218GHz 2010 (rightpanels), where there is somewhat more variance in the curves (which istypical of the 218GHz array) and where the Uranus observations deviatesignificantly from the mean beam (which is seen in all arrays in 2010).Differences between Uranus and Saturn are indicative of 2% changes inthe beam focus during the season; such changes have been accounted forin the season effective beam by fitting a correction parameter to maps ofpoint sources in the season maps as described in Section 3.3.5. . . . . . 53Figure 4.1 Measurements of the Uranus brightness temperature from this work,Weiland et al. (2011, WMAP), and Griffin and Orton (1993, G&O). TheG&O points include data from that work as well as Ulich (1981) andOrton et al. (1986). The dotted line shows the model of G&O. G&Odata are calibrated to a Ulich-Wright hybrid model for Mars brightnessthat interpolates between 90 and 857 GHz and carries an estimated 5%systematic error. The solid line is our best-fit empirical model, using onlythe two highest frequency points from WMAP , the two ACT points, andthe G&O points above 600 GHz. . . . . . . . . . . . . . . . . . . . . . . 63xiFigure 4.2 Binned data and resulting best-fit two-component model of effective Sat-urn brightness vs. ring opening angle (B) relative to observer. Themodel is symmetric about B = 0 by construction. As the absolute valueof B increases, the increased radiation from the rings and decreased fluxfrom the obscured disk leads to a local minimum in the total effectivebrightness at B ? 9? (13?) at 149 GHz (219 GHz). The model is fittedindependently for each frequency band. Error bars correspond to theerror in the mean of observations contributing to each point, but fits in-clude additional error due to calibration, which is covariant within eachseason and in some cases between seasons. Approximate mean dates ofobservation are, from left to right: Nov/08; Dec/08; Jun/10; Apr/10;Dec/09; Dec/10; and Dec/10. The sign convention is such that B < 0corresponds to negative values of the sub-Earth latitude. . . . . . . . . 64Figure 4.3 Measurements of the Saturn disk brightness temperature from ACT,Weiland et al. (2011, WMAP), and Goldin et al. (1997, G97). Pointsfrom G97 have been recalibrated as described in the text. Frequencyerror bars on ACT and G97 points indicate bandwidth. Temperatureerror bars on G97 points do not include calibration uncertainty. Thegreen dashed line is a spectral model from Weisstein and Serabyn (1996,WS96), which shows proximity of absorption features to G97 points. . 65Figure 5.1 The portion of the ACT Equatorial survey region considered in this work.It spans from 20h16m00s to 3h52m24s in R.A. and from ?2?07? to 2?18?in declination for a total of 504 deg2. The overlap with Stripe 82 (dashedline) extends only to 20h39m in R.A. and covers ?1?15? in declination, fora total of 270 deg2. Circles identify the optically confirmed SZ-selectedgalaxy clusters, with radius proportional to the signal to noise ratio ofthe detection (which ranges from 4 to 13). The grey-scale gives thesensitivity (in CMB?K) to detection of galaxy clusters, after filtering, forthe matched filter with ?500 = 5.?9 (see Section 5.1.3). Inside the Stripe 82region the median noise level is 44 ?K, with one quarter of pixels havingnoise less (respectively, more) than 41 ?K (46 ?K). Outside Stripe 82,the median level is 54 ?K, with one quarter of pixels having less (more)than 47 (64) ?K noise. The higher noise, X -shaped regions are due tobreaks in the scan for calibration operations. . . . . . . . . . . . . . . . 71xiiFigure 5.2 The azimuthally averaged real space matched filter kernel, proportionalto ?5.?9(?), for signal template with ?500 = 5.?9. Shown for referenceare the ACT 148GHz beam, and the cluster signal template S5.?9(?).While filters tuned to many different angular scales are used for clusterdetection (Section 5.1.3), the 5.?9 filter is used for cluster characterizationand cosmology (Section 5.2.1). . . . . . . . . . . . . . . . . . . . . . . . 72Figure 5.3 Section of the 148GHz map (covering 18.7 deg2) match-filtered with aGNFW profile of scale ?500 = 5.?9. Point sources are removed prior to fil-tering. Three optically confirmed clusters with S/N > 4.9 are highlighted(see Table 5.3). Within this area, there are an additional 11 candidates(4 < S/N < 4.9), which are not confirmed as clusters in the SDSS data(and thus may be spurious detections or high-redshift clusters). . . . . 73Figure 5.4 Central decrement and signal to noise ratio as a function of filter scalefor the 20 clusters in S82 detected with peak S/N > 5. Top panel :Although the central decrement is a model-dependent quantity, the valuetends to be stable for filter scales of ?500 > 3?. Bottom panel : On eachcurve, the circular point identifies the filter scale at which the peak S/Nwas observed. The vertical dashed line shows the angular scale chosen forcluster property and cosmology analysis, ?500 = 5.?9. Despite the apparentgap near S/N ? 6, the clusters shown represent a single population. . . 74Figure 5.5 Postage stamp images (30? on a side) for the 10 highest S/N detectionsin the catalogue (see Table 5.3), taken from the filtered ACT maps. Theclusters are ordered by detection S/N , from top left to bottom right, andeach postage stamp shown is filtered at the scale which optimizes thedetection S/N . Note that J2327.4?0204 is at the edge of the map. Thegreyscale is linear and runs from ?350 ?K (black) to +100?K (white). 76Figure 5.6 Response function used to reconstruct the cluster central decrement asa function of cluster angular size (solid line). At ?500 = 5.?9, the filter isperfectly matched and Q = 1. At scales slightly above 5.?9, Q > 1 becausesuch profiles have high in-band signal despite being an imperfect match,overall, to the template profile. For the definition of Q, see Section 5.2.1.The dotted line shows analogous function computed under the assump-tion that the cluster signal is described by the Planck Pressure Profile(see Section 5.2.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78xiiiFigure 5.7 Prediction, based on the UPP, for cluster signal in a map match-filteredwith ?500 = 5.?9, in units of uncorrected central Compton parameter y?0and apparent temperature decrement ??T at 148GHz (Section 5.2.1).Solid lines trace constant masses of, from top to bottom, M500c = 1015, 7?1014, 4?1014, and 2?1014 h?170 M?. Dotted lines are for the same masses,but with the scaling relation parameter C = 0.5 to show the redshiftsensitivity to this parameter. Above z ? 0.5, the scaling behaviour of theobservable y?0 with redshift is stronger for higher masses because theirangular size is a better match to the cluster template and the redshiftdependence in Q does not attenuate the scaling of the central decrement,y0 ? E(z)2, as much as it does for lower masses. The dashed linescorrespond to S/N > 4 and S/N > 5.1, based on the median noise levelin the S82 region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Figure 5.8 Example probability distributions for cluster mass (upper panel) andSZ signal strength parametrized as a mass according to equation (5.14)(lower panel). The solid line PDF is the result of a direct inversion ofthe scaling relation described by equation (5.14). The corrected PDF(dashed line) is obtained by accounting for the underlying populationdistribution (bold line; arbitrary normalization). The correction is com-puted according to equation (5.15) for the upper panel, and according toequation (5.17) for the lower panel. Curves shown correspond to ACT?CL J0022.2?0036. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Figure 5.9 Residuals of the scaling relation fit for the B12 model (Section 5.2.4).Only clusters with 0.2 < z < 1.4 andM500c > 4.3?1014 h?170 M? (indicatedby dotted line) are used for the fit. The scatter in the relation is measuredfrom the RMS of the residuals. . . . . . . . . . . . . . . . . . . . . . . . 87Figure 5.10 Corrected central Compton parameter vs. dynamical mass for the 16ACT-detected clusters presented in Sifo?n et al. (2012) for the Southernsample. Values on y-axis include factor of E(z)?2, which arises in thederivation of y0 in self-similar models. The high signal outlier is ?ElGordo? (ACT-CL J0102?4915, Menanteau et al., 2012), an exceptional,merging system. The solid line represents the best fit of equation (5.14)with Mpivot = 7.5 ? 1014 h?170 M?. The dashed line is for the fit withJ0102?4915 excluded. Dotted lines, from top to bottom, are computedfor scaling relation parameters corresponding to the UPP, B12 and Non-thermal20 (z = 0.5) models. . . . . . . . . . . . . . . . . . . . . . . . . 90xivFigure 5.11 Estimate of the mass (M500c) above which the ACT cluster sample withinS82 is 90% complete (see Section 5.2.6). Lower panel assumes a UPP-based scaling relation with 20% intrinsic scatter; the solid line is forS/N > 4 (full S82 sample, valid to z < 0.8), and the dotted line is forthe S/N > 5.1 subsample (valid to z ? 1.4). The upper panel showsanalogous limits, but assuming scaling relation parameters obtained forthe B12 model (Section 5.2.4). Circles (crosses) are based on filteringand analysis of B12 model clusters for the S/N > 4 (5.1) cut. Thecompleteness threshold decreases steadily above z ? 0.6, because clustersat this mass are easily resolved and the total SZ signal, at constant mass,increases with redshift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Figure 5.12 Cumulative number counts for two sub-samples of the full cluster cat-alogue for which confirmation is complete. The upper lines are dataand model counts for the S82 sample of clusters having y?0/?y?0 > 4 and0.2 < z < 0.8. The lower lines represent the cosmological sample of 15clusters with fixed-scale y?0/?y?0 > 5.1 and z > 0.2. The model for thecounts is obtained from a maximum likelihood fit, with only ?8 as a freeparameter. The model includes a full treatment of selection effects forthe sample under consideration. . . . . . . . . . . . . . . . . . . . . . . 92Figure 5.13 Ratio of ACT SZ determined masses to X-ray luminosity based massesfrom the MCXC. ACT masses assume the UPP scaling relation parame-ters. Error bars on mass include uncertainty from the ACT SZ measure-ments, and 50% uncertainty on MCXC masses. The weighted mean ratiois 1.03? 0.19 for the Equatorial clusters and 0.83? 0.13 for the full sample. 99xvFigure 5.14 Comparison of ACT SZ based masses (from B12 scaling relation) tomasses from the South Pole Telescope. Both are M500c. ACT masses arecomputed using the B12 scaling relation and may be found in Table 5.6.SPT masses are taken from Williamson et al. (2011) (mass is computedfrom SZ signal based on scaling relation calibrated to Shaw et al., 2010,models; only statistical uncertainty is included in error bars), and Reichardt et al.(2013, mass is computed from combination of YX and SZ measurements).The weighted mean mass ratio for the 11 clusters is 0.99 ? 0.06, thoughthere is evidence of a systematic difference between the mass calibrationin the two SPT catalogues. Dotted line traces equality of SPT and ACTmasses for the B12 scaling relation. Dashed lines trace approximate lociof agreement between SPT masses and ACT masses based on the UPP(upper line) and Nonthermal20 (lower line) scaling relations. Uncertain-ties in the ACT and SPT measurements for each cluster are likely to bepartially correlated, since both use properties of cluster gas to infer atotal mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Figure 6.1 Constraints on ?CDM cosmological parameters from WMAP7 (black linecontours) and ACTcl+BBN+H0 (without CMB information). Contoursindicate 68 and 95% confidence regions. ACT results are shown for threescaling relations: UPP (orange shading); B12 (green lines); Nonthermal20(violet shading). While any one scaling relation provides an interestingcomplement to CMB information, the results from the three differentscaling relations span the range of parameter values allowed by WMAPmeasurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Figure 6.2 Constraints on wCDM cosmological parameters from WMAP7+H0 (solidblack lines), and WMAP7+ACTcl+H0 for three scaling relations (B12scaling relation is green lines; UPP is orange shading; Nonthermal20 isviolet shading.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Figure 6.3 Constraints on ?CDM cosmological parameters from Equatorial and South-ern clusters. Results from ACTcl(dyn)+BBN+H0 (violet shading), andWMAP7+ACTcl(dyn) (green shading), which both include full marginal-ization over scaling relation and dynamical mass bias parameters, maybe compared to WMAP alone (solid black lines). Dotted line shows con-straints for ACTcl+BBN+H0, using the same cluster sample but with thescaling relation fixed to the central values obtained from the dynamicalmass fit of Section 5.2.5; note the similarity to contours in Figure 6.1 ob-tained for Equatorial SZ data with B12 fixed scaling relation parameters.The dashed blue line shows WMAP7+ACTcl(dyn), with full marginal-ization over scaling relation parameters, but with ?dyn fixed to 1.33. . . 125xviFigure 6.4 Constraints on ?CDM cosmological parameters from the combined South-ern and Equatorial cluster samples, including dynamical mass measure-ments for the Southern clusters and full marginalization over scaling rela-tion parameters. WMAP7 and WMAP7+ACTcl(dyn) are identified as inFigure 6.3 (solid black line and green contours, respectively). Also shownare WMAP7+BAO+H0 (dotted black line) andWMAP7+ACTcl(dyn)+BAO+H0(dashed blue lines). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Figure 6.5 Constraints within an extension to ?CDM that allows for non-zero neutrinodensity. The data sets shown are WMAP7+BAO+H0 (dotted black lines),WMAP7+ACTcl(dyn) (green shading), and WMAP7+ACTcl(dyn)+BAO+H0(solid blue lines). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Figure 6.6 Constraints on wCDM cosmological parameters from the combined South-ern and Equatorial cluster samples, with scaling relation parameters con-strained based on dynamical mass measurements. Data sets shown areWMAP7+SNe (dotted black lines), WMAP7+ACTcl(dyn) (green con-tours), and WMAP7+ACTcl(dyn)+SNe (solid blue lines). The units ofH0 are km s?1 Mpc?1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Figure 6.7 Constraints on SZ scaling relation parameters from the combined South-ern and Equatorial cluster samples, ACTcl(dyn), constrained based ondynamical mass measurements in a cosmological MCMC. Green shadedregions are for WMAP7+ACTcl(dyn) chain; black solid lines are forWMAP7+ACTcl(dyn) but with J0102?4915 excluded from the Southernsample. Dotted lines show constraints for ACTcl(dyn)+BBN+H0 (i.e.,without CMB information), but with a Gaussian prior on C of 0.0 ? 0.5. 131xviiAcknowledgmentsIt has been a privilege to work with the skilled and dedicated researchers in the AtacamaCosmology Telescope collaboration. I feel fortunate to be involved in a group with suchstrong commitments to both the quality of the science and to the mentorship of youngresearchers. In particular I thank Lyman Page, Toby Marriage, and my supervisor MarkHalpern for their encouragement, advocacy, and patience. I thank my supervisory com-mittee: Douglas Scott, Ludovic Van Waerbeke, and David Jones, for tolerating my absurdschedule but enforcing high standards, otherwise.I additionally thank Mark for filling the Experimental Cosmology Lab with people likeMandana Amiri, Viktoria Asboth, Elia Battistelli, Bryce Burger, Ed Chapin, Gaelen Mars-den, Don Wiebe, and many others with whom I regret not having had a chance to workmore closely. It has been a pleasure to work with this group.The Department of Physics and Astronomy at UBC is full of amazing people, and I hopethey will accept my forgiveness that they discouraged me from graduating in a more timelyfashion by providing such enjoyable companionship. The people of Physics Pub Night, theSunday Bridge Squad, Taking Care of Quizness, The Pack, and Choralation were essentialto the maintenance of my mental and emotional health during my studies and I miss themdearly. Anyone named Mike, Kory, James, Gaelen or Melanie is eligible for special gratitudeand appreciation.Finally, I thank my family for letting things get this out of hand. I have always felt freeto pursue my interests and follow life where it takes me, knowing I would have their loveand support.xviiiChapter 1IntroductionIn this work we will present aspects of the instrumentation, calibration, and data analysisfor the Atacama Cosmology Telescope (ACT; Swetz et al., 2011). ACT observes in mil-limetre wavelength bands, where the Cosmic Microwave Background (CMB) is brightest,and where galaxy clusters may be efficiently detected due to the Sunyaev-Zeldovich (SZ;Sunyaev and Zel?dovich, 1970) effect.While space-based observatories are optimal for measuring features of the CMB onthe largest angular scales, large aperture ground-based telescopes achieve higher angularresolution. By studying areas of hundreds of square degrees at arcminute resolution, suchexperiments characterize both the fine scale angular features of the CMB and the statisticalproperties of source populations that contaminate the primordial signal.In addition to statistical measurements, the arcminute resolution of telescopes suchas ACT and the South Pole Telescope (SPT; Carlstrom et al., 2011) makes them highlysensitive to the SZ effect signals from massive high-redshift galaxy clusters. Because galaxyclusters form at the most extreme peaks in the density field, they can be used to constrainparameters related to the matter power spectrum. Such measurements of structure in thez < 2 Universe provide important complements to CMB measurements, particularly for thepurposes of characterizing Dark Energy and constraining the properties of neutrinos.In this chapter we will briefly review the roles of the CMB and of galaxy cluster surveysin constraining cosmological models. Because we pay particular attention to galaxy clustersin this work, we review their properties in optical, X-ray and millimetre wavelengths. Fi-nally, we describe certain elements of the design and operation of the Atacama CosmologyTelescope to provide background for susbequent chapters on calibration and observations.11.1 Cosmological ParametersIn the Big Bang model, the Universe is expanding. Light emitted from a distant galaxy andtraveling towards an observer on Earth is elongated by this expansion according to?o = (1 + z)?e (1.1)where ?e is the wavelength at the time of emission, ?o is the wavelength we now observe,and z is the redshift parameter of the source. Redshifts of distant galaxies can be measuredextremely precisely by identifying patterns of atomic absorption or emission features in theiroptical spectra, and comparing those redshifted wavelengths to the ?rest frame? wavelengthsmeasured on Earth. What is more difficult to establish is the lookback time: how muchtime did it take for photons emitted at redshift z to reach us? This question can beaddressed within the framework of General Relativity. Assuming homogeneity and isotropy,the expansion of the Universe is determined by the average energy density and relativisticpressure of the things in the Universe. In the simplest models that are consistent withobservations, the Universe is geometrically flat but contains significant contributions to theenergy density and pressure from matter, radiation, and a cosmological constant term thatfalls within a class of phenomena known as Dark Energy. Defining the scale factor as afunction of time,1a(t) ? 11 + z , (1.2)one can show that geometrical flatness requires that the average energy density of theUniverse be equal to the critical energy density (e.g., Weinberg, 2008),?c(t) =3c2H2(t)8?G , (1.3)whereH(t) ? d log a(t)dt (1.4)is the time-dependent Hubble constant. Within an expanding Universe, the energy densityof non-relativistic matter scales as ?m(t) = ?m(0)c2a?3(t); due to redshifting of photonwavelength the energy density of electromagnetic radiation scales as ?r(t) = ?r(0)a?4(t).The cosmological constant contributes a constant energy density per unit volume, and thus??(t) = ??(0). These energy densities are customarily expressed as fractions of the critical1Readers sufficiently versed in Relativity to wonder what we mean by ?time? should consult a moredetailed treatment.2energy density, i.e.,?x ??x(0)?c(0), (1.5)for each of non-relativistic matter (?m), radiation (?r) and Dark Energy (??). Note thatgeometrical flatness requires that these three density parameters sum to unity.The General Relativistic field equations require that the scale factor a(t) evolve accord-ing toH(t) = H0??ra?4(t) + ?ma?3(t) + ??, (1.6)where H0 ? H(0) is the present value of the Hubble constant. Measurements show thatH0 ? 70 km s?1 Mpc?1, but since uncertainty in the Hubble constant often contributes astrong, correlated error to mass, distance, and time measurements, such results are oftenexpressed including factors ofh70 ?H070 km s?1 Mpc?1(1.7)orh100 = h ?H0100 km s?1 Mpc?1. (1.8)The expansion history of the Universe is thus sensitive the current matter and energycontent, with an additional free parameter related to the current value of the Hubble con-stant.The luminous structures, such as stars, galaxies, and galaxy clusters, that we observetoday represent extreme overdensities of matter relative to the cosmic mean density. Thesestructures evolved through gravitational collapse of what were once extremely slight over-densities in the matter and energy distribution. These primordial fluctuations originatedin the very early Universe, when the energy density was far above the highest energy scalesdescribed by our current understanding of particle physics. Theories of the early Universe,such as inflationary field models, seek to explain the generation of density perturbations.Measurements of the density field in the early Universe, and at present times, thus have thepotential to constrain models of high energy physics at very early times.The overdensity field may be written as?(x, t) ? ?(x, t)?m(t)? 1 (1.9)where x is a vector in the co-moving coordinate system, i.e., the coordinate system thatassigns to each point, for all times, the coordinate associated with its physical distance from3some origin at the present time. The spatial components may be Fourier transformed, forany given time, to obtain the co-moving k?space modes ?k and the matter power spectrum,P (k, t) = ?|?k(t)|2?. (1.10)Models of the early universe predict particular forms for P (k, t) at early times, and theevolution of P (k, t) with time can be computed in analytic or numerical frameworks thatmodel the gravitational and other interactions that result in enhancement or suppressionof features on each scale k.Simple models for the primordial matter power spectrum assume a nearly scale invariantform,P (k, t ? 0) = ?20(k/k0)ns (1.11)where k0 is a pivot scale and ns is expected to be near to 1. The amplitude ?0 and thespectral index ns are then parameters fit to observations. Another parameter in widespreaduse is ?8, the standard deviation of density fluctuations, neglecting non-linear mode growth,when the density field is smoothed within spheres of radius 8h?1 Mpc.Precise measurements of density and matter distribution parameters are derived fromobservations of the Cosmic Microwave Background.1.2 The Cosmic Microwave BackgroundObservationally, the CMB is a radiation signal, most prominent at millimetre wavelengths,that impinges on Earth with almost uniform intensity from every direction (e.g., Ryden,2003). Most of this radiation originates from long before the era of galaxy formation andprovides crucial information about the physics of the early Universe. While this primor-dial signal is the primary motivation for overcoming the numerous obstacles to makingmeasurements at these wavelengths, the somewhat weaker signals from objects that devel-oped more recently in cosmic history also contain important astrophysical and cosmologicalinformation.The CMB that we observe today consists of photons emitted at a redshift of z ? 1100,approximately 400,000 years after the Big Bang. At this epoch, known as recombination,the hot, dense plasma of radiation and baryons became sufficiently cool and rarefied thatelectrons could settle into bound states with the atomic nuclei and photons were free topropagate. The radiation that we now observe has been redshifted to longer wavelengths,but has a blackbody spectrum and a very uniform temperature across the sky.Photons leaving regions where the plasma density was higher than average experiencea stronger gravitational redshift than photons leaving a lower density region and this canbe seen in the subtle anisotropy of the CMB temperature. The temperature variations areat the level of 1/105, are highly Gaussian, and have a characteristic angular scale of about41 degree. The all-sky CMB temperature map from the WMAP satellite mission is shownin Figure 1.1.Figure 1.1: All-sky map of the CMB temperature variations from the WMAP satellite9-year results, from Bennett et al. (2013). Reproduced by permission of theAAS.The local density variations are determined by the history of interactions between thevarious matter and density components in the Universe prior to recombination. Analysesof these variations yield important measurements of the Dark Matter and baryon densities,and establish the near flatness of our spacetime. They provide constraints on high-energyphysics models (such as inflationary models) that seek to describe the behaviour of the veryearly Universe, and have the potential to constrain fundamental standard model parameters,such as the neutrino masses.Maps of the CMB temperature fluctuations are often analysed by multipole decomposi-tion (e.g., Durrer, 2008). The temperature signal T (n?) towards direction n? can be expandedasT (n?) =??,mY?m(n?)a?m, (1.12)where Y?m are spherical harmonics and a?m are the expansion coefficients. Models predictthat the coefficients a?m are random variables drawn from Gaussian distributions withvariance C? and no correlation between modes; i.e.,?a?ma??m?? = C??????mm? , (1.13)with the expectation value computed over all Universes for a given set of C?. Measurementsof our Universe?s a?m are used to estimate the angular power spectrum C?, which can becompared to the predictions from cosmological models and constrain free parameters. TheC? are referred to as the angular power spectrum. Recent measurements of C? are shownin Figure 1.2.50 500 1000 1500 2000 2500 3000 3500Multipole ?102103?(?+1)C ?/(2?)[?K2 ]WMAP9SPT 150GHzACT 148GHzFigure 1.2: Angular power spectrum measurements from WMAP , ACT, and SouthPole Telescope (SPT), highlighting the acoustic peaks originating in the pri-mordial plasma. From Das et al. (2013).The multipole expansion of the temperature field is a harmonic transform: the equivalentof a Fourier transform on the sphere. The coefficients C? represent the power of fluctuationson angular scales corresponding to approximately ? = 180?/?. Oscillations in the baryon-photon plasma prior to recombination lead to enhancement and suppression of anisotropiesat particular scales. The locations and relative strengths of these acoustic peaks in theangular power spectrum are very sensitive to the densities of photons, baryons, and coldDark Matter (e.g., Hu, 2008). The most prominent peak is at ? ? 200, corresponding to anangular scale of about 1?.At angular scales larger than ? 6 arcminutes (corresponding to multipole momentsof ? < 1800), the CMB signal is dominated by the primary anisotropies originating atrecombination. At smaller angular scales, the power spectrum is dominated by secondaryanisotropies due to objects in the local (z < 2) Universe (e.g., Aghanim et al., 2008). InFigure 1.3 we show the angular power spectrum measured by the Atacama CosmologyTelescope, extending to small angular scales. The main contributions at ? > 1800 comefrom radio point sources, dusty galaxies that make up the cosmic infrared background,and clusters of galaxies. Each population is interesting from a variety of astrophysical andcosmological standpoints, and the angular power spectrum measurements at fine angular6scales provide constraints on population models.0 2000 4000 6000 8000 10000Multipole ?101102103104?(?+1)C ?/(2?)[?K2 ]148?148148?218218?218Figure 1.3: Angular power spectrum measurements from ACT in 148GHz and218GHz bands. Secondary anisotropies dominate the power beginning at? ? 1800 in the 218GHz, and at somewhat larger ? at 148GHz. Grey pointsare from WMAP 7-year results (Larson et al., 2010). From Das et al. (2013).While interesting in their own right, an understanding of the secondary anisotropies alsopermits a more precise measurement of the finer angular features in the primary anisotropyspectrum. This is particularly relevant for parameters that affect the spectrum of initialperturbations over a large range of angular scales, such as the scalar index, ns, its variationwith comoving scale, d log ns/dk, and the effective number of neutrino species, Neff (e.g.,Hou et al., 2013).In addition to statistical analyses of microwave maps, bright objects are also detectedand can be studied on an individual basis. In this work we will pay particular attentionto galaxy clusters; in the next two sections we discuss the sensitivity of cluster populationsto cosmological parameters and the mechanism by which microwave observations providecosmologically informative galaxy cluster samples.1.3 Cosmology from Galaxy Cluster SurveysGalaxy clusters represent the most massive gravitationally collapsed systems in the Uni-verse. They form at the most extreme peaks in the matter density field and their abundancecan be related, using large N-body simulations, to the matter density power spectrum, P (k).Galaxies are believed to form in Dark Matter halos, where overdensities in the Dark7Matter distribution have collapsed due to gravitational instability and formed deep potentialwells (e.g., Binney and Tremaine, 2008). Simple models for halo formation are based onspherical collapse arguments, in which the mean matter overdensity ?(x, t) = ?(x, t)/??within some spherical volume of radius R can be shown to grow rapidly if that density everexceeds some threshold, ?(x, t) > ?c ? 1.686. The density stabilizes as the infalling materialenters virial equilibrium. A meaningful definition of the halo size is the radius within whichthe matter is in mutual virial equilibrium; the cluster mass can then be defined as the totalmass within this radius.In our Universe, the largest Dark Matter halos can have co-moving sizes of a few Mpc,and densities (within the virial radius) that exceed the background by factors of order? ? 200. The virial masses of such objects are of order 1015 M?. The immense gravitationalpotential depth at these points attracts baryonic matter as well as Dark Matter, whichresults in the formation of large numbers of galaxies within an envelope of ionized Hydrogen(and Helium) gas. Such concentrated overdensities of galaxies are known as galaxy clusters.Since the virial radius may be difficult to define or measure, cluster masses are practicallydefined with respect to some radius within which the structure has a particular overdensityrelative to either the mean matter density or the critical density at the cluster redshift. Foran overdensity parameter ?, let R? be the radius of the sphere within which the clusterdensity is ??c(z). Then the cluster mass M? isM? =4?R35003 ?c(z)? (1.14)As is conventional for X-ray and SZ studies, we work mostly with ? = 500, denoting themass as M500c.From a cosmological standpoint, galaxy clusters form at the most extreme peaks in thedensity field and thus their abundance constrains parameters describing the matter powerspectrum. While CMB observations provide strong constraints on ?8 within fairly simplecosmological models, significant degeneracies develop when additional parameters describingDark Energy or the role of neutrinos are included in the model (Hinshaw et al., 2013). Thesedegeneracies can be broken using measurements of the local Universe, including the Hubbleconstant, Baryon Acoustic Oscillation (BAO) experiments, and galaxy cluster abundance.Neutrinos play an interesting role in the energy budget of the Universe. Neutrinos arebelieved to be massive, but the masses are only weakly constrained from particle physics ex-periments. Following primordial nucleosynthesis, massive neutrinos will gradually transitionfrom a relativistic, non-interacting regime (hot Dark Matter) into a non-relativistic, non-interacting regime (like other cold Dark Matter) as the Universe expands (e.g., Hannestad,2006). Prior to decoupling the neutrinos suppress the formation of structure at the smallestscales, complicating the measurement of the matter power spectrum amplitude unless thedistance to the last scattering surface is precisely known. Local (z < 2) measurements of8the Hubble Constant or BAO scale help constrain the distance to last scattering. Studies oflocal structure, such as galaxy and cluster surveys and cosmological lensing studies, probethe power spectrum amplitude directly, through ?8, breaking the CMB degeneracy betweenneutrino properties and the matter power spectrum amplitude.In addition, massive clusters are mostly found at redshifts z < 2 and their formation issensitive to variations in expansion history during these (relatively) recent times. Clusterabundance thus has the potential to probe properties of Dark Energy such as the equationof state parameter, w, in models where the Dark Energy pressure is fixed to P? = w??, with?? the Dark Energy density. Indeed, studies in this area provided early evidence against aclosed, matter dominated universe (Bahcall and Cen, 1992), as the abundance of clustersin simulations could not be made consistent with observations in a flat, matter-dominatedUniverse.Cluster cosmology studies typically proceed by comparing an observed sample of clustersto number count predictions from N-body simulations of structure formation on large scales.Such simulations can be used to calibrate methods for converting a prediction of the matterpower spectrum P (k) into a function n(M,z) that gives the expected abundance (spatialdensity) of dark matter halos as a function of mass and redshift. In Figure 1.4 we show thehalo abundance resulting from the analysis of several independent N-body codes.Figure 1.4: An analytic form for the mass function (solid lines) fit to cluster abun-dances from several different cosmological simulations (data points). The threedata sets and best fit lines correspond to masses defined at overdensities of,from top to bottom, ? = 200, 800, and 3200 with respect to the mean matterdensity. From Tinker et al. (2008). Reproduced by permission of the AAS.9The comparison of a cluster sample to a model requires some measurement of the clustermasses and redshifts, or at the very least an understanding of the redshift volume and massthreshold of the survey. The issue of mass calibration is particularly challenging, and isdiscussed in the context of optical, X-ray, and millimetre cluster samples in the next section.1.4 Galaxy Cluster Observations1.4.1 Optical ObservationsModern galaxy cluster surveys in optical bands make use of multi-band imaging of hundredsor thousands of square degrees and identify clusters based on localized overdensities ofgalaxies (e.g., Gilbank et al., 2011; Koester et al., 2007). Multiband photometric techniquesprovide a means of identifying galaxies that are proximate in redshift as well as in thedirection projected on the sky. Because massive clusters tend to host a large number of redsequence galaxies (which have a tight colour-magnitude relationship), colour-based selectionis effective in identifying clusters and obtaining rough redshift estimates (Gladders and Yee,2000). Clusters also tend to contain a Brightest Cluster Galaxy (BCG), very massiveelliptical galaxies that form near the centre of the cluster, and the presence of a BCG mayalso be incorporated into the cluster identification criteria.Clusters selected in the optical are typically classified according to their richness, whichis essentially the number of cluster member galaxies within some comoving distance of anominal cluster centre (e.g., Abell, 1958; Koester et al., 2007). Not surprisingly, richnessstatistics are correlated to the halo mass, and have been calibrated using weak lensing mea-surements for the purpose of establishing precise cosmological constraints (Sheldon et al.,2009). While the relationship between richness and mass has more intrinsic scatter thanX-ray and millimetre observables that probe the cluster mass, the large number of opticallycharacterized clusters has the statistical strength to overcome individual uncertainties.Large numbers of nearby clusters are found in optical surveys, but the minimum clustermass achieved by a given survey rises sharply with redshift, since the integration timerequired to reach a given absolute magnitude increases as the fourth power of the luminositydistance. Deep optical surveys do probe to z ? 