UC Berkeley UC Berkeley Electronic Theses and Dissertations Title Measurements of Secodary Cosmic Microwave Background Anisotropies with the South Pole Telescope Permalink https://escholarship.org/uc/item/1m21q7w6 Author Lueker, Martin Van Publication Date 2010 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California Measurements of Secondary Cosmic Microwave Background Anisotropies with the South Pole Telescope by Martin Lueker A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor William Holzapfel, Chair Professor John Clarke, Professor Geoffrey Bower Fall 2010 Measurements of Secondary Cosmic Microwave Background Anisotropies with the South Pole Telescope Copyright 2010 by Martin Lueker 1 Abstract Measurements of Secondary Cosmic Microwave Background Anisotropies with the South Pole Telescope by Martin Lueker Doctor of Philosophy in Physics University of California, Berkeley Professor William Holzapfel, Chair The South Pole Telescope is a 10m millimeter-wavelength telescope for finding galaxy clusters via the thermal Sunyaev-Zel'dovich (tSZ) effect. This thesis is divided into two parts. The first part describes the development of the kilopixel SPT-SZ receiver and the frequency-domain multiplexor (fMUX). The second part describes the first SPT power spectrum measurement and the first detection of the tSZ power spectrum. The SPT-SZ focal plane consists of 960 spiderweb coupled transition-edge sensors. Due to strong electro- thermal feedback, these devices have good sensitivity and linearity, though risk spontaneous oscillations. Adding heat capacity to these devices can ensure stability, so long as the loopgain, , is less than Gint=G0, the ratio between the thermal conductances linking the TES toL the heat capacity and linking the heat capacity to the bath. I describe as experimental technique for measuring the internal thermal structure of these devices, allowing for rapid sensor evaluation. The fMUX readout system reduces wiring complexity in this receiver by AC- biasing each sensor at a unique frequency and sending signals from multiple bolome- ters along one pair of wires. The Series SQUID Arrays (SSAs) used to read changes in bolometer current are notably non-linear and extremely sensititve to ambient mag- netic fields. The SSAs are housed in compact magnetic shielding modules which reduces their effective area to 80 mΦ0=gauss. The SSA are fedback with a flux-locked loop to improve their linearity and dynamic range, and decrease their input reac- tance. The FLL is bandwidth of 1 MHz with a measured loopgain of 10. In the current implementation, this bandwidth is limited between the SQUID input coil and other reactances, which I study in Chapter 4. In the second part of the thesis I present power spectrum measurements for the first 100 deg2 field observed by the SPT. On angular scales where the primary CMB anisotropy is dominant, ` . 3000, the SPT power spectrum is consistent with the stan- dard ΛCDM cosmology. On smaller scales, we see strong evidence for a point source contribution, consistent with a population of dusty, star-forming galaxies. I combine the 150 and 220 GHz data to remove the majority of the point source power, and 2 use the point source subtracted spectrum to detect Sunyaev-Zel'dovich (SZ) power at 2:6 σ. At ` = 3000, the SZ power in the subtracted bandpowers is 4:2 1:5 µK2, which is significantly lower than the power predicted by a fiducial model using± WMAP5 cos- mological parameters. i To my dear|and extremely patient|wife, Sirena. Your support and encouragement made all of this possible. ii Contents List of Figures vi List of Tables ix 1 Cosmological Background 1 1.1 The Smooth Expanding Universe . .1 1.2 Experimental Evidence for Dark Energy . .3 1.2.1 Type Ia Supernovae . .3 1.2.2 The Cosmic Microwave Background . .3 1.2.3 Large-Scale Structure and Baryon Acoustic Oscillations . .5 1.2.4 Beyond the Cosmological Constant: The Dark Energy Equation of State . .6 1.3 The Non-linear Growth of Structure . .7 1.4 Constraining Dark Energy with the Galaxy Clusters and the Sunyaev- Zel'dovich effect . .9 1.5 The Power Spectrum of the tSZ Effect . 10 1.6 Other Contributions to the Microwave Power Spectrum . 13 1.7 The State of tSZ Power Spectrum Measurements Before the SPT . 14 I Building a TES Bolometer Array for the South Pole Telescope 17 2 Transition Edge Sensor Bolometers 18 2.1 Electrothermal Feedback . 19 2.1.1 Frequency Response of a TES Bolometer . 22 2.1.2 Electrothermal Feedback Stability . 23 2.2 TES Noise . 23 2.2.1 Photon Noise Terms . 