close

Вход

Забыли?

вход по аккаунту

?

A measurement of the cosmic microwave background polarization with the south pole telescope

код для вставкиСкачать
THE UNIVERSITY OF CHICAGO
A MEASUREMENT OF THE COSMIC MICROWAVE BACKGROUND POLARIZATION
WITH THE SOUTH POLE TELESCOPE
A DISSERTATION SUBMITTED TO
THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES
IN CANDIDACY FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
DEPARTMENT OF ASTRONOMY AND ASTROPHYSICS
BY
ABIGAIL TINNEY CRITES
CHICAGO, ILLINOIS
DECEMBER 2013
UMI Number: 3606308
All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent upon the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
UMI 3606308
Published by ProQuest LLC (2013). Copyright in the Dissertation held by the Author.
Microform Edition © ProQuest LLC.
All rights reserved. This work is protected against
unauthorized copying under Title 17, United States Code
ProQuest LLC.
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, MI 48106 - 1346
c 2013 by Abigail Tinney Crites
Copyright All Rights Reserved
TABLE OF CONTENTS
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
1
INTRODUCTION . . . . . .
1.1 CMB Polarization . . . .
1.1.1 Testing ΛCDM .
1.1.2 Neutrino Masses
1.1.3 Inflation . . . . .
1.2 SPTpol Science . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1
2
3
4
4
5
2
THE INSTRUMENT . . . . . . . . . . . . . . . . . . . . . . . .
2.1 The South Pole Telescope . . . . . . . . . . . . . . . . . . .
2.2 The SPTpol Receiver . . . . . . . . . . . . . . . . . . . . .
2.2.1 Voltage-Biased Transition Edge Sensor Bolometers .
2.2.2 90 GHz Design and Fabrication . . . . . . . . . . .
2.2.3 150 GHz Detector Design and Fabrication . . . . . .
2.2.4 SPTpol Array Properties . . . . . . . . . . . . . . .
2.2.5 Cryogenic and Mechanical Design and Performance
2.2.6 The DFMUX Readout . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
9
9
10
10
13
18
18
22
30
3
DATA COLLECTION AND ANALYSIS . . . . . . .
3.1 Observation Strategy . . . . . . . . . . . . . . .
3.1.1 Field Depth . . . . . . . . . . . . . . . .
3.2 Data Processing . . . . . . . . . . . . . . . . . .
3.2.1 Data Flagging . . . . . . . . . . . . . . .
3.2.2 Downsampling and Timestream Filtering
3.2.3 Telescope Pointing . . . . . . . . . . . .
3.2.4 Relative Calibration . . . . . . . . . . .
3.2.5 Polarization Calibration . . . . . . . . .
3.2.6 Bolometer Cuts . . . . . . . . . . . . . .
3.2.7 Map Making . . . . . . . . . . . . . . .
3.2.8 Data Cuts . . . . . . . . . . . . . . . . .
3.2.9 Map Bundles . . . . . . . . . . . . . . .
3.2.10 Temperature Projection . . . . . . . . . .
3.2.11 2012 Season CMB Maps . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
33
33
34
38
39
39
41
41
41
42
45
45
46
48
49
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
iii
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4
POWER SPECTRUM ANALYSIS . . . . . . . . . . . . . . .
4.1 The Cross-Spectrum Analysis . . . . . . . . . . . . . .
4.1.1 Sky Window Function . . . . . . . . . . . . . .
4.1.2 Beams . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Mode Mixing . . . . . . . . . . . . . . . . . . .
4.1.4 Transfer Function . . . . . . . . . . . . . . . . .
4.1.5 Covariance Matrix . . . . . . . . . . . . . . . .
4.1.6 Systematic Tests . . . . . . . . . . . . . . . . .
4.1.7 Map Based Jackknives . . . . . . . . . . . . . .
4.1.8 Systematic Effects from Detector Non-Idealities
4.1.9 Jackknife Results and Implications . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
56
56
57
58
58
59
59
65
65
67
67
5
RESULTS . . . . . . . . . . . . . . . . .
5.1 TE and EE Polarized Power Spectra
5.2 Lensing B-Mode Detection . . . . .
5.3 Discussion . . . . . . . . . . . . . .
5.4 Conclusions and Future Work . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
73
73
73
75
76
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
iv
LIST OF FIGURES
1.1
1.2
1.3
The CMB Angular Power Spectrum as Measured by the SPT . . . . . . . . . . . . . .
The CMB Angular Power Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . .
Current State of Measurements of the CMB Polarization Power Spectrum . . . . . . .
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
2.21
2.22
2.23
2.24
The SPT in the Dark Sector . . . . . . . . . . . . . . .
The SPT Optics Cryostat . . . . . . . . . . . . . . . .
Bolometer Sketch . . . . . . . . . . . . . . . . . . . .
TES Bolometer Resistance vs Temperature Curve . . .
90 GHz TES Bolometer Current, Voltage and Power .
Crossed 90 GHz Pixel . . . . . . . . . . . . . . . . . .
90 GHz Contoured Feedhorn . . . . . . . . . . . . . .
90 GHz Module Assembly . . . . . . . . . . . . . . .
NIST 150 GHz TES and Feedhorn Arrays . . . . . . .
150 GHz Detector . . . . . . . . . . . . . . . . . . . .
UofC Dark Testing Board: Front . . . . . . . . . . . .
UofC Dark Testing Board: Back . . . . . . . . . . . .
150 GHz Detector NETs . . . . . . . . . . . . . . . .
90 GHz Detector NETs . . . . . . . . . . . . . . . . .
SPTpol Bands . . . . . . . . . . . . . . . . . . . . . .
3 He-3 He-4 He Chase Cryogenics Refrigerator . . . . .
SolidWorks Model of the Focal Plane Support Structure
Focal Plane Support Structure . . . . . . . . . . . . .
A Typical 3He Refrigerator Cycle . . . . . . . . . . .
The 3He Refrigerator Cycle Time . . . . . . . . . . .
Bolometer Stage Temperature . . . . . . . . . . . . .
Digital Frequency-Domain Multiplexing Readout . . .
SQUID Voltage versus Phi . . . . . . . . . . . . . . .
Network Analysis . . . . . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
10
11
13
14
14
16
16
19
19
20
20
21
22
23
24
26
27
28
29
29
30
31
32
32
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
The SPT Survey Fields . . . . . . . . . . . . . . . . . . . . .
The Lead Trail Fields . . . . . . . . . . . . . . . . . . . . . .
The Power Spectrum of a Difference Map . . . . . . . . . . .
Timestream Glitches . . . . . . . . . . . . . . . . . . . . . .
Polarization Angle Calibration . . . . . . . . . . . . . . . . .
Cross Polarization . . . . . . . . . . . . . . . . . . . . . . . .
Polynomial Filtered Timestream . . . . . . . . . . . . . . . .
Map Cut Metrics . . . . . . . . . . . . . . . . . . . . . . . .
The SPTpol RA23h30DEC-55 Field: 150 GHz, Temperature .
The SPTpol RA23h30DEC-55 Field: 150 GHz, Q Polarization
The SPTpol RA23h30DEC-55 Field: 150 GHz, U Polarization
The SPTpol RA23h30DEC-55 Field: 90 GHz, Temperature . .
The SPTpol RA23h30DEC-55 Field: 90 GHz, Q Polarization .
The SPTpol RA23h30DEC-55 Field: 90 GHz, U Polarization .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
35
36
37
40
43
44
47
48
50
51
52
53
54
55
v
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
6
7
8
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
Sky Window Function . . . . . .
Transfer Function . . . . . . . . .
Mode Mixing Matrix . . . . . . .
The SPTpol Real Space Beams . .
The SPTpol Space Beams . . . .
The SPTpol Beam Uncertainties .
An Example Jackknife Test . . . .
Ground Pickup . . . . . . . . . .
Difference Map of Simulated Data
150 GHz Detector Non-Linearity .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
60
61
61
62
63
64
66
68
71
72
5.1
5.2
5.3
5.4
150 GHz EE Power Spectrum
150 GHz TE Power Spectrum
Lensing B-Mode Detection . .
Lensing B-Mode Detection . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
74
74
75
76
.
.
.
.
.
.
.
.
vi
LIST OF TABLES
2.1
2.2
2.3
2.4
2012 Season Filter Configuration
90 GHz Detector Dimensions . .
Array Properties . . . . . . . . .
Total Array NET . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3.1
3.2
3.3
Observing Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
150 GHz Map Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
90 GHz Map Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1
4.2
4.3
4.4
Jackknife Results, Naive Analysis . . . . . .
Jackknife Results, Aggressive Analysis . . .
Jackknife Results with Simulated Expectation
Jackknife Results with Simulated Expectation
vii
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
12
15
22
23
70
70
71
71
ACKNOWLEDGMENTS
None of this work could have been completed without all the members of the South Pole Telescope
collaboration. I was lucky to spend my time on SPT working with the wonderful grad students at
Chicago especially Lindsey and Tyler, my constant companions in lab at different ends of grad
school, who shared my joy and frustrations many late nights in LASR. I learned so much from the
postdocs Clarence, Brad, Jared, and Stephen. I was also incredibly lucky to be part of the SPTpol
receiver team with Liz, Jason, and Brad. I was constantly impressed by their work. I learned from
them and generally just had a ton of fun deploying SPTpol with them. And of course none of this
would have been possible without my brilliant, kind, inspiring advisor, John Carlstrom. Outside of
the lab, Ashlee Gabrysch gave me constant encouragement and support and Alissa Bans was with
me every step of the way as we finished out theses this summer. Though their influence started
much earlier, my parents and sister were with me on this journey and deserve more thanks that I
can express.
viii
ABSTRACT
We present maps of the cosmic microwave background (CMB) polarization at 90 and 150 GHz
measured with SPTpol and the first EE and TE CMB power spectrum measurements from SPTpol.