1 (e.g., Gilbank et al., 2011), but the trade-off in sky area and total cluster yield is significant.Spectroscopy on cluster members provides precise cluster redshifts and can also yieldmass estimates directly, through analysis of the velocity dispersion. The dispersion ofredshifts is due to radial velocities relative to the cluster centre of mass. By invoking thevirial theorem, the velocity dispersion may be related to the gravitational potential, andthus to the halo mass. The cluster formation and dynamics within an expanding Universeare sufficiently complicated that parameters of this relationship must be constrained usingN-body simulations (e.g., Evrard et al., 2008). Systematic issues with dynamical massmeasurements arise due to the possible presence of virialized substructures within the larger10cluster, and in the difficulty of characterizing the motion using only one component (theradial velocity) of galaxy motions (Saro et al., 2013). Apparent redshift dispersion dueto chance projected super-position of two or more non-interacting clusters may lead tovast overestimates of system mass. This approach nevertheless provides an interestingcomplement to other mass measures, and is an important mass calibrator in the studiespresented in Chapter 5.Gravitational lensing provides the most promising and convincing mass measurements.Distortions of background galaxy shapes provide a probe of the projected gravitationalpotential, and thus of the cluster total density profile (e.g., Bartelmann and Schneider,2001). There is thus less reliance on information from member galaxies, or baryons in thecluster gas, which constitute a relatively small fraction of the cluster mass and for whichthe physics is not well understood.Individual cluster masses may be measured through the analysis of arcs due to stronglydistorted background galaxies (strong lensing), or through statistical studies of backgroundgalaxy deformations (weak lensing). For lower mass clusters, where lensing signal may notbe sufficiently strong to provide precise cluster masses, stacking analyses may be used tocalibrate other observables (such as richness, X-ray luminosity, or millimetre wave signal)onto a halo mass scale, while eliminating certain systematic biases (Oguri and Takada,2011).1.4.2 X-ray ObservationsThe X-ray signal from clusters arises due to bremsstrahlung emission from the intraclus-ter medium of ionized gas. Low resolution surveys yield in-band luminosities for clusters(Bo?hringer et al., 2004; Mehrtens et al., 2012); deep, high resolution or spectroscopic obser-vations can be used to explore the distribution of gas and its temperature (Vikhlinin et al.,2005).Because bremsstrahlung intensity is proportional to the square of the electron density,X-ray observations are particularly sensitive to the densest regions, near the centre of thecluster. Characterization of the gas at radii approaching the virial radius is comparativelydifficult, and simple luminosity-based proxies for cluster mass have been shown to havelarge (? 50%) intrinsic scatter.High resolution X-ray data provide strong total mass constraints of individual clusters.Assuming hydrostatic equilibrium, the pressure gradient is simply related to the gravita-tional potential (e.g., Voit, 2005), and measurements of the radial pressure profile yield thetotal mass profile. In practice, one obtains the pressure by combining measurements ofthe gas temperature from spectroscopy, and of the gas density from X-ray surface bright-ness. The most advanced techniques analyse the projected X-ray signal within a sphericallysymmetric model for gas density and temperature (e.g., Croston et al., 2008).The quality of current observations is such that statistical errors on hydrostatic mass11Figure 1.5: Composite image of galaxy cluster Abell 383 in X-ray (purple) and op-tical wavelengths (white). X-ray: NASA/CXC/Caltech/A. Newman et al./TelAviv/A. Morandi & M. Limousin; Optical: NASA/STScI, ESO/VLT, SDSS.measurements can be below the 10% level. However, the assumption of hydrostatic equilib-rium is an idealization that is likely to bias hydrostatic masses to be lower than total clustermasses. Introducing nonthermal pressure support into cluster simulations predicts biasesin the range of 10% to 20% (Kravtsov et al., 2006). Without a solid understanding of suchbiases, the use of X-ray based mass proxies for cosmological parameter constraint is prob-lematic. Weak lensing measurements attempting to measure this bias have not produced aconvincing resolution to this problem (Mahdavi et al., 2008; Planck Collaboration III, 2013;Vikhlinin et al., 2009a).The pressure profiles obtained from X-ray cluster measurements are important for cur-rent millimetre wavelength cluster surveys such as ACT and Planck .2 X-ray measurements(Arnaud et al., 2010) and cluster simulations (Battaglia et al., 2012) have demonstrated ahigh degree of uniformity in cluster pressure profiles, once the effects of mass and redshifthave been removed. The microwave signal from galaxy clusters is discussed further in thenext section.1.4.3 Microwave ObservationsAt millimetre wavelengths clusters are detected through the thermal Sunyaev-Zeldovich(SZ) effect. The gas in galaxy clusters is hot (? 108 K) and ionized, and there is significantoptical depth for scattering of CMB photons by free electrons in this intracluster medium(e.g., Birkinshaw, 1999). The CMB photons preferentially gain energy in these interactions,because the typical kinetic energy of cluster electrons far exceeds the typical CMB photon2The South Pole Telescope cluster analysis, to date, does not make direct use of characteristic pressureprofiles.12energy. The process of inverse Compton scattering of electrons in the hot gas of clusters isknown as the Sunyaev- Zeldovich effect (Sunyaev and Zel?dovich, 1970).An analog of optical depth for inverse Compton scattering is the Compton parameter,y = ?Tmec2?ds ne(s) kBTe(s). (1.15)The integral is taken along the line of sight from an observer, through some portion of agalaxy cluster, to the surface of last scattering. The quantities ne(s) and Te(s) are theelectron density and temperature, respectively. The Thomson cross-section is denoted ?T,and me is the electron mass. The expression ne(s) kBTe(s) has the units of pressure, andcan be written Pe(s) and is referred to as the electron pressure.The scattering of CMB photons to higher energies produces a distortion in the CMBblackbody spectrum. At frequencies lower than about 220 GHz, there is a net loss ofphotons and the radiation intensity is diminished; above 220 GHz, the intensity is enhanced.A computation that neglects relativistic effects in the electron gas yields the simple resultthat the apparent brightness temperature T (?) of the CMB as a function of frequency ?will be altered according to?T (?)TCMB= y x/2arctan(x/2) , (1.16)where x = h?/kBTCMB and y is given by equation (1.15). Relativistic corrections becomerelevant for very hot clusters and may be as great as ? 10% in such cases. The spectrumof the SZ effect f(?) = x/(2 arctan(x/2)) is plotted along with the locations of the ACTbands in Figure 1.6.An important feature of the SZ signal from galaxy clusters is that the effective surfacebrightness is proportional to the Compton parameter y, which is not sensitive to the redshiftat which a given cluster is located. Unlike optical or X-ray measurements, the total SZ signalstrength does not fall off with the inverse square of the luminosity distance to the cluster,but only with the inverse square of the angular diameter distance. Figure 1.7 shows modelsfor the projected radial profiles of the Compton y parameter, for clusters of several massesas a function of redshift.Figure 1.8 shows a simulation of the SZ sky at 150GHz, comparing the signal to thatfrom the primary CMB anisotropies, a background which complicates the detection of galaxyclusters. With good multi-band data, the spectral dependence of the SZ effect can be usedto distinguish it from the CMB blackbody. In single band data with sufficient angular res-olution, compact clusters can be identified due to their small extent relative to the typicalscale of primary anisotropies. While nearby massive clusters become confused with thebackground CMB in single band data, the typical angular scale for even massive clustersat redshifts z > 0.2 is only a few arcminutes. In a single frequency band where clustersshow up as brightness decrements, high resolution observations can easily distinguish dis-130 50 100 150 200 250 300 350 400Frequency (GHz)?1.5?1.0? intensitySZ spectrum f(?)SZ intensityFigure 1.6: The intensity of the SZ signal as a function of frequency for constantCompton y parameter. This is computed from the product of the CMB intensityand the SZ spectrum f(?). Coloured regions indicate the ACT observing bands.Figure 1.7: Cross-sections of the Compton y parameter through the centres of clus-ters of several masses, from integration of the electron pressure profile inArnaud et al. (2010), in a standard ?CDM cosmology. The cluster masses,from top to bottom in each panel, are M500c = 1015, 3? 1014, and 1014 M?.tant, massive galaxy clusters from both radiative point sources, and the primary CMBanisotropies.Just as X-ray data can be used to obtain halo mass estimates, models and simulationsthat relate the SZ signal to cluster mass indicate that the SZ signal should scale stronglywith the cluster mass with only moderate (? 20%) intrinsic scatter for individual objects.14?400?300?200?100SZE?20 0 20?30?20?1001020?100?50050100CMB?20 0 20?30?20?1001020?400?300?200?1000100SZE+CMB?20 0 20?30?20?1001020Figure 1.8: SZ signal at 150GHz based on simulations (from Springel et al., 2001)with typical CMB anisotropies. Images are one degree square and grayscaleis CMB temperature in ?K. Republished with permission of Annual Reviews,from Carlstrom et al. (2002); permission conveyed through Copyright Clear-ance Center, Inc.Such studies typically deal with an integrated SZ quantityYsph =?Tmec2?Vd3r Pe(r), (1.17)where the integral is taken over a sphere of some radius related to the mass of the cluster.(For example, one often defines R500 to be the radius within which the cluster densityexceeds the critical density by a factor of 500. The integrated Compton parameter withinR500 is then denoted Y500.) Hydrostatic assumptions are invoked to lead to scaling relationsof the formYsph ? E?2/3(z)M5/3, (1.18)where M is the cluster mass and E(z) = H(z)/H0 is the ratio of the Hubble constant at z toits present value. While one might expect such a relation to experience scatter and bias inthe same way that simple X-ray measurements do, integrated Y values are somewhat morerobust indicators of cluster mass, since they depend only linearly on the electron densityne and more readily probe the cluster outskirts (e.g., Motl et al., 2005; Reid and Spergel,2006).In practice, direct measurement of Ysph values is complicated by at least three factors.The first is that the volume within which one integrates to obtain Ysph is defined withreference to the cluster mass, which is often the thing one is trying to estimate by measuringYsph in the first place. This may be mitigated if a rough mass estimate is available, fromX-ray luminosity measurements, for example.Secondly, the SZ signal is observed in projection and thus Ysph cannot be simply mea-sured from maps of the SZ Compton parameter y. Alternative integrated statistics, based onthe integration of the Compton parameter inside projected cylinders, rather than spheres,may be defined and used to link simulations and observations.Third, cluster pressure profiles tend to be quite extended and have non-negligible signalon angular scales that compete with the CMB (e.g., Melin et al., 2006). While a cluster may15be quite easily detected due to its sharp central features, determining integrated spherical(or cylindrical) Ysph values is not possible unless the contaminating CMB can be removed.A central result of the present work is a method that makes use of template pressureprofiles to estimate Ysph values from single band microwave maps for which CMB contami-nation cannot be subtracted. Pressure profiles, such as the results of Arnaud et al. (2010),are essential to the interpretation of resolved cluster signal for both ACT and Planck .For ACT this is primarily due to the modest signal-to-noise ratios obtained for individualclusters, and CMB contamination (which has not, in this work, been cleaned using otherfrequency bands). For Planck , multiband data help to separate CMB and cluster signals,but a pressure profile template is needed to interpret the signal from clusters that are notresolved by the larger Planck beams (Planck Collaboration VIII, 2012).As an alternative to using pressure profile models, SZ observables can be calibrated in amore empirical way using simulations; this is the approach adopted in work from the SouthPole Telescope, for example Vanderlinde et al. (2010) and Benson et al. (2013).The cosmological significance of galaxy cluster samples, and the usefulness of high red-shift SZ-selected cluster samples in particular, have helped guide the design of large aper-ture, ground-based CMB observatories such as ACT.1.5 The Atacama Cosmology Telescope (ACT)Figure 1.9: Left : Atacama Cosmology Telescope during installation, with partiallycompleted ground shield. Photo credit: Michele Limon. Right : View showingprimary mirror.The Atacama Cosmology Telescope (ACT) is located in the Chilean Andes, at an el-evation of 5200m. With a primary mirror diameter of 6m, the telescope has an angularresolution of 2 arcminutes or less at frequencies above 100GHz. The elevation and the 8month dry season provide conditions that are among the best in the world for ground-basedobervations at millimetre wavelengths.From 2007?2010, ACT imaged the CMB using the Millimeter Bolometeric Array Camera16(MBAC; Swetz et al., 2011). MBAC initially contained a single detector array operating at148GHz, with arrays centred at 218GHz and 277GHz added in 2008. Each array consistedof roughly 1000 Transition Edge Sensor (TES) bolometers operating at 300 mK. In orderto read out large numbers of bolometers at such cryogenic temperatures, time domainmultiplexing of Superconducting Quantum Interference Devices (SQUIDs) is used; this isthe subject of Chapter 2.The FWHM of the point spread functions for the 148, 218, and 277GHz arrays areapproximately 1.4?, 1.1?, and 1.0?, respectively. Each array lies at the end of an independentoptics tube, and filters limit the frequency bandwidth to about 30%. The filter bandlocations are shown in Figure 1.6. The main, 148GHz band is centred near the peak of theCMB intensity, where the SZ signature is strongly negative. At 218GHz, the SZ signal issmall, providing a measurement of the CMB without any SZ signal. The highest frequencyband is most sensitive to dusty sources, which have a rising spectrum in this frequencyrange, and also to SZ signal, which shows up as a temperature increment.Water vapour in the atmosphere emits at millimetre wavelengths and is a major con-taminant for ground-based observations (Pardo et al., 2001). The intensity of atmosphericradiation fluctuates in time with a 1/f spectrum, and thus can be mitigated by modulat-ing the astrophysical signal into a frequency band where the atmospheric contribution issub-dominant to detector noise. For ACT this is achieved by scanning the telescope acrossthe sky at approximately 1 degree per second. Because the time-ordered data from eachbolometer are recorded, the map making procedure is able to reject temporal noise that isnot coherent in the spatial (map) domain Du?nner et al. (2013). This reconstruction is mostreliable along directions parallel to the scan; in order to reconstruct modes in all directionsit is necessary to have observations that include more than one scan direction. Such mapsare said to be ?cross-linked.?The primary ACT observing fields are centred at declinations of roughly ?53? and 0?,at Right Ascensions from 21h to 7h. This range of Right Ascension is visible at the fiducialobserving altitude, in both rising and setting modes, at night during the ACT observingseason. These declinations provide good cross-linking; the constant-altitude scan directionin the rising observations is roughly perpendicular to the scan direction in the settingobservations.The ACT Southern field is a roughly 450 deg2 region centred at an R.A. of 3h30m andDeclination of ?53?, and was the primary observing target during the 2008 season. In2009?2010, focus shifted to the 500 deg2 Equatorial field, centred at an R.A. of 0h00m andDeclination 0?, which overlaps with approximately 270 deg2 of the Sloan Digital Sky Survey(SDSS) deep survey region known as Stripe82 (Annis et al., 2011).In this work we will describe elements of instrumentation, calibration, and analysiscontributing to scientific output from ACT. In Chapter 2 we describe the bolometer readout17system. In Chapters 3 and 4 we use ACT observations of planets to characterize thetelescope beam, and present measurements of the disk temperatures of Saturn and Uranus.In Chapters 5 and 6 we present the galaxy cluster sample from the ACT Equatorial field,and use it to obtain cosmological parameter constraints.18Chapter 2Bolometer Data AcquisitionModern millimetre and sub-millimetre cameras may contain hundreds or thousands of lowtemperature bolometers. The move towards larger numbers of bolometers is motivated firstby the need to reduce photon shot noise by providing larger collection areas, and secondby the improved map-making performance made possible by sampling many different areasof the sky simultaneously. Figure 2.1 shows the detector count from a number of recentmillimetre and sub-millimetre wavelength observatories that make use of bolometers.1995 2000 2005 2010Year100101102103104Bolometer CountBAMBOOMERanGMAXIMA AcBARSPTACTSCUBA-2PlanckBICEPKeckFigure 2.1: Bolometer count in recent ground-based (square), balloon-based (circle)and space-based (star) observatories. Filled symbols identify experiments thatuse MCE for readout.In order to achieve kilo-pixel arrays of bolometers, it has been necessary to develop newtechnologies for amplifying and reading out these low temperature, low noise detectors.19In this chapter we describe the Multi-Channel Electronics (MCE), a system developed atthe University of British Columbia Experimental Cosmology Laboratory for use in readingout large (kilo-pixel) arrays of time-domain multiplexed Transition Edge Sensing (TES)bolometers. While the electronics and software developed for this purpose were designedand first implemented for SCUBA-2 and ACT, respectively, the systems have been used bya number of other instruments since that time. Current and future observatories such asACTpol, Spider, and CLASS, to name a few, also use or plan to use the MCE hardwareand its associated software.In what follows, we describe the general features of the system and specialize, as neces-sary, to the ACT version of the implementation and configuration to present examples orrelevant details.2.1 Readout SystemIn this section we briefly describe the basic components of the readout system. We touchonly briefly on the cold electronics, including the detectors and the cryogenic multiplexingarray, to provide sufficient background for descriptions of the warm electronics and thecontrol software, which are the focus of this chapter.2.1.1 Cold ElectronicsTransition Edge Sensing (TES) bolometers (Irwin and Hilton, 2005; Lee et al., 1996) areused by ACT and many other millimetre and sub-millimetre wavelength experiments be-cause of their low noise and scalability. In such detectors, a radiation absorber is thermallycoupled to a piece of superconducting metal (the TES), through which a bias current ispassed to bring the metal onto the transition between the superconducting and normal(ohmic) regimes.The current-voltage and resistance-power characteristic curves are shown in Figure 2.2.When the absorber temperature increases (due to an incident CMB photon, for example),the TES resistance is slightly increased, and the current through the TES drops. By mon-itoring the TES current, one measures the variation in radiation intensity incident on theabsorber. Noise from thermal sources is suppressed in ACT by cooling the TES to 300 mK.The tiny changes in TES current are amplified, while still at cryogenic temperatures, us-ing a chain of Superconducting Quantum Interference Device (SQUID) amplifiers (Chervenak et al.,1999; Reintsema et al., 2003). SQUIDs are used in this case for their high sensitivity tomagnetic fields. The voltage response of a current-biased SQUID to an applied magneticfield is periodic in the magnetic flux ? through the loop, with the period equal to themagnetic flux quantum, ?0 = h/2e.In the ACT readout scheme, the TES current is coupled inductively into the First StageSQUID (S1), as shown schematically in Figure 2.3. An additional, externally controlledcurrent source is similarly coupled to the same S1, to apply a ?feedback? flux to the S1.200.0 0.5 1.01.5V (?V)010203040506070I (?A)0 10 20 30 40P (pW)051015202530R (m?)Figure 2.2: Left : Current-voltage characteristic curve of a TES detector (solid line),measured during ACT observations in 2008. As the device voltage decreases(from right to left), the device transitions from ohmic behaviour (dashed line),to a regime where the device dissipates a constant power IV ? 5.0 pW (dottedline). Right : The resistance of the device as a function of dissipated power.When run in an automated servo, the feedback flux is adjusted to maintain the SQUIDvoltage, and thus the total magnetic flux, at a constant level. A record of applied feedbackcurrent can then be converted to the equivalent TES current. Servo loops using feedbackflux allow the amplifier to operate in a consistent, linear response regime over a dynamicinput range that is not limited by the ?0-periodicity of the SQUID.The voltage from each First Stage SQUID (S1) is converted to a current and inductivelycoupled into a single Second Stage SQUID (S2), which also has a flux feedback line. Themain purpose of the S1 and S2 is to facilitate time-domain multiplexing (TDM) of largenumbers of TESs. While each detector has a dedicated S1, groups of 33 S1 are coupledinto a single S2. Such a group is typically called a ?column,? and each S1 is assigned aparticular ?row.? By activating each S1 in an independent time slice, the entire set of TESmay be read out serially. The S1 feedback line is also shared by all the S1 in a column. Thesystem is designed to support switching rates of up to 1 MHz, and for 30 to 40 rows thisyields a potential independent detector visitation rate in the 10s of kHz.Several columns may then be combined in a single detector array, as shown in Figure 2.4,with the additional savings that the biases for all S1 with the same row index can be sourcedby a single external bias line. Such multiplexing schemes permit the readout of kilo-pixeldetector arrays using approximately 500 wires (including supply and return) between thecold and warm stages.The voltage from the S2 on each column is passed into a SQUID Series Array (SA),21IFBITESIS1VS1?TES-?FB? 8 ? 4 0 4S1 FB (1000 DAC)? 10? 50510ERROR(1000ADC)Figure 2.3: Left : Diagram of First Stage SQUID operation. Current ITES from thedetector is inductively coupled to the SQUID loop (center), as is the current IFBfrom a feedback line controlled by external, room-temperature electronics. Theroom-temperature electronics also control the SQUID bias current IS1. TheSQUID voltage VS1 is a periodic function of the total flux, ?TES ??FB, and isfed into the next stage of the amplifier chain. The principle of operation of theS2 and SA stages is essentially the same as presented here for the S1. Right :Measured response from a First Stage SQUID, acquired by ramping the IFB atconstant ITES. All SQUID response curves shown in this work were acquiredon the ACT 148GHz array during regular ACT observations between 2008 and2010.a high-gain device that boosts the signal to a level suitable for room-temperature analogelectronics. The SA is also SQUID-based, and has a periodic voltage response to appliedflux. Like the S1, the S2 and SA have dedicated bias and feedback flux lines.2.1.2 Warm ElectronicsThe SQUID chain is read out at room temperature by the Multi-Channel Electronics (MCE)hardware originally developed for the SCUBA-2 experiment. A block diagram of the MCEis shown in Figure 2.5. The MCE connects to the cold SQUID and TES circuitry throughbetween two and five 100-pin connectors. The MCE also connects, over fibre-optic cables,to a control computer. The MCE has a modular architecture in which the various functionsof the electronics are concentrated in one or more identical, removable cards.Synchronization and control functions are performed by a single Clock Card (CC), whoseroles are to dispatch commands from the control computer to the other cards, and to managethe collection and off-loading of data frames during data acquisition. The CC is also able torun some high-level automatic functions independently of the command computer, such ascommanding an arbitrary waveform to some set of DACs in the system. The CC generatesthe main 50 MHz clock and various internal regulation signals, or it can be commanded topass through such signals from an external unit (the Sync Box).An MCE contains between one and four Readout Cards (RCs), which each possess ADCs22Each colored blockcorresponds to thecomponents for anindividual pixel.Row addresscurrents:Row 1Row 2Column 2Column 1Columnouputs:Figure 2.4: Schematic of SQUID multiplexing scheme for reading out TES signal.Figure Courtesy of R. Doriese.and DACs for biasing and reading out 8 SQUID Series Arrays. These cards provide the SAbias and S1 feedback signals, and sample the output voltage of the SA. These cards are ableto perform the computations for the S1 feedback servo, to keep the SQUID chain lockedat the desired operating point. The RCs package measured SQUID voltages and computedfeedbacks into digital frames which are then sent to the Clock Card to be sent to the controlcomputer.The Bias Cards (BCs) are used to drive the S2 bias, the S2 feedback, the SA feedback,and the TES bias. Each BC contains 32 DACs, intended to provide a single function (e.g.,the S2 bias) or 32 different readout columns. While in many applications these voltages aresimply set to a constant value to put the SQUIDs into the desired operating regime, modernBCs are able to perform ?fast-switching,? in which the voltages on each line may be updatedat the row switching rate (typically 10?20 kHz). Bias Cards also provide between 1 and12 lines intended as TES bias lines. On modern cards, the TES bias circuitry can providebi-polar output (which is especially interesting in the context of AC biasing schemes).Finally, each MCE contains an Address Card (AC), with 41 DACs designed to drive the?row select? (S1 bias) lines of the multiplexers. (The SCUBA-2 experiment used multiplex-ing technology that supported 41, instead of 33, independent rows.)23MCEInstrument BackplaneBus BackplaneAddress cardBias cardsReadout cardsClock CardControlComputerPower SupplySync BoxCryostatFigure 2.5: Block diagram showing MCE component connections and electrical con-nections to control computer, Sync Box, and cryostat.The DACs, ADCs, and communications channels on each device are managed by a FieldProgrammable Gate Array (FPGA). FPGAs allow for flexible, high-performance manage-ment of each card?s tasks.The cards in the MCE connect to two separate backplanes: the bus backplane provideconnections for power, communications, and synchronization; the instrument backplaneconnects the analogue inputs and outputs of each card to an appropriate MDM connectorfor interfacing with the cryostat. The instrument backplane is designed to group linesdestined for a single column into the same MDM even if those lines originate on differentcards.The MCE communicates with the control computer using a fibre-optic link. The useof fibre-optics provide electrical isolation and high bandwidth data transfer over large dis-tances. A second fibre-optic link provides a connection to a Sync Box.2.1.3 Control Computer and Low-Level SoftwareThe MCE Acquisition Software (MAS) consists of a kernel driver, a library of basic MCEfunctions, and a suite of applications to provide basic MCE control at the script level.Inside the control computer, an Astronomical Research Cameras ARC-64 PCI cardconnects to the fibre-optic cables from the MCE. The ARC-64 is based around a MotorolaDSP chip and is intended for use with CCD controllers in optical telescopes. In order tomeet the requirements of continuous bolometer readout at rates of several MB/s it wasnecessary to develop customized firmware and kernel driver code.The two main functions of the ARC-64 firmware and the kernel driver are to efficientlytransfer bolometer data from the MCE into control computer system memory, and to pro-vide a command pathway from the MCE library layer to the MCE.24Bolometer data are transferred from the MCE in structured units called readout frames.In the ACT readout configuration, frames are 4400 bytes and are transmitted at a rate of400 Hz. To achieve an efficient and uninterrupted transfer of bolometer data, the driverpre-allocates a buffer of between 10 and 50 MB of system memory (RAM) and informsthe ARC-64 of the buffer address. During data acquisition, the buffer is used as a circularbuffer. The ARC-64 writes data into the buffer continuously, but only occasionally (10 Hz)raises an interrupt to inform the driver of how many frames have been written into RAM.The driver serves the frame data to an application, and occasionally (10 Hz) informs theARC-64 of regions of RAM that are now free for reuse. The driver and firmware are awareof the frame size and the total number of frames expected. This latter figure is useful tocause the ARC-64 to raise interrupt immediately upon completion of a short (e.g., singleframe) acquisition.Neither the driver nor the firmware manage any high level MCE functions or maintainany details about the MCE configuration or state. Rather, commands are constructed atthe application or library level and simply passed, by the driver and firmware, to the MCE.Similarly, reply packets from the MCE are not inspected in detail by the firmware or driverbeyond the level necessary to verify the origin and determine the size of the packet.The library level provides a C language Application Programming Interface (API) forcontrolling the MCE. This includes functions for reading and writing MCE parameters, forresetting the PCI card and MCE communication pathways, and for triggering the acquisitionof frame data. While the most basic frame data handlers write the data directly to disk,the API can also present the data to the host application for analysis, compression, ortransmission prior to storage.Most MCE commands involve writing vectors of 32-bit integers to MCE card registers.Registers are addressed by their card name (e.g., ?bc2? for the second bias card) and theregister name (e.g., ?flux fb?, for the bank of 32 DACs on a bias card). The library exposesboth the absolute address of each register (e.g., ?bc2 flux fb?) but also permits the definitionof virtual cards and registers, to isolate particular device functions. So the virtual address?sq2 feedback? can serve as an alias for ?bc2 flux fb?, or can be mapped to some set ofDACs occupying multiple physical cards.Beyond the library level, a small set of C language applications provide low-level accessto the library, permitting individual registers to be manipulated and frame data to beacquired from a command line or from simple shell scripts. In addition to the basic tools, avariety of programs and scripts are maintained to perform more complicated or specializedtasks with the MCE. These operations are described in the remainder of the chapter.2.2 Multiplexing SetupAs discussed in Section 2.1.1, the SQUID array factors the set of detectors into a grid thatmay be indexed by row and column. In time-domain multiplexing, each row is activated in25sequence, and SA voltage on each column is monitored by the room-temperature electronics.Switching between rows occurs at a constant rate, which can be configured to be as highas 1 MHz. The steps performed by the MCE on each row switch are as follows:? Apply current to the S1 bias for the new row; disable all other S1 biases.? For each column, apply the most recently computed S1 feedback value for this detector.? If S2 fast-switching is enabled : adjust the S2 feedback value on each column accordingto a pre-programmed look-up table.? After a certain settling period, sample the SA voltage on each column and record theresults.? If the internal feedback servo is active: use the SA voltage reading on each column tocompute the feedback value that will be applied the next time this row is visited.The number of rows and the length of each row visit are configurable in the MCE, andare expressed as the number of cycles of the MCE?s 50 MHz clock. In ACT and severalother experiments, there are 33 rows and a row visit time of 100 cycles. Row switching thusoccurs at 500 kHz. The internal frame rate, i.e., the rate at which any one row is visited, is15.1 kHz.Faster multiplexing is desirable to minimize the aliasing of noise from the SQUIDs. Themultiplexing rate may be limited by the settling time of the S1 bias and feedback lines, orby the response of the S2 to the changing signal from the S1. The multiplexing sequenceand settling times can be studied using Raw Mode readout; see Section 2.4.5.Readout of ? 1000 bolometers at 15 kHz is possible with the current system. In normalreadout configuration, the MCE is programmed with a decimation parameter N such thatonly every Nth complete frame is returned. Noise aliasing in decimated readout is mitigatedby a low pass digital filter, as described in Section 2.4.2. A decimation factor of N = 38 isused by ACT to bring the readout frame rate to approximately 400 Hz.The Readout Card can be configured to return various different kinds of data, includ-ing the raw SA voltage reading, the computed feedback, the low-pass filtered form of thecomputed feedback, or various mixtures of these signals.When setting up the SQUID array, the internal servo is disabled and a constant, pro-grammable value is applied to the S1 feedback current of each column. The Readout Cardsare instructed to return the SA voltage. The SQUID setup procedure, wherein the proper-ties of the SQUIDs are measured and various parameter values are optimized, is describedin the next section.2.3 SQUID TuningThe proper setup of the SQUID amplifier and multiplexing chain is important for low noise,high bandwidth readout of the detectors. To facilitate future discussion we introduce a26model for the three-stage amplifier associated with a single detector. Each of the SA, S2,and S1 has a V?? curve described (ideally) by a periodic function V (?). The flux ? is a sumfrom two sources: the signal flux from the TES or lower amplifier stage and the feedbackflux set by the MCE. We take the liberty of working in units where the output voltage ofthe S1 and S2 stages are in terms of the S2 and SA input flux, respectively:?S2sig = V S1(?TESsig ? ?S1FB); (2.1)?SAsig = V S2(?S2sig ? ?S2FB); (2.2)E = V SA(?SAsig ? ?SAFB)? Voffset ? Eoffset. (2.3)Here E (for ?ERROR? signal) denotes the voltage measured by the MCE, and ?TES isthe flux due to the changing detector current. The fluxes ?ssig and ?sFB denote the signaland feedback inputs, respectively, to the squid stage s.Two offset terms affecting the measured voltage E can be controlled through the MCE.The ?SA offset,? denoted Voffset, is a fixed electrical offset applied to a given column to com-pensate for the increasing DC voltage in the SA bias line as the SA bias current is increased.Once configured properly it can be ignored; this is discussed further in Section 2.3.1. The?ADC offset,? denoted Eoffset, is a digital offset chosen separately for each detector suchthat the error signal E is 0 at the desired lock point of the final open loop response. Thisparameter is discussed later in this section.The SQUID tuning procedure consists essentially in measuring the V?? curve of eachSQUID, possibly for multiple values of the SQUID bias. The amplitude, phase, and DCoffsets of the V?? curve are used to select the bias, feedback, and compensating offset valuesfor the SQUID.The algorithm is implemented in the Python language, with data acquisition providedby special purpose C language programs. The original implementation is described inBattistelli et al. (2008).2.3.1 Setting up the Series ArrayThe tuning procedure begins with a study of the SA. The V?? curve of the SA is easilymeasured. The SA is biased to some trial value, and the S2 bias is set to 0 so that ?SAsig = 0.The SA feedback is then ramped and the SA voltage is recorded. The result of such anacquisition is shown in Figure 2.6.To use the SA as an amplifier, we seek to identify a broad region where the response toflux is monotonic. We select the point that is midway, in the flux axis, between the edgesof this region, to be the operating point for the amplifier. We adjust the value of Eoffset sothat E = 0 at the operating point. This will allow us to easily identify the operating pointagain once the input signal from the S2 starts to change.270 10 20 30 40 50 60SA FB (1000 DAC)?40?30?20?1001020ERROR (1000 ADC)Figure 2.6: SQUID tuning plot for the ?SA Ramp? stage. This curve is taken in openloop by ramping the SA feedback. A locking region (shaded) is found betweentwo values of the feedback (dashed lines) that lie on a single slope of the V??curve, and the midpoint of this region is used to determine the ERROR valueat which subsequent servos will be set to lock. Note that the SA feedback isnot fixed as a result of this analysis.When also optimizing the SA bias, the acquisition and analysis described above is per-formed at a number of discrete bias values. The data from such a set of ramps are over-plotted in Figure 2.7. The code identifies the bias associated with the largest amplitude ofresponse. This bias is then scaled by a programmable parameter ?SA to obtain the optimalbias. Typically ?SA = 1 is sufficient for the SA, but faster response may be obtained bybiasing to values slightly higher than the critical current.The cryostat cable resistance in the SA bias line leads to a build up of DC voltage inthe measured SA response. This is compensated at the MCE input operational amplifierusing the SA offset voltage (Voffset in equation (2.3)), which is set to be some multiple of theSA bias voltage. This approximate, but sufficient, compensation can be seen in the y-axisoffsets of the curves in Figure 2.7.Following the SA optimization, the SA are biased to be responsive and the ADC offsethas been configured so that the ERROR signal reads 0 at the SA operating point. The SAcan then be used to measure the behaviour of next stages of the SQUID amplifier chain.2.3.2 Setting up the First and Second Stage SQUIDTo measure the S2 V?? curve it is not sufficient to simply ramp the S2 feedback current.The S2 output would then be composed with the SA response, at an arbitrary point in thephase of the SA V?? curve. Instead, the S2 V?? curve is measured by ramping the S2feedback current and manipulating the SA feedback current to keep the ERROR signal at0. This stage is called the ?S2 Servo.?280 10 20 30 40 50 60SA FB (1000 