25 2.2.2 Thermal Fluctuation Noise . 26 2.2.3 Johnson Noise . 26 2.2.4 Readout Noise . 27 iii 2.3 Summary . 27 3 Frequency Domain Multiplexed SQUID Readout 28 3.1 System Overview . 28 3.2 Shunt-Feedback SQUID Controllers . 31 3.2.1 SQUIDs as Current Transducers . 31 3.2.2 Properties of Shunt-Fedback SQUIDs . 32 3.2.3 Implementation: SQUID Controller . 35 3.3 Oscillator Demodulator Boards . 38 3.4 Cold SQUID Housing . 40 3.4.1 Expected Shielding Performance . 41 3.4.2 Measured Performance . 43 4 Flux-locked Loop Stability 48 4.1 Stability . 49 4.1.1 Poles, Delays, Resonances and Zeroes . 49 4.1.2 Zeroes and the Lead-Lag Filter . 52 4.2 Simulating and Measuring SQ ..................... 52 4.3 Transmission lines: 4K to 300KL . 55 4.4 Role of the SQUID input coil . 61 4.5 Bolometers Gone Superconducting . 62 4.6 Other Sub-Kelvin Strays . 64 4.6.1 Enhancements From a Lead-Lag Filter . 66 4.7 Summary . 68 5 Thermal Design of the SPT Pixels 70 5.1 Spiderweb-coupled TES Bolometers . 70 5.2 ETF Stability . 71 5.2.1 Bound Thermal Oscillations . 72 5.2.2 BLING Coupling Requirements for ETF Stability . 72 5.3 Measuring of the Internal Thermal Structure of the TES . 75 5.3.1 Measuring sI (!).......................... 76 5.4 Summary . 80 6 The South Pole Telescope 82 6.1 Atmospheric Conditions at the South Pole . 82 6.2 Telescope and Optical Design . 84 6.3 Cryogenics . 86 6.3.1 The Optics Cryostat . 86 6.3.2 Receiver Cryostat . 86 6.4 Focal Plane Module Design . 88 6.5 Instrument Performance . 90 iv 6.5.1 Bandpass Performance . 90 6.5.2 Calibration and Optical Efficiency . 91 6.5.3 Noise and Sensitivity . 92 6.5.4 Beam Measurements . 94 6.6 Summary . 96 II SZ Power Spectrum Constraints 98 7 The High-` SPT Power Spectrum 100 7.1 2008 Observations . 100 7.2 Timestream processing and Map-making . 101 7.2.1 Data Selection . 102 7.2.2 Time-Ordered Data (TOD) Filtering . 102 7.2.3 Map-making . 103 7.3 Maps to Bandpowers . 104 7.3.1 Apodization Mask and Calculation of the Mode-mixing Kernel 105 7.3.2 Fourier Mode Weighting . 106 7.3.3 Transfer Function Estimation . 107 7.3.4 Frequency-differenced Spectra . 108 7.4 Systematic checks . 110 7.5 Power Spectrum . 113 8 Cosmological Interpretation of the SPT Power Spectrum 116 8.1 Foregrounds . 116 8.2 DSFG-subtracted Bandpowers . 119 8.2.1 Residual Point Source Power . 123 8.2.2 Residual Clustered Point Source Power . 124 8.3 Markov Chain Analysis . 126 8.3.1 Elements of the MCMC Analysis . 126 8.3.2 Constraints on SZ amplitude . 128 8.4 Implications of the ASZ Measurement . 131 A Generalized Equations of Motion for TES Devices with Detailed Thermal Structure 152 A.1 Solving for sT (!), G(!), and sI (!)................... 154 A.2 Relating sI (!) to G(!).......................... 155 A.2.1 Expressing the Equations in Terms of G(!).......... 155 B Johnson Noise in AC-biased TESs 158 B.1 Conventions . 158 B.1.1 Power-to-Current Sensitivity, Noise PSDs, and NEPs . 159 B.2 Equations of Motion . 161 v B.2.1 Steady-state solution . 161 B.2.2 Perturbations in Ohms Law . 162 B.2.3 Perturbations in the Conservation of Energy Equation . 163 B.2.4 Voltage Fluctuations Internal to the Bolometer Island . 164 B.2.5 Comparison to DC biased systems . 164 B.3 Noise . 165 B.4 Responsivity and NEP . 167 C Bandpower Covariance Matrix Estimation 170 C.1 Analytical Considerations . 170 C.2 The Empirical Covariance Estimator . 173 C.2.1 Multifrequency Cross Covariances . 174 C.2.2 Treatment of Off-diagonal Elements . 175 vi List of Figures 1.1 Cosmological constraints from Type Ia supernovae . .4 1.2 Large- to intermediate-scale CMB anisotropies. .5 1.3 Constraints on Ωm and ΩΛ from the CMB . .6 1.4 Constraints on Ωm and ΩΛ combining CMB, Type I Sne and BAO, .7 1.5 The abundance of galaxy clusters above a given mass threshold,Mth, as a function of w ............................. 11 1.6 An analytical prediction of the tSZ power spectrum from Komatsu & Seljak (2002). 12 1.7 The galaxy cluster populations probed by the tSZ spectrum, as a func- tion of multipole . 13 2.1 A Schematic Voltage-Biased Bolometer. 19 2.2 The resistance vs. temperature dependence of an Al-Ti bilayer near the superconducting transition temperature. 20 3.1 A schematic overview of the frequency-domain multiplexor. 29 3.2 I{V and V –Φ curves for a NIST 8-turn series SQUID array (SSA) . 32 3.3 A photograph of the 8-channel SQUID Controller. 36 3.4 Simplified schematic of a single SQUID Controller channel . 37 3.5 A magnetically shielded SQUID module. 41 3.6 A measurement of the magnetic shielding efficiency of the fMUX SQUID module.