We also describe the SPTpol instrument in detail. We discuss the development of the SPTpol
camera including the cryogenic design and the transition edge sensor (TES) detectors developed
at NIST and Argonne National Laboratory. The goals of the SPTpol project are to exploit the
high resolution of the telescope (1 arcminute beam) and the high sensitivity afforded by the 1536
detector camera to measure the E-mode power spectrum of the CMB, characterize the B-mode
polarization induced by the gravitational lensing of the primordial E-mode CMB polarization, and
to detect or set an upper limit on the level of the B-mode polarization from inflationary gravitational
waves. This thesis is a first step toward acomplishing these goals. Measuring the E-mode power
spectrum will allow us to improve constraints on parameters of the current cosmological models
that are sensitive to the damping tail of the CMB.
ix
CHAPTER 1
INTRODUCTION
Measurements of the cosmic microwave background (CMB) radiation have shaped our understanding of fundamental physics, cosmology and the large-scale structure of the universe. This “relic”
radiation consists of photons that last scattered ∼ 370,000 years after the big bang, when the universe expanded and cooled enough for photons and baryons to decouple. The CMB is extremely
uniform across the sky — with small fluctuations of less than a part in 104 . Over the last 50 years,
increasingly sensitive measurements of the CMB, combined with measurements of galaxies and
supernovae, have led to our current understanding of cosmology and the emergence of a standard
cosmological model. The universe began in a hot big bang, and has been cooling and expanding
over cosmic time. Its composition can be described by four components. Firstly, dark energy, a
form of energy which is responsible for the accelerating expansion of the universe, accounts for a
large fraction of the energy density of the universe today. A smaller fraction consists of dark matter, a non-luminous form of matter that does not interact electromagnetically. The third component
of the energy density of the universe today is in baryons, the matter which composes visible dust,
stars, and galaxies. The fourth component, radiation, is a small fraction of the energy density today
but was dominant in the early universe. This is well described by a theoretical framework known as
the ΛCDMcosmological model (where Λ represents the dark energy component, and CDM stands
for cold dark matter). This model has six free parameters: the comoving baryon density Ωb h2 , the
comoving density of cold dark matter Ωc h2 , the optical depth to recombination τ , the angular scale
of the sound horizon at last scattering Θs , the amplitude of the primordial density fluctuations As ,
and finally the scalar spectral index ns .
The existence of the CMB was predicted in the 1940s as a product of a hot big bang model of
the universe (Gamow, 1940). It was discovered in 1964 (Penzias & Wilson, 1965) providing solid
evidence of an expanding universe and the hot big bang model. This primordial blackbody radiation, which peaked in the optical wavelengths at the time of emission, cooled with the expansion
of the universe and presently has a temperature of ∼ 3 K. The blackbody spectrum and hence the
1
temperature of the CMB was measured with the COBE satellite in the early 1990’s (Mather et al.,
1994).
Current models predict along with CMB measurements, that density perturbations in the early
universe were very small, and described by a nearly scale-invariant Gaussian random field. Prior
to recombination, the tightly coupled baryon-photon plasma underwent acoustic oscillations. A
snapshot of these oscillations is observed today as anisotropy of the observed CMB temperature.
These small temperature differences as a function of position on the sky are termed primary CMB
anisotropy.
Because the CMB photons trace the density fluctuations in the early universe at the time of
decoupling, and the linear physics governing the evolution prior to decoupling is well understood,
measurements of primary CMB anisotropies allow us to probe density inhomogeneities in the early
universe that lead to the structure we see today. The first detection of primary anisotropy was made
by the DMR instrument on the COBE satellite (Smoot et al., 1992). A theoretical power spectrum
of the CMB, is shown in Fig. 1.2.
Over the last two decades, the temperature anisotropy of the CMB has been measured over
a wide range of angular scales and significant cosmological inferences have been made. Early
measurements of the acoustic peaks in the CMB power spectrum (e.g. de Bernardis et al. (2000);
Halverson et al. (2002); Hanany et al. (2000)) provided strong evidence that we live in a flat universe. Recent measurements include those by the Planck (Planck Collaboration et al., 2013),
WMAP (Komatsu et al., 2011), the South Pole Telescope (SPT) (Keisler et al., 2011; Reichardt
et al., 2012; Story et al., 2012), and the Atacama Cosmology Telescope (ACT; Das et al., 2011)
have tightly constrained the key parameters governing the ΛCDM model and have begun to place
constraints on subtleties of our cosmological paradigm.
1.1
CMB Polarization
Current CMB temperature measurements provide powerful constraints on cosmology but also
leave us with tantalizing questions about cosmology and fundamental physics. These questions
2
include:
1. Are extensions to the ΛCDM model (e.g., varying number of effective neutrino species,
Neff , non-zero neutrino mass, Σmν ) necessary to describe upcoming data sets?
2. Did our universe begin with a rapid period of inflation?
Measurements of the polarization of the CMB radiation are a promising way to address these
questions. Throughout this work we refer to two types of CMB polarization: the polarization signal
can be decomposed into what are commonly referred to as “E-mode” (gradient-like) and “B-mode”
(curl-like) signals, where the nomenclature is derived from electrostatics. This decomposition
facilitates cosmological analysis because the different patterns are sourced by different physical
phenomena. The E-mode polarization was detected in 2002 (Kovac et al., 2002) and has since
been measured by a number of experiments. See Quiet Collaboration (2012) for a compilation of
recent CMB polarization measurements. Some current measurements of the CMB power spectrum
are shown in Fig. 1.3.
In the next few subsections we discuss the specific motivations for CMB polarization observations that address the questions outlined above.
1.1.1
Testing ΛCDM
Temperature measurements of the CMB over a wide range of angular scales have been used to
constrain the six parameter ΛCDM model. While the E-mode power spectrum carries some of the
same information as the temperature power spectrum, these measurements can increase precision
on cosmological parameters in the range of angular scales where the measurements are already
cosmic variance limited. Additionally, foregrounds (i.e., dusty galaxies, galaxy clusters, galactic sources) that contaminate the temperature measurements at large angular scales are predicted
to be at a lower amplitude in polarization. Reduced foregrounds will allow the measurements
by polarization-sensitive instruments to be done over a larger range of angular scales and should
improve the cosmological parameter constraints. In particular, polarization data will improve con3
straints on: Neff , the number of effective neutrino species in the early universe, Σmν , discussed
above, and Yp , the primordial fraction of baryonic mass in helium. Current E mode measurements
have not had sufficient precision to improve cosmological parameters (Pryke et al., 2009).
1.1.2
Neutrino Masses
Atmospheric neutrino oscillation experiments have measured a difference in mass between two
neutrino eigenstates of 0.05 eV and hence directly constrain the sum of the neutrino masses to
Σmν ≥ 0.05 eV (Araki et al., 2005). CMB temperature measurements have begun to place interesting upper limits on the sum of the neutrino masses (Hou et al., 2012). Measurements of the
CMB polarization will provide a complementary way to constrain the neutrino masses through
the following mechanism. B-mode polarization is generated from the gravitational lensing of the
CMB by large-scale structure. This signal is dominant in the range of a few hundred to a few
thousand. The amplitude of the B-mode lensing signal in the polarization power spectrum depends
on the sum of neutrino masses, Σmν (Lesgourgues et al., 2006). This is due to the fact that a finite
amount of the matter density is in the form of neutrinos, suppressing the amount of structure on
scales smaller than the neutrino free-streaming length.
1.1.3
Inflation
CMB data, along with other cosmological probes, are consistent with the theory that the universe
underwent a period of rapid expansion, known as inflation (Guth, 1981), that took place ∼ 10−35
seconds after the big bang. In fact, it is difficult to explain the geometric flatness of the universe
and the homogeneity and isotropy of the universe without an inflationary theory. However, there
have been no direct measurements confirming the theory of inflation because it is experimentally
challenging to probe the physics of the universe either directly or with particle accelerators since
the energy where this effect took place is much higher than the energies reached by current accelerators. Gravitational waves in the early universe sourced by inflation will impart a very small
B-mode polarization signal at large angular scales of = 50-100 (scales of 1 degree on the sky,
4
the horizon scale at decoupling). The strength of the signal from the inflationary gravity waves
is parametrized by the tensor to scalar ratio, r. In simple models of inflation, the strength of the
inflationary gravity waves is directly related to the energy scale of inflation (Hu & Dodelson, 2002)
as E ∼ 3.0x1016 GeV r1/4 .
The CMB polarization is one of a few experimental probes of inflation and, as such, could lead
to a new understanding of physics at the highest energy scales.
1.2
SPTpol Science
The temperature power spectrum of the CMB has been measured over a wide range of angular
scales with increasing precision over the last few years with experiments such as the SPT. The
current generation of experiments, with added polarization sensitivity (in particular, SPTpol) are
designed to tackle the remaining questions that are not informed by temperature measurements
alone. In particular, Σmν and r.