DAC)?50?40?30?20?10010203040ERROR (1000 ADC)Figure 2.7: V?? curves acquired for the SA at several different bias values. The al-gorithm selects the bias that yields the largest peak-to-peak response (shownin bold). The flat response regions are associated with the lowest bias values,and are an indication that the Josephson junctions are still superconducting.The y-axis offsets of the curves are an artifact of the full readout circuit con-figuration.A typical S2 V?? curve is shown in figure Figure 2.8. Note that y-axis is in units of SAfeedback. The selection of an operating point on the S2 is performed according to the samecriteria as for the SA, except that the asymmetrical shape of the S2 means that the sign ofthe slope should be taken into consideration.The servo operates by setting the S2 feedback, and measuring the ERROR signal E. TheSA feedback is then updated according to ??SAFB = ??E, where ? is a programmable gain.The sign of this gain determines whether positive E will lead to increasing or decreasingvalues of the SA feedback; it is thus this sign that determines whether the effective operatingpoint of the SA is on the rising or falling slope.Having chosen the SA feedback and the S2 bias, the acquisition and analysis of the S1V?? curves proceeds in a similar way. The S1 feedback is ramped and now the S2 feedbackis adjusted to keep the ERROR reading near 0. The V?? curve of a single S1 is shown inFigure 2.9. When S2 fast switching is enabled, optimization of the S1 is trivial because theS2 FB can be set independently for every detector. This stage is called the ?S1 Servo.?When S2 fast switching is not in use, the S2 feedback must be a compromise suitable fora maximum number of detectors on a given column. This is achieved by running a servo oneach row, in turn, and examining the distribution of preferred S2 feedback values on eachcolumn. A detector is identified whose feedback is near the center of the distribution, andthat detector is used to choose the S2 feedback going forward. This procedure is not partof the automatic tuning process, but scripts are available for collecting and displaying thedata.290 246 8 10S2 FB (1000 DAC)3436384042SA FB (1000 ADC)Figure 2.8: SQUID tuning plot for the ?S2 Servo? stage. This curve is taken in closedloop while ramping the S2 feedback, and servoing with the SA feedback to keepthe error signal at 0. The analysis is similar to the SA Ramp curve; here we fixthe value of the SA FB such that it corresponds to the mean flux over a singleedge of the S2 V?? curve.?8 ?6?4?2 0 246S1 FB (1000 DAC) FB (1000 ADC)Figure 2.9: SQUID tuning plot for the ?S1 Servo? stage. An S2 feedback is chosenas the result of this operation.2.3.3 Finalizing the Lock PointOnce the squids have been biased and the feedback settings chosen for the SA and S2, thecomposed response curve defined in equation (2.3) is determined, up to the final choice ofdigital offset Eoffset. In order to verify the usability of the final composed response, andto choose Eoffset, the S1 feedback is ramped while measuring the ERROR signal. Becausethe S1 feedback enters the amplifier at the same place as the TES current, the resultingresponse is exactly the open loop response of the amplifier to changes in TES current. The30resulting S1 ramp curve is shown in Figure 2.10. Now Eoffset is simply taken to be midwaybetween curve maximum and minimum.?8 ?6?4?2 0 246S1 FB (1000 DAC)02468ERROR (1000 ADC)Figure 2.10: SQUID tuning plot for the ?S1 Ramp? stage. This curve is taken inopen loop by ramping the S1 feedback. The response here is the final openloop response of the SQUID chain. The dashed line is chosen to lie half waybetween the maximum and minimum of the V?? curve. The resulting valueis used to set the ADC offset (Eoffset) so that the ERROR signal returns 0through the center of the open loop response.The slope of the S1 ramp curve at the operating point (E = 0) can be used to choosethe gain value for the MCE internal servo. This is discussed in Section 2.4.1.The SQUID tuning algorithms work well in systems where the SQUID amplitudes aremutually well matched, and S2 fast switching obviates the need for compromise. Regard-less it is sometimes necessary to assess the final S1 response curves visually to identifyproblematic readout channels.In cases where the S1 response curve does have sufficiently deep or broad locking regions,the MCE internal servo may be unable to keep the amplifier locked at the operating point.A consequence of this is often that the servo will ramp the S1 through the DAC range,wrapping around to 0 as necessary, trying to restore lock. Despite the low (?2%) level ofcrosstalk between channels, a ramping servo may have a noticeable and deleterious impacton adjacent channel.The servo can be disabled for individual channels by marking them in a mask thatcauses their servo gains to be set to zero. SQUIDs likely to cause ramping can usuallybe identified by their low amplitude (comparable to the white noise level in the S1 rampcurves) or irregular features (especially problematic when S2 fast switching is not in place).312.4 Data Acquisition2.4.1 ServoDuring normal operation the MCE operates an independent servo on each of up to 1300detectors, to keep the SQUID chain amplifiers at the operating point. The full SQUIDresponse is non-linear, but provided that the servo keeps the system within an approximatelylinear regime, we may analyse the servo behaviour in linear theory.Some versions of MCE firmware support a full PID servo, but in practice the integralterm is sufficient. Despite the lack of a proportional term, the servo yields a feedbackcurrent that matches the TES current perfectly at low frequencies. This is normal for asystem where changes in the input produce an error reading which is then cancelled out bya corresponding change in the feedback.In the full PID computation, the feedback is computed at a given time step based onmeasurements from preceding time steps. At visit n+1, the feedback is computed accordingto?n+1 = pEn + in?j=0Ej + d(En ? En?1) (2.4)= ?n + (p + i)En + (d? p)En?1 ? dEn?2. (2.5)Here p, i, and d are gains and Ej is the error signal measured at step j. A simple analysis ofthe frequency response may proceed by assuming the sequence of feedback values is finiteand periodic. Then the discrete Fourier Transform is??(f) =?ne2?jnf/fs?n, (2.6)where fs is the sampling frequency. The error signal may be similarly expanded. Trans-forming both sides of equation 2.5 and rearranging yields??(f) = (p+ i) + (d? p)e?2?jf/fs + de?4?jf/fs(e2?jf/fs ? 1) E?(f). (2.7)The error signal measured at time step j is related to the TES signal (in S1 feedbackunits) byEj = V (?n ? ?TES(tn)) ? m(?n ? ?TES(tn)). (2.8)Here V (?) represents the full, non-linear SQUID response function, whilem = ?[dV/d?|V =0]?1is a constant representing the slope dV/d? of the linearized system near the operating point.In the linearized system the frequency response can be solved exactly to assess the32fidelity with which the measured ? traces ?TES. The servo is commonly operated with onlya nonzero i term, so we specialize to that case in what remains.In the linearized system the S1 feedback traces the TES flux exactly, though lagging byone sample, if the servo gain i is set to the critical value ofi0 ? ?1m. (2.9)Fourier transforming equation (2.8) and eliminating E? we have??(f)??TES(f)= ii+ i0(e2?jf/fs ? 1). (2.10)Neglecting phase, the frequency transfer function is???????(f)??TES(f)????? =(1 + 41?xx2 sin2(?f/fs))?1/2 , (2.11)where x ? i/i0. While x = 1 produces a perfect response in theory, x > 1 will causeamplification of oscillations at high frequencies. It is thus standard to recommend thatusers measure their S1 response curves at the lock point to get i0, and then set i such that1/4 < x < 1/2. For an ACT-like configuration, where the readout frequency is 1/38 timesthe sampling frequency, the transfer function at the readout Nyquist frequency (200 Hz) is0.96. This is negligible compared to the effects of detector time constants.2.4.2 Readout FilterThe servo and multiplexer are typically set to operate as quickly as possible, to minimizethe aliasing of high frequency noise into lower bands. In order to provide a data streamsuitable for readout at a more reasonable rate, the MCE implements a digital low-pass filter.The default filter has an f3dB/fs ? 0.08, corresponding to knee frequency of 120 Hz for a15 kHz internal frame rate. Alternative filters can be programmed, but due to the potentialfor internal overflows it is necessary to study new filter designs using firmware simulations.The Readout Card supports output modes which expose either the raw unfiltered feed-back signal, or the low-pass filtered version, in the frame data.2.4.3 Flux JumpingThe S1 feedback DAC has a 14-bit range. A broad dynamic range is desired in order toprobe both the low amplitude astrophysical signal from the CMB as well as bright sourcessuch as planets. In addition, during calibration operations one must ramp the TES currentthrough a range that far exceeds its usable operating range. The periodic response of theSQUIDs allows one to avoid making a compromise between dynamic range and resolution.33The SQUID voltage is equal for any two feedback values that differ by an integer multipleof the flux quantum ?0. When MCE ?flux jumping? is enabled, the MCE servo block willautomatically adjust the computed feedback value by an integer number of flux quanta toremain within the DAC range.The computed feedback ?S1 is updated on each row visit. The actual DAC valuedapplied is?DAC = ?S1 ? nFJ?0, (2.12)where ?0 is the flux quantum in DAC units and the integer nFJ is the ?flux jump counter?,maintained separately for each channel.When the servo detects that FBDAC is within 5% of the minimum or maximum validDAC value, nFJ is incremented or decremented to move ?DAC towards the center of theDAC range. This extends the useful dynamic range of the servo system by a factor of 256.The flux quanta ?0 must be measured from the SQUID tuning data and programmed addedto the MCE configuration files.Sudden large changes in the applied feedback current can have noticeable effects on otherchannels, due to crosstalk within the MCE or due to settling time effects on the feedbackline. In a well-behaved system, such jumps are rare and thus so is the incidence of glitchesdue to cross-talk.Note that the Readout Card treats ?S1 as the feedback signal for all purposes exceptthe computation of a DAC value; it is ?S1 that is returned in frame data and that is passedinto the readout filter. The RC can be configured so that the frame data includes both thefiltered feedback signal and the flux jump counter for each detector. This provides a meansto reconstruct, if desired, the true applied DAC value.2.4.4 High Speed ReadoutOverall system bandwidth (in the digital components) limits readout rates for entire kilo-pixel arrays to be less than about 1 kHz. To study the higher frequency spectrum of theSQUIDs, detectors, and noise environment, the readout cards can be configured to storeand return data for only a subset of the detectors in the array. This can be configuredwithin the regular multiplexing scheme, or even higher bandwidths may be obtained bysetting up the multiplexer to only switch between two rows.Within such configurations, it is possible to readout small numbers of detectors atsampling rates of up to approximately 250 kHz.2.4.5 Raw ModeIn ?Raw Mode? readout, the Readout Card is configured to store up to 65536 samples ofreadings from the ADC, at the full sampling rate of 50 MHz. This functionality is indepen-34dent of ordinary multiplexing and servoing, and so can be used to study settling times in themultiplexing sequence. The RC is triggered to acquire raw mode data using a special RCcommand, and recording begins at the beginning of the next internal multiplexing frame(i.e. the next return to row 0). In the original implementation, 8192 samples from eachof the 8 ADCs on the readout card were recorded. In recent firmware, the user insteadselects a column from which to record a single block of 65536 samples, which for the ACTconfiguration corresponds to 20 full multiplexing cycles of the array. To read out the data,the user sets the RC readout mode to a special value, and then uses the usual acquisitioncommands and data pathways.2.4.6 Internal CommandingDAC output values can be changed from the control PC at any time, including during normalframe data acquisition. But in order to meet synchronization or period requirements the CCincludes a facility for updating DACs to preprogrammed values at regular intervals. Dueto bandwidth restrictions within the command backplane, the commands issued internallyby the CC are restricted to writing a single value to a single register on a single card.The most common application of Internal Commanding is to manipulate the TES biasvoltage. For TESs biased onto transition, the device current and voltage characteristictraces out a line of approximately constant Joule heating, i.e., a line of constant IV . Bystepping the voltage using a low amplitude square wave and measuring the changes incurrent, the bias power P can be measured and the conversion between DAC units andTES power units obtained.In addition to simple ramps and steps, recent CC firmware includes an Arbitrary Wave-form Generator mode, wherein a repeating sequence of up to 65536 values is written tothe target register. This capability has applications for measuring dynamic impedance, asfrequency-rich signals may be injected into the system with a known phase.Large arrays of bolometers are essential for obtaining significant scientific yield fromground-based CMB observatories such as ACT. The warm readout system provided a strongfoundation upon which the SQUID and TES systems for ACT were characterized andoperated. For most of its run, ACT enjoyed continuous, automated observing due to thestability of the hardware, firmware, and software.35Chapter 3Beams and Window Functions3.1 IntroductionThe telescope point spread function, or beam, acts as a low-pass spatial filter on the astro-physical signal from the sky. The effects of this filtering are relevant, to varying degrees, forall ACT science results. Interpretation of the angular power spectrum, in particular, relieson its decomposition into components that are correlated across large ranges in angularscale. The extraction of cosmological parameters associated with such components dependson an understanding of the beam shape and its error covariance.Sky temperature data may be compared to predictions based on cosmological modelsthrough statistical measures such as the angular power spectrum of temperature fluctu-ations. The effect of the observing strategy and telescope beam on the measurement ofcorrelation functions in CMB data has been discussed in, e.g., White and Srednicki (1995).A Gaussian random temperature field T (n?) at position n? on the sphere may be charac-terized by coefficients C? of the decomposition of its auto-correlation function:?T (n?)T (n??)?=???=02? + 14? C?P?(n? ? n??), (3.1)where P? are Legendre polynomials. Measurements T? (n?) of the temperature field with agiven telescope and observing strategy will differ from the true sky temperature; for ACTthe primary effects are an uncertain calibration (which we neglect for now) and the telescopebeam. For the case of an azimuthally symmetric beam that does not vary in time or withposition on the sky, the auto-correlation function of the observed temperature map T? (n?)will be related to the C? describing the T (n?) by?T? (n?)T? (n??)?=??2? + 14? C?P?(n? ? n??)B2? , (3.2)36where B? are the multipole coefficients of the beam, defined byB(?) =???=1B??(2? + 1)4? P?(cos ?). (3.3)In this context, B2? is referred to as the window function.The absolute calibration of the telescope is achieved by comparison to WMAP at angularscales of approximately 15?, and an understanding of the beam B? permits the extensionof this calibration to smaller angular scales. Systematic errors in the beam will lead tosystematic offsets between flux densities measured for extended sources, such as the CMBon large angular scales, and flux densities measured for compact objects, such as pointsources, planets, and galaxy clusters.The telescope point spread function varies as a function of radiation frequency, variesover the focal plane of the array, and varies with time due to slight motions and deformationsof the primary mirror. Integration of various source spectra across the ACT band passesshows that the effective band centre varies by 1 to 2% for spectral indices ranging fromsynchrotron (? ?0.8) to dusty sources (? 3.5) (Swetz et al., 2011). Planetary sources havespectral indices in the middle of that range, and are thus a reasonable probe of the telescopebeam. Small adjustments to the beam obtained from planet measurements are necessarywhen working with the CMB or with particular point source populations, as described inSection 3.3.5.The beam varies only slightly over the focal plane, and both the survey field observationsand the planet observations used in this analysis make use of all working detectors in thefocal plane. At any given time, the combined signal from all detectors has an effective pointspread function, which we refer to as the instantaneous beam. While the instantaneousbeam may vary in time, we compute a mean instantaneous beam by aligning and averagingtogether beam maps taken over the course of the observing season in each year of operation.Measurements of the mean instantaneous beam provide a starting point for characterizingthe effective beam in ACT survey maps, where the beam may be diluted due to variancein the absolute pointing registration over the many observations that contribute to a givenregion of the full survey map. The result of applying pointing and spectral corrections tothe mean instantaneous beam is referred to as the season effective beam.In this chapter we describe the measurement of the ACT beams for each season andfrequency array. We begin with a discussion of the planet observations and maps, and thenmove on to obtain the mean instantaneous beam map and its multipole space decomposition.The effects of pointing variance are measured in the survey maps, and used to finalize theseason effective beam. We then return to study variations in the beam shape and calibrationover the season by studying fluctuations in the apparent brightness of Uranus over the courseof the season.37Table 3.1:Number of Saturn and Uranus ob-servations selected for calibra-tion purposes for each season andarray.2007 2008 2009 2010Saturn148GHz 22 22 13 35218GHz ? 23 9 28277GHz ? 16 5 23Uranus148GHz 16 37 94 113218GHz ? 33 75 102277GHz ? 21 16 74Note ? While Uranus was visiblethroughout each observing season, Sat-urn was available only near the begin-ning and end of each season. The numberof successful planet observations is lowerat higher frequencies because of increasedsensitivity in these arrays to atmosphericcontamination.3.2 Observations and Mapping3.2.1 ObservationsThe ACT observation strategy is to scan over small ranges of azimuth angle while keepingthe boresight altitude fixed at ? 50? to minimize systematic effects due to altitude variation.The CMB fields are observed as they rise and set through two central azimuth pointings.Planet observations are made at this same telescope altitude angle, by briefly interruptingCMB survey scans and re-pointing in azimuth to the planet location.ACT observed a planet approximately once per night of operation in 2007?2010, butonly high quality observations of Saturn and Uranus are considered in this analysis. Saturnand Uranus were preferentially targeted, as Saturn?s brightness makes it useful for beamprofile measurements, and Uranus? stable brightness is a convenient calibration source.While Uranus was visible throughout each observing season, Saturn was available only atthe beginning and end of each season. Jupiter and Mars were, respectively, too bright andtoo low in the sky to be useful for calibration work. In Table 3.1 we list the number of highquality Uranus and Saturn observations achieved in each season.383.2.2 Planet MapsAs described in Du?nner et al. (2013), maps are made from the ACT timestream data ac-cording to a maximum likelihood technique in which the noise is described in the timedomain while the signal is assumed to be spatially coherent (Tegmark, 1997). The bolome-ter timestream data for planet observations are pre-processed in a similar fashion to theCMB survey data. The timestream data are calibrated, based on detector load curves,after deconvolving the effects of the detector time constants and low-pass readout filtering.Detectors are then screened for quality based on their projections onto a common-modecomputed using a fiducial set of well-behaved detectors. Detector screening is performedwith the planetary signal masked out. Maps are made using a dedicated code that is op-timized for high resolution mapping of single observations; we have confirmed that themain season map pipeline code produces compatible results when run on the same data.Each map is solved iteratively, converging after fewer than 10 iterations. The noise modelis designed to remove common-mode signal at frequencies below 0.2 Hz, corresponding toangular scales that are much larger than the array size. Because high-pass filtering of thiskind may suppress signal at large angular scales, we study the transfer function of the mapmaking solutions in Section Map SelectionWhile planets were observed almost every night, observations do not always yield successfulmaps. The primary reason for failed mapping is a low number of live detectors duringperiods of high sky loading. This is a greater problem at higher frequencies, and for the277GHz array in particular leads to many maps with incomplete sampling of the planetsignal; such maps are discarded.Planet observations are sometimes made after sunrise. While such observations allowus to study the magnitude of pointing and beam focus changes due to thermal deformationof the telescope structure, they are excluded from the present analysis. The sunrise cut isalso applied to CMB observations.A small number of maps are cut due to having substantially higher noise levels thanother maps of the same planet for the same array and season. The remaining maps are usedto establish the telescope beam and calibration parameters, as described in the followingsections. Season mean beam maps, obtained by aligning and averaging the selected Saturnmaps for each season and array, are shown in Figure 3.1. The Airy pattern is easily seenin the maps at 148GHz and 218GHz. The horizontal streaks are parallel to the telescopescan direction.39Figure 3.1: Beam maps for each season and array, formed from the average of se-lected Saturn maps. Gray scale is logarithmic. Each panel is 12? by 12?. Eachcontributing Saturn map incorporates all live detectors in the array. The well-resolved Airy rings indicates that the relative detector offsets are accuratelyknown. The frequency labels correspond to the effective frequencies for CMBspectrum radiation (Swetz et al., 2011).3.3 BeamsIn this section we obtain measurements of the telescope beams for each season and array.Saturn is bright and much smaller than the beam solid angle, permitting the character-ization of our beams with high signal-to-noise ratio. Saturn maps are reduced to radialprofiles, which are then modeled with appropriately chosen basis functions and transformedto Fourier space. The resulting transform, the beam modulation transfer function, is cor-rected for a number of systematic effects to produce a window function and ?-space covari-ance suitable for use with the ACT CMB survey maps.403.3.1 Radial ProfilesWhile the instantaneous ACT beams are slightly (< 10%) elliptical in cross-section, weanalyse them as though they were circular, and work exclusively with the ?symmetrized?(i.e., azimuthally averaged) radial profiles. The resulting beam measurements are suitablefor any analysis that incorporates a similar simple azimuthal average of the signal understudy. In particular, the cross-linking of CMB survey observations is such that the telescopebeam contributes to the map, with roughly equal weight, at two orientations that differ inrotation by approximately 90?; the net effective beam is very nearly circular. The goal ofour analysis is thus to characterize the symmetrized beam.Radial profiles are obtained for each Saturn observation by averaging map data in radialannuli of width 9??, producing average profile measurements yi at radii ?i. On scales smallerthan a few arcminutes, the covariant noise is sub-dominant to the planetary signal and thusthe shape of the core beam is very well measured by even a single observation of Saturn.However, at larger angular scales there is non-negligible contamination from the atmosphere.This means that the asymptotic behaviour of the beam cannot be separated from thefluctuating background without making some assumptions about the beam behaviour farfrom the main lobe.The illumination of the ACT optics is controlled by a cryogenic Lyot stop at an imageof the circular exit pupil; this leads to a beam shape described by an Airy pattern (formonochromatic radiation) and to the expectation that the beam pattern (including theeffects of finite detector size and spectral response) will decay asymptotically as 1/?3, where? is the angle from the beam peak. We fit this model to the radial profile data in order tofix the background level of the map and to provide a model for extrapolating the beam tolarge angles.The background level of the map and the large-angle behaviour of the beam are measuredby fitting the model y(?) = A ? (1?/?)3 + c to the binned profile data in the range ?A <?i < ?B, with the range chosen such that the profile measurements have fallen to below1% of the peak but are still signal dominated. The points yi with ?i < ?A, corrected forthe background level c and renormalized so that y(? = 0) ? 1, constitute the ?core? ofthe beam profile. The radial profile beyond ?A is referred to as the ?wing.? The fit rangesused for each array, and the amplitude of the beam at ?A relative to the peak, are given inTable 3.2. An example of the wing fit for each array is shown in Figure 3.2.For each array, the multiple observations of Saturn in each season are combined bytaking the mean of their core profile points and wings. The season mean beam profile isthus described by points y?i (for each ?i < ?A) and a mean wing fit parameter A?. The fullcovariance matrix of {y?1, ..., y?n, A?} is computed from the ensemble of Saturn profiles and,as described in the next section, is used to propagate covariant error on large angular scalesinto the ?-space beam covariance matrix.The solid angle and FWHM of the beam (as well as the approximate ellipticity of the41Figure 3.2: Wing model fitted to binned radial profile data. Points shown, and thebest-fit model (solid line), are from a typical individual Saturn observationfor each array. A baseline is fit simultaneously and has been removed from thedata points. The shaded area represents the standard deviation of all individualbest-fits to wing models for the 2010 season.non-symmetrized telescope beam) are shown in Table 3.2. Solid angles may be comparedto the values presented in Hincks et al. (2010). The reduction in solid angle uncertainty isprimarily due to our choice to fit the wing over a range of radii closer to the beam centre.We have doubled the error from its formal value to account for systematic variation in solidangle results as different fitting ranges are used.42Table 3.2:Summary of beam parameters by array and season.Wing Fit (?3.3.1) Transform Fit (?3.3.2) Beam Properties Hincks et alArray Season ?A ?B B(?A) ?max nmode Solid angle FWHM Ellip. Solid angle(10?3) (10?9 sr) (arcmin) (10?9 sr)148GHz 2007 4? 8? 2.40 ? 0.05 21900 11 224.5 ? 1.4 1.364? 1.098 ?2008 4? 8? 2.03 ? 0.04 18400 9 216.6 ? 1.6 1.373? 1.065 218.2 ? 4.02009 4? 8? 2.15 ? 0.09 16400 8 215.8 ? 2.6 1.378? 1.039 ?2010 4? 8? 2.13 ? 0.04 15800 9 215.4 ? 1.8 1.381? 1.033 ?218GHz 2008 2? 4? 6.54 ? 0.12 25500 6 116.5 ? 1.1 1.092? 1.021 118.2 ? 3.02009 2? 4? 7.07 ? 0.29 25800 6 123.9 ? 1.7 1.057? 1.026 ?2010 2? 4? 7.34 ? 0.21 25100 6 125.0 ? 1.8 1.015? 1.027 ?277GHz 2008 2? 4? 5.49 ? 0.12 28400 7 98.1 ? 1.9 0.869? 1.049 104.2 ? 6.02009 2? 4? 5.22 ? 0.26 32100 7 95.2 ? 4.0 0.879? 1.118 ?2010 2? 4? 5.65 ? 0.18 28600 7 98.9 ? 2.0 0.870? 1.103 ?Note ? Radial profiles are obtained within a distance ?A from the peak; wing and baseline parameters are fit to dataover the range ?A to ?B. The level B(?A) of the beam, relative to the peak, at the edge of the wing fit region is shownfor reference. Parameters ?max and nmode describe the basis functions used for fitting a beam model to the radial profiledata in the beam core. The solid angle and FWHM of the symmetrized instantaneous telescope beam are provided,along with the ellipticity (defined as the ratio of major to minor axes of the unsymmetrized mean beam). The solidangles for the 2008 season may be compared to the values from the independent analysis of Hincks et al. (2010).433.3.2 Harmonic Transforms and Window FunctionsThe multipole expansionB? of the real space beam responseB(?) is defined in equation (3.3).The ACT beams are sufficiently concentrated that we may work in a flat sky approximationand take ? to be a radial coordinate in the plane. The radial component of the Fourierconjugate variable will be ?. The azimuthally symmetric two-dimensional Fourier transformB(?) of B(?) may be used to obtain the multipole coefficients according to B? = B(?) withentirely negligible error. We will thus work in the flat sky approximation, but write B?(with ? in subscript) to emphasize the correspondence to the multipole coefficients.We consider contributions from the wing and from the core separately. The transform ofthe wing (which is truncated below ?A) is easily obtained. For the beam core, computationof the transform from the binned radial profile requires us to interpolate the profile datayi. We achieve this by expressing the real space beam as a sum of basis functions that weknow to have spatial frequency cut-offs near those determined by the telescope optics ineach frequency band.The primary mirror has a diameter D = 6m; this size limits the optical response tospatial frequencies below ?max ? 2?D/?. A natural basis for the Fourier space beam is thenprovided by the Zernike polynomials R02n(?), where ? = ?/?max. (The Zernike polynomialsRmn (?, ?) are orthogonal and complete on the unit disk; here we impose azimuthal symmetryand need only consider even n and m = 0.) We thus model the real space beam withbasis functions fn(?), for non-negative integer n, that are proportional to inverse Fouriertransforms of R02n(?):fn(?) = J2n+1(??max)??max. (3.4)In practice, for some value of ?max and a mode count nmode the beam model is expressedasB(?) =nmode?1?n=0anfn(?), (3.5)where the coefficients an are fit parameters. The model is fitted to the data by minimizingthe ?2 of the residuals yi?B(?i), accounting for the full covariance of the yi measurements.Values of ?max and nmode are adjusted to obtain a fit with the minimum number of modesnecessary that gives a ?2 per degree of freedom equal to unity. The fit yields coefficients anand the covariance matrix of the errors, ??an?an??.Details of the fitting parameters, including ?max, nmode and reduced ?2 for each seasonand array, are presented in Table 3.2. The choice of basis functions results in a satisfactoryexpansion of the beam using approximately half as many modes as data points.After fitting the coefficients an in real space, we obtain the corresponding beam trans-44form,B? =?nanFn? + w?, (3.6)where Fn? are the Fourier transforms of fn(?), truncated above ?A, and w? is the Fouriertransform of the extrapolated wing, from ?A to infinity.The resulting beam transforms are shown in Figure 3.3. While the beams for the 2008season are shown, the beam features are not substantially different between seasons. Thefigure shows the separate contributions of the core and wing to the beam transform. Thewing contributes significantly only at low ? (i.e., below 1000 at 148GHz, and below 2000 at218GHz and 277GHz).While this is very similar to the procedure described in Hincks et al. (2010), in this workwe include covariance between radial profile data points, and between the radial profile andthe wing fit parameter. This results in a natural propagation of beam errors on all spatialscales into the fitted beam transform and its ?-space covariance matrix. Our treatment ofbeam errors is discussed in the next section.3.3.3 Beam and Calibration CovarianceUsing the covariance matrix of the fit coefficients obtained in Section 3.3.1, we also obtainthe covariance in ? space:???? ? ??B??B???=?n,n?Fn? Fn?????an?an??+ ??w??w???+?nFn? ??an?w???+?n??w??an?Fn?? . (3.7)This covariance includes contributions from the wing fit error and the correlation betweenthe wing fit error and the coefficients an.This covariance matrix is an ?-space representation of the covariant features in the radialprofiles that contribute to the B?. However, because the calibration of the CMB surveymaps is established at a particular angular scale, we must recast the beam covariance intoan appropriate form. This is effectively the same procedure applied in Page et al. (2003).The absolute calibration of the ACT maps at 148GHz is obtained by cross-correlation ofthe 2008 Southern and 2010 Equatorial maps with the WMAP 7-year maps (Jarosik et al.,2011) at 94 GHz of the same sky region, over angular scales with 300 < ? < 1100 (Das et al.,2013; Hajian et al., 2011). This leads to an absolute calibration of the ACT maps centrednear ? = 700. The 2009 season Equatorial maps at 148GHz are then calibrated, over500 < ? < 2500, to the 2010 season Equatorial maps. The subsequent calibration of the218GHz maps to the 148GHz maps is performed in the signal-dominated regime with45Figure 3.3: Upper panels: Beam transforms B? for each array. Beams shown are for the 2008 season. The total beam is the sumof the contribution from the core of the beam, and the extrapolated wing. Lower panels: Diagonal error from the covariancematrix for the renormalized beam. The beam normalization has been fixed at calibration ? = 700 (1500) for the 148GHz(218GHz and 277GHz) array(s), as described in Section 3.3.3. Note that these curves show uncertainty, not systematictrends, and they do not include additional uncertainty from the empirical corrections of Section 3.3.5. The full covariancematrix shows an anti-correlation between the beam error at angular scales above the calibration ? and beam error below thecalibration ?. The window function is B2? and thus its fractional error is 2?B?/B?.461000 < ? < 3000. For each season and array, we factor out the beam amplitude at effectivecalibration scale ? = L, where L = 700 for the 148GHz array, and L = 1500 for the 218GHzand 277GHz arrays.For a celestial temperature signal described by multipole moments T?,m, we measure amap M?,m in detector power units, which is related to T byM?,m = G?T?,m, (3.8)where G? ? G0B? is the product of the beam (normalized such that B?=0 = 1) and a globalcalibration factor G0 that converts CMB temperature to map units (i.e., to detector powerunits).Our calibration to WMAP is a comparison of M and T at ? = L and is thus a mea-surement of GL that is independent of our beam uncertainty. This leads us to recastEquation (3.8) asM?,m = GLb?T?,m, (3.9)whereb? ?B?BL. (3.10)Since the errors in b? and GL are not correlated, the uncertainty in G? is described by acovariance matrix ???? that is the sum of a calibration error from the measurement of GL,and a term due to correlated error in the b?:???? = b?b??(?GL)2 +G2LB2L[???? ? b??L??? ??Lb?? + b?b???LL] . (3.11)The term in square brackets is the normalized beam covariance that accompanies ACTdata releases. The diagonal beam error (i.e., the square root of the diagonal entries of thenormalized beam covariance) is shown for each season and array in Figure 3.3. At high ?,the error in the effective season beam is dominated by an empirical map-based correction,which is not included here (see Section 3.3.5).While the fitted beam and covariance are an accurate description of the binned radialbeam profile, they must be corrected for a number of systematic effects prior to being usedto interpret ACT maps.473.3.4 Correction for SystematicsThe beams computed in the preceding section are corrected for a number of systematiceffects that would otherwise bias the resulting transforms relative to the true telescopebeam. These are briefly described below.Mapping Transfer FunctionBecause our map-making procedure includes time domain high-pass filtering, we mightexpect poor reproduction of large spatial scales. We study the mapping transfer functionby injecting a simulated signal into telescope timestream data and comparing the outputmap to the input map in Fourier space. The transfer function deviates significantly fromunity only on angular scales larger than 20?. The wing fit is performed at somewhat smallerradii than this, and we have confirmed that the wing fit and extrapolation reproduces theinput signal, on all scales, to 0.1%.A very small (?0.1%) correction due to the 3.5?? pixelization of the planet maps isapplied by dividing the beam transform by the azimuthal average of the analytic pixelwindow function.Radial Binning of Planet MapsThe binning of the planet map pixel data into annuli has a slight impact on the inferredbeam transform. This is quantified by evaluating the harmonic transform of data pointstaken from a model of the radial beam profile, and comparing it to the harmonic transformof points that include simulated binning of the radial beam profile. This resulting correctionis approximately 1% at ? = 10000.Saturn Disk and Ring ShapeThe Saturn angular diameter of approximately 18?? is large enough that we do not treat itas a point source. For each season and array, we deconvolve Saturn?s shape assuming thatit is a disk with solid angle equal to the mean solid angle for all Saturn observations thatcontribute to the mean instantaneous beam measurement. This correction is approximately2% at ? = 10000.While Saturn?s rings complicate the spatial distribution of the planetary signal, theseeffects are negligible at ? < 20000, aside from an overall change in average brightness,and need not be considered in the deconvolution procedure. The brightness variation isdiscussed further in Chapter Mean Instantaneous vs. Effective BeamAfter applying the corrections described in Section 3.3.4, the resulting beam describes thetelescope response to a point-like radiation source with approximately Rayleigh-Jeans spec-48trum, averaged over the focal plane of each array. The combination of observations takenat many different times may lead to an effective window function that is different from theinstantaneous one.For use in particular contexts, we compute an effective beam that includes correctionsfor alternative frequency spectra, and for pointing variation or other cumulative effectsresulting from the combination of observations taken at many different times.We apply a simple first-order correction to obtain the effective beam for different ra-diation spectra. For radiation with a band effective frequency ?, the beam is taken tobeB?(?) = B(??RJ/?), (3.12)where ?RJ is the effective frequency for radiation with a Rayleigh-Jeans (RJ) spectrum.Effective frequencies for various spectral types are presented in Swetz et al. (2011).In the absence of planetary sources, the absolute pointing registration of individual ACTobservations is not known. Since each pixel of the ACT survey maps contains contributionsfrom data acquired on many different nights throughout each season, the resulting seasoneffective beam for these maps is less sharp than the instantaneous beam obtained fromcarefully aligned individual planet observations.Pointing repeatability can be estimated from the variation in apparent planet positions,relative to expectations, in each season and array. As summarized in Table 3.3, theseindicate that the repeatability of telescope pointing is at the ?planet = 3?? to 8?? (RMS)level. Pointing variation in CMB observations may in principle be smaller than ?planet,since CMB observations are performed at the same azimuth angles each night, while planetobservations span a wider range of azimuths.In addition to pointing repeatability, the season effective beam may also be diluteddue to errors in the global pointing model, which is used to combine observations madeat different azimuth angles. These global adjustments are estimated using point sourcepositions measured in (non-cross-linked) maps made from only rising or only setting data.While pointing variance and global alignment may contribute to dilution of the seasonbeam, we must also acknowledge that the beam may change slightly over the course of theseason in a way that is not captured by the Saturn observations. (Changes in the beam overthe course of the season, and the resulting impact on calibration, are assessed using Uranusobservations in Section 3.4.) We thus seek an empirical measure of the difference betweenthe season effective beam and the instantaneous beam obtained from Saturn observations.We parametrize the difference between the season effective beam Beff? and the instanta-neous beam B? as a Gaussian in ?:Beff? = B? ? e??(?+1)V/2. (3.13)49If the correction is interpreted as arising purely from Gaussian pointing error, then Vis simply the pointing variance in square radians. While this motivates the form of thecorrection, our broader interpretation permits V to differ from the value expected basedon pointing variance measured from planets, or to be less than zero if the season effectivebeam is somewhat sharper than the ensemble of Saturn observations indicates.We measure V for each season and array using bright point sources in the season CMBsurvey maps. Point sources with signal to noise ratios greater than 10 are identified using amatched filter. A beam model is fit to the map in the vicinity of each source, producing avalue of V . The weighted mean and error of these individual fits, for each season and array,are used to form the effective beam for use with the survey maps. While this point sourceanalysis gives us a secondary probe of the beam core, we note that the Saturn observationsare still key for measuring the behaviour in the wings of the beam.The values of the season correction parameter V are presented in Table 3.3. The mea-surement of V is somewhat susceptible to changes in the fitting parameters and thus thequoted errors have been inflated from the formal values by factors of 2 and 6 for the 148GHzand 218GHz arrays, respectively. While values of V for the 148GHz array are very similarbetween seasons, values for 218GHz are more variable. The analysis of Uranus observa-tions in Section 3.4.1 shows that in 2010 the telescope beam was more sharply focused,relative to the mean beam estimated from Saturn, during most of the observing season (seeSection 3.4.1); this results in a negative value for V at 218GHz.3.4 Planet Brightness MeasurementsIn this section we measure variations in the telescope gain and beam shape over the courseof each season by comparing maps of Uranus and Saturn to expectations based on the meaninstantaneous beam. This permits an assessment of systematic and random error in ourmean instantaneous beam, and allows us to measure the dependence of the telescope gainon atmospheric water vapour level.3.4.1 Planet AmplitudesWe characterize the apparent brightness of a planet in a map by examining the ratio ofthe Fourier transform of the map to expectations based on the beam and planet shape.While ultimately equivalent to procedures that involve measuring source peak heights infiltered real-space maps, the Fourier space approach emphasizes the role of spatial filteringin providing precise planet amplitude measurements. It also allows us to quantify differencesbetween the planet shape and expectations based on the beam measurements in a physicallymeaningful way.Once again working in the flat sky limit, we let ? represent a vector in the plane of thesky centred on the planet. The Fourier conjugate variable is denoted as ? and is written insubscript. The signal from a planet is modeled as a circular disk of uniform RJ temperature50Table 3.3:Pointing variance and beam correction parame-ters.?2planet V AttenuationSeason Array (arcsec2) (arcsec2) at ? = 50002007 148GHz 53? 12 ? ?2008 148GHz 24? 4 25? 10 0.993 ? 0.003218GHz 23? 5 143 ? 51 0.962 ? 0.013277GHz 11? 2 ? ?2009 148GHz 58? 9 26? 6 0.993 ? 0.002218GHz 43? 8 46? 27 0.988 ? 0.007277GHz 49? 18 ? ?2010 148GHz 31? 3 29? 6 0.992 ? 0.002218GHz 18? 2 ?5? 23 1.002 ? 0.006277GHz 25? 3 ? ?Note ? Pointing variance ?2planet is measured from planetobservations, and the season effective beam correction pa-rameter V is measured from point sources in the full-seasonCMB survey maps, where available. The parameter V isused to correct the high-? beam for use with the surveymaps; the resulting attenuation or inflation of the beam at? = 5000 is provided for reference. The covariant error dueto this correction is included in the season effective beamcovariance matrix.TP. For each planet observation, we use the total disk solid angle ?P to compute angularradius ?P ? (?P/?)1/2. The Fourier transform of the planetary signal has componentsT? = TP?P? , (3.14)where ?P? ? ?P ? (2J1(??P)/(??P)) is the Fourier transform of a disk of radius ?P. ForUranus, ?P? ? ?P at the ACT angular scales; for Saturn, the finite disk size cannot beneglected, but the effects due to its oblateness are negligible. Planetary radii are taken atthe 1 bar atmospheric surface, as reported in Archinal et al. (2011). The Saturn equatorialradius is (60268 ? 4) km and the polar radius is (54364 ? 10) km; the Uranus equatorialradius is (25559 ? 4) km and the polar radius is (24973 ? 20) km.Adapting equation (3.8) to the flat sky, the ACT map M(?) of the planetary signal will51have Fourier componentsM? = G0B?TP?P? . (3.15)For each planet map, we compute the amplitude M? of the planet at multiple binsin ?. The map is centred, apodized, and Fourier transformed. To suppress atmosphericcontamination, which contributes faint horizontal streaks to the map, we mask Fouriercomponents having |?x| < 17001. The remaining complex Fourier amplitudes are averagedinside annuli of width ?? ? 600 and the imaginary part is discarded. We then compute theratio of M? to B??P? (which has been corrected to account for the apodization and maskingapplied to obtain M?).The result is a curve of planet amplitude measurements,??? ?M?B??P?, (3.16)for 2000 < ? < 14000. In the absence of any gain or beam variation, ?? should be equal toG0TP, the apparent brightness of the planet in detector power units.The mean and variance of ??? curves for selected seasons and arrays are shown in Fig-ure 3.4. The ??? curves are not in all cases consistent with a constant value. This maybe attributed to variations in the focus from night to night. To parametrize these devi-ations and to make possible an assessment of the impact they might have on the systemcalibration, we fit parameters ?? and ?? for each ??? curve according to the following model:??? = ??(1 + ?? ?? ??5000). (3.17)The mean angular scale ?? is taken as the centre of the fitting range. The parameters ?? and?? represent the mean amplitude of the planet and the deviation from expected focus of thebeam, respectively. For example, ?? = 0.01 would indicate that the the planetary signal isstronger by 1% at ? ? 10000 relative to ? ? 5000, given the mean season beam, and thusthe telescope beam at the time of observation was slightly more sharply focused. We wouldexpect observations associated with negative ?? to also have a smaller ?? than expected, sincea less sharply focused beam will have poorer overall efficiency.The extraction of amplitudes ?? and focus parameters ?? allows us to quantify deviationsof focus over the season, and to estimate the effects of such deviations on the overall systemcalibration. This is accomplished in the next section, where a model for system calibrationis obtained from the brightness and focus measurements of Uranus.1No such masking or filtering is performed on the Saturn maps prior to their use in the determination ofthe telescope beam; the masking is more important for Uranus maps, because the signal is weaker.52Figure 3.4: Variation of planet amplitude measurements with angular scale. Eachpanel shows mean fractional deviation of ??? relative to ?? (solid line) and thestandard deviation of all individual ???/?? curves (grey band) for a particularseason, array, and planet. See Section 3.4.1 for definitions of ??? and ??. Weshow results from 148GHz 2008 (left panels), where there is a high degree ofconsistency between the planet observations and the season mean beam. Wealso show results for 218GHz 2010 (right panels), where there is somewhat morevariance in the curves (which is typical of the 218GHz array) and where theUranus observations deviate significantly from the mean beam (which is seenin all arrays in 2010). Differences between Uranus and Saturn are indicativeof 2% changes in the beam focus during the season; such changes have beenaccounted for in the season effective beam by fitting a correction parameter tomaps of point sources in the season maps as described in Section Calibration Parameters from Uranus ObservationsIn addition to variations in gain resulting from changes in focus quality, absorption ofradiation by water vapour in the atmosphere also decreases the apparent brightness ofastrophysical signals. The optical thickness for such absorption is parametrized by theprecipitable water vapour (PWV) level, which is the water volume per unit projected areain a column above the observer. The measurements of ?? and ?? from Uranus observations,along with measurements of the PWV level for most of these observations, permit us tocharacterize the impact of PWV level and focus variation on the telescope calibration. Thisanalysis does not require that the brightness temperature of Uranus be precisely known,but assumes that the brightness is roughly constant over the observing season. (We do notperform the same analysis on Saturn, because the effective brightness varies with the ringopening angle; see Section 4.2).The Atmospheric Transmission at Microwaves model (ATM; Pardo et al., 2001) pro-53vides estimates of atmospheric emission and absorption at millimetre and sub-millimetrewavelengths. The ACT frequency bands avoid strong molecular resonances and are thusprimarily susceptible to continuum emission and absorption due to water vapour. For thepurposes of calibration we are interested in the atmospheric transmission in a given fre-quency band. The transmission at the ACT observation altitude ?0 is written asT = exp (?(?ww + ?d)/ sin ?0) , (3.18)where w is the precipitable water vapour column density at zenith and ?ww and ?d are the?wet? and ?dry? optical depths at zenith. The parameters ?w and ?d vary negligibly overthe range of temperatures and pressures experienced at the telescope site.Because planet observations discussed in this work are obtained at the same fiducialaltitude used for CMB observations, the effects of ?d are common to both observations andcannot be measured from the planet observations. We define the overall system gain G0such that it applies at the typical PWV level of w0 = 0.44 mm. The w-dependent gainfactor is thenG0(w) = G0 exp (?(?w + ?x)(w ? w0)/ sin ?) . (3.19)Here ?w is as provided by the ATM model, while ?x is a fit parameter that could indicate adeviation from the ATM model but is more likely due to a bias in the detector calibrationprocedure that is sensitive to sky loading. Estimates of ?w for the ACT bands were com-puted using the ATM model by Marriage (2006); these values are provided for reference inTable 3.4.To assess the impact of small variations in telescope focus on planet calibration, weinclude a dependence on the difference between the focus parameter ?? (defined in Equa-tion (3.17)) and the season mean focus parameter ??. Because a planet was observed ap-proximately once per night, we take ?? to be the average of measured ?? for all planetobservations for the array and season under consideration. We adopt an exponential formout of convenience; calibration variation is small so a linear correction would be equivalent.The full model for the Uranus brightness data ??, ?? is then given by? = TUG0em(????)?exp (?(?w + ?x)(w ? w0)/ sin ?) , (3.20)where the fit parameters TUG0, m, and ?x represent overall calibration, sensitivity to vari-ations in telescope focus, and sensitivity to PWV beyond predictions based on ATM, re-spectively.This model is fitted to the Uranus brightness amplitude data for each season and fre-quency array. The parameter values are presented in Table 3.4. The residuals have scatter54of approximately 2%, 2% to 6%, and 6% in the 148GHz, 218GHz and 277GHz arrays, re-spectively; this scatter is not explained by uncertainties in planet amplitude measurement.Values obtained for ?x are in good agreement between seasons for the 148GHz and 218GHzarrays. They are inconsistent with zero (at the ? 2 to 4?? level), which we attribute to sys-tematic detector calibration error. For the 277GHz array there is some slight disagreementbetween the 2009 and 2010 results, which we attribute to the low number of observations in2009. The values of ?x are used in combination with ?w to correct the time-ordered data foropacity prior to creation of full-season survey maps, as described in Du?nner et al. (2013).While for some seasons and arrays we obtain better fits to the data by including theparameter m, the impact of this additional parameter on inferred overall system calibrationis small. To show this, we refit the model of equation (3.20) with parameter m fixed to0. The resulting calibration factor TUG(m=0)0 may be compared to the case where m wasfree to vary. The differences are presented in Table 3.4; the change in overall calibrationis 0.6% or smaller, and always less than the 1-? error on TUG0, with the exception of the2009 data for the 218GHz array. This exceptional case also has a large (9%) uncertaintyin its absolute WMAP -based calibration.The fit values of TUG0 may be used to provide an absolute calibration of each array(should TU be known) or to provide a measurement of the Uranus disk temperature basedon an independent calibration of G0. The latter possibility is discussed in the next section,leading to the measurements of Uranus and Saturn brightness temperatures presented inChapter Relation to WMAP-Based CalibrationThe absolute calibration of the ACT full-season CMB survey maps is obtained through cross-correlation in ?-space (Hajian et al., 2011) to the 94 GHz maps from WMAP (Jarosik et al.,2011). As described by Das et al. (2013), the WMAP maps are used to calibrate the ACT2008 Southern and 2010 Equatorial field maps at 148GHz directly; the latter maps are thenused to calibrate the 148GHz map for 2009 and the 218GHz maps for all seasons.While the data entering the survey maps are corrected for atmospheric opacity, theyhave not been corrected for any kind of time variation in the telescope beam. Instead,we have obtained an effective season beam suitable for use with the survey maps by com-paring our mean instantaneous beam to point sources in the survey maps, as described inSection 3.3.5. This correction has negligible effect at low ? where the calibration to WMAPtakes place. Furthermore, the WMAP calibration should be associated with the telescopegain at the season-average focus parameter. Thus the calibration factor obtained from theWMAP calibration is compatible with G0, as defined by equation (3.20).Beam measurement is essentially a measurement of the dependence of the instrumentcalibration as a function of angular scale. For ACT, our understanding of the beam also55Table 3.4:Properties of planetary data and calibrationmodel fit parameters by season and array.ArrayQuantity 148GHz 218GHz 277GHz?w (mm?1) 0.019 0.044 0.075?x (mm?1)2007 0.016 ? 0.010 ? ?2008 0.014 ? 0.004 0.040 ? 0.008 0.033 ? 0.0632009 0.009 ? 0.005 0.021 ? 0.017 -0.008 ? 0.0412010 0.012 ? 0.003 0.045 ? 0.008 0.083 ? 0.016Error in TUG0 (%)2007 0.9 ? ?2008 0.2 0.4 1.32009 0.3 1.1 2.22010 0.2 0.4 0.8m2007 0.7 ? 0.6 ? ?2008 0.5 ? 0.3 -0.5 ? 0.6 1.2? 1.32009 0.5 ? 0.3 3.4 ? 0.5 1.2? 0.72010 0.8 ? 0.1 0.5 ? 0.2 1.5? 0.4? mean (rms)2007 ?0.017 (0.010) ? ?2008 0.002 (0.006) 0.011 (0.010) 0.011 (0.015)2009 0.004 (0.011) 0.008 (0.016) 0.007 (0.020)2010 0.015 (0.015) 0.021 (0.019) 0.017 (0.019)(G(m=0)0 /G0 ? 1)(%)2007 ?0.6 ? ?2008 0.1 ?0.3 0.52009 0.2 1.4 0.42010 0.3 0.2 0.4Note ? The opacity parameters ?w from the ATMmodel are provided for reference. Fit parameters ?x andm parametrize sensitivity of Uranus apparent brightness toPWV and focus parameter, respectively. The mean andstandard deviation of the focus parameter ? for all planetobservations in each season is provided for reference. Theoverall calibration shift G(m=0)0 /G0?1 is the systematic cal-ibration change if m is fixed to zero instead of being free tovary.56permits a transferring of the calibration obtained from WMAP at large angular scalesto the smaller angular scales where ACT is more sensitive. In the next chapter we usethis calibration and our measurements of planet amplitudes to obtain precisely calibratedmeasurements of planet brightness temperatures in the ACT bands.57Chapter 4Planet Temperature MeasurementsThe use of Solar system planets as absolute calibrators for observations at millimetre wave-lengths is limited by uncertainties in the planet disk brightness, typically parametrized interms of the thermodynamic brightness temperature. While survey instruments such asACT are able to obtain precise absolute temperature calibration by comparing maps tothose from WMAP or Planck , planetary sources are more convenient calibrators in manycircumstances because they are compact on the sky and very bright compared to the CMBanisotropies on small angular scales.In this chapter, we use the WMAP -based calibration of the ACT survey maps at 148GHzand 218GHz, to convert the Saturn and Uranus amplitude measurements to calibratedbrightness temperatures. A geometrically detailed, two-parameter model for Saturn diskand ring temperatures is fit to the Saturn brightness data. Because CMB survey maps forthe 277GHz array have not yet been calibrated to WMAP , we do not consider that arrayin this analysis.In what follows, we refer to both the Rayleigh-Jeans (RJ) and brightness temperaturesof the planet.1 The RJ temperature TRJ is related to the brightness temperature TB byequating the specific intensity of an RJ spectrum and a blackbody spectrum at the bandeffective frequency ?eff :B?eff (TB) = 2?2effkBTRJ/c2, (4.1)where B?(T ) is the blackbody spectral radiance. The spectra of Saturn and Uranus areeach sufficiently close to the RJ limit that we take the source effective frequencies to be theRJ band centres of 149.0 GHz and 219.1 GHz (Swetz et al., 2011).1Our planet amplitude measurements include a deconvolution of the telescope beam and thus we do notwork with the planet?s ?antenna temperature? directly.584.1 UranusDue primarily to its smaller solid angle, the total flux density from Uranus is substantiallysmaller than that from Mars, Jupiter, Saturn, or Venus. Its brightness, however, is consid-erably more stable than Mars (which has substantial diurnal variation) and Saturn (whoserings are neither negligible nor well understood). The potential usefulness of Uranus as acalibrator is increased if its absolute brightness is also well measured.4.1.1 Temperature MeasurementBased on our fitted values of TUG0 (Section 3.4.2) and the absolute calibration of G0 usingWMAP data, we obtain measurements of TU. Because the calibration factor is obtainedfrom the primary anisotropies of the CMB, we must account for the different frequencyspectrum of the planets relative to the CMB blackbody. The effective spectral index ofthe flux of the CMB in the ACT bands is 1.0 (0.0) in the 148GHz (218GHz) bands,while the spectral index of Uranus is approximately 1.65 in both bands (based on, e.g.,Griffin and Orton, 1993). The 3.5 GHz uncertainty in the ACT band centres and theeffective frequencies provided in Swetz et al. (2011) result in an additional 1.6% (2.7%)error in the Uranus brightness determinations at 148GHz (218GHz).The Rayleigh-Jeans temperatures obtained for each season and array are presented inTable 4.1. The value quoted for the 148GHz (218GHz) array is valid at effective frequencyof 149.0 (219.1) GHz. All RJ temperatures have been inflated by 0.5 (0.3) K, correspondingto the RJ brightness of the CMB, to compensate for the background level against whichplanet brightnesses are measured. Applying equation (4.1), brightness temperatures maybe computed from the RJ values by adding 3.5 (5.1) K.The results are consistent between seasons (even after removing the correlated errordue to the frequency spectrum correction), with uncertainty dominated by the overall in-strument calibration uncertainty rather than statistical uncertainty from planet brightnessmeasurements.From the RJ temperature measurements in each season, we compute a weighted meandisk temperature for Uranus. The WMAP -based calibration error is correlated betweenthe 2009 and 2010 seasons, because the 2009 map is calibrated to the 2010 ACT map, andthe ACT band centre uncertainty is correlated across all seasons. We account for this inthe mean and error presented. At 148GHz, we obtain a RJ (brightness) temperature of103.2 K (106.7 K), with 2.1% error. At 218GHz, we obtain temperature 95.0 K (100.1 K),with 3.2% error.4.1.2 Comparison to Previous Measurements and ModelsWe compare our Uranus temperature measurements to the widely used model of Griffin and Orton(1993, hereafter G&O). The G&O model provides brightness temperatures for Uranus and59Neptune in the ? 100 to 1000 GHz range based on precise measurements of brightnessratios of each planet to Mars. The absolute calibration is obtained by interpolating, inthe logarithm of the frequency, between the Wright (1976) model for Mars temperatureat 3.5?m (857 GHz), and the (Ulich, 1981) model for Mars temperature at 90GHz. Theyadopt a 5% systematic error for this Ulich-Wright hybrid model.The G&O model predicts a brightness temperature of 112 K at 148GHz, approximately5% larger than our measured value. This suggests that the Ulich-Wright model for Marsbrightness is 5% high at 148GHz. Weiland et al. (2011) have observed a similar 5% discrep-ancy between Mars temperatures and the Ulich model at 94GHz. At 218GHz, the G&Omodel gives a brightness temperature of 99 K, which is 1% smaller than our measured value;this difference is smaller than our calibration uncertainty.Long term studies of Uranus show a variation in mean disk brightness at 8.6GHz(Klein and Hofstadter, 2006) and 90GHz (Kramer et al., 2008) on decade time scales. Ifthis variation is attributed to differences in the Uranus surface brightness at different planetlatitudes, it implies that the mean disk temperature is roughly 10% larger when the Southpole, rather than the equator, is directed to towards the observer.2 The ACT measurementsover the 2008?2010 period span Uranus sub-Earth latitudes from 1? to 13?. In comparison,the observations presented by G&O were made in 1990?1992 and span sub-Earth latitudesfrom -70? to -60?. It is then possible that, rather than a difference in calibration, Uranuswas brighter in these bands at the time the G&O data were taken. However, if one acceptsthe 5% downward recalibration of the Ulich Mars model at 94GHz, then one should ac-cept a downward recalibration (of 4?5%) of the G&O data around 148GHz. This bringsthe ACT and G&O measurements into agreement, with no evidence for any variation inUranus brightness temperature due to sub-Earth latitude.Our results at 148GHz are consistent with the analysis of Sayers et al. (2012), whouse WMAP measurements of Uranus and Neptune at 94 GHz (Weiland et al., 2011) torecalibrate the G&O model at 143 GHz. It is important to note that while our measurementsrely on a detailed understanding of the telescope beam, our absolute calibration standard isthe CMB, for which the brightness as a function of frequency is known. Our errors thus donot include any significant systematic contribution due to interpolation of unknown sourcespectra into our frequency bands.In Figure 4.1 we show our brightness temperature measurements along with WMAPmeasurements below 100GHz from Weiland et al. (2011) and with data used by G&O tofit their model in the 90 to 1000GHz range.2The centre of the projected planet disk, as observed from Earth, is called the sub-Earth point. TheUranian latitude of this point is called the sub-Earth latitude.604.1.3 Empirical Model for Uranus TemperatureAs discussed above, systematic error in the G&O model is dominated by uncertainty in theMars spectrum below 1000GHz. The ACT and WMAP data provide new, absolutely cali-brated temperature measurements between 20 and 220GHz. We thus fit a simple empiricalmodel for the temperature using the ACT, WMAP , and the higher frequency G&O data.To avoid the strong spectral feature at 30 GHz, we include only the two highest frequencybands of WMAP . We use the three data points in G&O above 600GHz. We model theUranus brightness temperature as a function of ? ? (?/100 GHz) byTU1 K = a0 + a1 log10 ?+ a2 log210 ?, (4.2)and obtain best fit coefficients (a0, a1, a2) = (121,?78.2, 18.2).The ACT, WMAP , and G&O brightness temperature measurements are shown in Fig-ure 4.1, along with the G&O model and our empirical model.4.2 SaturnMeasurements of the Saturn disk temperature are complicated by the presence of the rings,whose dust both obscures the main disk and radiates at a lower temperature. The ACTobservations of Saturn span ring opening angles from ?2? to 12? and provide an opportunityto explore the separate contribution of these two components to the total effective brightnessof the planet.4.2.1 Ring Model and Temperature ConstraintsWe follow closely the approach of Weiland et al. (2011, hereafter W11), who apply a two-parameter model in which the opacity and geometry of the rings are fixed, while the disktemperature and an effective temperature for the rings are free to vary. The ring dimensionsand normal opacities are taken from Dunn et al. (2002). For each of the 148GHz and218GHz arrays, we fit Tdisk and Tring, which describe the mean disk temperature andmean effective brightness temperature of the rings (see W11 for the detailed definition),respectively.The measurements of ?? and ?? for each Saturn observation are converted to RJ temper-atures, including corrections for PWV level and focus parameter, and with the CMB-basedcalibration applied. Because the scatter in the temperatures is not fully accounted for by theerrors in the amplitude measurements and correction parameters, we combine observationsmade in single 15 to 30 day periods, taking the uncertainty in each combined measurementto be the error in the mean of the contributing data. As a result, a small number of tempo-rally isolated observations are discarded. The binned data points, and the best fit model,are shown in Figure 4.2.61Table 4.1:RJ temperature measurements of Uranus andSaturn.TRJ (K)148GHz 218GHzUranus (?4.1.1)2008 101.5 ? 2.0 93.2 ? 2.32009 103.8 ? 2.2 91.5 ? 8.62010 105.7 ? 2.1 97.6 ? 2.6Combined 103.2 ? 2.2 95.0 ? 3.1Saturn, W11 model (?4.2)Tdisk 133.8 ? 3.2 132.2 ? 4.7Tring 17.7 ? 2.2 12.3 ? 4.0[?2 / d.o.f.] [7.6 / 5] [6.5 / 5]Saturn, single T model (?4.2)Tdisk 131.2 ? 3.1 127.5 ? 4.4[?2 / d.o.f.] [12.0 / 6] [11.2 / 6]Note ? Values for Uranus (Section 4.1.1) are shown foreach season, as well as a weighted mean that takes full ac-count of calibration covariance between seasons. Saturn re-sults (Section 4.2) are provided for both a two-componentdisk+ring model and a disk-only model. All temperaturesare RJ and have been corrected for the CMB to indicate thebrightness that would be seen relative to an empty (T = 0)sky. To obtain thermodynamic brightness temperatures at148GHz (218GHz), add 3.5 K (5.1 K) to the RJ values.The fit of the W11 model includes a full accounting of the non-trivial correlations inthe calibration uncertainty of the data points. The resulting models are good fits, with?2 per degree of freedom of 7.6/5 (6.5/5) in the 148GHz (218GHz) array. The model fitparameters and uncertainties are presented in Table 4.1.For comparison, we also fit a single temperature model to the binned Saturn data, findingpoorer fits and mean temperatures that are 1?? less than the disk temperatures obtainedin the full model. These temperatures and ?2 statistics are also presented in Table Comparison to Previous MeasurementsIn Figure 4.3 we show the ACT disk temperature measurements along with high precisionresults from W11 below 100 GHz and from Goldin et al. (1997, hereafter G97) between170 and 700 GHz. The G97 measurements have statistical errors at the 2% level, but are62Figure 4.1: Measurements of the Uranus brightness temperature from this work,Weiland et al. (2011, WMAP), and Griffin and Orton (1993, G&O). The G&Opoints include data from that work as well as Ulich (1981) and Orton et al.(1986). The dotted line shows the model of G&O. G&O data are calibrated toa Ulich-Wright hybrid model for Mars brightness that interpolates between 90and 857 GHz and carries an estimated 5% systematic error. The solid line isour best-fit empirical model, using only the two highest frequency points fromWMAP , the two ACT points, and the G&O points above 600 GHz.calibrated with reference to the same Mars model used by G&O. We have applied a roughrecalibration factor to the G97 measurements using the WMAP result (Weiland et al., 2011)that the Ulich (1981) model for Mars temperature is 5% high at 94 GHz. Our recalibrationfactor varies linearly with the log of frequency from 0.95 at 90 GHz to 1 at 857 GHz. Withthis calibration factor applied, the G97 measurement at 170GHz and ACT measurementsat 149 and 219 GHz are consistent with a flat spectrum over this frequency range. It isdifficult to comment further on the continuum spectrum of Saturn based on the ACT andG97 data, due to the proximity of the high frequency G97 bands to PH3 resonances (e.g.,Weisstein and Serabyn, 1996).63Figure 4.2: Binned data and resulting best-fit two-component model of effective Sat-urn brightness vs. ring opening angle (B) relative to observer. The model issymmetric about B = 0 by construction. As the absolute value of B increases,the increased radiation from the rings and decreased flux from the obscureddisk leads to a local minimum in the total effective brightness at B ? 9? (13?)at 149 GHz (219 GHz). The model is fitted independently for each frequencyband. Error bars correspond to the error in the mean of observations contribut-ing to each point, but fits include additional error due to calibration, which iscovariant within each season and in some cases between seasons. Approximatemean dates of observation are, from left to right: Nov/08; Dec/08; Jun/10;Apr/10; Dec/09; Dec/10; and Dec/10. The sign convention is such that B < 0corresponds to negative values of the sub-Earth latitude.In this study of Uranus and Saturn, we have used a high quality calibration source (theCMB blackbody) to measure the disk brightness temperature of Uranus and to constraina two-component model of Saturn?s disk and ring temperatures. The precision of ourresults is limited by the absolute calibration error in the ACT maps. The accuracy ofour results depends on the correct extrapolation from large angular scales, where the ACTand WMAP maps are cross-calibrated, to the intermediate angular scales where the planetamplitudes are measured. Consistency between our temperature measurements and futuremeasurements is thus also a consistency check of our beam analysis.64Figure 4.3: Measurements of the Saturn disk brightness temperature from ACT,Weiland et al. (2011, WMAP), and Goldin et al. (1997, G97). Points fromG97 have been recalibrated as described in the text. Frequency error barson ACT and G97 points indicate bandwidth. Temperature error bars on G97points do not include calibration uncertainty. The green dashed line is a spec-tral model from Weisstein and Serabyn (1996, WS96), which shows proximityof absorption features to G97 points.65Chapter 5The ACT Equatorial GalaxyCluster SampleThe promise of Sunyaev-Zeldovich cluster surveys is the delivery of approximately mass-limited samples of galaxy clusters extending to high redshifts. High resolution microwavesurvey instruments such as ACT, South Pole Telescope, and Planck have begun to de-liver such samples (Marriage et al., 2011; Planck Collaboration VIII, 2012; Reichardt et al.,2013; Vanderlinde et al., 2010; Williamson et al., 2011). As described in Section 1.3, clus-ters trace extremes in the density field, and an accurate census has the potential to constrainparameters describing the matter power spectrum, Dark Energy, and neutrino physics.In this chapter we present the cluster sample derived from the ACT Equatorial field,using the data at 148GHz from the 2008?2010 seasons. We concentrate on the sampleand the inferred properties of individual clusters; the cosmological analysis is deferred toChapter 6. We first discuss the field maps and the process of cluster detection and con-firmation using a suite of matched filters. Following this, we develop a new approach tothe analysis of the SZ signal that incorporates a template for the cluster pressure profile torelate the cluster signal to the halo mass. To explore the effect of systematic variation in themass relation, free parameters are introduced and constrained through the application ofseveral different SZ models and data sets. We demonstrate general agreement of the samplewith expectations in a ?CDM cosmology, and compare the derived mass and integratedSZ quantity measurements to other measurements. Finally, we apply this analysis tech-nique to the ACT Southern cluster sample originally presented by Marriage et al. (2011)and Menanteau et al. (2010).Throughout the discussion of clusters, we parametrize the Hubble constant as H0 =70 h70 km s?1 Mpc?1. Where it is necessary to adopt a fiducial cosmology, we assume?m = 0.3, ?? = 0.7, and h70 = 1 unless otherwise stated. The ratio of the redshift66dependent Hubble constant to its present value is denoted E(z); i.e.,E(z) = [?m(1 + z)3 +??]1/2, (5.1)for a Universe with ?k = 0 and negligible radiation density.5.1 Maps and Cluster DetectionIn this section we discuss the detection of galaxy clusters in the ACT Equatorial mapsat 148GHz. The maps are filtered to enhance structures whose shape matches the Uni-versal Pressure Profile of Arnaud et al. (2010). The final cluster catalogue consists of SZcandidates that have been confirmed in optical or IR imaging.5.1.1 Equatorial MapsACT?s observations during the 2009 and 2010 seasons were concentrated on the celestialequator. For this study we make use of the 504 deg2 deep, contiguous region spanning from20h16m00s to 3h52m24s in right ascension and from ?2?07? to 2?18? in declination. Thisregion includes 270 deg2 of overlap with S82, which extends to 20h39m in R.A. and ?1?15?in declination. As shown in Figure 5.1, the S82 region corresponds to the lowest-noise regionof the ACT Equatorial maps.The bolometer timestream data are acquired while scanning the telescope in azimuthat fixed elevation. Cross-linked data are obtained by observing the same celestial region attwo telescope pointings that produce approximately orthogonal scan directions. Because thescan strategy was optimized for simultaneous observation with the 148GHz and 218GHzarrays (the centres of which are separated by approximately 33? when projected onto thesky), the regions beyond declinations of ?1?40? are not well cross-linked.The ACT data reduction pipeline and map-making procedure are described in Du?nner et al.(2013), in the context of ACT?s 2008 data. The timestream bolometer data are screened forpathologies and then combined to obtain a maximum likelihood estimate of the microwavesky map (with 0.5? pixels) for each observing season. As a result of the cross-linked scanstrategy, and the careful treatment of noise during map making, the ACT maps are unbi-ased at angular scales ? > 300, in the sense that there is no scale-dependent gain due tofiltering or noise.Due to realignments of the primary and secondary mirrors, the telescope beams varyslightly between seasons but are stable over the course of each season. The telescope beamsare determined from observations of Saturn, using the method described in Hincks et al.