This dissertation will discuss the unique challenges associated with the measurement of the
CMB E-mode and B-mode polarization signals. I will detail the design and development of the
SPTpol instrument which was developed to meet these challenges. I will describe the assembly
of the camera, the data collection process and analysis pipeline. In the instrument section I focus
my work on the receiver mechanical design and assembly and 90 GHz detector assembly. In the
analysis section I focus on describing my work on map making, cuts, and the power spectrum
analysis. I also report preliminary science results from the first season of SPTpol observations:
temperature and polarization maps from both the 90 and 150 GHz bands of SPTpol and a precise
measurement of the E-mode power spectrum.
The instrument is discussed in Chapter 2, the data processing in Chapter 3, the power spectrum
analysis in Chapter 3, and finally the science results in Chapter 4.
5
Figure 1.1: The CMB Angular Power Spectrum measured with the South Pole Telescope.
SOURCE: Story et al. (2012).
6
10
10
10
10
3
2
1
0
2
( +1)C /2π (μK )
10
4
10
10
10
10
-1
-2
-3
-4
TT
10
10
10
10
-5
EE
-6
-7
BB
lensing BB
inflationary BB
-8
10
2
10
3
10
4
Figure 1.2: The CMB Angular Power Spectrum. Red: The temperature power spectrum of the
primary CMB anisotropy sourced from the acoustic oscillation in the early universe. Green: The E
mode power spectrum also sourced from the acoustic oscillation in the early universe. Blue: The
B mode signal from the lensing of E mode polarization by large scale structure for a model with
Σmν = 0 (dot-dashed). The B mode signal from gravitational waves in the early universe for an r
value of 0.1 (dashed).
7
2
l(l+1)Cl / 2π (μK )
10
2
EE: >2σ detections
10
1
BICEP
QUaD
QUIET-W
WMAP
-1
10
CBI
CAPMAP
Boomerang
DASI
-2
10
10
2
BB: 95% confidence upper limits
10
1
10
10
10
-1
-2
-3
10
2
10
3
Multipole l
Figure 1.3: The current state of measurements of the CMB polarization power spectrum compiled
by Cynthia Chiang. The black line shows the theoretical curve for a ΛCDM cosmology with r =
0.1. As shown in the bottom panel the B-mode polarization has yet to be detected.
8
CHAPTER 2
THE INSTRUMENT
2.1
The South Pole Telescope
The South Pole Telescope (SPT) is a 10 meter telescope at the South Pole designed to measure
the cosmic microwave background built in 2006 (Carlstrom et al., 2011). The observing site for
the South Pole telescope is the Dark Sector Laboratory at the South Pole, Antarctica. An aerial
photograph of the SPT and surrounding buildings can be seen in Fig. 2.1.
The SPT is an off-axis Gregorian design with a 1 degree field of view and arcminute resolution
at 150GHz. The primary mirror has a surface error of ≤ 20 μm RMS (Carlstrom et al., 2011).
The secondary mirror is 1.2 meters in diameter and is housed in a cryostat, which is cooled to 10K
with a Cryomech Pulse Tube Cooler (PTC), (Cryomech Inc., model PT4101 ). The inside of the
secondary cryostat is absorptive. This 10 K absorptive material acts as a cold stop in the optics. The
camera for the SPT is housed in a separate cryostat that shares a vacuum with the optics cryostat.
This assembly can be seen in Fig. 2.2. The wide field of view and arcminute resolution make the
SPT an ideal instrument for doing large surveys and measuring the anisotropy of the CMB from
degree scales out to of 10,000. The optical elements in the SPT telescope, described in detail
in Padin et al. (2008) and George et al. (2012), are summarized here. The incoming radiation is
reflected by the primary mirror and goes through a 100 mm thick expanded polypropylene foam
(Zotefoam PPA302 ) window into the optics cryostat. It then passes through a set of filters that are
intended to block high frequency radiation. The radiation then reflects off of the secondary mirror
and passes through a lens and lens filter. It then passes through another set of filters that block high
frequency radiation and define the bandpass of the instrument. Finally the radiation is incident on
the focal plane. These optical elements and their temperature and frequency cutoff, if applicable,
are summarized in Table 2.1.
1. Cryomech Inc., Syracuse NY 13211
2. Zotefoams PLC, Croydon CR9 3AL UK
9
Figure 2.1: The SPT resides approximately 1 km from the geographic south pole. It is located at
the Dark Sector Laboratory (DSL). Figure credit: NSF
2.2
The SPTpol Receiver
The SPTpol receiver is the second camera to be installed on the South Pole Telescope. This camera
was deployed in the Austral summer of 2011-2012 and achieved first light in January of 2012. It
is designed to measure the polarization of the cosmic microwave background over a wide range of
angular scales (from degree scales out to of 10,000). The camera consists of ∼ 1600 polarization
sensitive transition edge sensor (TES) bolometers developed at Argonne National Labs (ANL) and
National Institute for Standards and Technology (NIST).
2.2.1
Voltage-Biased Transition Edge Sensor Bolometers
The sensors in the SPTpol camera are Transition edge sensor (TES) bolometers. These devices are
the most common technology used in the current generation of CMB instruments. Their popularity
is owed to their high sensitivity per focal plane area and ease of high throughput fabrication.
A schematic of a bolometer can be seen in Fig. 2.3. A classic bolometer is a temperature sensor
10
Window
Heat Blocking
Filters
Pulse Tube
Refrigerator
Lens
Focal
Plane
Secondary
Mirror
Cold Stop
and Radiation
Shields
Figure 2.2: A cross-section view of the SPT optics and receiver cryostats.
11
Element
Te [K]
Frequency Cutoff
Bolometer
.25
–
Horn
.25
–
Band-def filters
.25
5.7 icm @ 150 GHz, 3.7 icm @ 90 GHz
Harmonic blocker
.25
6.2 icm
IC blocker
.50
7.8 icm
Lens
6.00
.–
Lens filter
6.00
7 icm
Secondary
10.0
.–
10 K filter
10.0
10 icm
IR shader
100.0
. ∼ 100 icm
70 K filter
100.0
12 icm
IR shader
100.0
∼ 100 icm
IR shader
100.0
∼ 100 icm
Window
300.0
–
Primary
220.0
–
Table 2.1: The 2012 Season Filter Configuration. Each optical element is shown with its temperature and frequency cutoff, if applicable.
coupled to optical radiation through an absorber. The absorbed radiation heats the sensor and the
resistance of the sensor changes with the temperature of the sensor (Mather, 1982).
A TES bolometer is a specialized bolometer where the thermometer is made from superconducting material. Superconducting materials undergo a transition between normal electrical resistance and zero electrical resistance at a characteristic temperature, known as the “transition temperature”. At the transition temperature the TES changes electrical resistance very rapidly with
small changes in temperature. Fig. 2.4 shows a sketch of the steep resistance versus temperature
curve for a bolometer. A constant voltage bias is applied to the TESs and the device is held in the
superconducting transition by electro-thermal feedback (ETF) (Lee et al., 1996).
The power dissipated on the device, Ptotal , is a combination of the electrical power applied
through the electronics and optical power from the sky and telescope (Ptotal = Poptical +Pelectrical ).
In the case of strong electro-thermal feedback P is constant, so an increase in Poptical will cause a
decrease in Pelectrical . Since the voltage (V) is constant the change in Pelectrical is measured as a
changing current by the readout system.
12
Figure 2.3: A classic bolometer consists of an absorber with a weak thermal link to a cold bath.
When optical radiation hits the detector it heats up briefly. This change in temperature is measured
by a thermometer.
The electrical bias required to operate the TES bolometer stably on its superconducting transition without saturating the detector is a function of the strength of the weak thermal link to the
cold bath, and the optical power on the detector. Fig. 2.5 shows the current (I) measured through
a TES versus the voltage (V) applied to the TES measured as well as the resistance R versus the
power (P) for the same detector. The detector shown is a SPTpol 90 GHz detector.
2.2.2
90 GHz Design and Fabrication
The 90 GHz detectors for SPTpol are absorber coupled TES bolometers fabricated at Argonne
National Labs (ANL) (Sayre et al., 2012). There are 180 polarization-sensitive 90 GHz pixels (360
detectors) deployed in the SPTpol receiver. A pair of 90 GHz detectors is shown in Fig. 2.6. Each
90 GHz detector consists of a Pd-Au alloy dipole absorber and a Mo/Au bilayer TES suspended on
a low-stress silicon nitride island. The absorber is designed to couple to radiation through a singlemoded waveguide. The coupling of the radiation to the absorber was modeled and optimized using
HFSS(McMahon et al., 2009). HFSS is a finite element method solver used for radio frequency
(RF) design. The dimensions of the detector structure are detailed in Table 2.2. Details of the
13
Figure 2.4: The resistance of a transition edge sensor (TES) bolometer versus its temperature.
The resistance of the device falls sharply at the transition temperature of the superconductor. This
characteristic leads to the high responsivity of this type of device.
Figure 2.5: Top: The current versus voltage of a 90 GHz transition edge sensor (TES) bolometer.
Bottom: The resistance versus power curve for the same device.
14
detector design and fabrication are described in Yefremenko et al. (2009) and Sayre et al. (2012).