(2010), but with additional corrections to account for ? 6?? RMS pointing variation betweenobservations made on different nights (Hasselfield et al., in prep.). The effective beam forthe 148GHz array differs negligibly between the 2009 and 2010 seasons, with a FWHM of1.4? and solid angle (including the effects of pointing variation) of (224 ? 2) nsr.67Calibrations of ACT observations are based on frequent detector load curves, and at-mospheric opacity water vapour measurements (Du?nner et al., 2013). Absolute calibrationof the ACT maps is achieved by comparing the large angular scale (300 < ? < 1100) signalfrom the 2010 season maps to the WMAP 95 GHz 7-year maps (Jarosik et al., 2011). Usinga cross-correlation technique, as described in Hajian et al. (2011), an absolute calibrationuncertainty of ? 2% in temperature is achieved (Das et al., 2013). The inter-calibration of2009 and 2010 is measured through a similar cross-correlation technique, with less than 2%error.5.1.2 Gas Pressure ModelAt several stages in the detection and analysis we will require a template for the intraclus-ter gas pressure profile. To this end we adopt the ?Universal Pressure Profile? (UPP) ofArnaud et al. (2010, hereafter A10), which includes mass dependence in the profile shapeand has been calibrated to X-ray observations of nearby clusters. In this section we re-view the form of the UPP, and obtain several approximations that will be used in clusterdetection (Section 5.1.3) and cluster property recovery (Section 5.2).In A10, the cluster electron pressure as a function of physical radius r is modeled with ageneralized Navarro-Frenk-White (GNFW) profile (Nagai, Kravtsov, and Vikhlinin, 2007),p(x) = P0 (c500x)?? (1 + (c500x)?)(???)/? , (5.2)where x = r/R500 and P0, c500, ?, ?, ? are fit parameters. The overall pressure normaliza-tion, under assumptions of self-similarity (i.e., the case when gravity is the sole processresponsible for setting cluster properties), varies with mass and redshift according toP500 =[1.65 ? 10?3h270 keV cm?3]m2/3E8/3(z), (5.3)where E(z) is the ratio of the Hubble constant at redshift z to its present value, andm ? M500c/(3 ? 1014 h?170 M?) (5.4)is a convenient mass parameter. Some deviation from strict self-similarity may be encodedvia an additional mass dependence in the shape of the profile, yielding a formP (r) = P500m?p(x)p(x). (5.5)In this framework, A10 use X-ray observations of local (z < 0.2) clusters to obtain best-fitGNFW parameters [P0, c500, ?, ?, ?] = [8.403 h3/270 , 1.177, 0.3081, 1.0510, 5.4905], and anadditional radial dependence described reasonably well by ?p(x) = 0.22/(1 + 8x3).Because hydrostatic mass estimates are used by A10 to assess the relationship betweencluster mass and the pressure profile, there may be systematic differences when one makes68use of an alternative mass proxy, such as weak lensing or galaxy velocity dispersion. Sim-ulations suggest that hydrostatic masses are under-estimates of the true cluster mass (e.g.,Nagai et al., 2007). However, there is little consensus among recent studies which com-pare X-ray hydrostatic and weak lensing mass measurements. For example, Mahdavi et al.(2013) find that hydrostatic masses are lower than weak lensing masses by about 10%at R500, Zhang et al. (2010) and Vikhlinin et al. (2009a) find reasonable agreement, andPlanck Collaboration III (2013) find hydrostatic masses to be about 20% larger than weaklensing masses. Therefore in our initial treatment of the UPP we neglect this bias; later wewill address this issue by adding degrees of freedom to allow for changes in the normalizationof the pressure profile.The thermal SZ signal is related to the optical depth for Compton scattering along agiven line of sight. For our pressure profile, and in the absence of relativistic effects, thisCompton parameter at projected angle ? from the cluster centre isy(?) = ?Tmec2?ds P(?s2 + (R500?/?500)2), (5.6)where ?500 = R500/DA(z) with DA(z) the angular diameter distance to redshift z, ?T is theThomson cross section, me is the electron mass, and the integral in s is along the line ofsight. Relativistic effects change this picture somewhat, but for convenience we will use theabove definition of y(?) and apply the relativistic correction only when calculating the SZsignal associated with a particular y.To simplify the expression for the cluster pressure profile, we first consider the massparameter m = 1 and factor the expression in equation (5.6) to gety(?,m = 1) = 10A0E(z)2?(?/?500) (5.7)where ?(x) is a dimensionless profile normalized to ?(0) = 1, and 10A0 = 4.950 ? 10?5h1/270gives the normalization. The deviations from self-similarity are weak enough that we maymodel the changes in the profile shape with mass as simple adjustments to the normalizationand angular scale of the profile. For the masses of interest here (1 < m < 10) we obtainy(?,m) ? 10A0E(z)2m1+B0?(mC0?/?500) (5.8)with B0 = 0.08 and C0 = ?0.025. This approximation reproduces the inner signal shapeextremely well, with deviations increasing to the 0.5% level by ?500. For 0.1?500 < ? < 3?500,the enclosed signal (? ?0 d?? 2???y(??,m)) differs by less than 1% from the results of the fullcomputation. This parametrization of the cluster signal in terms of a normalization anddimensionless profile is not used for cluster detection (Section 5.1.3), but will motivate theformulation of scaling relations and permit the estimation of cluster masses (Section 5.2.1).The observed signal due to the SZ effect is a change in radiation intensity, expressed in69units of CMB temperature:?T (?)TCMB= fSZ y(?). (5.9)In the non-relativistic limit, the factor fSZ depends only on the observed radiation frequency.Integrating this non-relativistic SZ spectral response over the nominal 148GHz array band-pass, we obtain an effective frequency of 146.9 GHz (Swetz et al., 2011). At this frequency,the formulae of Itoh et al. (1998) provide a spectral factor, including relativistic effectsfor gas temperature Te, of fSZ(t) = ?0.992frel(t) where t = kBTe/mec2 and frel(t) =1+3.79t?28.2t2 . This results in a 6% correction for a cluster with T = 10 keV. We use thescaling relation of Arnaud et al. (2005), t = ?0.00848? (mE(z))?0.585 , to express the meantemperature dependence in terms of the cluster mass and redshift. This yields a final form,fSZ(m, z) = ?0.992frel(m, z), which we use in all subsequent modelling of the SZ signal.The corrections for the ACT cluster sample range from roughly 3% to 10%.5.1.3 Galaxy Cluster DetectionIn addition to the temperature decrements due to galaxy clusters, the ACT maps at 148GHzcontain contributions from the CMB, radio point sources, dusty galaxies, and noise fromatmospheric fluctuations and the detectors. To detect galaxy clusters in the ACT maps wemake use of a set of matched filters, with signal templates based on the UPP through theintegrated profile template ?(?/?500).We consider signal templates S?500(?) ? ?(?/?500) for ?500 = 1.?18 to 27? in increments of1.?18. Each fixed angular scale corresponds to a physical scale that varies with redshift, butcan be computed for a given cosmology. For each signal template we form an associatedmatched filter in Fourier space,??500(k) =1??500B(k)S?500(k)N(k) , (5.10)where B(k) is the product of the telescope beam response with the map pixel window func-tion, N(k) is the (anisotropic) noise power spectrum of the map, and ??500 is a normalizationfactor chosen so that, when applied to a map containing a beam-convolved cluster signal??T [S?500 ?B](?) (in temperature units), the matched filter returns the central decrement??T .Since the total power from the galaxy cluster SZ signal is low compared to the CMB,atmospheric noise, and white noise that contaminate the cluster signal, we estimate thenoise spectrum N(k) from the map directly. Bright (signal to noise ratio greater than five)point sources are masked from the map, with the masking radius ranging from 2? for thedimmest sources to 1? for the brightest source. A plane is fit to the map signal (weightingby the inverse number of samples in each pixel) and removed, and the map is apodized7020h30m21h00m21h30m22h00m22h30mR.A. (J2000)020100+01+0223h00m23h30m00h00m00h30m01h00m020100+01+02Dec. (J2000)01h30m02h00m02h30m03h00m03h30m020100+01+0220 40 60 80Sensitivity to central decrement (K)Figure 5.1: The portion of the ACT Equatorial survey region considered in this work.It spans from 20h16m00s to 3h52m24s in R.A. and from ?2?07? to 2?18? indeclination for a total of 504 deg2. The overlap with Stripe 82 (dashed line)extends only to 20h39m in R.A. and covers ?1?15? in declination, for a total of270 deg2. Circles identify the optically confirmed SZ-selected galaxy clusters,with radius proportional to the signal to noise ratio of the detection (whichranges from 4 to 13). The grey-scale gives the sensitivity (in CMB?K) todetection of galaxy clusters, after filtering, for the matched filter with ?500 = 5.?9(see Section 5.1.3). Inside the Stripe 82 region the median noise level is 44 ?K,with one quarter of pixels having noise less (respectively, more) than 41 ?K (46?K). Outside Stripe 82, the median level is 54 ?K, with one quarter of pixelshaving less (more) than 47 (64) ?K noise. The higher noise, X -shaped regionsare due to breaks in the scan for calibration operations.within 0.2? of the map edges.For ACT, the effect of the noise term in the matched filter is to strongly suppresssignal below ? ? 3000 (corresponding to scales larger than 7?). When combined with thesignal template (and beam), the filters form band-passes centred at ? ranging from roughly2500 to 5000. The angular scales probed by the filters are thus sufficiently small thatfiltering artifacts near the map boundaries are mitigated by the map apodization. Whilethe suppression of large angular scales disfavours the detection of clusters with large angularsizes, we apply the full suite of filters in order to maximize detection probability and tostudy the features of inferred cluster properties as the assumed cluster scale is varied.The azimuthally averaged real space filter kernel corresponding to ?500 = 5.?9 is shown710 246 8 10 (arcmin) kernelCluster templateACT beamFigure 5.2: The azimuthally averaged real space matched filter kernel, proportionalto ?5.?9(?), for signal template with ?500 = 5.?9. Shown for reference are the ACT148GHz beam, and the cluster signal template S5.?9(?). While filters tuned tomany different angular scales are used for cluster detection (Section 5.1.3), the5.?9 filter is used for cluster characterization and cosmology (Section 5.2.1).in Figure 5.2, and compared to both the ACT 148GHz beam and the signal template S?500 .The true noise spectrum may vary somewhat over the map due to variations in atmo-spheric and detector noise levels, and thus the matched filter ??500(k) might be said to besub-optimal at any point. The filter remains unbiased, however, and a reasonable estimateof the signal to noise ratio (S/N) may still be obtained by recognizing that the local noiselevel will be highly correlated with the number of observations contributing to a given mappixel.Prior to matched filtering, the ACT maps are conditioned in the same way as for noiseestimation, except that the point sources are subtracted from the maps instead of beingmasked. (Subsequent analysis disregards regions near those point sources, amounting to1% of the map area.) With the application of each filter we obtain a map of ?T values. Asection of a filtered map (for ?500 = 5.?9) is shown in Figure 5.3.We characterize the noise in each filtered map by modelling the variance at position xas ?2(x) = ?20 + ?2hits/nhits(x), where nhits(x) is the number of detector samples falling inthe pixel at x. We fit constants ?0 and ?hits by binning in small ranges of 1/nhits. The fitis iterated after excluding regions near pixels that are strong outliers to the noise model.Typically such pixels are near eventual galaxy cluster candidates. Figure 5.1 shows thenoise map for the ?500 = 5.?9 filter.After forming the signal to noise ratio map ??T (x)/?(x), cluster candidates are iden-tified as all pixels with values exceeding 4. The catalogue of cluster candidates containspositions, central decrements (?T ), and the local map noise level. Candidates seen at7202h10m02h15m02h20m02h25m02h30mR.A. (J2000)-01?0?+01?Dec. (J2000)J0218.2-0041(S/N = 5.8)J0223.1-0056(S/N = 5.8)J0215.4+0030(S/N = 5.5)?200 ?160 ?120 ?80 ?40 0 40 80 120 160 200?T (?K)Figure 5.3: Section of the 148GHz map (covering 18.7 deg2) match-filtered with aGNFW profile of scale ?500 = 5.?9. Point sources are removed prior to fil-tering. Three optically confirmed clusters with S/N > 4.9 are highlighted(see Table 5.3). Within this area, there are an additional 11 candidates(4 < S/N < 4.9), which are not confirmed as clusters in the SDSS data (andthus may be spurious detections or high-redshift clusters).multiple filter scales are cross-identified if the detection positions are within 1?; the clustercandidate positions that we list come from the map where the cluster was most significantlydetected. We adopt the largest S/N value obtained over the range of filter scales as thedetection significance for each candidate.For a given candidate, the S/N tends to vary only weakly with the filter scale. Thereconstructed central decrement ?T varies weakly above filter scales of ?500 ? 3?, as maybe seen for the most significantly detected clusters in Figure 5.4. This stabilization occurswhen the assumed cluster size is larger than the true cluster size, because the filter isoptimized to return the difference in the level of the signal at the cluster position and thelevel of the signal away from the cluster centre. The filter interprets the signal at the clusterposition as being due to the convolution of the telescope beam with the cluster signal. Theinferred central decrement thus rises rapidly as the assumed ?500 decreases, since total SZflux scales as ?T?5002. As is discussed in Section 5.2.1, only the results from the ?500 = 5.?9matched filter are used for inferring masses, scaling relations, and cosmological results. Thecorresponding physical scale may be determined, as a function of redshift, based on clusterdistance.73500 (arcmin)0200400600800100012001400T  (K)0510 15 20500 (arcmin)0246810S/NFigure 5.4: Central decrement and signal to noise ratio as a function of filter scale forthe 20 clusters in S82 detected with peak S/N > 5. Top panel : Although thecentral decrement is a model-dependent quantity, the value tends to be stablefor filter scales of ?500 > 3?. Bottom panel : On each curve, the circular pointidentifies the filter scale at which the peak S/N was observed. The verticaldashed line shows the angular scale chosen for cluster property and cosmologyanalysis, ?500 = 5.?9. Despite the apparent gap near S/N ? 6, the clustersshown represent a single population.5.1.4 Galaxy Cluster ConfirmationThe cluster candidates obtained from the 148GHz map analysis are confirmed using opticaland infrared imaging. A complete discussion of this process may be found in Menanteau et al.(2013). For the purposes of this work, we briefly summarize the confirmation process andthe redshift limits of the sample (which must be understood in order to derive cosmologicalconstraints). These limits differ according to the depth of the optical imaging available overa given part of the map.Most cluster candidates are confirmed through the analysis of SDSS imaging. TheACT Equatorial survey is almost entirely covered by SDSS archival data (Abazajian et al.,2009), with a central strip designed to overlap with the deep optical data in the S82 region(Annis et al., 2011), as shown in Figure 5.1. For each ACT cluster candidate with peakS/N > 4, SDSS images are studied using an iterative photometric analysis to identify abrightest cluster galaxy (BCG) and an associated red sequence of member galaxies. A74minimum richness of Ngal = 15, evaluated within a projected 1 h?1 Mpc of the nominalcluster centre and within 0.045(1+ zc) of the nominal cluster redshift zc, is required for thecandidate to be confirmed as a cluster. The redshifts of confirmed clusters are obtainedfrom either a photometric analysis of the images, from SDSS spectroscopy of bright clustermembers, or from targeted multi-object spectroscopic follow-up. The redshift limit of clusterconfirmation using SDSS data alone is estimated to be z ? 0.8 within S82 and z ? 0.5outside of S82. Cluster candidates that are not confirmed in SDSS imaging are targeted,in an on-going follow-up campaign, under the assumption that they may be high redshiftclusters.Within the S82 region, 49 of 155 candidates are confirmed, with 44 of these confirmationsresulting from analysis of SDSS data only. Targeted follow-up of the high S/N candidateswas pursued at the Apache Point Observatory, yielding five more confirmations, all atz > 0.9. All cluster candidates with S/N > 5.1 were confirmed as clusters. This is consistentwith our estimate of 1.8 false detections in this region, based on filtering of simulated noise.The follow-up in the S82 region is deemed complete to a S/N of 5.1, in the sense that allSZ candidates with ACT S/N > 5.1 have been targeted. It is thus this sample, and thisregion, that are considered for the cosmological analysis (in addition to a subset of theMarriage et al., 2011, sample; see Chapter 6). The completeness within S82, as a functionof mass and redshift, is estimated in Section 5.2.6.Outside of S82, 19 clusters are confirmed using SDSS DR8 data. High significance SZdetections in this region that are not confirmed in the DR8 data constitute good candidatesfor high redshift galaxy clusters and are being investigated in a targeted follow-up campaign.The confirmed cluster sample may contain a small number of false positives, due tochance superposition of a low mass cluster at the location of an otherwise spurious SZcandidate. Most of our confirmed clusters are associated with rich optical counterparts,and thus are truly massive clusters. However, our search was carried out over considerablesky area in the ? 150 regions around SZ candidates. Assigning an effective area of 13arcmin2 to each of these fields yields a total area of approximately 0.5 deg2. From themaxBCG catalogue (Koester et al., 2007), which includes optical richness measurementsfor clusters with 0.1 < z < 0.3, we expect that the density of clusters satisfying our richnesscriteria in the range 0.1 < z < 0.8 is approximately 6 per deg2. We conclude that roughlythree of our low richness confirmed clusters could potentially be spurious associations. Suchcontamination is not likely to affect the high significance (S/N > 5.1) sample, where thelowest richness is ? 30.In Table 5.3 we present the catalogue of 68 confirmed clusters. For each object we listits coordinates, redshift (see Menanteau et al., 2013, for details), S/N of the detection (weadopt the maximum S/N across the range of filters used), and SZ properties. Figure 5.5shows postage stamp images of some high-significance clusters, taken from the filtered ACT148GHz maps.75Figure 5.5: Postage stamp images (30? on a side) for the 10 highest S/N detections inthe catalogue (see Table 5.3), taken from the filtered ACT maps. The clustersare ordered by detection S/N , from top left to bottom right, and each postagestamp shown is filtered at the scale which optimizes the detection S/N . Notethat J2327.4?0204 is at the edge of the map. The greyscale is linear and runsfrom ?350 ?K (black) to +100?K (white).5.2 Recovered Cluster PropertiesIn this section we develop a relationship between cluster mass and the expected signal inthe ACT filtered maps. The form of the scaling relationship between the SZ observableand the cluster mass is based on the UPP, and parameters of that relationship are studiedusing models of cluster physics and dynamical mass measurements. We obtain masses forthe ACT Equatorial clusters assuming a representative set of parameters.5.2.1 Profile Based Amplitude AnalysisScaling relations between cluster mass and cluster SZ signal strength are often expressedin terms of bulk integrated Compton quantities, such as Y500, which are expected to becorrelated with mass with low intrinsic scatter (e.g., Motl et al., 2005; Reid and Spergel,2006). Due to projection effects, and the current levels of telescope resolution and surveydepth, measurements of Y500 for individual clusters can be obtained only by comparing themillimeter wavelength data to a simple, parametrized model for the cluster pressure profile.Such fits may be done directly, or indirectly as part of the cluster detection process throughthe application of one or more matched filters (where the filters are ?matched? in the senseof being tuned to a particular angular scale). In such comparisons, the inferred values ofY500 are very sensitive to the assumed cluster scale (i.e., ?5001), and this scale is poorlyconstrained by microwave data alone.1M500c = (4pi/3) ? 500?c(z)R3500; ?500 = R500/DA(z).76Recent microwave survey instruments make use of spatial filters to both detect and char-acterize their cluster samples, coping with ?500 uncertainty in different ways. For example,the Planck team uses X-ray luminosity based masses (Planck Collaboration VIII, 2012) aswell as more detailed X-ray and weak lensing studies (Planck Collaboration III, 2013) toconstrain R500, and obtain Y500 measurements assuming profile shapes described by theUPP.In cases where suitable X-ray or optical constraints on the cluster scale are not available,authors have constructed empirical scaling relations based on alternative SZ statistics, suchas the amplitude returned by some particular filter (Sehgal et al., 2011), or the maximumS/N over some ensemble of filters (Vanderlinde et al., 2010). Recognizing that the clusterangular scale is poorly constrained by the filter ensemble, recent work from the South PoleTelescope has included a marginalization over the results returned by the ensemble of filters(e.g., Reichardt et al., 2013; Story et al., 2011). Such approaches rely on simulated mapsto guide the interpretation of their results.For the purposes of using the SZ signal to understand scaling relations and to obtain cos-mological constraints, we develop an approach in which the cluster SZ signal is parametrizedby a single statistic, obtained from the ACT map that has been filtered using ?5.?9(k). In-stead of using simulations to inform our interpretation of the data, we develop a frameworkwhere the SZ observable is expressed in terms of the parameters of some underlying modelfor the cluster pressure profile. In particular, we model the clusters as being well describedby the UPP, up to some overall adjustments to the normalization and mass dependence(see Section 5.1.2).An estimate of the cluster central Compton parameter, based only on the non-relativisticSZ treatment, is given byy?0 ??TTCMBf?1SZ (m = 0, z = 0), (5.11)where fSZ(m = 0, z = 0) = ?0.992 as explained in Section 5.1.2. This ?uncorrected? centralCompton parameter is used in place of ?T to develop an interpretation of the SZ signal.This quantity is uncorrected in the sense that it is associated with the fixed angular scalefilter and does not include a relativistic correction.For a cluster with SZ signal described by equation (5.8), the value of y?0 that we wouldexpect to observe by applying the filter ?5.?9 to the beam-convolved map isy?0 = 10A0E(z)2m1+B0Q(?500/mC0)frel(m, z) (5.12)whereQ(?) =? d2k(2?)2?5.?9(k)B(k)?d2?? ei?? ?k?(??/?). (5.13)770 246 8 10 1214	500 (arcmin) 5.6: Response function used to reconstruct the cluster central decrement as afunction of cluster angular size (solid line). At ?500 = 5.?9, the filter is perfectlymatched and Q = 1. At scales slightly above 5.?9, Q > 1 because such profileshave high in-band signal despite being an imperfect match, overall, to the tem-plate profile. For the definition of Q, see Section 5.2.1. The dotted line showsanalogous function computed under the assumption that the cluster signal isdescribed by the Planck Pressure Profile (see Section 5.2.3).is the spatial convolution of the filter, the beam, and the cluster?s unit-normalized integratedpressure profile. We note that in this formalism, ?500 = R500/DA(z) is determined by thecluster mass and the cosmology (rather than being some independent parameter describingthe angular scale of the pressure profile).The response function Q(?) for the Equatorial clusters is shown in Figure 5.6. It encap-sulates the bias incurred in the central decrement estimate due to a mismatch between thetrue cluster size and the size encoded in the filter, for the family of clusters described by theUPP. While this bias is in some cases substantial (Q ? 0.3 for clusters with ?500 ? 1.5?),the function Q(?) is not strongly sensitive to the details of the assumed pressure profile(as demonstrated in Section 5.2.3), and the assumptions underlying this approach are nota significant departure from other analyses that rely on a family of cluster templates toextract a cluster observable.Equation (5.12) thus relates y?0 to cluster mass and redshift while accounting for theimpact of the filter on clusters whose angular size is determined by their mass and redshift.This relationship can be seen in Figure 5.7.The essence of our approach, then, is to filter the maps with ?5.?9(k) and for eachconfirmed cluster obtain ?T and its error. This is equivalent to measuring y?0, which canthen be compared to the right hand side of equation (5.12). If the cluster redshift is alsoknown, then for a given cosmology the only free parameter in the expression for y?0 is themass parameter, m.22 With y?0 and z measurements in hand, one could certainly proceed to solve equation (5.12) to obtain a780.2 0.4 0.6 0.8 1.0 1.2 1.4Redshift0. y0 (10?4)0100200300400500600700??T (?K)Figure 5.7: Prediction, based on the UPP, for cluster signal in a map match-filteredwith ?500 = 5.?9, in units of uncorrected central Compton parameter y?0 andapparent temperature decrement ??T at 148GHz (Section 5.2.1). Solid linestrace constant masses of, from top to bottom, M500c = 1015, 7? 1014, 4? 1014,and 2?1014 h?170 M?. Dotted lines are for the same masses, but with the scalingrelation parameter C = 0.5 to show the redshift sensitivity to this parameter.Above z ? 0.5, the scaling behaviour of the observable y?0 with redshift isstronger for higher masses because their angular size is a better match to thecluster template and the redshift dependence in Q does not attenuate the scalingof the central decrement, y0 ? E(z)2, as much as it does for lower masses. Thedashed lines correspond to S/N > 4 and S/N > 5.1, based on the median noiselevel in the S82 region.We refer to this alternative approach, where a family of pressure profiles is used tomodel the amplitude of a source in a filtered map, as ?Profile Based Amplitude Analysis?(PBAA). While we have applied a filter tuned to a particular angular scale, the effects ofangular diameter distance, telescope beam, and the spatial filtering are modeled in a waythat accounts for the (mass and redshift dependent) cluster angular scale. For a givencosmology, and having computed Q(?) based on the UPP, the parameters (A0, B0, and C0)of the scaling relation between y?0 and mass have a physical significance and can be verifiedthrough measurements of y?0, redshift, and mass for a suitable set of clusters.While the usage of a single filter clearly simplifies data processing, the most compellingadvantage is that one does not suffer from inter-filter noise bias. For example, when opti-mizing filter scale, a CMB cold spot near a cluster candidate will draw the preferred filterto larger angular scales than would the isolated cluster signal. The preferred filter scale isthus driven by the amplitude of local noise excursions as much as it is driven by the clustersignal. In a single filter context, a CMB cold spot affects the amplitude measurement bycontributing spurious signal to the apparent cluster decrement; but if CMB hot and coldmass for each cluster. Because we are treating mass as one of the independent variables, however, such anapproach would produce biased mass estimates; see Section are equally likely, and uncorrelated with cluster positions, then the CMB as a wholeacts as a Gaussian noise contribution to cluster signal. The effects of coherent noise on largescales are thus somewhat better behaved if we do not permit the re-weighting of angularscales to maximize the apparent signal.To achieve the goal of detecting as many clusters as possible, one should certainly explorea variety of candidate cluster profiles and apply an ensemble of matched filters. However,for cosmological studies, or when trying to understand the relationship between observablesin samples that are selected based on one of the observables under study, it is critical tounderstand the selection function that describes how the population of objects in the samplerelates to the broader population of objects in the Universe. While we sacrifice a certainamount of signal when choosing a single filter scale to use for cosmological and scalingrelation analysis, we benefit from having a simpler selection function.Much of our approach can be simply generalized so that a suite of filters are used,but with each filter intended to correspond to a particular redshift interval. The redshift-dependent angular scales might be selected to match clusters of a particular mass, forexample. Such an approach benefits from the lack of inter-scale noise bias, because thereis no data-based optimization over angular scale. However, interpretation of the signal isthen complicated by the need to consider the impact of the full suite of filters on the clustersignal and noise models. Such an approach is tractable, but is not considered in this work.We also note that ?500 = 5.?9 is chosen because it lies in a regime of ?500 where themeasured y?0 statistic for our high significance clusters is approximately constant. Ourapproach does not require this, however, and could instead have used a filter correspondingto some smaller ?500, where signal to noise ratios are, on average, slightly higher.In order to compare the predictions of the UPP based formalism to models and otherdata sets, we introduce a more general relationship relating cluster mass to the uncorrectedcentral Compton parameter. We allow for variations in the normalization, mass dependence,and scale evolution through parameters A, B, and C and model y?0 asy?0 = 10A0+AE(z)2(M/Mpivot)1+B0+B?Q[(1 + z1.5)C?500/mC0]frel(m, z). (5.14)To abbreviate the argument to Q(?), we will often simply write Q(m, z). The exponents(A0, B0, C0) remain fixed to the UPP model values of equations (5.7) and (5.8), except whereotherwise noted. For a given data set or model, Mpivot will be chosen to reduce covariancein the fit values of A and B. In Table 5.1 we present the fit parameters for various modelsand data sets discussed in subsequent sections. In order to compare fits from data setswith different Mpivot, we also compute the normalization exponent Am associated withMpivot = 3 ? 1014 h?170 M? for each data set. In these terms, the UPP model described byequation (5.12) corresponds to (Am, B,C) = (0, 0, 0).80In cases where independent surveys each measure y?0 values for a cluster based on follow-ing the algorithm described here, the y?0 measurements should not, in general, be compareddirectly. This is because the filter ??500 and the resulting bias factor Q depend on the tele-scope beam and the noise spectra of the resulting maps. However, it is possible to filter oneset of maps in a way that matches the beam and filtering of a preceding analysis. In suchcases an independent measurement of y?0 is obtained, which may be compared between ex-periments. Such comparisons are likely to be most interesting in cases where two telescopeshave similar resolution.Alternatively, y?0 measurements and redshifts may be converted, for some particularvalues of the scaling relation parameters, into physical parameters such as M500c, Y500, orthe corrected y0. Such derived quantities may be compared between experiments that probedifferent angular scales. The physical parameters can be updated as one?s understandingof the scaling relation parameters is improved. The use of y?0 thus facilitates the re-use ofthe data in analyses that explore different models for the cluster signal.The uncorrected central Compton parameter measurements (y?0) for the ACT Equatorialclusters are presented in Table 5.3. They are used in subsequent sections to estimatecluster properties (such as corrected SZ quantities and mass) and to constrain cosmologicalparameters. For the Southern cluster sample, analogous measurements are presented in theAppendix. Between the Equatorial and Southern cluster samples, the ACT collaborationhas reported a total of 91 optically confirmed, SZ detected clusters.5.2.2 Cluster Mass and SZ Quantity EstimatesGiven measurements of cluster y?0 and redshift, one cannot naively invert Equations (5.12)or (5.14) to obtain a mass estimate. Because of intrinsic scatter, measurement noise, andthe non-trivial (very steep) cluster mass function, the mean mass at fixed SZ signal y?0will be lower than the mass whose mean predicted SZ signal is y?0. The bias due to noiseis often referred to as ?flux boosting? and can be corrected in a Bayesian analysis thataccounts for the underlying distribution of flux densities (Coppin et al., 2005). The biasdue to intrinsic scatter, however, is not restricted to the low significance measurements.Considering the population of clusters (at fixed redshift) in the (logm, log y?0) plane, thelocus ?logm| log y?0? (i.e., the expectation value of the log of the mass for a given centralCompton parameter) lies at lower mass than ?log y?0| logm?. This phenomenon has beendiscussed in the context of galaxy cluster surveys by, e.g., Mantz et al. (2010a, see also thereview by Allen, Evrard, and Mantz 2011).The mass of a cluster, however, can be estimated if one has an expression for the clustermass function. We adapt the Bayesian framework of Mantz et al. (2010a) to this purpose.81The posterior probability of the mass parameter m given the observation y?ob0 isP (m|y?ob0 ) ? P (y?ob0 |m)P (m)=(?dy?tr0 P (y?ob0 |y?tr0 )P (y?tr0 |m))P (m) (5.15)where y?tr0 represents the ?true? SZ signal in the absence of noise, P (y?ob0 |y?tr0 ) is the dis-tribution of y?ob0 given y?tr0 and the observed noise ?y?ob0 , and P (m) is proportional to thedistribution of cluster masses at the cluster redshift. The distribution P (y?tr0 |m) of thenoise-free cluster signal y?tr0 is assumed to be log-normal about the mean relation given byEquation (5.14), i.e.,log y?tr0 ? N(log y?0(m, z);?2int) (5.16)with ?int denoting the intrinsic scatter.We use the results of Tinker et al. (2008) to compute the cluster mass function, assumingthe fiducial ?CDM cosmology, with ?8 = 0.8. Scaling the mass function by the comovingvolume element at fixed solid angle, we obtain dN(< m, z)/dz, the number of clusters, perunit solid angle and per unit redshift, that have mass less than m. The probability of acluster in this light cone having mass m and redshift z may then be taken as P (m, z) ?d2N(< m, z)/dz dm. We account for redshift uncertainty by marginalizing the cluster massfunction P (m, z) over the cluster?s redshift error to obtain an effective P (m) at the observedcluster redshift.The marginalized masses obtained using Equation (5.15) are presented in Table 5.4. Forthe ACT Southern cluster sample, these masses are presented in the Appendix. In each case,masses are presented for the UPP scaling relation as well as for scaling relation parametersfit to SZ signal models (see Section 5.2.4) or dynamical mass data (see Section 5.2.5).A similar approach may be taken to estimate the true values of SZ quantities, giventhe observed quantities. In this case we are effectively only undoing the noise bias, whileintrinsic scatter affects the underlying population function. We are interested inP (y?tr0 |y?ob0 ) ? P (y?ob0 |y?tr0 )P (y?tr0 )= P (y?ob0 |y?tr0 )?dm P (y?tr0 |m)P (m). (5.17)The resulting probability distribution is used to obtain marginalized estimates of y0, ?500(which should be interpreted as giving the scale of the pressure profile rather than the scaleof the mass density profile), Y500 (estimated within the SZ-inferred ?500) and Q. Thesequantities are presented in Table 5.4, for the UPP scaling relation parameters.In Figure 5.8 we demonstrate the impact of the steep mass function on the inferredmass and SZ quantities. As the measurement noise decreases, the y?0 measurements are820123456102 3 4 5 7M500c (1014h?170M?)0246810P(log10M[m])P(log10M[y0])Figure 5.8: Example probability distributions for cluster mass (upper panel) and SZsignal strength parametrized as a mass according to equation (5.14) (lowerpanel). The solid line PDF is the result of a direct inversion of the scalingrelation described by equation (5.14). The corrected PDF (dashed line) isobtained by accounting for the underlying population distribution (bold line;arbitrary normalization). The correction is computed according to equation(5.15) for the upper panel, and according to equation (5.17) for the lower panel.Curves shown correspond to ACT?CL J0022.2?0036.less biased; but any intrinsic scatter in the y?0?M relation will lead to bias in the naivelyestimated mass.5.2.3 The Planck Pressure ProfileIn Planck Collaboration V (2013), data for 62 massive clusters from the Planck all-sky EarlySunyaev-Zeldovich cluster sample (Planck Collaboration VIII, 2012) are analysed to obtaina ?Planck pressure profile? (PPP) based on measurements of the SZ signal. Integrating thePPP along lines of sight, the central pressure is 20% lower than the UPP but is higher thanthe UPP outside of 0.5R500. Planck finds overall consistency between results obtained withthe UPP and the PPP.We assess the difference in inferred mass due to this alternative pressure profile by re-analysing the ACT y?0 using the PPP. A bias function Q is computed as in Equation (5.13),but with the normalized Compton profile ? associated to the PPP (see Figure 5.6). Weadditionally determine scaling parameters, compatible with Equation (5.8), of (10A0 , B0, C0)= (4.153? 