Each pixel consists of an individual contoured feedhorn module containing a pair of crossed
detectors. The contoured, monotonic feedhorn design was chosen for its polarization properties
as well as the low cost to machine the horn. A drawing of the contoured feedhorn is shown in
Fig. 2.7. Conical feedhorns are inexpensive to make but were not be used for SPTpol because they
introduce significant beam ellipticity. Corrugated feedhorns have excellent polarization properties
but are expensive to machine.
Absorber width
18 μm
Absorber length
1300 μm
Distance between absorbers
25 μm
Waveguide diameter
2350 μm
Distance from absorber to backshort
1080 μm
Width of waveguide break
150 μm
Width of choke
840 μm
Distance from TES to waveguide
150 μm
1 μm
SiN film thickness
thermal island length x width
thermal standoff leg length x width
3300 μm x 200 μm
1350 μm x 10 μm
70μm x 40 μm
TES length x width
Table 2.2: Dimensions of 90 GHz Detector Structures The dimensions of the 90 GHz detector
structure shown in Fig. 2.6.
The 90 GHz detectors were fabricated on a 3 inch array and diced into individual detectors.
Each array consisted of 25 detectors. Once the pixels are mounted in their optical modules removing them can be a destructive process, so the single detectors were electrically and thermally tested
before mounting in the final holders. Detectors that were not functional or did not meet a required
specification were discarded. A special printed circuit board (PCB) was designed at the University
of Chicago and fabricated commercially by Advanced Circuits 3 for this testing. The design and
3. http://www.4pcb.com/
15
Figure 2.6: A crossed 90 GHz pixel. Pd-Au antennas suspended on a silicon nitride membranes
absorb radiation. TESs measure the power incident on the detector. Image reproduced from Crites
et al. (2011).
Figure 2.7: The 90 GHz contoured feedhorn (Bleem et al., 2012) defines the beam function of the
instrument. This feed horn is inexpensive to machine and has low ellipticity (Sayre et al., 2012).
16
fabrication involved close collaboration with the Advanced Circuits because special features such
as untinned pads over portions of the PCB were required. One side of the PCB was a copper sheet
with bond pads for the detectors Fig. 2.11. The other side of the board contained the detector leads
and inductors and capacitors for the LC resonance circuits needed to readout the detectors (see
Fig. 2.12 and Sec. 2.2.6 for more information). The boards have the capacity to test 32 detectors
at once.
In the case where all detectors on a wafer could not be tested due to time constraints and testbed availability, the wafers were spot-checked. It was possible to take this shortcut because the
detector properties were found to be very uniform within a given wafer.
After screening the individual pixels, the 90 GHz single pixels modules were placed in the
machined aluminum holders (Fig. 2.8). The detector holders were machined from aluminum in
large batches and gold plated. The aluminum holders were designed to fit two pixels, one for each
polarization. The modularity of the holders allows the ability to swap detectors.
Superconducting pins made from tinned stainless steel take the signals from the detector boards
to the printed circuit board that is used for readout. The pins have a tear-shaped copper tab soldered
to one end to provide a surface to wire-bond the detector to the lead.
The assembly of over 200 detector modules took place over a period of months. The steps were
staggered in an assembly line procedure doing multiple different steps on ∼10 modules per day.
The steps were performed as follows:
1. Electroplate stainless steel pins with tin.
2. Solder the tear-shaped copper tab to one end of each stainless pin.
3. Cover with a Teflon tube to electrically isolate the pin from the aluminum holder.
4. Slip the pins through the holes in the aluminum holder and glue into place with Stycast 2850
and allow to dry overnight.
5. Place the first pixel in the detector holder, registering with tweezers to a reference edge, and
glue in place with GE varnish.
17
6. Dry the bottom pixel overnight.
7. Place wire-bonds on the frame of the bottom pixel to physically separate them ensuring the
adsorbers don’t contact each other. The separation of the pixels is ∼ 25 um.
8. Place a second pixel with orthogonal polarization on top, registering it to the bottom pixel
by under a microscope using lithographed reference crosses and glue in place
9. When the glue is dry, place wirebonds connecting the copper tabs on the electrical leads to
the niobium pads on the detector chips.
10. Place the feedhorn on the module and screw in place. Alignment pins register the feedhorn
with the bottom of the module.
11. Tape the module with aluminum tape to create an RF tight seal.
This process is illustrated in Fig. 2.8.
2.2.3
150 GHz Detector Design and Fabrication
The 150 GHz portion of the focal plane is composed of seven detector modules each containing
84 pixels. The 150 GHz modules each consist of a 2.3 inch wide monolithic feedhorn array and
a detector array fabricated at NIST see Fig. 2.10 and Fig. 2.9. Incoming power from the sky is
coupled to an orthomode transducer (OMT), which splits the light into two orthogonal polarization
states. The signal then travels through microstrip to the transition edge sensors (TES). The TES
sensors are made of an aluminum manganese alloy. See Henning et al. (2012) for additional details.
2.2.4
SPTpol Array Properties
There are several properties of the TES detectors that must be optimized for low noise performance in a mm-wave camera. First, the normal resistance of the detector must be compatible with
the readout technology. The SPTpol target normal resistance was∼ 1 Ω. The noise performance of
18
90 GHz Holders
Gold-Plated Holder with Bias Pins
90 GHz Detectors
Glued Bottom Pixel
Wire-bonds for Separation
Glued Top Pixel
Crossed Pixel
Fully Assembled Modules
Module in Mounting Plate
Figure 2.8: The ANL/KICP 90 GHz Pixels were assembled by hand over a period of 3 months in
2011 by UofC graduate students and postdocs.
Figure 2.9: Left: A 150 GHz detector array fabricated at NIST. Right: A 150 GHz feedhorn array.
19
Figure 2.10: A 150 GHz detector. Incoming power from the sky is coupled to an orthomode
transducer (OMT) fins, which splits the light into two orthogonal polarization states. The signal
then travels along microstrip and is deposited on the TESs.
Figure 2.11: 90 GHz detectors are placed on the copper surface of the PCB and glued with
removable rubber cement. Wire-bonds make the electrical connection from the detectors to the
circuit board.
20
Figure 2.12: The LC resonance circuits on the 90 GHz test board. Capacitors are soldered to the
test board and inductors are glued and wirebonded.
the detectors depends on both the transition temperature of the TES and the strength of the thermal
link to the cold bath, so these must be targeted and carefully controlled during detector fabrication.
Additionally, the time constants of the detectors must be fast enough that the detectors can equilibrate when scanning across the sky. The array averaged properties for the SPTpol detectors are
given in Table 2.3.
The optical bandpasses of the arrays were chosen to use as much of the available bandwidth
between the atmospheric lines without incurring noise penalties by including too much power in
the wings of the atmospheric lines. The SPTpol bands with respect to the atmospheric lines are
shown in Fig. 2.15. A measurement of the bandpasses using a Fourier Transform Spectrometer
(FTS) showed that the high edge of both the 90 and 150 GHz bands were lower than specified.
This was corrected for the 2013 observing season by replacing the bandpass filters.
The noise equivalent temperature (NET) of the detectors quantifies the sensitivity of the detectors to sky signals. The NETs for SPTpol are calculated using noise stares, combined with
measurements of RCW38. Fig. 2.13 and Fig. 2.14 show the NET distributions for the 150 and 90
GHz portions of the focal plane. Table 2.4 shows the array averaged NETs. The array average
21
TES Normal Resistance (Rn )
Transition Temp (Tc )
Nominal Operation Point
Saturation Power at 278mK
Optical Time Constant
90 GHz
1.0 ± 0.1 Ω
535 ± 35 mK
.74 ± .02 Rn
44 ± 11 pW
2.10 ± .78 ms
150 GHz
1.2 ± 0.2 Ω
478.0 ± 28.6 mK
.78 ± .01 Rn
22.4 ± 5.7 pW
.45 ± .23 ms
Table 2.3: 90 and 150 GHz detector array parameters adapted from George et al. (2012).
Figure 2.13: 150 GHz Detector NETs for the 2012 Season Array Configuration.
NET determines the mapping speed of the instrument.
2.2.5
Cryogenic and Mechanical Design and Performance
The 300 mK operating temperature of the detectors make the cryogenic and mechanical design a
crucial part of the instrument development.
The ultra sensitive TES detectors operate at a temperature of 300 mK. The focal plane containing the 1600 detectors, is located in a pulse tube cooled cryostat that isolates the detectors from
the ambient environment. The ∼ 300 mK operating temperature is reached with a multiple stage,
22
Figure 2.14: 90 GHz Detector NETs for the 2012 Season Array Configuration.
150 GHz 90 GHz
Total Array NET(uKcmb (s))
20.9
42.0
Table 2.4: The array NETs for 90 and 150 GHz. The array average NET determines the mapping
speed of the instrument
23
Figure 2.15: The 90 GHz (Red) and 150 GHz (Green) bands for SPTpol during the 2012 season.
Predicted second year SPTpol bands are shown in black The bandpass filters for both 90 and
150 GHz were replaced with ones of a higher cutoff frequency in Austral summer 2012-13. The
curve defined by the line between the gray shaded region and the white region is the atmospheric
transmission for 0.25 mm percipitable water vapor (PWV), typical for the atmosphere above the
South Pole.
closed cycle 3 He-3 He-4 He fridge manufactured by Chase Cryogenics (model CRC0314 )
The focal plane is heat sunk to the ∼ 300 mK “ultra cold” or “UC” stage of the 3 He-3 He-4 He
refrigerator. This stage is isolated from 4 K with a stage at ∼ 500 mK and a stage at ∼ 1.5 K.