10?5h1/270 , 0.12, 0). Note that while the bias function shows increased sensitivity,compared to the UPP, for ?500 < 9?, this is compensated for by the lower normalizationfactor 10A0 . For the Equatorial cluster sample, we find the PPP masses to be well describedby a simple mean shift of MPPP500c = 1.015 MUPP500c , with 3% RMS scatter. Note that this is83only a statement about the dependence of the ACT results on the assumed pressure profile;experiments that probe different angular scales may be more or less sensitive to such achange.While the change in inferred masses is in this case negligible, we reiterate that our fullyparametrized relationship between SZ signal and mass (Equation (5.14)) allows for freedomin the normalization, mass dependence, and evolution of cluster concentration with redshift.Mass or cosmological parameter estimation can be computed after fixing these parametersbased on any chosen pressure profile, model, simulation, or data set; all that is required isto compensate for the mismatch of our assumed pressure profile to the true mean pressureprofile.5.2.4 Scaling Relation Calibration from SZ ModelsThe previous sections have described a general approach that relates cluster mass andredshift to SZ signal in a filtered map, given values for the scaling relation parameters. Inthis section we obtain scaling relation parameters based on three models for cluster gasphysics. While the ACT data will be interpreted using each of these results, we do not yetconsider any ACT data explicitly.Current models for the SZ signal from clusters include contributions from non-thermalpressure support, star formation, and energy feedback and are calibrated to match detailedhydrodynamical studies and X-ray or optical observations (Bode et al., 2012; Shaw et al.,2010). Such models provide a useful testing ground for the assumptions and methodologyof our approach to predicting SZ signal based on cluster mass. While models may sufferfrom incomplete modelling of relevant physical effects, they are less vulnerable to somemeasurement biases (e.g., by providing a cluster mass and alleviating the need for secondarymass proxies). In order to explore the current uncertainty in the SZ?mass scaling relation,we consider simulated sky maps based on three models of cluster SZ signal that includedifferent treatments of cluster physics.Our study will centre on maps of SZ signal produced from the SZ models and struc-ture formation simulations of Bode et al. (2012, hereafter B12). The N-body simulations(Bode and Ostriker, 2003) are obtained in a Tree-Particle-Mesh framework, in which darkmatter halos have been identified by a friends-of-friends algorithm. The intracluster medium(ICM) of massive halos is subsequently added, following a hydrostatic equilibrium prescrip-tion, and calibrated to X-ray and optical data (Bode, Ostriker, and Vikhlinin, 2009). Thedensity and temperature of the ICM of lower mass halos and the IGM are modeled as avirialized ideal gas with density (assuming cosmic baryon fraction ?b/?m = 0.167) andkinematics that follow the dark matter.To complement the model of B12, we also consider the ?Adiabatic? and ?Nonthermal20?models described in Trac et al. (2011), which make use of the same N-body results as B12.In the Adiabatic model the absence of feedback and star formation leads to a higher gas84fraction than in the B12 model. In the Nonthermal20 model, 20% of the hydrostatic pressureis assumed to be nonthermal, leading to substantially less SZ signal compared to the B12model. The SZ-mass relations derived from these two models are thus interpreted as,respectively, upper and lower bounds on the SZ signal.The model of B12 differs from those in Trac et al. (2011) through a more detailed han-dling of non-thermal pressure support, which is tied to the dynamical state of the clusterand is allowed to vary over the cluster extent. Both B12 and the similar treatment ofShaw et al. (2010) make use of hydrodynamic simulations (Battaglia et al., 2012; Lau et al.,2009; Nagai et al., 2007) to understand these non-thermal contributions.To calibrate our scaling relation approach to these models, we make use of light-coneintegrated maps of the thermal and kinetic SZ at 145 GHz (constructed as in Sehgal et al.,2010), and the associated catalogue of cluster positions and masses. A set of 192 non-overlapping patches of area 18.2 deg2 each are extracted from the simulated map, andconvolved with the ACT 148GHz beam to simulate observation with the telescope. Themaps are then filtered with the same filter ?5.?9(k) that was used for the ACT Equatorialclusters. Because the filtering is a linear operation, it is counter-productive to the pur-pose of calibration and intrinsic scatter estimation to add noise (CMB, detector noise) tothe simulated signal map, and so we do not; the effects of flux boosting on sample selec-tion depend on the noise levels of the map under study and are dealt with separately, asneeded. The uncorrected central decrements are extracted and used to constrain the pa-rameters of Equation (5.14). To probe the high-mass regime, only the 257 clusters havingM500c > 4.3 ? 1014 h?170 M? and 0.2 < z < 1.4 are considered; the fit is performed aroundMpivot = 5.5 ? 1014 h?170 M?. The intrinsic scatter of the relation is also obtained from theRMS of the residuals. For the B12 model, the residuals of the fit are plotted against massin Figure 5.9.For each of the three models, fit parameters are presented in Table 5.1. The massdependence is consistent, in all cases, with the UPP prediction (B ? 0), and additionalredshift dependence is only present in the Nonthermal20 model. Only the Adiabatic modelis consistent in its normalization with the UPP value. This is despite the explicit calibration,85Table 5.1:Scaling relation parametersDescription Mpivot A Am B C ?int(1014h?170M?)Universal Pressure Profile (UPP) ? ? 0 0 0 0.20aModels (?5.2.4)B12 5.5 0.111? 0.021 ?0.17? 0.06 ?0.00? 0.20 ?0.04? 0.37 0.20Nonthermal20 5.5 ?0.003? 0.020 ?0.29? 0.06 0.00? 0.20 0.67? 0.47 0.21Adiabatic 5.5 0.241? 0.020 ?0.02? 0.06 ?0.08? 0.20 0.10? 0.43 0.21Dynamical mass data (?5.2.5)All clusters 7.5 0.237? 0.060 ?0.21? 0.21 0.03? 0.51 0 0.31? 0.13Excluding J0102 7.5 0.205? 0.045 ?0.11? 0.15 ?0.28? 0.35 0 0.19? 0.10Full cosmological MCMC (?6.3)?CDM model 7.0 0.079? 0.135 ?0.45? 0.19 0.36? 0.36 0.43? 0.62 0.42? 0.19wCDM model 7.0 0.065? 0.153 ?0.46? 0.21 0.36? 0.35 0.34? 0.65 0.45? 0.20Note ? Scaling relation parameters, fit to: (i) various SZ models (see Section 5.2.4); (ii) the dynamical mass data ofSifo?n et al. (2012) (Section 5.2.5); (iii) a cosmological MCMC including WMAP data along with the ACT Southern andEquatorial cluster samples and dynamical mass data (Section 6.3). Scaling relation parameters A, B, and C are defined asin equation (5.14), with Mpivot chosen to yield uncorrelated A and B. Am is the normalization parameter correspondingto Mpivot = 3 ? 1014 h?170 M? and may be compared among rows. Parameters Am, B and C indicate the level of deviationfrom the predictions based on the Universal Pressure Profile of Arnaud et al. (2010) (equations (5.7) and (5.8); shown forreference). The intrinsic scatter ?int is defined as the square root of the variance of the observed log y?0, in the absence ofnoise, relative to the mean relation defined by equation 5.14. The parameter C is fixed to 0 when fitting scaling relations todynamical masses.a This value, based on the B12 model value, is used for results computed for the UPP scaling relation parameters that alsorequire a value for the intrinsic scatter.8610154?10146?1014M500 (h?170M?)?,z)fsz(m,z))Figure 5.9: Residuals of the scaling relation fit for the B12 model (Section 5.2.4).Only clusters with 0.2 < z < 1.4 and M500c > 4.3? 1014 h?170 M? (indicated bydotted line) are used for the fit. The scatter in the relation is measured fromthe RMS of the residuals.in B12, of the mean pressure profile to the UPP at R500. The origin of this inconsistency isdue to the relative shallowness of the mean pressure profile in B12 compared to the UPP.Thus, the profiles in B12 have less total signal within R500, where ACT is sensitive.The scaling relation parameters obtained for the Adiabatic model are sufficiently closeto zero (i.e., to the UPP scaling prediction), that we drop them from further consideration.While the B12 normalization lies somewhat below the UPP prediction, we note that evenlower normalizations (such as that found in the Nonthermal20 model) are favoured by recentmeasurements of the SZ contribution to the CMB angular power spectrum (Dunkley et al.,2011; Reichardt et al., 2012).We thus proceed to consider quantities derived from each of the UPP, B12, and Non-thermal20 scaling relation parameter sets. Mass estimates for the B12 and Nonthermal20models are computed for the ACT Equatorial cluster sample, as described in Section 5.2.2,and are presented alongside the UPP estimates in Table Scaling Relation Calibration from Dynamical MassesSifo?n et al. (2012, hereafter S12) measure galaxy velocity dispersions to obtain mass es-timates for clusters in ACT?s Southern field. S12 also present the uncorrected centralCompton parameter measurements y?0 and the corrected versions y0 obtained as describedin Section 5.2.2 and presented in the Appendix. S12 perform power-law fits of both theuncorrected (y?0) and corrected (y0) central Compton parameters to the dynamical massesto establish scaling relations for those cluster observables.87Here, we fit the full scaling relation of equation (5.14) to the dynamical mass data forthe 16 z > 0.3 clusters from the Southern field that were detected by ACT and observed byS12. We do not use the scaling relation as estimated in S12, because the parametrization ofthe scaling relation in that study is different. Also, the linear regression that is used in S12(the bisector algorithm of Akritas and Bershady, 1996) is not suited to predicting the SZsignal given only the mass, which is the aim in formulating the cluster abundance likelihoodin Section 6.1.3Dynamical masses are estimated in S12 for each cluster based on an average of 60member galaxy spectroscopic redshifts. For each cluster, the galaxy velocity dispersion SBIis interpreted according to the simulation based results of Evrard et al. (2008), who findthat the dark matter velocity dispersion ?DM is related to the halo mass M200c by?DM = ?15(0.7? E(z) M200c1015 h?170 M?)?, (5.18)where ?15 = (1082.9?4) km s?1 and ? = 0.3361?0.0026. By inverting equation (5.18) andassuming that SBI = ?DM, S12 obtain dynamical estimates, which we will denote by Mdyn200c,of the halo mass. As discussed in S12 and Evrard et al. (2008), the systematic bias betweengalaxy and dark matter velocity dispersions, bv ? SBI/?DM, is believed to be within 5% ofunity. To account for this, and any other potential systematic biases in the dynamical massestimates, we introduce the parameter?dyn ??Mdyn200cM200c?. (5.19)Based on a velocity dispersion bias of bv = 1.00 ? 0.05, the equivalent mass bias is ?dyn =1.00 ? 0.15. For the present discussion, we disregard this bias in order to distinguish itseffects from other calibration issues. However, in the cosmological parameter analysis ofSection 6.3 we include ?dyn as a nuisance parameter and discuss its impact on the cosmo-logical parameter constraints.The y?0 measurements associated with the Southern sample of clusters are obtained usinga filter matched to the noise power spectrum of the Southern field maps used in Sifo?n et al.(2012). Thus, while the signal template is the same, the full form of the filter ? and theassociated response function Q differ slightly from the ones used on the Equatorial data. Weapply the same correction for selection bias that was used by S12, and denote the correctedvalues as y?corr0 .To convert the dynamical masses to M500c values, we model the cluster halo with aNavarro-Frenk-White profile (Navarro et al., 1995) with concentration parameters and un-3The cluster abundance likelihood assumes a scaling relation where y?0 is the dependent variable and takesfull account of the mass function; in this section we will use the likelihood-based approach of Kelly (2007)which includes iterative estimation of the distribution of the independent variable.88certainties obtained from the fits of Duffy et al. (2008). For the fit we use a pivot mass of7.5?1014 h?170 M?, and fix the parameter C to 0 (otherwise the fit is poorly constrained). Weuse the likelihood-based approach of Kelly (2007) to fit for the intrinsic scatter along withthe parameters A and B, given measurement errors on both independent and dependentvariables. The scatter is modeled, as before, as an additional Gaussian random contributionto log y?0 relative to the mean relation ?y?0|m, z?.The fit parameters are presented in Table 5.1. A substantial contribution to the scatter inthe dynamical mass fits comes from the exceptional, merging cluster ACT-CL J0102?4915(?El Gordo,? Menanteau et al., 2012): when this cluster is excluded from the fit, the scatterdrops to 0.19 ? 0.10, which is more consistent with fits based solely on models.In Figure 5.10 we plot the cluster SZ measurements against the dynamical masses,along with the best fit scaling relation. The scaling relations from the UPP and fromthe parameters fit to the B12 and Nonthermal20 models are also shown. While the fitparameters for the dynamical mass data are consistent with either the B12 or Nonthermal20models, the dynamical mass data lie well below the mean scaling relation predicted bythe UPP. These results reinforce the need to consider a broad range of possible scalingrelation parameters, within our framework based on the UPP. We note, however, that thepossibility of a systematic difference between dynamical masses and other mass proxies mustbe considered when comparing the parameters obtained in this section to other results.5.2.6 Completeness EstimateIn this section we estimate the mass, as a function of redshift, above which the ACT clustersample within SDSS Stripe 82 (which we will refer to as the S82 sample) is 90% complete.We consider the S82 sample as a whole (S/N > 4), and also consider the subsample thathas complete high redshift follow-up (S/N > 5.1).For a cluster of a given mass and redshift, we use the formalism of Section 5.2.1 to predictits SZ signal and to infer the amplitude y??500 that we would expect to measure in a map towhich filter ??500 has been applied, in the absence of noise and intrinsic scatter. We thenassume that the cluster occupies a map pixel with a particular noise level, and consider allpossible realizations of the noise (assumed to be Gaussian) and intrinsic scatter, to obtainthe probability distribution of observed y??500 values. Applying the sample selection criteria,we thus obtain the probability of detection for this mass, redshift, filter scale, and mapnoise level.We obtain the total probability that the cluster will be detected at a given filter scaleby averaging over the distribution of noise levels in the corresponding filtered map. Thedistribution of noise levels in the real filtered maps is used to perform this computation. Toobtain a total detection probability for the cluster, we take the maximum of the detectionprobabilities over the ensemble of filters. This assumes that noise and intrinsic scatter arestrongly covariant between the filter scales, so that a cluster that is not detected in the8910153?10146?1014M500c  (h?170M?)10.2 0.3 0.5 0.7 23? ycorr0[E(z)2Q(z,m)frel(m,z)]?1 (10?4)Figure 5.10: Corrected central Compton parameter vs. dynamical mass for the 16ACT-detected clusters presented in Sifo?n et al. (2012) for the Southern sam-ple. Values on y-axis include factor of E(z)?2, which arises in the deriva-tion of y0 in self-similar models. The high signal outlier is ?El Gordo?(ACT-CL J0102?4915, Menanteau et al., 2012), an exceptional, merging sys-tem. The solid line represents the best fit of equation (5.14) with Mpivot =7.5 ? 1014 h?170 M?. The dashed line is for the fit with J0102?4915 excluded.Dotted lines, from top to bottom, are computed for scaling relation parameterscorresponding to the UPP, B12 and Nonthermal20 (z = 0.5) models.optimal filter is very unlikely to be detected in a sub-optimal filter. This assumption maylead to a slight underestimate of the total detection probability. The calculation is repeatedto obtain the detection efficiency as a function of mass and redshift.At redshift z, the completeness at mass level M is the average fraction of all existingclusters with mass greater than M that we would expect to detect. The total number ofclusters is obtained by integrating the Tinker et al. (2008) mass function for our fiducialcosmology; the average number of detected clusters is obtained by integrating the massfunction scaled by the detection efficiency. Such computations are used to obtain the mass,as a function of redshift, at which the completeness level is 90%.The completeness mass levels are shown in Figure 5.11. Note that we also show resultsobtained for the B12 scaling relation parameters. In this case we also obtained completenessestimates based in part on the filtered simulated maps. The central Compton parameterswere measured in the filtered maps, and the S82 noise model was applied to generate adetection probability for each simulated cluster. Because of the small number of sufficientlyhigh mass clusters in the model simulations, we have compensated for sample variance byreweighting the contribution of each cluster to correspond to the Tinker et al. (2008) massfunction.In summary, the S82 sample with S/N > 4, for which optical confirmation should be9056789M90%B12 (1014h170M)0.0 0.2 0.4 0.6 0.8 1.0 1.2Redshift456M90%UPP (1014h170M)Figure 5.11: Estimate of the mass (M500c) above which the ACT cluster samplewithin S82 is 90% complete (see Section 5.2.6). Lower panel assumes a UPP-based scaling relation with 20% intrinsic scatter; the solid line is for S/N > 4(full S82 sample, valid to z < 0.8), and the dotted line is for the S/N > 5.1subsample (valid to z ? 1.4). The upper panel shows analogous limits, but as-suming scaling relation parameters obtained for the B12 model (Section 5.2.4).Circles (crosses) are based on filtering and analysis of B12 model clusters forthe S/N > 4 (5.1) cut. The completeness threshold decreases steadily abovez ? 0.6, because clusters at this mass are easily resolved and the total SZsignal, at constant mass, increases with redshift.100% complete for z < 0.8, is estimated to have SZ detection completeness of 90% abovemasses of M500c ? 4.5 ? 1014 h?170 M? for z > 0.2. The S82 sample having S/N > 5.1, forwhich optical confirmation is 100% complete for z < 1.4, is estimated to have SZ detectioncompleteness of 90% above masses of M500c ? 5.1 ? 1014 h?170 M? for z > 0.2. (Note in thelatter case, however, that the mass threshold falls steadily beyond redshift of 0.5.)5.2.7 Redshift distributionWhile a full cosmological analysis will be undertaken in Chapter 6, we briefly confirm theconsistency of our cluster redshift distribution with expectations. As in the cosmologicalanalysis, we will select our samples based on the signal to noise ratio of the uncorrectedcentral decrement y?0? ?y?0 obtained for each cluster using the filter corresponding to ?500 =5.?9. We first consider the S82 clusters that have y?0/?y?0 > 4, over the redshift range0.2 < z < 0.8. Secondly we consider the ?cosmological? sample of clusters, consisting of 15clusters with y?0/?y?0 > 5.1 and z > 0.2. The cumulative number density as a function of910.2 0.4 0.6 0.8 1.0 1.2 1.4Redshift05101520253035N(<z)S82CosmoFigure 5.12: Cumulative number counts for two sub-samples of the full cluster cata-logue for which confirmation is complete. The upper lines are data and modelcounts for the S82 sample of clusters having y?0/?y?0 > 4 and 0.2 < z < 0.8.The lower lines represent the cosmological sample of 15 clusters with fixed-scale y?0/?y?0 > 5.1 and z > 0.2. The model for the counts is obtained from amaximum likelihood fit, with only ?8 as a free parameter. The model includesa full treatment of selection effects for the sample under consideration.redshift is shown in Figure 5.12. For each of the two subsamples, we bin the clusters intoredshift bins of width 0.1 and perform a maximum likelihood fit (assuming Poisson statisticsin each bin) to estimate ?8. To facilitate comparison with cosmological results presentedin Chapter 6, we assume a flat ?CDM cosmology with ?m = 0.25 and ns = 0.96, andfix the scaling relation parameters to the values associated with the UPP.4 Cluster countpredictions are obtained starting from the cluster mass function of Tinker et al. (2008),and include all selection effects (intrinsic scatter, noise, and y?0/?y?0 cut). The fits yield?8 = 0.782 for the cosmological sample, and ?8 = 0.789 for the S82 sample. Both of theseare consistent with the result of the full cosmological analysis for the UPP scaling relation.The best-fit model is a good fit to the data in the sense that the likelihood score of thedata, given the best-fit model, lies near the median of the likelihood scores for all samplesdrawn from the best-fit model that have the same total cluster count as the data. For theS82 (respectively, cosmological) sample, 55% (59%) of such random samples are less likely.Each of these samples is dominated by clusters with spectroscopic redshift estimates, andthus any features in the distribution cannot be attributed to redshift error.4This value of the matter density is taken from the WMAP7+ACTcl(UPP) line in Table 6.1.925.3 Comparison with Other CataloguesIn this section we compare the Equatorial cluster catalogue and the SZ derived clusterproperties to those obtained by other studies in microwave, X-ray, and optical wavelengths.While optical studies have good overlap with our sample in S82 to z < 0.6, previous X-rayand SZ survey data include only a small fraction of the clusters in our sample. We alsoexamine the question of radio contamination of cluster decrements through a comparisonof extrapolated fluxes near our cluster positions relative to random positions in the field.5.3.1 Comparison to Planck Early SZ SampleWe compare our catalogue and our derived cluster properties, to the catalogue presented inthe Planck all-sky Early Sunyaev-Zeldovich cluster sample (ESZ; Planck Collaboration VIII,2012). The ESZ presents 189 clusters, of which 4 lie within the ACT Equatorial footprint,and of which 2 are detected by ACT. The two clusters detected by both Planck and ACTconsist of two of the three clusters having ACT Y500 exceeding the 50% completeness levelof the ESZ. (The third, not matched to the ESZ, is RCS2 J2327.4?0204.)The two clusters not detected by ACT are low redshift clusters: Abell 2440 at z = 0.091and Abell 119 at z = 0.044. Based on their integrated X-ray gas temperature measurementsof (3.88? 0.14) and (5.62? 0.12) keV (White, 2000), we estimate masses of ? 4? 1014 and7?1014 h?170 M?, respectively; these are well below our 90% completeness level (Section 5.2.6)at these redshifts.For the two clusters detected by both Planck and ACT, a summary comparison ofmeasured cluster properties may be found in Table 5.2. MACS J2135.2?0102 is detectedby ACT, at low significance, inside S82. Abell 2355 (ACT-CL J2135.2+0125) is detectedby ACT at high significance (S/N = 9.3) just outside the S82 region. The specifics of eachcase are discussed below.For ease of comparison, we convert the Planck measurement of the SZ signal within5R500 through the ESZ-provided conversion factor Y500 = Y5R500/1.81. We also use the ESZvalue for ?500 (which is either determined from X-ray luminosity measurements, or from theSZ signal alone) to obtain an approximate value for M500c. The ESZ analysis makes useof the ?Standard? version of the Universal Pressure Profile, which assumes a self-similarscaling relation (see the Appendix of Arnaud et al., 2010). We thus re-analyse the ACT y?0measurements using the profiles and scaling relation of the Standard UPP to estimate ?500,Y500, and M500c. The results of this analysis differ only slightly from the results obtainedusing the full UPP (Table 5.4).93Table 5.2:Comparison of Planck and ACT cluster measurementsCluster ID Redshift Planck ACT?500 Y500 M500 ?500 Y500 M500(arcmin) (10?4 arcmin2) (1014 h?170 M?) (arcmin) (10?4 arcmin2) (1014 h?170 M?)Early SZ clustersMACS J2135.2-0102 0.325 1.6 ? 1.0 9.8 ? 1.9 0.8 ? 0.8 3.1 ? 0.4 2.5 ? 1.2 2.7 ? 1.0Abell 2355 0.231 5.1 15 ? 4 5.2 5.3 ? 0.2 14.3 ? 2.4 6.3 ? 1.3Intermediate ResultsAbell 267 0.235 4.5 ? 0.2 9.3 ? 2.3 3.6 ? 0.5 5.4 ? 0.2 13.1 ? 2.4 5.6 ? 1.2RXC J2129.6+0005 0.234 4.7 ? 0.2 7.8 ? 2.0 4.3 ? 0.5 5.2 ? 0.2 11.4 ? 2.5 5.2 ? 1.2Abell 2631 0.275 5.4 ? 0.6 15.5 ? 2.3 9.8 ? 3.3 4.8 ? 0.2 11.5 ? 2.2 6.0 ? 1.3Note ? Comparison of cluster properties as determined by Planck and by ACT, for two clustersfrom the ESZ (Planck Collaboration VIII, 2012, Section 5.3.1) and three clusters from Intermediate Results(Planck Collaboration III, 2013, Section 5.3.2). For Planck , ?500 is derived from X-ray measurements of M500 forall clusters except MACS J2135.2?0102, for which the angular scale was determined from the SZ data only. Planckvalues for Abell 2355 are corrected to redshift 0.231 as discussed in the text; M500 for this cluster is estimated fromX-ray luminosity and thus carries a large (? 50%) uncertainty. For the ACT measurements, the angular scale, massand Y500 of each cluster are obtained simultaneously from the 148GHz data assuming that the cluster pressure profileis described by the Standard UPP.94For MACS J2135.2?0102 (z = 0.329), X-ray luminosity data were not available andthe ESZ presents the angular scale of the cluster based on SZ data alone. The scale,?500 = 1.6 ? 1.0? is the smallest ?500 in the ESZ, and corresponds to a very low mass (?1? 1014 M?). Such a mass seems inconsistent with the SZ signal observed by either Planckor ACT. Lensed sub-millimetre galaxies have been observed near this cluster (Ivison et al.,2010), and the ESZ notes include a reference to possible point source contamination. TheACT measurement is likely to be less contaminated by such emission, since we use only148GHz data where dusty sources are comparatively dim. This may explain the largedifference in Y500 inferred by the two telescopes. Overall this cluster is a peculiar case,and it is difficult to draw any useful conclusions from the disagreement of ACT and Planckmeasurements without more detailed X-ray information.Abell 2355 (ACT?CL J2135.2+0125) is one of the most significant ACT detections,and one for which the ACT analysis implies a very high mass. A spectroscopic redshift of0.1244 for this cluster has been obtained by Kowalski et al. (1983), and has subsequentlybeen adopted in both the MCXC and the Planck ESZ. However, Sarazin et al. (1982)identify z = 0.231 as a more probable spectroscopic redshift, and this value is adoptedby Menanteau et al. (2013), who find it to be much more consistent with their photometricestimate of z = 0.25 ? 0.01. Furthermore, the NED5 entry for this cluster refers to anunpublished spectroscopic redshift z = 0.228 obtained from three galaxies. In order tocompare the Planck and ACT measurements, we correct the Planck SZ measurements toz = 0.231.The cluster angular scale used by Planck is obtained from X-ray luminosity based massesin the MCXC. We compute a new mass estimate using the MCXC scaling relations, correct-ing the X-ray luminosity for the changes in luminosity distance and K-correction (accordingto the T = 5 keV tabulation of Bo?hringer et al., 2004). The resulting inferred mass is morethan double the estimate obtained for z = 0.1244. The corresponding ?500 is slightly smaller,and so we obtain a crude estimate of the Y500 that Planck might have measured if theyhad used this angular scale. From the inspection of Figure 9 of Planck Collaboration VIII(2012), the axis of degeneracy for the scale and signal measurements lies along Y500 ? ??500with ? in the range of 0.75 (for resolved clusters) to 1.5 (unresolved clusters). We computethe new value assuming ? = 1, and add 20% error to account for the uncertainty in ?. Thisgives Y500 = (15? 4)? 10?4 arcmin2. The ACT mass and Y500 are in good agreement withthe X-ray mass and our estimate of the resulting Planck SZ signal.Comparison to SZ measurements of three more clusters detected by Planck may befound in the next section.5NASA Extragalactic Database; http://ned.ipac.caltech.edu/. Retrieved July 15, 2012.955.3.2 Comparison to Weak Lensing MassesIn this section we examine weak lensing mass measurements of four clusters in the ACTEquatorial sample. While one is a high redshift cluster discovered by ACT, the other threeare well-known moderate redshift clusters that have been observed by XMM-Newton andPlanck .Weak lensing measurements of ACT-CL J0022.2?0036 (z = 0.81) are presented inMiyatake et al. (2013). Subaru imaging is analysed and radial profiles of tangential shearare fit with an NFW profile. They obtain a mass estimate of M500c = 8.4+3.3?3.0?1014 h?170 M?.While consistent with our SZ masses for any of the three model scaling relations, this mass ishigher than the one deduced from the UPP scaling relation parameters and more consistentwith the B12 and Nonthermal20 models. The SZ and lensing mass estimates are alsoconsistent with the dynamical mass reported for ACT-CL J0022.2?0036 in Menanteau et al.(2013).The ACT Equatorial sample also includes three clusters (A267, A2361, and RXCJ2129.6+0005)treated by Planck Collaboration III (2013, hereafter PI3) in a comparison of weak lensingmass, X-ray mass proxies, and SZ signal. X-ray data are obtained from the XMM-Newtonarchive, and weak lensing masses for the clusters we consider here originate in Okabe et al.(2010). Each of these clusters is detected by ACT inside S82 with S/N > 8.Comparing the ACT UPP based SZ masses to the weak lensing masses for these threeclusters we obtain a mean weighted mass ratio of MUPPACT/MWL = 1.3?0.2. This is consistentwith the mass ratio found by PI3 between X-ray masses and weak lensing masses for theirfull sample of 17 objects. For the B12 scaling relation parameters the ratio is MB12ACT/MWL =1.8? 0.3.PI3 also report Y500, measured from Planck ?s multi-band data using a matched filter,with the scale (?500) of the cluster template fixed using either the X-ray or the weak lensingmass. For each object we see agreement in the Y500 measurements at the 1 to 2-? level,and our mean ratio is consistent with unity. For ?500 determined from X-ray (weak lensing)mass we find weighted mean ratio Y UPP500,ACT/Y500,P lanck = 0.90? 0.16 (0.98 ? 0.16).The angular scales, Y500 and M500c obtained by Planck and ACT are provided in Ta-ble 5.2. The ACT values are computed for the Standard version of the UPP, following ourtreatment of the ESZ clusters in section 5.3.1; these results are almost indistinguishablefrom those obtained with the full UPP treatment.5.3.3 Comparison to SZA MeasurementsHigher resolution SZ data can be obtained through interferometric observations. Reese et al.(2012) present Sunyaev-Zeldovich Array (SZA) observations of two ACT Equatorial clus-ters at 30 GHz. For the high redshift, newly discovered cluster ACT-CL J0022-0036, aGNFW profile is fit to the 30 GHz SZ signal, and is used to infer the cluster mass as-suming an NFW density profile and virialization of the gas. This yields a mass estimate96of M500c = 7.3+1.0?1.0 ? 1014 h?170 M?. For Abell 2631 (ACT-CL J2337.6+0016), X-ray andSZ data are both used to constrain the density profile, producing a mass estimate ofM500c = 9.4+4.8?2.4 ? 1014 h?170 M?. These masses are somewhat higher than the ACT re-sults for the UPP scaling relation, and are more consistent with the masses arising fromthe B12 scaling relation parameters.5.3.4 Optical Cluster CataloguesThe extensive overlap of the ACT observations described in this work with the SDSS meansthat there are a number of existing optically selected cluster catalogues with which the ACTSZ selected cluster sample can be compared (see also Menanteau et al., 2013). For all thecomparisons described below, we matched each catalogue to the ACT cluster sample usinga 0.5Mpc matching radius, evaluated at the ACT cluster redshift.Several optical cluster catalogueues have been extracted from the SDSS legacy sur-vey (e.g., Goto et al., 2002; Koester et al., 2007; Miller et al., 2005; Szabo et al., 2011;Wen et al., 2009, 2012). For the purposes of this comparison, we focus on the MaxBCGcatalogue (Koester et al., 2007) and its successor the GMBCG catalogue (Hao et al., 2010).Both of these catalogues make use of the colour-magnitude red-sequence characteristic ofthe cluster early type galaxy population, plus the presence of a Brightest Cluster Galaxy(BCG), to identify clusters. The MaxBCG catalogue contains 13,823 clusters, of which492 fall within the footprint of the 148GHz map used in this work, and is thought to be> 90% complete and > 90% pure for clusters with Ngal > 20 over its entire redshift range(0.1 < z < 0.3). The GMBCG catalogue builds on this work using the entire SDSS DR7survey area, and is thought to have > 95% completeness and purity for clusters with rich-ness > 20 galaxies and z < 0.48. A total of 1903 of the 55,424 GMBCG clusters fall withinthe ACT footprint.We find that the ACT cluster catalogue contains 8 clusters in common with MaxBCG,and 16 clusters in common with the GMBCG catalogue. There are no ACT clusters at z <0.3 in the SDSS DR7 footprint that are not cross-matched with MaxBCG objects; however,there are 2 ACT clusters at z < 0.48 (ACT-CL J0348.6?0028 and ACT-CL J0230.9?0024)that are not cross-matched with objects with richness > 20 in the GMBCG cataloguewithin the common area6 between the two surveys. ACT-CL J0348.6?0028 (z = 0.29)is an optically rich system (Ngal = 56.9 ? 7.5; as measured by Menanteau et al. 2013),while ACT-CL J0230.9?0024 is optically fairly poor (Ngal = 19.9 ? 4.5). In both cases,Menanteau et al. (2013) find the BCG to have a small offset from the SZ position (0.1Mpcfor J0348.6 and 0.16Mpc for J0230.9). However, neither of these objects has a plausiblecross-match in the full GMBCG catalogue, although we note that there is a GMBCG cluster(J057.14850?00.43348) at z = 0.31 located within a projected distance of 0.65Mpc of ACT-6To determine the overlap between the ACT maps and various SDSS data releases, we make useof the angular selection function from http://space.mit.edu/~molly/mangle/download/data.html (seeBlanton et al., 2005; Hamilton and Tegmark, 2004; Swanson et al., 2008, for details).97CL J0348.6?0028.We also compared the ACT catalogue with that of Geach, Murphy, and Bower (2011).This catalogue is constructed using the Overdense Red-sequence Cluster Algorithm (ORCA;Murphy, Geach, and Bower, 2012) and is the first optical cluster catalogue available basedon the deep (r ? 23.5 mag) SDSS S82 region. It reaches to higher redshift (z ? 0.6) thanthe catalogues based on the SDSS legacy survey data (such as GMBCG), and all of theMaxBCG clusters within a 7 deg2 test area are re-detected (Murphy et al., 2012). We findthat 26 z < 0.6 ACT clusters are cross-matched with objects in the Geach et al. catalogue.However, there are 24 ACT clusters, which we have optically confirmed using the S82 data,that were not detected by Geach et al., and most of these (19 objects) are at z > 0.6. Wealso confirmed a further 4 objects at z > 1 in the S82 region with the addition of Ks-bandimaging obtained at the Apache Point Observatory. This suggests that the ACT clustercatalogue has a higher level of completeness for massive clusters at high redshift comparedto current optical surveys.5.3.5 X-ray Cluster CataloguesClusters are detected in X-rays through thermal bremsstrahlung emission from the intraclus-ter gas, and so X-ray selected cluster surveys are complementary to SZ searches. However,current large area X-ray surveys are relatively shallow. The REFLEX cluster catalogue(Bo?hringer et al., 2004) is derived from the ROSAT All Sky Survey data (Voges et al.,1999) and overlaps completely with the ACT survey. The full catalogue contains a total of448 clusters reaching to z = 0.45, from which 17 objects fall within the footprint of the ACTEquatorial maps. We find that only five of these clusters are cross-matched with ACT clus-ter detections. The detected objects are all luminous systems, with LX > 3.3?1044 erg s?1.The undetected objects are all lower luminosity (hence lower mass) and are at z < 0.1,where SZ completeness is low.As discussed in Section 5.3.1, the Planck ESZ relies on the M500c values presented in theMCXC (derived from the LX?M relation in Arnaud et al. (2010), which has intrinsic scatter? 50%) to constrain the angular scale of detected clusters, and reduce the uncertainty inY5R500 . The MCXC catalogue includes 9 clusters from the ACT Equatorial cluster sample,and 6 clusters from the ACT Southern cluster sample.Comparing the masses we derive from the UPP scaling relation to the MCXC masses,we obtain a mean ratio MACT,UPP500c /MMCXC500c = 1.03? 0.19. Adding in the Southern clusters(see Appendix) we find a ratio of 0.83 ? 0.13.While the Equatorial cluster result is consistent with the UPP scaling relation, the fullsample prefers higher masses. For the B12 scaling relation parameters and the full samplewe find MACT,B12500c /MMCXC500c = 1.12 ? 0.17. For the Equatorial sample alone, this ratio is1.41 ? 0.27. The mass ratios are shown in Figure 5.13.9834 5678 9 10MMCXC500c (1014h170M),UPP500c/MMCXC500cEquatorialSouthernFigure 5.13: Ratio of ACT SZ determined masses to X-ray luminosity based massesfrom the MCXC. ACT masses assume the UPP scaling relation parameters.Error bars on mass include uncertainty from the ACT SZ measurements, and50% uncertainty on MCXC masses. The weighted mean ratio is 1.03 ? 0.19for the Equatorial clusters and 0.83? 0.13 for the full sample.5.3.6 Radio Point SourcesRelative to the field, galaxy clusters are observed to contain an excess of radio point sources(e.g., Cooray et al., 1998). Studies of potential SZ signal contamination by radio sourceshave been carried out at frequencies below 50 GHz (e.g., Lin et al., 2009). There are,however, few such studies at 150 GHz. Recently Sayers et al. (2013) used Bolocam at140GHz to study possible radio source contamination in 45 massive clusters. They foundthat the SZ signals from only 25% of the sample were contaminated at a level greaterthan 1%. The largest contamination observed was 20% of the SZ signal. We study thisphenomenon in the ACT cluster sample, using the FIRST catalogue of flux densities at1.4GHz (White et al., 1997). The lower flux density limit of the catalogue is at most 1mJy,and overlaps with the ACT Equatorial field between R.A. of 21h20m and 3h20m.For each source in the FIRST catalogue, we extrapolate the flux density to 148GHzusing flux-dependent spectral indices computed based on a stacking analysis in the ACT148GHz and 218GHz maps. For the sources of interest here, the spectral index rangesfrom approximately ?0.5 (at S1.4 = 10mJy) to ?0.8 (at S1.4 = 100mJy). While a singlespectral index is inadequate for describing the spectral behaviour of radio sources over adecade in frequency, the extrapolation based on stacked ACT data is a reasonable techniquefor the purposes of predicting flux densities at ACT frequencies. Given the few sourcesfound per cluster, the error in the extrapolation will be dominated by intrinsic scatterin 148GHz flux densities (? 1mJy) corresponding to a given S1.4 range. This analysisdoes not take into account the probability of source orientation dependence that results99in significantly greater observed flux density, as in the case of blazars. For each of the 63galaxy clusters lying in the FIRST survey area, we take all sources within 2? of the clusterposition and sum the predicted flux density at 148GHz. We find a mean flux density ofS148 = 0.94mJy, and the 9 most potentially contaminated clusters have flux density between2.5 and 4.2mJy. Converting these to a peak brightness in CMB temperature units using the148GHz beam, we obtain contamination of 11?K on average and 50?K at worst. Theselevels are substantially higher than would be expected if total radio flux were not correlatedwith cluster position. For random positions, the contamination is only S148 = 0.2mJy onaverage, and 1% of locations have total flux exceeding 2.4mJy.For the purposes of inferring masses, we are interested in the impact the point sourcesmay have in the measurement of the uncorrected central decrement. To explore this, wecreate a simulated ACT map of the sources using their inferred flux densities at 148GHz andthe ACT beam shape. This map is then filtered with the same matched filter ?5.?9 describedin Section 5.2.1. We obtain a prediction for the contamination level of each cluster by takingthe maximum value in the filtered map within 2? of the cluster position. More than half ofthe clusters have predicted contamination less than 13?K and 90% have less than 30?K(which is smaller than the typical measurement uncertainty). The worst contaminationprediction is associated with ACT-CL J0104.8+0002, at a level of 59?K (corresponding to35% of the signal strength, and larger than the cluster noise level of 41?K).We emphasize that the contamination levels given here are extrapolations based on 1.4GHz flux density, and thus the contamination at 148GHz for any particular source associ-ated with a cluster may vary somewhat from the values stated. Since such contaminationis difficult to model in detail without knowing the spectral indices of individual sources,and since the rate of significant contamination seems to be quite low, we make no attemptto correct for this effect. This may introduce a small, redshift dependent bias into scalingrelation parameters obtained from these SZ data.100Table 5.3:Confirmed galaxy clusters in the ACT Equatorial region.ACT ID RA Dec Redshift Region S/N ?500 y?0 Alternate ID (ref.)(?) (?) (arcmin) (10?4)ACT?CL J0008.1+0201 2.0418 2.0204 0.36 ? 0.04 DR8 4.7 4.71 0.96 ? 0.21 WHL J000810.4+020112 (1)ACT?CL J0012.0?0046 3.0152 ?0.7693 1.36 ? 0.06 S82 5.3 16.47 0.91 ? 0.18ACT?CL J0014.9?0057 3.7276 ?0.9502 0.533 S82* 7.8 3.53 1.34 ? 0.18 GMB11 J003.71362-00.94838 (2)ACT?CL J0017.6?0051 4.4138 ?0.8580 0.211 S82 4.2 4.71 0.73 ? 0.17 SDSS CE J004.414726-00.876164 (3)ACT?CL J0018.2?0022 4.5623 ?0.3795 0.75 ? 0.04 S82 4.4 4.71 0.74 ? 0.17ACT?CL J0022.2?0036 5.5553 ?0.6050 0.805 S82* 9.8 1.18 1.35 ? 0.16 WHL J002213.0-003634 (1)ACT?CL J0026.2+0120 6.5699 1.3367 0.65 ? 0.04 DR8 6.3 4.71 0.99 ? 0.16ACT?CL J0044.4+0113 11.1076 1.2221 1.11 ? 0.03 S82 5.5 1.18 0.70 ? 0.15ACT?CL J0045.2?0152 11.3051 ?1.8827 0.545 DR8 7.5 3.53 1.31 ? 0.18 WHL J004512.5-015232 (1)ACT?CL J0051.1+0055 12.7875 0.9323 0.69 ? 0.03 S82 4.2 1.18 0.53 ? 0.15 WHL J005112.9+005555 (1)ACT?CL J0058.0+0030 14.5189 0.5106 0.76 ? 0.02 S82 5.0 2.35 0.72 ? 0.15ACT?CL J0059.1?0049 14.7855 ?0.8326 0.786 S82* 8.4 2.35 1.24 ? 0.15ACT?CL J0104.8+0002 16.2195 0.0495 0.277 S82 4.3 12.94 0.62 ? 0.15 SDSS CE J016.232412+00.058164 (3)ACT?CL J0119.9+0055 19.9971 0.9193 0.72 ? 0.03 S82 5.0 3.53 0.73 ? 0.15ACT?CL J0127.2+0020 21.8227 0.3468 0.379 S82 5.1 2.35 0.72 ? 0.15 SDSS CE J021.826914+00.344883 (3)ACT?CL J0139.3?0128 24.8407 ?1.4769 0.70 ? 0.03 DR8 4.3 1.18 0.54 ? 0.17ACT?CL J0152.7+0100 28.1764 1.0059 0.230 S82* 9.0 3.53 1.30 ? 0.15 Abell 267 (4)ACT?CL J0156.4?0123 29.1008 ?1.3879 0.45 ? 0.04 DR8 5.2 2.35 0.67 ? 0.15 WHL J015624.3-012317 (1)ACT?CL J0206.2?0114 31.5567 ?1.2428 0.676 S82* 6.9 2.35 0.94 ? 0.14ACT?CL J0215.4+0030 33.8699 0.5091 0.865 S82* 5.5 1.18 0.75 ? 0.15ACT?CL J0218.2?0041 34.5626 ?0.6883 0.672 S82* 5.8 2.35 0.82 ? 0.15 GMB11 J034.56995-00.69963 (2)ACT?CL J0219.8+0022 34.9533 0.3755 0.537 S82 4.7 2.35 0.66 ? 0.15 GMB11 J034.94761+00.35956 (2)ACT?CL J0219.9+0129 34.9759 1.4973 0.35 ? 0.02 DR8 4.9 2.35 0.62 ? 0.14 NSCS J021954+013102 (5)ACT?CL J0221.5?0012 35.3925 ?0.2063 0.589 S82 4.0 1.18 0.33 ? 0.15 GMB11 J035.40587-00.21967 (2)ACT?CL J0223.1?0056 35.7939 ?0.9466 0.663 S82* 5.8 2.35 0.84 ? 0.15 GMB11 J035.79247-00.95712 (2)ACT?CL J0228.5+0030 37.1250 0.5033 0.72 ? 0.02 S82 4.0 1.18 0.56 ? 0.15 GMB11 J037.11459+00.52965 (2)101Table 5.3: ? ContinuedACT ID RA Dec Redshift Region S/N ?500 y?0 Alternate ID (ref.)(?) (?) (arcmin) (10?4)ACT?CL J0230.9?0024 37.7273 ?0.4043 0.44 ? 0.03 S82 4.2 8.24 0.63 ? 0.15 WHL J023055.3-002549 (6)ACT?CL J0239.8?0134 39.9718 ?1.5758 0.375 DR8 8.8 4.71 1.61 ? 0.18 Abell 370 (4)ACT?CL J0240.0+0116 40.0102 1.2693 0.62 ? 0.03 DR8 4.8 4.71 0.70 ? 0.15 WHL J024001.7+011606 (1)ACT?CL J0241.2?0018 40.3129 ?0.3109 0.684 S82 5.1 1.18 0.59 ? 0.15 WHL J024115.5-001841 (1)ACT?CL J0245.8?0042 41.4645 ?0.7013 0.179 S82 4.1 10.59 0.61 ? 0.15 Abell 381 (4)ACT?CL J0250.1+0008 42.5370 0.1403 0.78 ? 0.03 S82 4.5 2.35 0.62 ? 0.15ACT?CL J0256.5+0006 44.1354 0.1049 0.363 S82* 5.4 7.06 0.82 ? 0.15 SDSS CE J044.143375+00.105766 (3)ACT?CL J0301.1?0110 45.2925 ?1.1716 0.53 ? 0.04 S82 4.2 2.35 0.51 ? 0.15 GMB11 J045.30649-01.17805 (2)ACT?CL J0301.6+0155 45.4158 1.9219 0.167 DR8 5.8 4.71 1.12 ? 0.20 RXC J0301.6+0155 (7)ACT?CL J0303.3+0155 45.8343 1.9214 0.153 DR8 5.2 7.06 1.00 ? 0.20 Abell 409 (4)ACT?CL J0308.1+0103 47.0481 1.0607 0.633 S82 4.8 1.18 0.60 ? 0.15 GMB11 J047.03754+01.04350 (2)ACT?CL J0320.4+0032 50.1239 0.5399 0.384 S82 4.9 3.53 0.72 ? 0.15 SDSS CE J050.120594+00.533045 (3)ACT?CL J0326.8?0043 51.7075 ?0.7312 0.448 S82* 9.1 1.18 1.24 ? 0.15 GMBCG J051.70814-00.73104 (8)ACT?CL J0336.9?0110 54.2438 ?1.1705 1.32 ? 0.05 S82 4.8 3.53 0.68 ? 0.14ACT?CL J0342.0+0105 55.5008 1.0873 1.07 ? 0.06 S82* 5.9 4.71 0.89 ? 0.15ACT?CL J0342.7?0017 55.6845 ?0.2899 0.310 S82 4.6 5.88 0.70 ? 0.15 SDSS CE J055.683678-00.286974 (3)ACT?CL J0348.6+0029 57.1612 0.4892 0.297 S82 5.0 2.35 0.69 ? 0.15 WHL J034837.9+002900 (6)ACT?CL J0348.6?0028 57.1605 ?0.4681 0.345 S82 4.7 2.35 0.67 ? 0.15 WHL J034841.5-002807 (6)ACT?CL J2025.2+0030 306.3006 0.5130 0.34 ? 0.02 DR8 6.4 9.41 1.05 ? 0.17 WHL J202512.8+003134 (1)ACT?CL J2050.5?0055 312.6264 ?0.9311 0.622 S82* 5.6 1.18 0.83 ? 0.16 GMB11 J312.62475-00.92697 (2)ACT?CL J2050.7+0123 312.6814 1.3857 0.333 DR8 7.4 4.71 1.16 ? 0.16 RXC J2050.7+0123 (7)ACT?CL J2051.1+0056 312.7935 0.9488 0.333 S82 4.1 1.18 0.62 ? 0.17 WHL J205111.1+005646 (6)ACT?CL J2051.1+0215 312.7885 2.2628 0.321 DR8 5.2 5.88 1.36 ? 0.26 RXC J2051.1+0216 (7)ACT?CL J2055.4+0105 313.8581 1.0985 0.408 S82 4.9 3.53 0.77 ? 0.16 WHL J205526.6+010511 (6)ACT?CL J2058.8+0123 314.7234 1.3836 0.32 ? 0.02 DR8 8.3 10.59 1.25 ? 0.15 WHL J205853.1+012411 (1)ACT?CL J2128.4+0135 322.1036 1.5996 0.385 DR8 7.3 5.88 1.34 ? 0.18 WHL J212823.4+013536 (1)ACT?CL J2129.6+0005 322.4186 0.0891 0.234 S82* 8.0 1.18 1.23 ? 0.17 RXC J2129.6+0005 (9)102Table 5.3: ? ContinuedACT ID RA Dec Redshift Region S/N ?500 y?0 Alternate ID (ref.)(?) (?) (arcmin) (10?4)ACT?CL J2130.1+0045 322.5367 0.7590 0.71 ? 0.04 S82 4.4 4.71 0.74 ? 0.17ACT?CL J2135.1?0102 323.7907 ?1.0396 0.33 ? 0.01 S82 4.1 8.24 0.68 ? 0.17 WHL J213512.1-010258 (6)ACT?CL J2135.2+0125 323.8151 1.4247 0.231 DR8 9.3 4.71 1.47 ? 0.16 Abell 2355 (4)ACT?CL J2135.7+0009 323.9310 0.1568 0.118 S82 4.0 10.59 0.68 ? 0.17 Abell 2356 (4)ACT?CL J2152.9?0114 328.2375 ?1.2458 0.69 ? 0.02 S82 4.4 3.53 0.70 ? 0.17ACT?CL J2154.5?0049 328.6319 ?0.8197 0.488 S82* 5.9 3.53 0.95 ? 0.17 WHL J215432.2-004905 (6)ACT?CL J2156.1+0123 329.0407 1.3857 0.224 DR8 6.0 7.06 0.95 ? 0.16 Abell 2397 (4)ACT?CL J2220.7?0042 335.1922 ?0.7095 0.57 ? 0.03 S82 4.0 1.18 0.63 ? 0.18 GMB11 J335.19871-00.69024 (2)ACT?CL J2229.2?0004 337.3042 ?0.0743 0.61 ? 0.05 S82 4.0 15.29 0.66 ? 0.17ACT?CL J2253.3?0031 343.3432 ?0.5280 0.54 ? 0.01 S82 4.0 2.35 0.64 ? 0.17ACT?CL J2302.5+0002 345.6427 0.0419 0.520 S82 4.9 4.71 0.82 ? 0.17 WHL J230235.1+000234 (6)ACT?CL J2307.6+0130 346.9176 1.5161 0.36 ? 0.02 DR8 6.1 2.35 0.95 ? 0.17 WHL J230739.9+013056 (1)ACT?CL J2327.4?0204 351.8660 ?2.0777 0.705 DR8 13.1 3.53 2.65 ? 0.21 RCS2 J2327.4?0204 (10)ACT?CL J2337.6+0016 354.4156 0.2690 0.275 S82* 8.2 7.06 1.43 ? 0.18 Abell 2631 (4)ACT?CL J2351.7+0009 357.9349 0.1538 0.99 ? 0.03 S82 4.7 2.35 0.89 ? 0.21Note ? Coordinates are in the J2000 standard equinox. Redshifts for which uncertainties are quoted arephotometric; all others are spectroscopic (full details can be found in Menanteau et al. 2013). The Region (Reg.)column indicates whether the cluster lies within the coverage of SDSS Stripe 82 or in the shallower coverageof SDSS DR8; an asterisk denotes clusters used for the cosmological analysis of Chapter 6. The signal to noiseratio and filter scale ?500 are provided for the matched filter template that yielded the most significant detection.The uncorrected central Compton parameter y?0 is obtained from maps filtered with the matched filter having?500 = 5.?9 (see Section 5.2.1).References: (1) Wen et al. (2012); (2) Geach et al. (2011); (3) Goto et al. (2002);(4) Abell (1958); (5) Lopes et al. (2004); (6) Wen et al. (2009); (7) Bo?hringer et al. (2000); (8) Hao et al. (2010);(9) Ebeling et al. (1998); (10) Gralla et al. (2011).1035.4 Revisiting the ACT Southern ClustersIn this section we apply the methodology of Sections 5.2.1 and 5.2.2 to estimate masses andSZ quantities for the 23 clusters from the original ACT Southern cluster sample, describedin Marriage et al. (2011, hereafter M11) and Menanteau et al. (2010). For this analysis, weuse updated maps that include additional data acquired in this field during the 2009 and2010 observing seasons.104Table 5.4:SZ-derived mass estimates for ACT clusters.ID ?500 Q(m, z) Y500 MUPP500c MB12500c Mnon500c Mdyn500c(arcmin) (10?4 arcmin2) (1014h?170 M?) (1014h?170 M?) (1014h?170 M?) (1014h?170 M?)ACT-CL J0008.1+0201 3.3 ? 0.3 0.78 ? 0.05 4.0 ? 1.6 3.9 ? 1.1 5.2 ? 1.6 6.2 ? 2.0 4.9 ? 2.0ACT-CL J0012.0?0046 1.2 ? 0.1 0.28 ? 0.03 1.4 ? 0.5 3.0 ? 0.8 3.9 ? 1.1 3.7 ? 1.0 3.3 ? 1.2ACT-CL J0014.9?0057 2.8 ? 0.1 0.69 ? 0.02 5.0 ? 0.9 5.7 ? 1.1 7.6 ? 1.4 9.0 ? 1.7 8.2 ? 1.9ACT-CL J0017.6?0051 4.6 ? 0.5 0.93 ? 0.04 5.0 ? 2.3 2.9 ? 1.0 3.9 ? 1.4 4.8 ? 1.8 3.4 ? 1.6ACT-CL J0018.2?0022 1.8 ? 0.2 0.45 ? 0.05 1.5 ? 0.6 3.1 ? 0.9 4.0 ? 1.3 4.4 ? 1.4 3.6 ? 1.4ACT-CL J0022.2?0036 2.1 ? 0.1 0.52 ? 0.02 3.8 ? 0.6 5.5 ? 0.9 7.3 ? 1.2 8.0 ? 1.4 7.7 ? 1.6ACT-CL J0026.2+0120 2.2 ? 0.1 0.56 ? 0.03 2.8 ? 0.6 4.4 ? 0.9 5.8 ? 1.2 6.6 ? 1.3 5.8 ? 1.5ACT-CL J0044.4+0113 1.3 ? 0.1 0.32 ? 0.04 1.1 ? 0.4 2.7 ? 0.8 3.5 ? 1.0 3.5 ? 1.1 3.0 ? 1.1ACT-CL J0045.2?0152 2.8 ? 0.1 0.68 ? 0.02 4.8 ? 0.9 5.6 ? 1.1 7.5 ? 1.4 8.8 ? 1.6 8.0 ? 1.9ACT-CL J0051.1+0055 1.7 ? 0.2 0.42 ? 0.06 0.9 ? 0.5 2.2 ? 0.8 2.8 ? 1.1 3.0 ? 1.3 2.2 ? 1.1ACT-CL J0058.0+0030 1.8 ? 0.1 0.45 ? 0.04 1.5 ? 0.5 3.2 ? 0.8 4.1 ? 1.1 4.5 ? 1.3 3.7 ? 1.3ACT-CL J0059.1?0049 2.1 ? 0.1 0.53 ? 0.02 3.5 ? 0.6 5.2 ? 0.9 6.9 ? 1.2 7.6 ? 1.3 7.2 ? 1.5ACT-CL J0104.8+0002 3.5 ? 0.4 0.81 ? 0.06 2.8 ? 1.3 2.6 ? 0.9 3.5 ? 1.2 4.2 ? 1.5 3.0 ? 1.4ACT-CL J0119.9+0055 1.9 ? 0.1 0.47 ? 0.04 1.7 ? 0.5 3.3 ? 0.8 4.3 ? 1.1 4.7 ? 1.3 3.9 ? 1.3ACT-CL J0127.2+0020 3.0 ? 0.2 0.73 ? 0.04 2.8 ? 0.9 3.3 ? 0.9 4.4 ? 1.2 5.3 ? 1.4 4.1 ? 1.4ACT-CL J0139.3?0128 1.6 ? 0.2 0.40 ? 0.06 0.8 ? 0.5 2.1 ? 0.9 2.6 ? 1.1 2.8 ? 1.2 2.1 ? 1.1ACT-CL J0152.7+0100 5.4 ? 0.2 0.98 ? 0.01 13.0 ? 2.3 5.7 ? 1.1 7.9 ? 1.6 9.7 ? 1.9 8.7 ? 2.3ACT-CL J0156.4?0123 2.6 ? 0.2 0.64 ? 0.05 2.1 ? 0.8 3.1 ? 0.9 4.0 ? 1.2 4.7 ? 1.4 3.6 ? 1.4ACT-CL J0206.2?0114 2.2 ? 0.1 0.54 ? 0.02 2.6 ? 0.6 4.3 ? 0.8 5.7 ? 1.1 6.4 ? 1.2 5.7 ? 1.4ACT-CL J0215.4+0030 1.9 ? 0.1 0.47 ? 0.03 1.8 ? 0.5 3.5 ? 0.8 4.5 ? 1.1 5.0 ? 1.2 4.2 ? 1.3ACT-CL J0218.2?0041 2.1 ? 0.1 0.54 ? 0.03 2.2 ? 0.6 3.8 ? 0.8 4.9 ? 1.1 5.6 ? 1.3 4.7 ? 1.3ACT-CL J0219.8+0022 2.2 ? 0.2 0.57 ? 0.05 1.7 ? 0.7 3.0 ? 0.9 3.9 ? 1.2 4.5 ? 1.4 3.5 ? 1.4ACT-CL J0219.9+0129 3.0 ? 0.3 0.73 ? 0.05 2.3 ? 0.9 2.8 ? 0.8 3.7 ? 1.1 4.5 ? 1.4 3.3 ? 1.3ACT-CL J0221.5?0012 1.6 ? 0.2 0.40 ? 0.06 0.5 ? 0.3 1.4 ? 0.6 1.8 ? 0.8 2.0 ? 0.9 1.4 ? 0.7ACT-CL J0223.1?0056 2.1 ? 0.1 0.53 ? 0.03 2.2 ? 0.6 3.8 ? 0.8 5.0 ? 1.1 5.7 ? 1.3 4.8 ? 1.4ACT-CL J0228.5+0030 1.7 ? 0.2 0.42 ? 0.06 1.0 ? 0.5 2.4 ? 0.8 3.0 ? 1.1 3.3 ? 1.3 2.5 ? 1.2ACT-CL J0230.9?0024 2.5 ? 0.3 0.64 ? 0.06 1.9 ? 0.8 2.8 ? 0.9 3.7 ? 1.2 4.3 ? 1.4 3.2 ? 1.4ACT-CL J0239.8?0134 3.9 ? 0.1 0.85 ? 0.01 9.4 ? 1.6 6.7 ? 1.3 9.1 ? 1.7 11.1 ? 2.0 10.3 ? 2.5ACT-CL J0240.0+0116 2.1 ? 0.2 0.53 ? 0.04 1.8 ? 0.6 3.3 ? 0.8 4.3 ? 1.1 4.8 ? 1.3 3.9 ? 1.3ACT-CL J0241.2?0018 1.8 ? 0.2 0.44 ? 0.06 1.1 ? 0.5 2.5 ? 0.9 3.2 ? 1.2 3.6 ? 1.3 2.7 ? 1.2ACT-CL J0245.8?0042 5.0 ? 0.6 0.95 ? 0.04 4.9 ? 2.4 2.5 ? 0.9 3.4 ? 1.3 4.1 ? 1.6 2.8 ? 1.4105Table 5.4: ? ContinuedID ?500 Q(m, z) Y500 MUPP500c MB12500c Mnon500c Mdyn500c(arcmin) (10?4 arcmin2) (1014h?170 M?) (1014h?170 M?) (1014h?170 M?) (1014h?170 M?)ACT-CL J0250.1+0008 1.7 ? 0.2 0.41 ? 0.05 1.2 ? 0.5 2.7 ? 0.8 3.5 ? 1.1 3.7 ? 1.2 3.0 ? 1.2ACT-CL J0256.5+0006 3.1 ? 0.2 0.76 ? 0.03 3.4 ? 1.0 3.8 ? 0.9 5.0 ? 1.2 6.1 ? 1.4 4.8 ? 1.5ACT-CL J0301.1?0110 2.0 ? 0.3 0.51 ? 0.07 1.1 ? 0.6 2.2 ? 0.8 2.8 ? 1.1 3.2 ? 1.3 2.3 ? 1.2ACT-CL J0301.6+0155 6.7 ? 0.4 1.01 ? 0.01 15.7 ? 5.0 4.7 ? 1.2 6.6 ? 1.8 8.1 ? 2.1 6.7 ? 2.4ACT-CL J0303.3+0155 6.9 ? 0.6 1.01 ? 0.01 14.9 ? 5.5 4.2 ? 1.2 5.8 ? 1.8 7.1 ? 2.1 5.6 ? 2.3ACT-CL J0308.1+0103 1.9 ? 0.2 0.48 ? 0.05 1.3 ? 0.6 2.7 ? 0.8 3.4 ? 1.1 3.8 ? 1.3 3.0 ? 1.3ACT-CL J0320.4+0032 3.0 ? 0.2 0.72 ? 0.04 2.8 ? 0.9 3.3 ? 0.9 4.4 ? 1.2 5.3 ? 1.4 4.1 ? 1.4ACT-CL J0326.8?0043 3.1 ? 0.1 0.75 ? 0.02 5.5 ? 0.9 5.5 ? 1.0 7.4 ? 1.4 8.9 ? 1.6 7.9 ? 1.9ACT-CL J0336.9?0110 1.2 ? 0.1 0.27 ? 0.03 1.0 ? 0.4 2.5 ? 0.7 3.2 ? 0.9 3.1 ? 0.9 2.7 ? 1.0ACT-CL J0342.0+0105 1.5 ? 0.1 0.37 ? 0.02 1.8 ? 0.4 3.7 ? 0.7 4.8 ? 1.0 4.8 ? 1.0 4.5 ? 1.1ACT-CL J0342.7?0017 3.4 ? 0.3 0.80 ? 0.04 3.2 ? 1.2 3.1 ? 0.9 4.1 ? 1.2 5.0 ? 1.5 3.7 ? 1.4ACT-CL J0348.6+0029 3.5 ? 0.3 0.81 ? 0.04 3.3 ? 1.2 3.1 ? 0.9 4.1 ? 1.2 5.0 ? 1.5 3.7 ? 1.4ACT-CL J0348.6?0028 3.1 ? 0.3 0.75 ? 0.05 2.6 ? 1.0 3.0 ? 0.9 4.0 ? 1.2 4.8 ? 1.5 3.5 ? 1.4ACT-CL J2025.2+0030 3.6 ? 0.2 0.83 ? 0.02 5.5 ? 1.3 4.6 ? 1.0 6.3 ? 1.4 7.7 ? 1.6 6.4 ? 1.8ACT-CL J2050.5?0055 2.2 ? 0.1 0.56 ? 0.04 2.2 ? 0.7 3.8 ? 0.9 4.9 ? 1.2 5.6 ? 1.4 4.7 ? 1.4ACT-CL J2050.7+0123 3.9 ? 0.2 0.85 ? 0.02 6.7 ? 1.4 5.1 ? 1.0 7.0 ? 1.4 8.5 ? 1.7 7.4 ? 1.9ACT-CL J2051.1+0056 3.0 ? 0.4 0.73 ? 0.07 2.1 ? 1.1 2.5 ? 0.9 3.3 ? 1.3 4.0 ? 1.6 2.8 ? 1.4ACT-CL J2051.1+0215 4.0 ? 0.3 0.87 ? 0.03 7.6 ? 2.5 5.3 ? 1.4 7.1 ? 1.9 8.6 ? 2.4 7.2 ? 2.6ACT-CL J2055.4+0105 2.9 ? 0.2 0.70 ? 0.04 2.8 ? 1.0 3.5 ? 0.9 4.6 ? 1.3 5.5 ? 1.5 4.3 ? 1.5ACT-CL J2058.8+0123 4.1 ? 0.2 0.88 ? 0.02 7.8 ? 1.4 5.5 ? 1.1 7.5 ? 1.5 9.2 ? 1.8 8.0 ? 2.0ACT-CL J2128.4+0135 3.5 ? 0.1 0.81 ? 0.02 6.8 ? 1.4 5.7 ? 1.1 7.7 ? 1.6 9.4 ? 1.8 8.3 ? 2.1ACT-CL J2129.6+0005 5.2 ? 0.2 0.97 ? 0.01 11.4 ? 2.4 5.3 ? 1.1 7.3 ? 1.6 9.1 ? 1.9 7.9 ? 2.2ACT-CL J2130.1+0045 1.9 ? 0.2 0.47 ? 0.05 1.6 ? 0.6 3.2 ? 0.9 4.1 ? 1.2 4.5 ? 1.4 3.7 ? 1.4ACT-CL J2135.1?0102 3.1 ? 0.4 0.75 ? 0.06 2.6 ? 1.2 2.8 ? 1.0 3.7 ? 1.3 4.5 ? 1.6 3.2 ? 1.5ACT-CL J2135.2+0125 5.3 ? 0.2 0.97 ? 0.01 14.2 ? 2.4 6.3 ? 1.2 8.7 ? 1.7 10.8 ? 2.1 9.9 ? 2.6ACT-CL J2135.7+0009 7.3 ? 1.0 1.01 ? 0.01 10.8 ? 6.3 2.6 ? 1.1 3.6 ? 1.6 4.3 ? 1.9 2.9 ? 1.8ACT-CL J2152.9?0114 1.9 ? 0.2 0.47 ? 0.05 1.5 ? 0.6 3.0 ? 0.9 3.9 ? 1.3 4.2 ? 1.4 3.4 ? 1.4ACT-CL J2154.5?0049 2.7 ? 0.2 0.68 ? 0.03 3.4 ? 0.9 4.3 ? 0.9 5.7 ? 1.3 6.8 ? 1.5 5.7 ? 1.6ACT-CL J2156.1+0123 4.9 ? 0.3 0.95 ? 0.02 7.9 ? 2.2 4.1 ? 1.0 5.7 ? 1.4 7.0 ? 1.7 5.7 ? 1.8ACT-CL J2220.7?0042 2.0 ? 0.3 0.50 ? 0.07 1.2 ? 0.7 2.5 ? 1.0 3.1 ? 1.3 3.5 ? 1.5 2.6 ? 1.4ACT-CL J2229.2?0004 2.0 ? 0.2 0.49 ? 0.06 1.3 ? 0.7 2.7 ? 1.0 3.4 ? 1.3 3.8 ? 1.5 2.9 ? 1.4ACT-CL J2253.3?0031 2.1 ? 0.3 0.54 ? 0.06 1.5 ? 0.7 2.7 ? 0.9 3.5 ? 1.3 4.0 ? 1.5 3.0 ? 1.4106Table 5.4: ? ContinuedID ?500 Q(m, z) Y500 MUPP500c MB12500c Mnon500c Mdyn500c(arcmin) (10?4 arcmin2) (1014h?170 M?) (1014h?170 M?) (1014h?170 M?) (1014h?170 M?)ACT-CL J2302.5+0002 2.5 ? 0.2 0.62 ? 0.04 2.5 ? 0.8 3.7 ? 0.9 4.8 ? 1.3 5.6 ? 1.5 4.6 ? 1.5ACT-CL J2307.6+0130 3.4 ? 0.2 0.80 ? 0.03 4.5 ? 1.2 4.2 ? 1.0 5.7 ? 1.3 6.9 ? 1.6 5.7 ? 1.7ACT-CL J2327.4?0204 2.8 ? 0.1 0.67 ? 0.01 10.1 ? 1.0 9.4 ? 1.5 12.5 ? 2.0 14.3 ? 2.2 14.9 ? 3.0ACT-CL J2337.6+0016 4.8 ? 0.2 0.94 ? 0.01 11.5 ? 2.2 6.1 ? 1.2 8.4 ? 1.7 10.3 ? 2.0 9.3 ? 2.5ACT-CL J2351.7+0009 1.5 ? 0.2 0.36 ? 0.05 1.5 ? 0.7 3.2 ? 1.0 4.0 ? 1.4 4.1 ? 1.5 3.4 ? 1.6Note ? Mass estimates obtained as described in Section 5.2.2. The y?0-M scaling relation is fixed to either the UPPresult, the fit to the B12 model, the fit to Nonthermal20 model (superscript ?non?), or the fit to dynamical masses ofSifo?n et al. (2012) (superscript ?dyn?). Masses and SZ quantities are computed from the cluster?s uncorrected centralCompton parameter y?0 and redshift measurements, including correction for mass function bias. The cluster scale ?500,value of the bias function Q(m, z), and integrated Compton parameter Y500 are those inferred from the UPP scalingrelation. Uncertainties do not include uncertainty in the scaling relation parameters, but do include the effects of intrinsicscatter and the measurement uncertainty. SZ and mass errors are highly correlated.107In Table 5.5 we summarize the basic properties of the Southern cluster sample, andinclude our measurement of the uncorrected central temperature decrement taken frommaps filtered with the ?500 = 5.?9 UPP matched filter. While this filter incorporates thesame cluster profile that was used in the analysis of the Equatorial sample, the filter itselfis slightly different due to the different noise properties in the Southern maps. In Table 5.6we present cluster mass and SZ quantity estimates.There is substantial overlap between the ACT Southern field and the cluster samplespresented by the SPT collaboration. The M11 sample includes six of the clusters anal-ysed in Williamson et al. (2011, hereafter W11), and five of the clusters in Reichardt et al.(2013, hereafter R12). In W11 a scaling relation based on the SPT signal to noise ratio andcalibrated to the models of Shaw et al. (2010) is used to obtain SZ based mass estimates.In R12, masses are presented that are derived from a combination of SZ and X-ray mea-surements, though X-ray measurements are expected to dominate because of the smalleruncertainty in the X-ray scaling relation. (Four of the five ACT clusters appearing in R12have X-ray mass measurements.)We find the SPT masses to be in good agreement with our masses based on theB12 model scaling relation parameters, with weighted mean mass ratio MB12/MSPT =0.99 ? 0.06. We note, however, a difference in the mean ratio for each of the two SPTcatalogues. For the clusters in R12 the mass ratio is 0.88 ? 0.09, while for the highermass, lower redshift sample of W11 the ratio is 1.10 ? 0.09. In Figure 5.14 we show themasses. We note that this difference in mass ratio is consistent with the observation in W11that their average SZ determined masses are smaller than YX based masses by a factor of0.78 ? 0.06. In contrast, the R12 masses for four of the five common clusters include in-put from observations of YX, which is likely to dominate over the contribution from SZ data.In summary, the ACT Equatorial cluster sample is consistent, assuming a standard?CDM cosmology, with an approximately mass-limited sample of galaxy clusters from red-shifts 0.2 < z. We find good agreement between the masses inferred from the PBAA ofthe SZ signal and masses measured by other instruments and at other wavelengths. Wehave approached the issue of mass calibration with some caution, considering a variety ofobservational and model-based probes of cluster mass. Bearing in mind these uncertaintiesin the mass calibration, we will proceed in the next chapter to explore the constraint ofcosmological parameters by combining the ACT cluster sample information with variousother data sets.108102 3 5 7 20MSPT (1014h170M)10235720MB12ACT (1014h170M)Williamson et al. (2011)Reichardt et al. (2013)Figure 5.14: Comparison of ACT SZ based masses (from B12 scaling relation) tomasses from the South Pole Telescope. Both are M500c. ACT masses arecomputed using the B12 scaling relation and may be found in Table 5.6.SPT masses are taken from Williamson et al. (2011) (mass is computed fromSZ signal based on scaling relation calibrated to Shaw et al., 2010, models;only statistical uncertainty is included in error bars), and Reichardt et al.(2013, mass is computed from combination of YX and SZ measurements). Theweighted mean mass ratio for the 11 clusters is 0.99 ? 0.06, though there isevidence of a systematic difference between the mass calibration in the twoSPT catalogues. Dotted line traces equality of SPT and ACT masses forthe B12 scaling relation. Dashed lines trace approximate loci of agreementbetween SPT masses and ACT masses based on the UPP (upper line) andNonthermal20 (lower line) scaling relations. Uncertainties in the ACT andSPT measurements for each cluster are likely to be partially correlated, sinceboth use properties of cluster gas to infer a total mass.109Table 5.5:Uncorrected central Compton parameters for the clusters from Marriage et al. (2011).ACT ID RA Dec Redshift S/N y?0 Alternate ID (ref.)(?) (?) (10?4)ACT?CL J0102?4915* 15.7208 ?49.2553 0.870 9.0 3.51 ? 0.43 SPT-CL J0102-4915 (1)ACT?CL J0145?5301 26.2458 ?53.0169 0.118 4.0 0.86 ? 0.19 Abell 2941 (2)ACT?CL J0215?5212 33.8250 ?52.2083 0.480 4.9 0.79 ? 0.18ACT?CL J0217?5245 34.2958 ?52.7556 0.343 4.1 0.79 ? 0.18 RXC J0217.2-5244 (3)ACT?CL J0232?5257 38.1875 ?52.9522 0.556 4.7 0.61 ? 0.17ACT?CL J0235?5121 38.9667 ?51.3544 0.278 6.2 0.98 ? 0.19ACT?CL J0237?4939 39.2625 ?49.6575 0.334 3.9 0.93 ? 0.26ACT?CL J0245?5302 41.3875 ?53.0344 0.300 9.1 1.57 ? 0.17 Abell S0295 (4)SPT-CL J0245-5302 (1)ACT?CL J0304?4921 46.0625 ?49.3617 0.392 3.9 1.52 ? 0.32ACT?CL J0330?5227* 52.7250 ?52.4678 0.442 6.1 1.23 ? 0.18 Abell 3128 NE (5)ACT?CL J0346?5438 56.7125 ?54.6483 0.530 4.4 1.05 ? 0.22ACT?CL J0438?5419* 69.5792 ?54.3181 0.421 8.0 1.62 ? 0.13 SPT-CL J0438-5419 (1)ACT?CL J0509?5341* 77.3375 ?53.7014 0.461 4.8 0.82 ? 0.14 SPT-CL J0509-5342 (6)ACT?CL J0516?5430 79.1250 ?54.5083 0.294 4.6 0.87 ? 0.15 Abell S0520 (4)SPT-CL J0516-5430 (6)ACT?CL J0528?5259 82.0125 ?52.9981 0.768 3.1 0.50 ? 0.13 SPT-CL J0528-5300 (6)ACT?CL J0546?5345* 86.6542 ?53.7589 1.066 6.5 0.92 ? 0.14 SPT-CL J0546-5345 (6)ACT?CL J0559?5249* 89.9292 ?52.8203 0.609 5.1 0.89 ? 0.14 SPT-CL J0559-5249 (6)ACT?CL J0616?5227* 94.1500 ?52.4597 0.684 5.9 1.00 ? 0.15ACT?CL J0638?5358 99.6917 ?53.9792 0.222 10.0 1.77 ? 0.15 Abell S0592 (4)SPT-CL J0638-5358 (1)ACT?CL J0641?4949 100.3958 ?49.8089 0.146 4.7 0.58 ? 0.26 Abell 3402 (2)ACT?CL J0645?5413 101.3750 ?54.2275 0.167 7.1 1.19 ? 0.17 Abell 3404 (2)SPT-CL J0645-5413 (1)110Table 5.5: ? ContinuedACT ID RA Dec Redshift S/N y?0 Alternate ID (ref.)(?) (?) (10?4)ACT?CL J0658?5557 104.6250 ?55.9511 0.296 11.5 2.65 ? 0.21 1E0657-56/Bullet (7)SPT-CL J0658-5556 (1)ACT?CL J0707?5522 106.8042 ?55.3800 0.296 3.3 0.54 ? 0.21Note ? Clusters used for cosmological and scaling relation constraints in Chapter 6 are marked with an asterisk.Redshifts are all spectroscopic, obtained from literature as described in Menanteau et al. (2010) or as presented inSifo?n et al. (2012). We provide the S/N of detection as presented in Marriage et al. (2011), for reference. Uncorrectedcentral Compton parameters y?0 are obtained from the application of a matched filter with ?500 = 5.?9 (see Section 5.2.1).Alternate IDs are provided for clusters detected before the initial release of the Southern sample, and for any clusterappearing in current SPT results. References: (1) Williamson et al. (2011); (2) Abell (1958); (3) Bo?hringer et al. (2004);(4) Abell et al. (1989); (5) Werner et al. (2007); (6) Reichardt et al. (2013); (7) Tucker et al. (1995).111Table 5.6:SZ-derived mass estimates for the ACT Southern cluster sample of Marriage et al. (2011).ID ?500 Q(m, z) Y500 MUPP500c MB12500c Mnon500c Mdyn500c(arcmin) (10?4 arcmin2) (1014h?170 M?) (1014h?170 M?) (1014h?170 M?) (1014h?170 M?)ACT-CL J0102?4915 2.5 ? 0.1 0.60 ? 0.02 11.5 ? 2.0 10.5 ? 1.8 13.8 ? 2.4 15.0 ? 2.6 16.0 ? 3.5ACT-CL J0145?5301 8.1 ? 0.9 1.02 ? 0.01 16.9 ? 8.2 3.5 ? 1.2 4.8 ? 1.8 5.7 ? 2.2 4.2 ? 2.2ACT-CL J0215?5212 2.5 ? 0.2 0.62 ? 0.05 2.4 ? 1.0 3.5 ? 1.0 4.5 ? 1.4 5.2 ? 1.7 4.1 ? 1.7ACT-CL J0217?5245 3.2 ? 0.3 0.75 ? 0.05 3.2 ? 1.3 3.4 ? 1.0 4.4 ? 1.4 5.3 ? 1.8 4.0 ? 1.7ACT-CL J0232?5257 2.0 ? 0.3 0.49 ? 0.07 1.2 ? 0.7 2.5 ? 1.0 3.1 ? 1.3 3.5 ? 1.5 2.6 ? 1.4ACT-CL J0235?5121 4.1 ? 0.3 0.87 ? 0.03 5.9 ? 2.0 4.1 ? 1.1 5.6 ? 1.5 6.8 ? 1.8 5.4 ? 1.9ACT-CL J0237?4939 3.2 ? 0.5 0.74 ? 0.09 3.1 ? 2.1 3.1 ? 1.4 3.9 ? 1.9 4.6 ? 2.4 3.2 ? 2.1ACT-CL J0245?5302 4.6 ? 0.2 0.92 ? 0.01 12.1 ? 2.0 6.7 ? 1.3 9.2 ? 1.8 11.3 ? 2.1 10.4 ? 2.6ACT-CL J0304?4921 3.5 ? 0.3 0.79 ? 0.05 6.8 ? 2.6 5.7 ? 1.6 7.4 ? 2.3 8.7 ? 2.8 7.3 ? 3.1ACT-CL J0330?5227 3.2 ? 0.1 0.74 ? 0.02 5.4 ? 1.2 5.4 ? 1.1 7.3 ? 1.5 8.7 ? 1.7 7.7 ? 2.0ACT-CL J0346?5438 2.6 ? 0.2 0.62 ? 0.04 3.3 ? 1.1 4.4 ? 1.2 5.7 ? 1.6 6.6 ? 1.9 5.5 ? 2.0ACT-CL J0438?5419 3.6 ? 0.1 0.80 ? 0.01 8.8 ? 1.0 7.0 ? 1.2 9.5 ? 1.6 11.5 ? 1.9 10.9 ? 2.3ACT-CL J0509?5341 2.8 ? 0.1 0.66 ? 0.03 3.1 ? 0.7 4.0 ? 0.8 5.3 ? 1.1 6.3 ? 1.3 5.2 ? 1.4ACT-CL J0516?5430 3.9 ? 0.2 0.85 ? 0.03 5.1 ? 1.3 4.0 ? 0.9 5.4 ? 1.2 6.7 ? 1.5 5.3 ? 1.6ACT-CL J0528?5259 1.6 ? 0.2 0.37 ? 0.05 0.9 ? 0.4 2.3 ? 0.8 2.9 ? 1.0 3.1 ? 1.1 2.4 ? 1.1ACT-CL J0546?5345 1.6 ? 0.1 0.36 ? 0.02 2.0 ? 0.4 3.9 ? 0.7 5.1 ? 0.9 5.2 ? 1.0 4.9 ? 1.1ACT-CL J0559?5249 2.3 ? 0.1 0.56 ? 0.02 2.8 ? 0.6 4.3 ? 0.8 5.7 ? 1.1 6.5 ? 1.3 5.6 ? 1.4ACT-CL J0616?5227 2.2 ? 0.1 0.53 ? 0.02 3.0 ? 0.6 4.6 ? 0.9 6.1 ? 1.2 6.9 ? 1.3 6.2 ? 1.5ACT-CL J0638?5358 6.1 ? 0.2 1.00 ? 0.01 22.4 ? 3.0 7.5 ? 1.4 10.5 ? 2.0 13.0 ? 2.4 12.5 ? 3.2ACT-CL J0641?4949 4.8 ? 1.0 0.93 ? 0.06 2.9 ? 3.2 1.4 ? 0.9 1.8 ? 1.2 2.2 ? 1.4 1.3 ? 1.1ACT-CL J0645?5413 6.9 ? 0.3 1.02 ? 0.01 18.2 ? 4.3 5.1 ? 1.2 7.3 ? 1.7 8.9 ? 2.0 7.7 ? 2.4ACT-CL J0658?5557 5.4 ? 0.1 0.97 ? 0.01 26.6 ? 3.2 10.3 ? 1.9 14.3 ? 2.6 17.6 ? 3.1 18.2 ? 4.3ACT-CL J0707?5522 2.8 ? 0.5 0.69 ? 0.09 1.4 ? 1.1 1.7 ? 0.9 2.2 ? 1.2 2.6 ? 1.4 1.7 ? 1.1Note ? Columns are as described in Table 5.4.112Chapter 6Cosmological Constraints from theACT Equatorial Galaxy ClusterSampleCluster count statistics, such as the number density of clusters above some limiting mass,are particularly sensitive to the total matter density (?m) and the amplitude of densityfluctuations (as parameterized by, e.g., ?8). As probes of local structure, cluster studiesare highly complementary to constraints from the CMB, and have the potential to provideinteresting constraints on the sum of the neutrino species masses, ?? m? . Because SZselected cluster samples reach to high redshift, they also probe parameters, such as thedark energy equation of state parameter w, that describe the recent expansion history.In order to constrain cosmological parameters, we incorporate our sample into a Bayesiananalysis and compute the posterior likelihood of cosmological parameters given the clusterdata. We begin by outlining the formalism used to model the probability of our data givenvalues of cosmological and scaling relation parameters. We then demonstrate the constraintsachieved by combining the ACT cluster data with other data sets. Posterior distributionsare summarized in terms of their mean and standard deviation unless otherwise indicated.6.1 Likelihood FormalismIn this section we outline a formalism for determining the Bayesian likelihood of cosmologi-cal and scaling relation parameters given the ACT cluster measurements, including redshift,SZ, and dynamical mass information, when available. Our approach follows previous workin developing an expression for the probability of the cluster measurements based on theapplication of Poisson statistics to finely spaced bins in the multi-dimensional space of clus-ter observables. Such approaches naturally support non-trivial sample selection functions,the self-consistent calibration of scaling relations between object properties (i.e., betweenmass, SZ signal, and redshift), and missing data (i.e., the absence of independent mass113measurements for some detected clusters). This approach to the comparison of a sample ofdetected objects to a number density predicted by a model is described by Cash (1979), andused for cluster studies by, e.g., Markevitch (1998) and Pierpaoli et al. (2001); Mantz et al.(2010b) present a useful general formalism for dealing with cluster data, applying it to X-ray mass and luminosity measurements to obtain cosmological constraints while calibratingthe mass?luminosity scaling relation. The SZ studies of Sehgal et al. (2011) and SPT (e.g.,Benson et al., 2013) have applied similar techniques to SZ and X-ray data. Here, we developan approach that pays particular attention to the uncertainties in the observed quantities,and in which the SZ signal is interpreted through the Profile Based Amplitude Analysisapproach (PBAA; Section 5.2.1).We assume that the cluster data consist of a sample of confirmed clusters, and that foreach cluster an uncorrected central Compton parameter y?0 ? ?y?0 and redshift z ? ?z havebeen measured. The y?0 are obtained from maps filtered with ?5.?9. In some cases, clustersmay also have dynamical mass measurements, Mdyn500c (see Section 5.2.5). To parameterizethese measurements in a way that is independent of cosmology, we define the observeddynamical mass parameter, m? ? E(z)Mdyn500c/(1014 h?170 M?).To compare the observed sample to predicted cluster number densities, we consider allclusters to possess an intrinsic uncorrected central Compton parameter y?0tr, redshift ztr,and mass parameter m?tr. These true intrinsic quantities represent the values one wouldmeasure in the absence of any instrumental noise or astrophysical contamination (from,e.g., the CMB). For the SZ signal, y?0tr should be thought of as the measurement we wouldmake if we applied our filter ?5.?9 (i.e., the fixed-scale filter matched to the noise spectrumof our maps) to a map from which all noise and astrophysical contamination had beenremoved. The true cluster mass parameter, m?tr ? M500c h70E(ztr) with E(ztr) computedfor the true cosmology, is representative of the halo mass rather than the mass inferred froman observational proxy (such as galaxy velocity dispersion).We proceed by obtaining the number density of galaxy clusters in the space of truecluster properties y?0tr, m?tr, and ztr. As described in Section 5.2.2, we make use of thecluster mass function of Tinker et al. (2008) to predict, for cosmological parameters ?, thenumber of clusters per unit redshift and unit mass within the area of the survey:n(m?tr, ztr|?) = d2N(< m?tr, ztr)/dztrdm?tr. (6.1)Here we use the notation n(?|?), more commonly used with probability densities, to indicatethe conditional distribution of clusters with respect to variables ? when variables ? are heldfixed.Given m?tr, ztr, and scaling relation parameters ? = (Am, B,C, ?int), the conditional dis-tribution of Compton parameter values, P (y?0tr|m?tr, ztr,?), is specified by equations (5.14)and (5.16). Summarizing these equations in our current notation, log y?0tr is normally dis-114tributed,log y?0tr ? N(log y?0(m?tr, ztr,?);?2int), (6.2)and the mean relation is described byy?0tr(m?tr, ztr,?) = 10A0+AmE2(ztr)(m?tr)1+B0+B?Q[(1 + ztr1.5)C?500/(m?tr)C0]? frel(m?tr, ztr). (6.3)This may be used to compute the number density of clusters in the full space of truecluster properties:n(y?0tr, m?tr, ztr|?,?) = P (y?0tr|m?tr, ztr,?)?n(m?tr, ztr|?). (6.4)In order to compare our observed sample to the model, it is necessary to properly accountfor the sample selection function, and for the effects of measurement uncertainty. This isespecially important because our selection function depends explicitly on ?y?0, and the massfunction (and thus the cluster density as a function of y?0) is very steep. This full treatmentof uncertainty allows us to include, in the same analysis, regions of the map that have quitedifferent noise levels.In general, we imagine that the cluster observables x = (y?0, m?, z, ?y?0, ?m?, ?z) are relatedto the true cluster properties y?0tr, m?tr, ztr by some probability distribution P (x|y?0tr, m?tr, ztr, ?dyn).In addition to describing the scatter of each variable about its true value, and accountingfor the dynamical mass bias through the parameter ?dyn (which is defined in Section 5.2.5),this distribution also includes a description of what measurement uncertainties we are likelyto encounter for given values of the true cluster properties. For example, while most of oursample have spectroscopic redshifts for which the measurement uncertainty is negligible,some clusters (particularly at high redshift) have photometric redshift estimates with rel-atively large uncertainties (?z ? 0.06). Although it may seem awkward to worry aboutmeasurement uncertainty for clusters that have not been detected, it is necessary, formally,to account for the distribution of errors if the sample is defined based on observed clusterproperties. In our particular case, the full probability distribution factors to:P (x|y?0tr, m?tr, ztr, ?dyn) = P (y?0|y?0tr, ?y?0)P (?y?0)?P (m?|m?tr, ?m?, ?dyn)P (?m?)?P (z|ztr, ?z)P (?z|ztr). (6.5)115The expression above encodes the following properties of the ACT observations.? For a given cluster, the measurements of y?0, m?, and z are independent; we do notexpect any covariance in the errors. In practice we assume cluster observables arenormally distributed about their true values (with the exception of m?; see next point).? The probability distribution of m? includes the effects of the dynamical mass biasparameter, ?dyn; specifically the measured dynamical mass parameter m? is expectedto be normally distributed about mean ?dynm?tr with standard deviation ?m?.? The distribution of y?0 errors, P (?y?0), is independent of all true cluster properties. Inpractice P (?y?0) is obtained from the histogram of the noise map.? The distribution of m? errors, P (?m?), is independent of true cluster properties. Inpractice the uncertainty in the dynamical masses is related to the number of galaxiesused for the velocity dispersion measurements. In any case, we do not need to un-derstand this distribution in detail, because observed mass is not a factor in sampleselection.? The distribution of z errors, P (?z|ztr), may depend on the true cluster redshift. Whilespectroscopically measured redshifts are available for many sample clusters, high red-shift clusters are more likely to have only photometric redshift estimates. In practice,this distribution only enters when computing the prediction for the total number ofclusters observed within some volume. For suitably chosen sample redshift limits, thedetails will not matter (see discussion below).For a sample selected based on signal to noise ratio threshold s and observed red-shift range [zA, zB], we define the selection function S(y?0, z, ?y?0) to take value unity wheny?0/?y?0 > s and z ? [zA, zB], and to take value zero otherwise. Then the predicted numberdensity in the 6-dimensional space of observables x isn(x|?,?, ?dyn) = S(y?0, z, ?y?0)??dy?0trdm?trdztrP (x|y?0tr, m?tr, ztr, ?dyn)?n(y?0tr, m?tr, ztr|?,?). (6.6)This cluster density function may be used to evaluate the extent to which the observedcluster data are consistent with the model ?,?, ?dyn. This is achieved, as in Cash (1979)by imagining a very fine binning in the space of observables. We take bins indexed by ?centered at x? and having (6-dimensional) volume V?. In the limit of very fine bins, the totalpredicted counts in bin ? is well-approximated by N?(?,?, ?dyn) ? V?n(x?|?,?, ?dyn).Furthermore, the number of observed clusters in bin ?, denoted c?, is either 0 or 1.116Letting D denote the set of bins in which a cluster has been observed (i.e., the ? wherec? = 1), we assume Poisson statistics in each bin, and obtain the probability of the datagiven the model parameters:P ({xi}|?,?, ?dyn) = P ({c?} |?,?, ?dyn)=??e?N?(?,?,?dyn)N?(?,?, ?dyn)c?= e?Ntot(?,?,?dyn)???DV? n(x?). (6.7)We have definedNtot(?,?, ?dyn) =??N?