The 500 mK stage is cooled by the the interhead cold (“IC”) and the stage 1.5 K stage by heat
exchanger (“Hex”) of the 3 He-3 He-4 He refrigerator. Fig. 2.16 shows a schematic of the fridge.
Vespel5 , a plastic with very low thermal conductivity, provides the mechanical support for the
stages. A photograph of the tiered stage structure can be seen in Fig. 2.18. A SolidWorks model
(Fig. 2.17) shows the design more clearly.
The wiring from the bolometers on the UC stage is intercepted at the intermediate stages to
reduce the heat loading on the cold stage from the ambient environment. The loading from the
Vespel legs, detector and thermometer readout wiring, and optical power contribute ∼ 100 μW of
4. Chase Research Cryogenics Ltd., Sheffield S10 5DL UK
5. Professional Plastics, 5500 South Cobb Dr., Smyrna, GA. 30080
24
power on the IC stage and ∼ 6 μW of power on the UC stage.
The equilibrium stage temperatures are dependent on the cooling power of the refrigerator and
the total loading on the stages. UC and IC stage temperatures during the 2012 season can be seen
in Fig. 2.21
The SPTpol focal plane cannot be operated continuously at 300 mK. The 3He refrigerator is
cycled approximately every 36 hours. The fridge cycle is controlled by a cryoelectronics board6
designed to set the voltages of the heaters and sensors in the cryostat and read out the thermometers
in various locations in the cryostat. Silicon diodes are used to measure the temperature of the
cryostat that are above 1 K. Precisely calibrated Cernox temperature senseors7 are used to measure
the sub-Kelvin temperatures.
The 3 He-3 He-4 He refrigerator is cycled using a Python script, FridgeClientSPTpol, that has
been optimized to achieve the highest duty cycle from the fridge. The steps in this optimized cycle
are laid out in the appendix. A typical cycle is shown in Fig. 2.19. The refrigerator hold times and
cycle times throughout the season are shown in Fig. 2.20.
The thermal structure and focal plane described above are mounted in the receiver cryostat.
The receiver cryostat has nested radiation shields at ∼ 50 K and ∼ 4 K and a vacuum jacket at
300 K. The 300 K, 50 K and 4 K shields are mechanically attached using a thin G10 mount with
very low thermal conductivity. A pulse tube cooler (Croyomech model PT-415) is used to cool
the shields. The pulse tube cooler provides 1.35 W of cooling power at 4.2 K and 36 W at 45 K.
In the SPTpol cryostat there is about 20 W of loading on the 50 K shield from radiation, the G10
support structure, and wiring. Radiation is the most significant source of loading at 50 K and for
this reason the shields are covered in several layers of reflective aluminum coated Mylar sheets to
make them more reflective. There is about 0.25 W of loading on the 4 K stage, the majority of
that load coming from wiring and the G10 standoff. The cooled shields reduce the radiation and
thermal loading on the focal plane to an acceptable level.
6. http://www.mcgillcosmology.ca/cryoelectronics
7. http://www.lakeshore.com/products/Cryogenic-Temperature-Sensors/Pages/
default.aspx
25
Figure 2.16: A 3 He-3 He-4 He Chase Cryogenics Refrigerator is used to cool the focal plane to
300 mK. Figure adapted from Bhatia et al. (2000). The refrigerator is cycled by first heating the
charcoal pumps to expel the helium gas. The 4 He condenses into the still because the condensation
point (CP) is heat sunk to a bath that is below the temperature at which 4 He condenses. The 4 He
pump is then cooled which caused the charcoal to absorb helium. This creates low pressure in
the vessel and lowers the temperature of the 4 He to below the condensation point of 3 He. 3 He
condenses in both 3 He stills. After the 4 He has evaporated, the 3 He pumps are cooled. The low
pressure above the 3 He brings the fridge to its base operating temperature. It remains at base
temperature until the 3 He has evaporated.
26
Figure 2.17: The SolidWorks model of the SPTpol focal plane support structure. The optical axis
points up in this view. The ultra cold or “UC” is in the center of the structure. The Vespel legs
(teal) on the outer support structure isolate the UC stage from the 4 K shell of the cryostat. UC
stage and cooled to ∼ 300 mK with a 3He closed cycle refrigerator.
27
Figure 2.18: The SPTpol focal plane removed from the cryostat. The optical axis points down
to the lab bench in this view. The ultra cold or “UC” is in the center of the structure. The brown
Vespel legs on the outer support structure isolate the UC stage from the 4 K shell of the cryostat.
UC stage and cooled to ∼ 300 mK with a 3He closed cycle refrigerator.
28
Figure 2.19: The 3He refrigerator needs to be cycled approximately every 36 hours. The temperature of the refrigerator and attached stages are shown during the cycle.
Figure 2.20: The length of the fridge cycle (green) and the time available for observation (blue).
The region from November 2012 - February 2013 shows large scatter because the receiver was
being upgraded and the refrigerator was not being cycled in normal operation mode.
29
Figure 2.21: The median UC stage temperature was 0.278 K. The median IC stage temperature
was 0.451 K. The region from November 2012 - February 2013 shows large scatter because the
receiver was being upgraded and the refrigerator was not being cycled in normal operation mode.
Upgrades done between the 2012 and 2013 observing season reduced the loading on the IC and
UC stages, causing them to reach lower base temperatures in 2013.
2.2.6
The DFMUX Readout
The SPTpol detectors are read out with a digital frequency-domain multiplexing (DFMUX) system. The multiplexing factor allows twelve detectors to be read out with a single pair of wires,
reducing the thermal load on the cold stage. A schematic of the DFMUX readout is shown in
Fig. 2.22.
The SPTpol readout system consists of cryogenically cooled analog electronics paired with
digital electronics at room-temperature that control the biasing of the detectors and readout the
signals from the cryostat (Dobbs et al., 2008).
The sub-Kelvin electronics consist of the TES bolometers, each with its own LC resonance
circuit. PCBs with the LC resonance circuits are mounted off the back of the focal plane and can
be seen in Fig. 2.18. For the SPTpol experiment there are 12 bolometers on each pair of wires.
This is referred to as a comb of detectors. The capacitors and inductors were chosen such that the
12 bolometers would be spaced at 60 kHz intervals from 200 kHz to 1 MHz. Fig. 2.24 shows a
30
Figure 2.22: The SPTpol digital frequency-domain multiplexing (DFMUX) system. The multiplexing factor allows twelve detectors to be read out with a single pair of wires, reducing the
thermal load on the cold stage. The SPTpol readout system consists of cryogenically cooled analog electronics paired with digital electronics at room-temperature that control the biasing of the
detectors and readout the signals from the cryostat. SOURCE: de Haan et al. (2012).
comb of detectors measured during SPTpol deployment.
Superconducting wire takes the signals from the bolometer LC resonance circuits to the 4K
stage of the cryostat. At 4K the signals from the 12 bolometers on a comb are measured by a
single, very sensitive ammeter, a Superconducting Quantum Interference Device (SQUID).
SQUIDs consist of two Josephson junctions on opposite sides of a wire loop. When the current
across a SQUID exceeds the critical current of the superconducting junctions, the voltage, V ,
around the loop is determined by the magnetic flux, Φ and is periodic (Clarke, 1996). Current
is coupled to the SQUID using an inductive coil. 144 SQUIDs are required to read out the full
complement of SPTpol detectors. The 144 SQUIDs are mounted on 18 circuit boards with 8
SQUIDs each. The SQUIDs were screened prior to deployment, and in the receiver testing at the
South Pole. The voltage versus Φ or “VPhi” curves are measured for each SQUID to insure that
they can be properly biased. Measurements of a functioning SQUID are shown in Fig. 2.23.
The signals going to and from the SQUID board at 4K are fed through to the 300K warm
electronics. The 300K electronics consist of a SQUID controller board which controls the bias on
the SQUIDS and a DFMUX board which contains an FPGA which controls the detector biasing
and readout.
31
Figure 2.23: Voltage versus Φ curves for a SQUID. When the current across the SQUID exceeds
the critical current, the voltage across the SQUID is periodic in the flux, Φ, through the loop. The
SQUID bias current is chosen to maximize the amplitude of this sine wave because the dynamic
range of the SQUID readout depends on this quantity.
Figure 2.24: The response of the detector comb as a function of frequency. Each peak represents
a bolometer with the frequency set by its LC resonance circuit.
32
CHAPTER 3
DATA COLLECTION AND ANALYSIS
3.1
Observation Strategy
The first year of the SPTpol survey covered the 100 deg2 square patch of sky centered at right
ascension 23h30min and declination -55 degrees, henceforth referred to as the SPTpol 23h30 field.
This location was chosen to overlap the SPT-SZ deep field, where there are rich data sets in multiple
wavelengths allowing for the complementary and joint analysis of data from SPT-SZ, SPTpol, and
other surveys.
The SPT-SZ and SPTpol fields were chosen to be in a region of very low Galactic dust emission in the southern sky. The SPT survey field locations can be seen in Fig. 3.1.1 The SPTpol
observations of the 23h30 field used in this analysis were acquired between March and November
2012.