(?,?, ?dyn)=?d6x n(x|?,?, ?dyn), (6.8)the total number of clusters that the model predicts will be detected.In equation (6.7), the product over occupied bins is only sensitive to the values of thedensity function at the locations of the detected clusters. The volume elements V? dependon the data and the binning, but not on the cosmological or scaling relation parameters.They will thus cancel exactly in any ratio of probabilities comparing different models. Sowe may write the likelihood of parameters ?,?, ?dyn given the cluster data {xi} asL(?,?, ?dyn|{xi}) = P ({xi}|?,?, ?dyn)? e?Ntot(?,?,?dyn)??in(xi|?,?, ?dyn), (6.9)where i indexes the clusters in the sample.When evaluating this expression in practice, we face the two related problems of comput-ing the total cluster count prediction Ntot, and of computing the number density n(xi|?,?, ?dyn)for each cluster in the sample. Certain simplifications make possible the efficient computa-tion of these quantities.When computing n(xi|?,?, ?dyn), we approximate P (?z|ztr) as being constant overthe range of ztr under consideration. This is acceptable because the integral over ztr isrestricted to the vicinity of the observed cluster redshift zi by the distribution P (zi|ztr, ?z).We thus replace P (?zi|ztr) with pi ? P (?zi|ztr)|ztr=zi . The pi can then be factored out ofthe integral over true cluster properties in equation (6.6). When evaluating the likelihoodin equation (6.9), these pi contribute a constant multiplicative factor that is independentof parameters ?,?, ?dyn. So their contribution is irrelevant, and like the V? the pi may bedropped from the likelihood expression.117When computing Ntot, the procedure is simplified by first integrating over m?tr to ob-tain the distribution n(y?0tr, ztr|?,?). The integrals over m? and ?m? are trivial to perform(independent of the form of P (?m) and the value of ?dyn), because the selection functiondoes not depend on m? or ?m?. We may then write Ntot(?,?), dropping the dependence on?dyn. The integral over ?y?0 can be accomplished with P (?y?0) based on the noise map. Notethat this is essential to properly predict the total cluster count in cases where the map areaunder consideration includes a variety of local noise levels.It is necessary to consider the impact of P (?z|ztr) in the evaluation of Ntot. The numberof clusters within an observed redshift range z ? [zA, zB] will be approximately equal tothe number of clusters with true redshift ztr ? [zA, zB]. The difference between these twonumbers may be interpreted as the result of clusters ?scattering? over the redshift boundarydue to measurement uncertainty. The magnitude of this effect is related to the noise level?z and the steepness of the distribution n(z) at the boundaries.Two properties of the ACT cluster sample allow us to avoid dealing with the detailsof P (?z|ztr). The first is that we have spectroscopic redshift measurements for all but asmall number of high redshift clusters. This means that P (?z|ztr) strongly favours the caseof ?z ? 0 at the low redshift sample boundary. Second, our upper redshift limit, whicharises based on the depth of optical confirmation observations, is at z = 1.4. Clusters atz = 1.4 are sufficiently rare that uncertainty in ?z does not greatly affect the total numberof clusters within the full survey volume. For example, at z = 1.4 the predicted clusternumber density has fallen off significantly and the effects of redshift uncertainty can onlyaffect the total predicted counts by less than 1%. This is well below the error due to samplevariance. So, provided we use a cluster sample for which SZ candidate follow-up (optical/IRconfirmation) is complete out to at least z = 1.4, we may disregard redshift uncertaintywhen computing Ntot, and integrate over ztr instead of z and ?z.For a more complicated data set (involving a large number of photometrically obtainedredshifts), the distribution P (?z|ztr) could be estimated based on the redshift error data inhand.Finally, in the case that mass data are not available for some or all of the clusters, wecan simply integrate over our ignorance of m?. The model and scaling relation parametersgive cluster density prediction, marginalized over the missing data, ofn(y?0, z, ?y?0, ?z|?,?) =?d(?m?)?dm n(x|?,?, ?dyn). (6.10)118The likelihood expression for the mixed case isL(?,?, ?dyn|{xi}) ? e?Ntot(?,?)??i?Mn(xi|?,?, ?dyn)??i/?Mn(y?0i, zi, ?y?0i, ?zi|?,?), (6.11)where M denotes the subset of clusters that have mass measurements.6.2 Parameter Constraints for Fixed Scaling RelationsIn this section we obtain cosmological parameter constraints by combining the Equatorialcluster sample with various external data sets, with the SZ scaling relation parameters fixedto values indicated by the UPP prescription, and by the B12 and Nonthermal20 models.For each case, we fix the scaling relation parameters (Am, B,C, ?int) to the values givenin Table 5.1, and do not account for any uncertainty in these parameters. These resultsshould thus be viewed as illustrating the potential constraint achievable from these clusterdata, should the uncertainty on the scaling relations be reduced. The constraints alsodemonstrate the sensitivity of cosmological parameter estimates to the different physicalassumptions entering each model.The posterior distributions of cosmological parameters are obtained through MarkovChain Monte Carlo (MCMC) sampling, driven by the CosmoMC software (Lewis and Bridle,2002), with matter power spectra and CMB angular power spectra computed using theCAMB software (Lewis et al., 2000). The ACT Equatorial data contribute to the likeli-hood according to equation (6.11). The cluster sample includes the 15 objects (identifiedin Table 5.3) that lie inside sample boundaries defined by redshift range 0.2 < z < 1.4 andsignal to noise ratio cut y?0/?y?0 > 5.1. As discussed in Section 5.1.4, the cut on y?0/?y?0corresponds to the level above which the optical confirmation campaign has successfullyconfirmed or falsified all SZ detections.Posterior distributions of parameters for data sets that do not include ACT cluster in-formation are obtained from chains released with the WMAP seven-year results (WMAP7;Komatsu et al., 2011). In some cases, chains also incorporate data from Baryon Acous-tic Oscillation experiments (BAO; Percival et al., 2010), and Type Ia supernovae (SNe;Hicken et al., 2009). When not constrained by CMB information, ACT cluster data arecombined with results from big bang nucleosynthesis (BBN; Hamann et al., 2008) to con-strain the baryon density and with Hubble constant measurements (denoted H0; Riess et al.,2009). The H0 measurements are also used to restrict the parameter space of wCDM modelstudies, emphasizing the role clusters can play in such cases.We first consider a ?CDM model with seven free parameters representing the baryonand cold dark matter densities (?b and ?c), the angular scale of the sound horizon (?A), the1190.2 0.3 0.4?m0. 6.1: Constraints on ?CDM cosmological parameters from WMAP7 (black linecontours) and ACTcl+BBN+H0 (without CMB information). Contours indi-cate 68 and 95% confidence regions. ACT results are shown for three scal-ing relations: UPP (orange shading); B12 (green lines); Nonthermal20 (violetshading). While any one scaling relation provides an interesting complementto CMB information, the results from the three different scaling relations spanthe range of parameter values allowed by WMAP measurements.normalization (As) and spectral index (ns) of the matter power spectrum, the optical depthof reionization (?), and the SZ spectral amplitude (ASZ). For simplicity, the SZ spectralamplitude is not explicitly tied to the cluster scaling relation parameters.The potential for our cluster data to constrain ?m and ?8 is demonstrated in Fig-ure 6.1. In order to emphasize the impact of cluster studies, we have computed theparameter likelihood for the ACT cluster data in combination with BBN and H0 only(these constrain the baryon density to ?bh2 = 0.022 ? 0.002 and the Hubble constant toH0 = (73.9 ? 3.6) km s?1 Mpc?1). We plot the marginalized two-dimensional distributionof parameters ?8 and ?m, with contours showing the 68% and 95% confidence regions.The ACT cluster constraints, without CMB information, are seen to nicely complementthe results from WMAP7. But the variation in the constraints between models shows thedegree to which uncertainty in the cluster physics diminishes the constraining power. Themarginalized parameter values are provided in Table 6.1. We compute marginalized valuesfor the composite parameter ?8(?m/0.27)0.3, because this parameter provides a convenientprojection of the (?m, ?8) space that captures the axis of degeneracy in the CMB constraints.120Table 6.1:Cosmological parameter constraints for the ?CDM model.Parameter (?CDM)Data set ?ch2 ?m ?8 h ?8(?m/0.27)0.3Without ACT Cluster DataWMAP7 0.111 ? 0.006 0.266 ? 0.029 0.801 ? 0.030 0.710 ? 0.025 0.797 ? 0.053WMAP7 + BAO + H0 0.112 ? 0.003 0.272 ? 0.016 0.809 ? 0.024 0.704 ? 0.014 0.811 ? 0.034Fixed Scaling Relations (?6.2)BBN + H0 + ACTcl(B12) 0.115 ? 0.024 0.252 ? 0.047 0.872 ? 0.065 0.741 ? 0.036 0.848 ? 0.032WMAP7 + ACTcl(UPP) 0.107 ? 0.002 0.250 ? 0.012 0.786 ? 0.013 0.720 ? 0.015 0.768 ? 0.015WMAP7 + ACTcl(B12) 0.114 ? 0.002 0.285 ? 0.014 0.824 ? 0.014 0.693 ? 0.015 0.837 ? 0.017WMAP7 + ACTcl(Non) 0.117 ? 0.002 0.303 ? 0.016 0.839 ? 0.014 0.680 ? 0.015 0.869 ? 0.018Dynamical Mass Constraints (?6.3)BBN + H0 + ACTcl(dyn) 0.141 ? 0.042 0.301 ? 0.082 0.975 ? 0.108 0.737 ? 0.037 0.999 ? 0.130WMAP7 + ACTcl(dyn) 0.115 ? 0.004 0.292 ? 0.025 0.829 ? 0.024 0.688 ? 0.021 0.848 ? 0.042WMAP7 + ACTcl(dyn) + BAO + H0 0.114 ? 0.003 0.282 ? 0.016 0.829 ? 0.022 0.696 ? 0.013 0.840 ? 0.031Note ? Numbers indicate the mean and standard deviation of the marginalized posterior distribution. ACTcl results forscaling relations based on the Universal Pressure Profile (UPP), and the B12 and Nonthermal20 (Non) models do not includemarginalization over scaling relation uncertainties (Section 6.2). ACTcl(dyn) results use Southern and Equatorial clusterdata, including dynamical mass measurements for the Southern clusters (Section 6.3).121?1.5?1.2?0.9w0.18 0.24 0.30?m0. ?1.2 ?0.9wFigure 6.2: Constraints on wCDM cosmological parameters from WMAP7+H0 (solidblack lines), and WMAP7+ACTcl+H0 for three scaling relations (B12 scalingrelation is green lines; UPP is orange shading; Nonthermal20 is violet shading.)In a wCDM model (which differs from the ?CDM model in that the equation of stateparameter w may deviate from ?1), cluster counts are sensitive to the effect of dark energyon the expansion rate of the recent Universe. As shown in Table 6.2, the ACT cluster dataprovide slightly improved constraints on ?8 relative to WMAP7 alone; but the true powerof the cluster data is to break degeneracies between ?8, ?m, and w. We present compositeparameters defined by ?8(?m/0.27)0.4 and w(?m/0.27) to express these improvements.In Figure 6.2, we show 2-d marginalized constraints for ?m, ?8, and w. Note that, forthis plot only, we have included the H0 prior, to partially break the degeneracy betweenthese three parameters and to emphasize the role that normalization of the SZ scalingrelation plays in this space.122Table 6.2:Cosmological parameter constraints for the flat wCDM model.Parameter (wCDM)Data set ?ch2 ?8 ?8(?m/0.27)0.4 w(?m/0.27)Without ACT Cluster DataWMAP7 0.111 ? 0.006 0.832 ? 0.134 0.790 ? 0.065 ?0.95 ? 0.13WMAP7 + SNe 0.111 ? 0.006 0.791 ? 0.042 0.798 ? 0.060 ?0.99 ? 0.11Fixed Scaling Relations (?6.2)WMAP7 + ACTcl(UPP) 0.108 ? 0.002 0.854 ? 0.106 0.766 ? 0.018 ?0.90 ? 0.06WMAP7 + ACTcl(B12) 0.115 ? 0.003 0.915 ? 0.111 0.849 ? 0.021 ?1.04 ? 0.07WMAP7 + ACTcl(Non) 0.119 ? 0.003 0.915 ? 0.116 0.887 ? 0.023 ?1.11 ? 0.08Dynamical Mass Constraints (?6.3)WMAP7 + ACTcl(dyn) 0.116 ? 0.005 0.921 ? 0.108 0.851 ? 0.052 ?1.05 ? 0.11WMAP7 + ACTcl(dyn) + SNe 0.115 ? 0.004 0.835 ? 0.034 0.858 ? 0.049 ?1.08 ? 0.10Note ? Cluster data provide important constraints in the space of ?8, ?m and w. ACTcl resultsare presented for scaling relations based on the Universal Pressure Profile (UPP), and the B12 andNonthermal20 (Non) models; these do not include marginalization over scaling relation uncertainties.Results constrained using dynamical mass data (dyn) include a full marginalization over SZ scalingrelation parameters.123Overall, we find no disagreement between WMAP7 and the ACT cluster data for anyof the three model-based scaling relations considered. While the three scaling relationsproduce results that almost completely span the range of ?m and ?8 preferred by WMAP7,a better understanding of scaling relation parameters can provide significant improvementsin parameter constraints given even a relatively small cluster sample. This is addressed inthe next section.6.3 Parameter Constraints from Dynamical Mass DataAs an alternative to fixing the SZ scaling relation parameters based on models, in this sectionwe perform a cosmological analysis using the ACT Southern and Equatorial cluster samples,including the dynamical mass information for the Southern clusters from Sifo?n et al. (2012).The two samples are included as separate contributions to the likelihood. In this analysis,the dynamical masses directly inform the cosmology, while the selection function is under-stood in terms of the observed SZ signal, through the modeling of the cluster signal withthe UPP. In this framework the scaling relation parameters will be naturally constrained tobe consistent with the observed sample sizes and with the y?0 measurements of the clustersthat also have dynamical mass measurements.For the Equatorial clusters we apply the same sample selection criteria used in Sec-tion 6.2, and thus include the same 15 clusters. As before, these clusters contribute to thelikelihood through their observed redshifts and y?0 measurements.For the Southern cluster sample, we obtain y?0 measurements from the three-season148GHz maps as described in the Appendix. For the cosmological analysis we restrictthe Southern sample based on a signal to noise ratio threshold of y?0/?y?0 > 5.7 and anobserved redshift requirement of 0.315 < z < 1.4. The y?0/?y?0 threshold is high enough toexclude new, unconfirmed candidates in our analysis of the three-season Southern maps.The lower redshift bound restricts the sample to the clusters for which Sifo?n et al. (2012)have measured dynamical masses. This yields a sample of seven clusters, which are identifiedin Table 5.5. Of the nine clusters used in Sehgal et al. (2011), our sample includes the fiveclusters at z > 0.315. The sample includes the exceptional cluster ACT-CL J0102?4915; theinclusion or exclusion of this cluster does not change the cosmological parameter constraintssignificantly. The contribution from the Southern clusters to the likelihood is in the formof equation (6.9).The data set consisting of this combination of Equatorial SZ data and Southern SZ anddynamical mass data is denoted ACTcl(dyn). These data are combined with other datasets in an MCMC approach to parameter estimation as described in Section 6.2, exceptthat now we allow the SZ scaling relation parameters to vary, assuming flat priors overthe ranges 1.7 < Am < 0.9, ?1 < B < 3, ?2 < C < 2 and 0 < ?2int < 2. These priorsare not intended to be informative, but rather to permit the scaling relation parameters torange freely over values supported by the data. For the dynamical mass bias parameter, we1240.2 0.3 0.4?m0.81.01.2?8Figure 6.3: Constraints on ?CDM cosmological parameters from Equatorial andSouthern clusters. Results from ACTcl(dyn)+BBN+H0 (violet shading), andWMAP7+ACTcl(dyn) (green shading), which both include full marginaliza-tion over scaling relation and dynamical mass bias parameters, may be com-pared to WMAP alone (solid black lines). Dotted line shows constraints forACTcl+BBN+H0, using the same cluster sample but with the scaling rela-tion fixed to the central values obtained from the dynamical mass fit of Sec-tion 5.2.5; note the similarity to contours in Figure 6.1 obtained for EquatorialSZ data with B12 fixed scaling relation parameters. The dashed blue line showsWMAP7+ACTcl(dyn), with full marginalization over scaling relation parame-ters, but with ?dyn fixed to 1.33.apply a Gaussian prior corresponding to 1/?dyn = 1.00? 0.15,1 motivated by the results ofEvrard et al. (2008) as described in Section 5.2.5.?CDM ConstraintsThe effect of the increased freedom in the scaling relation parameters may be seen in Fig-ure 6.3, which shows the confidence regions on ?8 and ?m, in a ?CDM model, from ACTcluster data combined with BBN and H0. The scaling relation parameters are not wellconstrained without some prior information, so for this chain only we include a Gaussianprior on the redshift evolution corresponding to C = 0.0?0.5, based on the B12 model fits.Compared to results for fixed scaling relation parameters, the distribution of acceptable ?8and ?m is broader and skewed, at fixed ?m, towards high ?8.In a ?CDM model, the addition of ACTcl(dyn) data improves the constraints on ?8,?m, and h relative to WMAP7 alone by factors of 0.8 to 0.9, as can be seen in Figure 6.3.1This description of the prior is an artifact of our initial implementation of the likelihood, where theparameter describing the bias corresponded to 1/?dyn.1250.20 0.25 0.30 0.35?m0.700.750.800.850.90?8Figure 6.4: Constraints on ?CDM cosmological parameters from the combinedSouthern and Equatorial cluster samples, including dynamical mass measure-ments for the Southern clusters and full marginalization over scaling relationparameters. WMAP7 and WMAP7+ACTcl(dyn) are identified as in Fig-ure 6.3 (solid black line and green contours, respectively). Also shown areWMAP7+BAO+H0 (dotted black line) and WMAP7+ACTcl(dyn)+BAO+H0(dashed blue lines).WMAP7+ACTcl(dyn) prefers slightly larger values of ?8 than does WMAP7+BAO+H0.For the composite parameter ?8(?m/0.27)0.3, the combination of WMAP7+BAO+H0+ACTcl(dyn)improves the uncertainty by a factor of 0.6 compared to WMAP7. Parameter values arepresented in Table 6.1 and confidence regions for ?8 and ?m are plotted in Figure 6.4.Within the WMAP7+ACTcl(dyn) chain for ?CDM the dynamical mass bias parameteris pushed to ?dyn = 1.12 ? 0.17 (corresponding to 1/?dyn = 0.91 ? 0.12), a substantialchange given the prior on ?dyn. To explore the consequences of a large systematic bias inthe dynamical mass measurements, we study a ?CDM chain run with fixed ?dyn = 1.33. Wefind that ?8 and ?m move towards the central values preferred by WMAP7, with parameteruncertainty slightly reduced. The confidence contours associated with this chain can be seenin Figure 6.3.In the chains presented we have not included any intrinsic scatter in the relationshipbetween dynamical mass and halo mass, because the measurement errors on the massesare already at the 20?50% level, and because we do not use dynamical mass in the sampleselection criteria. However, large levels of intrinsic scatter in m?dyn, or correlations betweenm?dyn and y?0tr as mass proxies will affect the derived constraints to some degree. In chainsthat include a 30% scatter in the dynamical mass relative to halo mass, the central valuesof ?8, ?m, and ?8(?m/0.3)0.27 decrease by up to 20% of their quoted uncertainties. Adding1260.00.30.6?m?(eV)0.3 0.4?m0.60.70.8?80.0 0.3 0.6?m? (eV)Figure 6.5: Constraints within an extension to ?CDM that allows for non-zero neu-trino density. The data sets shown are WMAP7+BAO+H0 (dotted black lines),WMAP7+ACTcl(dyn) (green shading), and WMAP7+ACTcl(dyn)+BAO+H0 (solidblue lines).positive correlation to the scatter in m?dyn and y?0tr lowers the preferred parameter valuesfurther. Running WMAP7+ACTcl(dyn) with an additional constraint that the two proxiesscatter with correlation coefficient ? = 0.5, we obtain constraints ?8 = 0.820 ? 0.025,?m = 0.284 ? 0.025, and ?8(?m/0.3)0.27 = 0.832 ? 0.042. The addition of these two effectschanges the central parameter constraints by roughly 40% of the quoted uncertainty; limitson the intrinsic scatter and its correlation between proxies will be important in higherprecision studies.6.3.1 Neutrino Mass ConstraintsAs an extension to ?CDM, we also run chains where the cosmic mass density of neutrinos isallowed to vary. Constraints are interpreted in terms of the sum of the neutrino mass speciesaccording to the relation ??h2 =?? m?/(93 eV). Combining the ACT cluster data withWMAP7 and BAO+H0 leads to significant improvements in this constraint, as shown inFigure 6.5 and Table 6.3. For WMAP7+BAO+H0+ACTcl(dyn) we obtain an upper limit,at 95% confidence, of ?m? < 0.29 eV. The improvement in this constraint is driven bythe preference of the ACT cluster data for values of ?8 and ?m that are in the upper rangeof those consistent with WMAP . Interpretations of this preference are discussed below.127Table 6.3:Cosmological parameter constraints for ?CDM, extended with one additional parameter for non-zeroneutrino density.Parameter (?CDM + ?m?)Data set ?m ?8 h?m? (eV)95% CLWMAP7 + BAO + H0 0.282 ? 0.018 0.742 ? 0.053 0.693 ? 0.016 < 0.58WMAP7 + ACTcl(dyn) 0.325 ? 0.041 0.787 ? 0.041 0.663 ? 0.029 < 0.57WMAP7 + ACTcl(dyn) + BAO + H0 0.289 ? 0.018 0.802 ? 0.031 0.690 ? 0.015 < 0.29Note ? The cluster data greatly assist in breaking the degeneracy between ?8, ?m, and theneutrino density (as parametrized by?m?). ACTcl(dyn) results use South and Equatorial clusterdata, including dynamical mass measurements for the Southern clusters (Section 6.3).128?1.2?1.0?0.8w0. 80.25 0.30?m657075H0?1.2 ?1.0 ?0.8w0.7 0.8 0.9 1.0?8Figure 6.6: Constraints on wCDM cosmological parameters from the combinedSouthern and Equatorial cluster samples, with scaling relation parametersconstrained based on dynamical mass measurements. Data sets shown areWMAP7+SNe (dotted black lines), WMAP7+ACTcl(dyn) (green contours),and WMAP7+ACTcl(dyn)+SNe (solid blue lines). The units of H0 arekm s?1 Mpc? wCDM ConstraintsWithin a wCDM model, we consider the ACTcl(dyn) data in combination with WMAP7and with SNe (which provides important, complementary constraints on the recent cosmicexpansion history). The WMAP7+ACTcl(dyn) are consistent with WMAP7+SNe, butwith a preference (as was found in ?CDM) for slightly higher values of ?8 and ?m. Theimportance of cluster information is demonstrated by the improvement, over both WMAP7and WMAP7+SNe, in the composite parameter ?8(?m/0.27)0.4 (see Table 6.2). As a result,the main impact of adding the cluster data to either WMAP7 or WMAP7+SNe is to reducethe uncertainties in ?8 and ?m by factors of ? 0.8. The wCDM parameter constraints foreach combination of ACTcl(dyn) and SNe with WMAP7 are presented in Table 6.4, withmarginalized 2-d confidence regions shown in Figure 6.6.The slight preference of ACTcl(dyn) for higher values of ?8 and ?m than are preferredby WMAP7+SNe alone also induces a shift in the posterior distribution for w. The valueof the composite parameter w(?m/0.27) decreases by almost one standard deviation whenACTcl(dyn) are added to WMAP7 + SNe.129Table 6.4:Cosmological parameter constraints for the flat wCDM model, for various combinations of WMAP7,ACT cluster data (with scaling relation constrained using dynamical mass data), and Type Ia Supernovaeresults.Parameter (wCDM)Data set ?ch2 ?m ?8 h wWithout ACT Cluster DataWMAP7 0.111 ? 0.006 0.259 ? 0.096 0.832 ? 0.134 0.753 ? 0.131 -1.117 ? 0.394WMAP7 + SNe 0.111 ? 0.006 0.276 ? 0.020 0.791 ? 0.042 0.697 ? 0.016 -0.969 ? 0.054Dynamical Mass ConstraintsWMAP7 + ACTcl(dyn) 0.116 ? 0.005 0.237 ? 0.080 0.921 ? 0.108 0.792 ? 0.119 -1.306 ? 0.356WMAP7 + ACTcl(dyn) + SNe 0.115 ? 0.004 0.289 ? 0.017 0.835 ? 0.034 0.691 ? 0.014 -1.011 ? 0.052130?1012C0.00.51.0? int?1 0Am? 0 1 2C0.0 0.5 1.0?intFigure 6.7: Constraints on SZ scaling relation parameters from the combined South-ern and Equatorial cluster samples, ACTcl(dyn), constrained based on dynami-cal mass measurements in a cosmological MCMC. Green shaded regions are forWMAP7+ACTcl(dyn) chain; black solid lines are for WMAP7+ACTcl(dyn)but with J0102?4915 excluded from the Southern sample. Dotted lines showconstraints for ACTcl(dyn)+BBN+H0 (i.e., without CMB information), butwith a Gaussian prior on C of 0.0 ? Scaling Relation ConstraintsThe marginalized constraints on the SZ scaling relation parameters derived for the ACTcl(dyn)chains are presented in Table 5.1. The parameters indicating deviations from self-similarscaling with mass and redshift (B and C) are each consistent with 0, and consistent withthe fits to all models. The intrinsic scatter, ?int is somewhat higher than the 20% seen inthe model results, but it is not well-constrained by these data. Furthermore, since the dataspan a fairly restricted range of masses, there is significant covariance between Am, B, and?int. The value of A is provided for Mpivot = 7? 1014 h?170 M?, chosen to produce negligiblecovariance between A and B. While the cosmological results change only slightly whenJ0102?4915 is excluded from the Southern cluster sample, we note that scaling relation pa-rameters are somewhat more affected, and in particular that the slope parameter B dropsfrom 0.36 ? 0.36 to 0.06 ? 0.27 and the scatter ?int drops from 0.42 ? 0.19 to 0.33 ? 0.17.The 2-d confidence regions for scaling relation parameters are shown in Figure 6.7.We note that the constraints on cosmological parameters are due mostly to the inclusionof the dynamical mass measurements for the Southern clusters, rather than due to the SZdata of the larger Equatorial sample. However, while the removal of the Equatorial samplefrom the likelihood computation produces no change in the cosmological parameter con-131straints, it leads to a significant weakening in the SZ scaling relation parameter constraints.This is because the Equatorial sample constrains the scaling relation parameters to val-ues that predict sample selection functions consistent with the Equatorial sample size. Byincluding the Equatorial SZ measurements in the likelihood, we obtain simultaneous, self-consistent constraints on cosmological parameters and the SZ scaling relation parameters.Despite the low weight of the SZ information in the cosmological parameter constraints, itremains true that the sample is SZ selected and thus approximately mass-limited over abroad range of redshifts.6.4 Comparison to Other Cluster-Based ConstraintsWhile the ACT SZ cluster data prefer matter density parameters that are at the upper endof those supported by WMAP7 data, our results are consistent with other cluster studiesat X-ray and millimetre wavelengths.The combined X-ray, fgas, Supernovae, BAO, and CMB results of Mantz et al. (2010b)produce ?8 = 0.80 ? 0.02 (0.79 ? 0.03) and ?m = 0.257 ? 0.015 (0.272 ? 0.016) in ?CDM(wCDM); these results are marginally consistent with but lower than the results of ouranalysis. For the ACTcl(dyn)+H0+BBN run in ?CDM, we compare to the X-ray clusterstudy of Vikhlinin et al. (2009b) by computing their composite statistic ?8(?m/0.25)0.47.Our value of 0.87? 0.04 is higher than but consistent with their value of 0.813 ? 0.027.Using SPT cluster SZ and X-ray mass information, Reichardt et al. (2013) obtain ?8 and?m measurements in a combined WMAP7, high-? power spectrum, and clusters analysisthat lie slightly below the central values preferred by CMB measurements alone (includ-ing Sievers et al, in prep.). From their Figure 5 we also estimate that their cluster datain combination with H0 and BBN (i.e., without CMB information) produce a compositeparameter constraint of ?8(?m/0.27)0.3 = 0.77 ? 0.05, lower by roughly 1.3-? than eitherour WMAP7+ACTcl(dyn) or BBN+H0+ACTcl(dyn) results. Our results are in generalagreement with SPT despite several differences in the SZ signal interpretation and masscalibration, which we summarize here.SPT makes use of cluster signal simulations, analogous to the B12 models used here,in order to interpret an observable based on signal to noise ratio. In contrast, our analysisrelies instead on the assumption of a simple relation between mass and the cluster pres-sure profile. We test the PBAA approach on simulated maps based on models of clusterphysics, but we do not use these models to place priors on the scaling relation parameters.The SPT mass calibration is ultimately derived from measurements of YX, defined as theproduct of the core-excised X-ray temperature and the cluster gas mass (Kravtsov et al.,2006). The use of YX as a mass proxy has, in turn, been calibrated to weak lensing masses(Vikhlinin et al., 2009a). The slight preference of our data for higher values of ?8 and?m (for both the ACTcl(dyn) and ACTcl(B12) studies) compared to SPT may indicate acomplicated relationship between the various mass proxies.132Our results are consistent with the recent ACT angular power spectrum results (Sieverset al, in prep.), which also favour the upper limits of ?8 and ?m permitted by WMAP7,with a study of the SZ signal from the ACT Southern cluster sample (Sehgal et al., 2011),and with the ?8 constraints from the skewness analysis of the ACT Equatorial 148GHzmaps. (Wilson et al., 2012).6.4.1 ConclusionWe have presented constraints in ?CDM and wCDM models using the ACT Equatorialcluster sample for several fixed normalizations of the SZ scaling relations. In each case thecosmological constraints are consistent with WMAP . The results obtained for fixed scalingrelations demonstrate the potential for such a cluster sample to provide important newcosmological information, even for modest cluster samples, provided the systematics of theSZ?mass calibration can be better understood.We have also demonstrated cosmological constraints based on the combination of SZmeasurements and dynamical mass data, in which the four parameters of the SZ scalingrelation are calibrated simultaneously with cosmological parameters. The results providesignificant constraints that are complementary to CMB, BAO, and Type Ia Supernovaedata. The scaling relation parameters obtained in this analysis are consistent with the B12model and inconsistent with the normalization arising directly from the UPP.Immediate improvement in the cosmological constraining power can be obtained throughimproved calibration of the SZ mass relation. This is underway in the form of a campaignto collect dynamical mass data for the Equatorial sample (Sifo?n et al, in prep.). Thecurrent analysis would also benefit from an improved understanding of any systematicbiases in the measurement of halo mass using galaxy velocity dispersions. In addition tothe dynamical mass data, we are pursuing weak lensing (e.g., Miyatake et al., 2013), X-ray(e.g., Menanteau et al., 2012), and additional SZ (e.g., Reese et al., 2012) measurementsto improve constraints on the SZ?mass scaling relation from the ACT cluster sample. Allsuch mass measurements can be easily included in our formulation. The sample of clustersappropriate for our approach to the cosmological analysis will grow as targeted follow-upon the Equatorial field candidates is completed to lower S/N ratios.While this work presents a new way to quantify the SZ-mass relation for 1015 M? clus-ters, we note that it is but one component of a growing web of observation that tie opticaland SZ data together. Recently the Planck team presented results (Planck Collaboration XI,2013) on the SZ emission from SDSS galaxies that extended the SZ-mass relation down to1013 M? systems and showed that the gas properties of dark matter haloes are similar tothose in massive clusters.133Chapter 7ConclusionWe have presented work related to aspects of the ACT instrumentation, characterization,and scientific results. We review these results critically in the broader contexts of modernCMB observatories and the era of precision experimental cosmology. While we have so farneglected to mention the first cosmological results from the Planck satellite1, we introducethem at this time. We touch briefly on our discussion of the MCE, beams, and planetsbefore returning to clusters and cosmological constraints.Within the world of millimetre wavelength observatories, the MCE has proven to be avery effective instrument for controlling and reading out large arrays of TES bolometers.CMB experiments are pushing to ever higher bolometer counts in order to expand frequencycoverage, collecting area, and field of view. Following on the successful use of this hardwarein SCUBA2 and ACT, the MCE has become a popular choice in ground-based telescopes,and will soon fly on a balloon-based telescope as well. The system is sufficiently flexiblethat recent major changes in SQUID multiplexing technology have easily been integratedinto the software without any need for hardware redesign.For ACT, beam measurements are clearly important to the understanding of the angularpower spectrum, point source studies, and for the measurement of planet brightness. Thebeam is also essential to the accurate transfer of calibration from large angular scales, whereACT and WMAP both have some sensitivity, to the intermediate and smaller angular scalesat which ACT is most sensitive. The techniques adopted in this work take careful accountof the covariance in the beam error across angular scales, to ensure that systematic biasesare not mistaken for uncorrelated random error.Our ability to characterize the beam was limited by the the small window of time duringwhich Saturn was visible over the course of each season. While we overcame the dearthof Saturn observations by constraining an empirical model for focus quality using frequentmeasurements of the much dimmer Uranus, a stronger understanding of the variations inbeam shape and gain might be achieved if some physical model for the mirror deformation1The Planck results were released in March, 2013, after the analyses presented in this work had beencompleted and submitted for publication.134were incorporated.The measurements of Uranus and Saturn brightness temperatures are of unprecedentedprecision, due to the calibration of the ACT maps using the CMB aniostropies. Subsequentmeasurements of the Uranus temperature by Planck in similar bands have since been pub-lished, and are in excellent agreement with the ACT results. This provides an importantcross-check of the ACT and Planck calibrations, and demonstrates that ACT has goodcontrol over beam systematic issues.The main scientific results of this work are the ACT Equatorial cluster sample, themethods for interpretation of the Sunyaev-Zeldovich signal, and the resulting study of cos-mological constraints and the mass relation calibration. ACT realizes the SZ promise ofproducing a roughly mass-limited sample of clusters to arbitrarily high redshift. While onlya modest fraction of the clusters are new discoveries, this is due in part to the choice tocenter the Equatorial field on the site of a very deep optical survey. While optically-selectedcluster catalogues on this region contain hundreds or thousands of clusters, the SZ sampleis not weighted towards low redshift, low mass clusters.Compared to the Planck SZ cluster survey (Planck Collaboration XXIX, 2013), whichcovers up to 86% of the sky, the smaller fields studied by ACT and SPT yield fewer extremelymassive clusters. However, the Planck survey, though covering a much larger sky fraction,does not probe to high redshift as effectively, due to its somewhat larger beam (FWHM of7.3? at 143 GHz). Regardless, we still have cause to believe that the SZ signal is the massproxy with the least intrinsic scatter, and any one of these SZ selected samples provides ahigh quality list of targets for follow-up observations. Each group has obtained, or is in theprocess of securing, a variety of optical and X-ray observations to better understand highmass clusters over a broad redshift range.The Profile Based Amplitude Analysis presented in Chapter 5 is not trivial to implementand interpret, but is promising in several ways. The method is based on the assumptionthat the sample will be obtained from matched filtering of a map, and makes use of thecluster redshift information in a self-consistent way. In constrast to approaches that try tomeasure Y500 directly, our method explicitly acknowledges the difficulties of distinguishingcluster signals in the presence of strong noise on large angular scales.While one sacrifices a certain amount of signal by using a single filter instead of anoptimization over cluster scale, the very act of not optimizing means that there is lessopportunity for noise bias. With large SZ samples in hand, one should be more concernedabout redshift dependent, mass dependent systematic biases than about signal to noiseratios on individual clusters. We expect the y?0 statistic to be more stable than scale-optimized techniques in the presence of CMB fluctuations, in the sense that it shouldsuffer fewer non-Gaussian excursions due to scale-dependent Gaussian noise. In this work,however, we have not provided compelling evidence for significantly reduced bias; this shouldbe studied further.135We have, at least, demonstrated the success of the PBAA in modeling the mass andredshift dependence of the survey selection function, and we are able to fit the sample?sredshift distribution with only ?8 as a free parameter. The agreement of our SZ massmeasurements with measures from SPT and from X-ray and weak lensing measurements isalso encouraging.Our cosmological constraints are limited by uncertainties in the calibration of the massscaling relation. We have addressed this by showing results for a variety of scaling relationparameter sets, in the hope that future work will justify the choice of one set of param-eters over the others. Ultimately we choose to pay the most attention to the dynamicalmass measurements, because they constitute independent mass measurements over a broadredshift range. Within the values of ?8 and ?m favoured by CMB measurements from theWMAP seven-year results, the dynamical mass measurements lead to a preference for thehighest values, while the direct propagation of the Universal Pressure Profile from X-raymeasurements leads to a preference for the lowest values. The difference in mass scalebetween those two extremes is roughly a factor of two.The recent Planck cluster cosmology results (Planck Collaboration XX, 2013) find a sim-ilar level of discrepancy, though between the cluster-based constraints and the constraintsfrom the CMB (Planck Collaboration XVI, 2013). The Planck cluster analysis relies onthe UPP and makes effectively the same assumptions as our baseline UPP analysis. ThePlanck CMB analysis yields ?m and ?8 that are well above the values preferred by thePlanck cluster analysis, consistent with a factor of 2 difference in the mass calibration.Whether this apparent discrepancy turns out to be due to unexpected biases in X-raycluster masses and scaling relations or to some unforeseen physical phenomena in galaxyclusters or the early Universe, this issue warrants further investigation. With any luck, thesolution may be very interesting.The mission of large-aperture ground-based millimetre wavelength observatories contin-ues, in the Planck era, as measurements of the intermediate and small scale features of theCMB provide an important complement to other cosmological probes. 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