The field was observed by scanning the telescope back and forth in azimuth and then stepping
in elevation, until the full field was covered. The field was observed using lead-trail scanning (e.g.
Pryke et al. 2009), a method that allows for an analysis that protects against systematics induced by
coupling to emission from ground sources (such as buildings or other structures near the telescope
site). In this work an observation is defined as a single lead or trail scan. For the observations,
the field is divided into two pieces each covering five degrees of right ascension and 10 degrees of
declination. The timing of the observation is such that by the time the first field has been observed
the sky has rotated so that the second field is over the same ground as the first. As such, the size of
the elevation steps are chosen so that the field can be observed in half an hour. The elevation steps
for this field are ∼ 15 arcminutes. During the CMB power spectrum analysis the data from the two
fields can be subtracted to remove the common ground component. The field divided into a lead
and trail pair can be seen in Fig. 3.2. We dither the observations of the field in elevation, changing
1. http://irsa.ipac.caltech.edu/data/Planck/release_1/all-sky-maps/maps/COM_
CompMap_dust-commrul_2048_R1.00.fits
33
Observation
Time (hh:mm)
Cycle Fridge
07:15
CenA
00:35
CMB Field Observations
18:40
Calibration and Overhead
5:50
RCW38
00:42
Cal vs El
00:44
Cal Sweep
0:22
Percent of Cycle
21
2
55
17
2
2
1
Table 3.1: A detailed accounting of the times spent on the different type of observations. 55 % of
the cycle is spent on the CMB field. The rest of the time is spent cycling the 3He refrigerator and
on auxiliary observations needed for array calibration.
the starting position of the observation by ∼ 1 arcminute to get more even field coverage. The
precise pointing of the telescope during each schedule (how long is each scan, what are the field
centers, etc.) are defined in an observation schedule that the telescope control computer uses to
command the telescope. We used two different observation schedules in 2012. The first schedule
did not have enough overlap between the lead and trail fields which created a shallow strip at the
border between the field. The second half of the season had a deep strip to compensate for the
shallow strip in the beginning of the season such that the full set of data from the 2012 season
would have uniform coverage.
Due to the nature of the cryogenics of the SPTpol the telescope operated on a ∼ 36 hour cycle
(see Chap. 2 for details). Each pair of lead and trail fields is observed ∼ 20 times every 36 hours.
The duty cycle on the CMB field is detailed in Table 3.1.
The full field (one set of lead and trail pairs) was observed approximately 2500 (5000 total
observations) times in 2012. In addition to the CMB observations, we obtained calibration data as
detailed in Sec. 3.2.
3.1.1
Field Depth
Each individual CMB observation has noise comparable to the level of the CMB signal. This
noise is dominated by contributions from the atmosphere and the instrument itself. We achieve
34
Figure 3.1: The SPT survey field locations are shown superimposed on the Planck thermal dust
map. The range of the Planck spans 0 to 1 M Jy/sr. The SPT fields were chosen to be in the
regions of very low dust emission (dark regions) in the southern sky. The plane of our galaxy can
be seen in red.
35
Figure 3.2: The SPT survey field locations are shown again this time superimposed on the Planck
150 GHz CMB map 3 . The units on the Planck map are in units of μKCMB, from -400 to +400.
The galaxy saturates the plot using this scale. The SPTpol 23h30 field is shown divided in to the
lead and trail fields.
36
Figure 3.3: The power spectrum of a difference map of the CMB field. The CMB signal has been
subtracted away leaving only the noise in the map. The noise level in the temperature signal is
lower above of 2000, but rises sharply at low due to atmospheric noise. The noise level in the
polarization signal does not have the same behavior at low because the atmosphere is unpolarized
(Battistelli et al., 2012).
a high signal-to-noise measurement of the CMB by repeated measurements of the field. When
the observations are added together the sky signal adds coherently and the sources of noise add
incoherently. We choose a metric for the noise in an observation which is the noise level in the range of 1000-3000 assuming white noise. To measure the noise level in the CMB field we divide
the data in half and make coadds of each half. We the subtract the two halves to remove the CMB
signal leaving only the noise. We call the resulting map a difference map or noise map. The power
spectrum of a difference map of the field can be seen in Fig. 3.3. The atmospheric noise dominates
the T map at much higher than in the polarization map where the noise is white down to of 1000.
For the data used in this analysis that noise level is 10 μK-arcminat 150 GHz in the polarization
and 7.5 μK-arcminin temperature.
37
3.2
Data Processing
Before CMB maps are made, the raw timestream data must be calibrated and bad data must be
flagged. This process is done in the following steps which are described in detail in the rest of this
chapter:
Pre-processing:
1. Read in raw time ordered data at full sampling rate of 190.92 Hz
2. Flag data that have glitches from cosmic rays, etc.
3. After subtracting a polynomial, calculate the RMS for each scan in an observation and flag
scans with RMS 3.5 times higher than the median or 0.25 times lower than the median of the
RMS for all scans
4. Downsample the raw data by a factor of 4
5. Apply pointing corrections to the data
6. Apply a notch filter to the data that removes lines in the data from instrumental noise that is
isolated in frequency space
7. Use auxiliary data to calibrate the data and convert it to units of TCMB
8. Mark timestreams failing data cuts
9. Save the data in intermediate data files (IDFs)
Map-making:
1. Read in IDF
2. Apply polynomial and low pass filters to the data
3. Bin the timestreams into map pixels
4. Cut maps that do not pass certain data quality thresholds
38
3.2.1
Data Flagging
Data is flagged on a “by scan” basis if there are glitches or DC jumps in the data. There are
three different phenomena that cause these artifacts, examples of which are plotted in Fig. 3.4.
First, cosmic rays incident on the bolometer absorber can cause sharp spikes in the bolometer
timestream. Second, we occasionally observe discrete DC jumps in the bolometer timestream that
are likely caused by a change in the SQUID bias point. Affected detectors are flagged for the rest
of the observation. The third type of glitch is of unknown origin and an example can be see in
the lower right panel of Fig. 3.4. If a bolometer is flagged more than 5 times per observation the
bolometer timestream is flagged as bad for the entire observation. Additionally, data is flagged
if the RMS of the data in a given scan is 3.5 time higher than the median RMS or less than 0.25
times the median for bolometers within the same module during the same observation. This last
flagging step is done after a polynomial (see below) removed. Data that is flagged in this step is
not included in the maps. This removes 5 percent of the data.
3.2.2
Downsampling and Timestream Filtering
The SPTpol data is acquired at a rate of 190.92 Hz. Since we scan at a rate of 0.4178 degrees per
second on the sky, this sampling rate retains information about modes out to of ∼ 80,000. For
this analysis we only need to measure power at <5,000. For this reason we downsample the data
by a factor of 4. Before downsampling we apply a low-pass filter with a cutoff at 21 Hz to avoid
aliasing high frequency noise into the signal band. We apply a fourth order polynomial filter to
the time ordered data (TOD) to remove atmospheric and other low frequency noise along the scan
direction. Fig. 3.7 shows an example bolometer timestream before and after polynomial filtering.
A low pass filter that cuts off at 14 Hz is also applied to each bolometer timestream.
39
a. Nominal Timestream
b. Cosmic Ray Hit
c. DC Jump
d. Unknown Cause
Figure 3.4: Data is flagged for individual bolometer timestreams on a scan-by-scan basis if a glitch
appears. The glitches can be caused by a cosmic ray hitting the detector or by a SQUID moving in
its bias point. This bias shift causes a DC jump in the timestream level. Additionally oscillations
of unknown origin may appear in a timestream. Cutting timestreams with glitches removes ∼ 3 %
of the data.
40
3.2.3
Telescope Pointing
The pointing for the SPTpol data is calculated with a model that uses daily measurements of
Galactic HII regions, RCW38 and Mat5a, and information from sensors on the telescope structure
that measure temperature, position, and tilt (Carlstrom et al., 2011). The pointing of the telescope
can be off by ∼ 10 arcminutes prior to applying the corrections determined by the model. After the
pointing corrections are applied the scatter between the pointing of different observations during
the season is ∼ 12 arcseconds.
3.2.4
Relative Calibration
The relative calibration between the SPTpol detectors is done using measurements of the HII region
RCW38 and measurements of a source inside the cryostat. This calibration is especially important
for polarization measurements because a calibration error between pixels can induce temperature
to polarization leakage. This method was first used in the SPT-SZ analysis. We take the power
on the detectors in Watts measured by the readout system (Sec. 2.2.6) and convert it to CMB
equivalent temperature units, TCMB .
We use several different types of observations for this calibration. First we measure the response of the bolometers to a chopped internal thermal source. We also observe RCW38 by rastering the array across the source to measure its flux with each bolometer.
Next, we combine the calibrator stare and RCW38 observation, that occurred just prior to the
CMB field observation with a set of season averages of the calibrator and RCW38 responses.
This bootstrapping of the calibration accounts for variations in bolometer tuning, gain drifts, and
atmospheric opacity on a bolometer by bolometer basis.
3.2.5
Polarization Calibration
The polarization angles of the bolometers must be measured to accurately reconstruct the Stokes
Q and U maps. This calibration is done once per season with a chopped external source near the
41
far-field, 3 km from the telescope. The polarization calibration source consists of a blackbody
source with two wire grids placed in front of it. One grid is stationary, while the other is allowed
to rotate. The stationary grid provides a source of known polarization. The entire source is placed
in the center of a reflecting panel designed to reflect most of the telescope beam onto the sky, so
the detectors are not saturated by pointing at the warm horizon. The telescope is then pointed at
this source and, locking in on the chopped signal, the response to the polarization calibrator is
measured at many angles with as many detectors as possible. This measurement is complicated
by the fact that some bolometers saturate when looking very low in elevation owing to the loading
from the atmosphere and the ground. The results of the polarization calibration measurement are
shown in Fig. 3.5 and Fig. 3.6. We measure individual bolometer polarization angles to within 2
degrees (with the array-averaged polarization angle measured to better than 0.1 degrees). We also
measure the median polarization efficiency of our bolometers to be 98.1 % at 150 GHz and 98.7 %
90 GHz. Cross checks of the polarization angle measurement are currently being done using the
astronomical source Centarus A.
3.2.6
Bolometer Cuts
Individual bolometers are cut from each observation based on a number of different criteria. First
all flagged bolometers are cut. As discussed above, examples of events that cause bolometers
to be flagged are having too many glitches in a single observation or if the SQUID attached to
that bolometer has been turned off. Bolometers are also cut if they do not have have polarization
calibration data or if they do not have pointing data. During the 2012 season, all bolometers in the
C4 module were cut due to excess noise for all detectors in the module. This module was replaced
for the 2013 season. Bolometers with a low response to the internal calibrator or with low response
to two degree elevation dips known as elnods are also cut. For this analysis “low” is signal-to-noise
ratio of less than 10 for the calibrator and 100 for the elnod response.
42
Figure 3.5: The measured polarization angles minus their nominal angles are plotted versus nominal angle for the 90 and 150 GHz detectors. The sinusoidal pattern and the scatter in angle between
detector modules may be due to the receiver and telescope optics, but are not yet fully understood.
43
Figure 3.6: The measured cross polarization versus nominal polarization angle for 90 and 150
GHz. The varying scatter in the measurement as a function of detector angle is not well understood.
44
3.2.7
Map Making
We bin the timestreams into Stokes Parameters T, Q, and U pixels based on their pointing information and their polarization angles. Timestreams are weighted by the inverse of the variance of
the timestream between 1 Hz and 3 Hz and the polarization efficiency of each detector. Weight
maps that represent the number of times a pixel is hit by a bolometer multiplied by its inverse noise
variance, are created as well.
We make maps in a flat-sky approximation, using the oblique Lambert azimuthal equal-area
projection with 0.5 arcminute pixels at 150 GHz and 1.0 arcminute pixels at 90 GHz. This sky
projection introduces small angle distortions which we account for by rotating the Q and U Stokes
components across the map to maintain a consistent angular coordinate system in this projection.
The result of the map-making step in the analysis are T, Q and U maps for each observation in the
season with corresponding weight maps.
3.2.8
Data Cuts
We make maps from all observations that have at least one functioning bolometer, but data cuts are
applied to the final map products based on five criteria. The first cut is based on live bolometers. If
an observation has less than 600 150 GHz bolometers the map is cut as a low bolometer number is
typically indicative of bad weather or a badly tuned array. Additionally, the field coverage for an
observation with low bolometer number is also not optimal.
The maps are also cut based on the total weight (based on the sum of the weight map) and
the median weight in the map . This cut is to remove observations that were terminated part way
through the observation. This may also remove observations with very noisy detectors. The fourth
cut is a cut based on the RMS noise in the map. Such high levels of noise are usually due to bad
weather. The final cut is the median weight times the RMS squared. This cut is intended to discard
maps where the noise in the observation is not encapsulated in the weight. The values for each of
these cut metrics for every observation in the season is shown in Fig. 3.8. The five map cuts are
partially redundant. If there are very few good bolometers in an observation, the median weight,
45
total weight and bolometer cut will also fail. If all bolometers in an observation have abnormally
high noise the data will fail the weights cuts and the RMS cut. The median and standard deviation
of the distributions are calculated for each cut. Maps that lie outside the cut thresholds are excluded
from the analysis. After these cuts are applied 3800 of the 5000 maps remain. See Table 3.3 and
Table 3.2 for a specific breakdown showing how many maps are cut at each step.
Cut
# Maps Cut
Median Weight Too High
102
Median Weight Too Low
792
Too Few Bolometer
712
RMS Too High
340
RMS Too Low
76
RMS * Median Weight Too High
747
RMS * Median Weight Too Low
30
Total Weight Too High
142
Total Weight Too Low
868
3800/5000 (76 %)
Good Maps
Table 3.2: 150 GHz data cuts. The cut metrics are described in the text.
3.2.9
Map Bundles
For this analysis we choose to combine multiple observations of the CMB field into “bundles.”
In this analysis each bundle is a coadd of 28 observations. Each of these bundles is then used
as the fundamental unit for the power spectrum analysis. This bundling makes the analysis less
computationally intensive (using large amounts of both memory and disk space) than it would be
if we were to use individual observation. In addition to the computational advantage, the coverage
of the field is more uniform when we stack multiple observations.
We restrict each bundle to contain one map of each of the dither steps. This is to assure good
coverage in each bundle. This leaves us with 3416 maps (∼ 90 percent of the good data from 2012)
used for the analysis. For the B-mode power spectrum analysis this restriction may be dropped so
46
Figure 3.7: Top: A timestream before polynomial filtering. The DC level changes every time the
telescope steps in elevation. Bottom: The same timestream after subtracting a 4th order polynomial
from each scan. The glitches show scans where the polynomial fitting failed. These scans are
flagged and will not contribute to the maps. The y-axis is in Kelvin CMB units.
47
Figure 3.8: Values for the map cut metrics versus observation number during the 2012 season.
The y axis is arbitrarty, but maps with outlying values in any of the populations are removed.
that more data can be included. However for the EE power spectrum this increase in noise is
a small noise penalty since we are sample variance limited by our field size over a large range
in . However, many of the interesting extensions to our cosmological models are sensitive to
measurements at 2000 < < 3000, where we are dominated by noise in our data, so future EE
analysis may include more data, if possible. For the time being we are using a very conservative
data set.
3.2.10
Temperature Projection
We see evidence for temperature to polarization leakage in the maps. We measure leakage from
temperature into polarization by correlating the temperature map with the Q and U polarization
maps. We then remove a fraction of the temperature map from the two polarization maps. For
each bundle we scale the temperature map scaled by .009 and add it to the Q map and scale the
temperature map by 0.0147 and subtract it from the U maps. To get the scalings the average
correlations between adjacent maps is calculated for the entire season.
48
Cut
# Maps Cut
Median Weight Too High
72
Median Weight Too Low
1505
Too Few Bolometer
1430
RMS Too High
1709
RMS Too Low
3
RMS * Median Weight Too High
2173
RMS * Median Weight Too Low
10
Total Weight Too High
460
Total Weight Too Low
1745
3466/5000 (69 %)
Good Maps
Table 3.3: 90 GHz data cuts. The cut metrics are described in the text.
3.2.11
2012 Season CMB Maps
The final result of the data processing in this chapter is T, Q and U CMB maps at 90 and 150
GHz. For the particular power spectrum analysis in the next section they are used in the bundle
subsets described above, however for other analysis a full season coadd is made. The CMB maps
are shown in Fig. 3.9 - Fig. 3.14
49
150
6
120
4
90
60
30
0
uK_CMB
Degrees
2
0
30
2
60
90
4
120
6
6
4
2
0
Degrees
2
4
6
150
Figure 3.9: The 150 GHz temperature map of RA23h30DEC-55 Field measured by SPTpol. The
pixel size is 0.5 arcminutes. Dozens of bright point-sources are visible to the eye as well as the
decement from the Sunayev-Zeldovich effect from at least one galaxy cluster.
50
30
6
24
4
18
12
6
0
uK_CMB
Degrees
2
0
6
2
12
18
4
24
6
6
4
2
0
Degrees
2
4
6
30
Figure 3.10: The 150 GHz Q polarization map of RA23h30DEC-55 Field measured by SPTpol.
51
30
6
24
4
18
12
6
0
uK_CMB
Degrees
2
0
6
2
12
18
4
24
6
6
4
2
0
Degrees
2
4
6
30
Figure 3.11: The 150 GHz U polarization map of RA23h30DEC-55 Field measured by SPTpol.
52
150
6
120
4
90
60
30
0
uK_CMB
Degrees
2
0
30
2
60
90
4
120
6
6
4
2
0
Degrees
2
4
6
150
Figure 3.12: The 90 GHz temperature map of RA23h30DEC-55 Field measured by SPTpol. The
pixel size is 1.0 arcminutes. Dozens of bright point-sources are visible to the eye as well as at least
one galaxy cluster.
53
30
6
24
4
18
12
6
0
uK_CMB
Degrees
2
0
6
2
12
18
4
24
6
6
4
2
0
Degrees
2
4
6
30
Figure 3.13: The 90 GHz Q polarization map of RA23h30DEC-55 Field measured by SPTpol.
The maps show striations that are due to uneven coverage in the vertical direction.
54
30
6
24
4
18
12
6
0
uK_CMB
Degrees
2
0
6
2
12
18
4
24
6
6
4
2
0
Degrees
2
4
6
30
Figure 3.14: The 90 GHz U polarization map of RA23h30DEC-55 Field measured by SPTpol.
55
CHAPTER 4
POWER SPECTRUM ANALYSIS
On the path to constraining cosmological parameters we must first compute the power spectrum
of our CMB maps. In this chapter we provide an overview of this process including the crossspectrum analysis, E mode power spectrum estimation, and estimation of our uncertainties.
4.1
The Cross-Spectrum Analysis
A pseudo-C method is used to estimate the bandpowers following the MASTER method described
in Hivon et al. (2002). Additionally we implement a cross spectrum analysis in which we take the
cross spectrum of the subsets of data (bundles) described in the previous chapter. These bundles
satisfy the required property that they have independent realizations of the atmospheric and detector noise. We follow the analysis developed in Lueker et al. (2010) which was based on methods in
Polenta et al. (2005) and Tristram et al. (2005) used in previous SPT results (Keisler et al. (2011),
Reichardt et al. (2012), Story et al. (2012)).
Formally, for two maps, mA and mB , with Fourier conjugates m̃A and m̃B , we compute the
cross-spectrum between the two maps and average the result within bins b in ell-space, to get a
binned pseudo power spectrum,
AB ≡
D
b
( + 1)
A
B∗
Re[m̃ m̃ ]
.
2π
∈b
(4.1)
We have 122 map bundles and therefore 7381 unique spectra. We then average the result for all
b . Since the noise in each bundle is uncorrelated
A = B to get the binned pseudo power spectrum D
and the signal is correlated, we get an estimate of the power spectrum that is not biased by noise in
the maps, a powerful benefit of the cross spectrum method.
To go from this pseudo power spectrum to the true sky power spectrum we need a mode-mixing
matrix, transfer function and the beam response of the instrument.
56
Db ≡ K −1
bb
D
b
(4.2)
where Kb b is a matrix that accounts for the mode-mixing from the sky window function, M , the
transfer function from timestream filtering,F , and B2 is the beam response of the instrument,.
These three elements will be described in the following sections.
4.1.1
Sky Window Function
The sky window function is a mask in real space that is applied to the data before computing the
Fourier transform for the cross spectrum analysis. It serves three purposes. The mask tapers the
edges of the map so that derivatives are well defined at the map border and do not cause issues
when taking the Fourier transform. The mask excludes regions with uneven sky coverage. Finally,
the mask is used to exclude any bright point sources that are in the survey field. The list of masked
bright point sources consists of all point sources with 150 GHz flux > 50 mJy as measured by
SPT-SZ in this region of the sky (see Story et al. (2012)). Each of the point sources is masked with
a 5
-radius disk. The disk is tapered to zero using a 15
cosine taper.
To create a window from the uniform coverage region for all map bundles, we calculate an
unsmoothed mask, Mb , for each of the map bundles, where Wb is the weight map for each bundle.
⎧
⎪
⎨ 1 if W
b,ij > tWb
Mb,ij =
,
⎪
⎩ 0 otherwise
(4.3)
where i and j index map rows and columns, respectively and b is an individual bundle in the set of
bundles B. Mb,ij is dependent on the weight map for each bundle, Wb , and the threshold, t which
is set to 0.3 for this analysis. Then the product of the threshold weight is
Wthreshold =
Mb
(4.4)
b∈B
We then take the result and taper the edges with a 30
cosine taper. This edge apodization mask
57
and the point source mask are combined to get the final window function Wsky , shown in Fig. 4.1
4.1.2
Beams
The beam response Bl for the 2012 instrument was measured using observations of Mars. The
measured beams for 90 and 150 GHz are show in Fig. 4.4 and Fig. 4.5.
Eight observations of Mars taken in the fall of 2012 were used to measure the beam profile.
Additionally, this profile was convolved with a measure of the pointing jitter over the entire 2012
season. This pointing jitter was measured using the brightest point sources in the SPTpol deep
field. At 90 and 150 GHz, the FWHM of the beams are 1.83 and 1.06 arcmin, respectively. The
errors on the beam are the standard deviation between individual Mars observations. As can be
seen in Fig. 4.6, the 90 and 150 GHz beam errors are less than five percent at all between 0 and
10,000.
4.1.3
Mode Mixing
To get a final power spectrum result from the pseudo-C power spectrum calculated in Sec. 4.1,
we must account for the mixing of power between bins. This mixing is an effect of measuring
a fraction of the sky. This effect, known as mode mixing or mode coupling, is calculated from
noiseless simulations. We map out the mixing of modes between power spectrum bins by creating
many realizations of T, Q, and U maps each with only pure T, E and B power in the given bins.
The sky window is then applied to each of the maps and the power spectrum is computed. The
output power spectrum is compared to the input power spectrum to produce a mode-mixing matrix
of size nbins by nbins. We calculate a matrix for TT, TE and EE power spectra. The left-hand
panel of Fig. 4.3 shows the diagonal elements of the mode-mixing matrix for EE. The right-hand
panel shows the mode-mixing matrix in 2D. The off-diagonal elements are less than 10 % of the
on-diagonal elements.
58
4.1.4
Transfer Function
We must account for the effect that filtering the data timestream has on the resulting power spectrum. We compute this transfer function by generating 100 realizations of the CMB sky using
Healpix1 . These maps are then “observed” to create simulated, noise free timestreams for each
bolometer. The simulated timestreams include the pointing information, weights, and data cuts for
each observation. We then filter the simulated data in the same way the real data is filtered, applying the exact filtering as was applied to the real data for each scan in each simulated observation.
We then make a map for each observation from the filtered data. The final output of the simulation
is 100 realizations for each of the 122 map bundles.
We add all of the observations in the full season of data for each of the 100 realizations of the
CMB and compute the autospectrum of this coadd. The resulting transfer function is the resulting
C s divided by the input C s. The C s from the simulations are corrected for mode mixing before
dividing by the input C s. The transfer function and beam, Bl2 Fl , are shown in Fig. 4.2.
The input cosmology to the simulations was a best fit, Planck model. Story et al. (2012) found
the transfer function insensitive to the cosmological model.
4.1.5
Covariance Matrix
The covariance matrix encapsulates the errors on the bandpowers and the correlations between
the bins. We calculate the covariance matrix as in Lueker et al. (2010) and other SPT-SZ power
spectrum results, following the MASTER algorithm (Hivon et al., 2002). The covariance matrix
consists of a term measured from the scatter between the individual cross spectra, as well as a
sample variance term calculated from the CMB simulations. For visual purposes the errors on the
plots of the SPTpol bandpowers are the diagonal elements of the covariance matrix, but the full
covariance matrix is used in cosmological modeling.
1. http://healpix.jpl.nasa.gov
59
1.0
0
0.9
200
0.8
400
0.7
600
pixel
0.6
0.5
800
0.4
1000
0.3
1200
0.2
1400
0
0.1
200
400
600
800
1000
1200
1400
0.0
pixel
Figure 4.1: The 150 GHz sky window function is applied to the data during the cross-spectrum
analysis. This window masks bright point sources in the map and tapers the borders of the map
using a cosine function.
60
Figure 4.2: The transfer function that accounts for the filtering of the time ordered data. The spikes
are montecarlo noise from using a small number of simulations. A larger number of simulations
will be used for the final result.
Figure 4.3: Left: The off-diagonal elements of the EE mode-mixing matrix. Also shown are the
rows of the matrix at of 500 (green), 1500 (red) and 3000 (cyan). Right: The same mode-mixing
matrix in 2D. The off-diagonal elements are small compared to the on-diagonal elements of the
matrix.
61
100
Amplitude (normalized)
10-1
Beam radial profile from planet observations
Mars, 150 GHz
Mars, 90 GHz
10-2
10-3
10-4
10-5
10-6 0
5
15
10
20
Radius from center (arcmin)
25
30
Figure 4.4: The SPTpol 90 GHz and 150 GHz 2012 beams measured from Mars and convolved
with pointing jitter measured from the bright point sources in the SPTpol field. The beams are
shown in real space. The x axis is distance from the center of the beam in arcminutes. The y axis
is the source response.
62
1.0
150 GHz beam
150 GHz beam errors
90 GHz beam
90 GHz beam errors
0.8
Bl
0.6
0.4
0.2
0.00
5000
10000
l
15000
20000
Figure 4.5: The SPTpol 90 GHz and 150 GHz 2012 beams measured from Mars and convolved
with pointing jitter measured from the bright point sources in the SPTpol field. The beams are
shown in space with the beam response, Bl on the y axis and on the x axis.
63
0.05
150 GHz
90 GHz
delta
Bl / Bl
0.04
0.03
0.02
0.01
0.00
0
2000
4000
l
6000
8000
10000
Figure 4.6: The SPTpol 90 GHz and 150 GHz 2012 beam uncertainties. The beams are shown in
Fourier space with the fractional beam uncertainty, δBl /Bl on the y axis and on the x axis.
64
4.1.6
Systematic Tests
We have done a suite of jackknives to test for systematic uncertainties in our measurement. A
jackknife test entails dividing the data up into two sets using a metric that might be associated
with a systematic effect. We pair each bundle in the first set with a bundle in the second set then
difference the pairs of bundles to remove the common CMB signal.
We perform the cross spectrum analysis on the resulting sets of null maps, with the exact same
procedure we use to get power spectra of the data. The resulting power spectra should be consistent
with zero if this systematic effect is not present. We test the consistency of the resulting spectra
for each test by calculating the χ2 of the residual power relative to the expectation spectrum in
nine bins with δ = 500, from of 500 to 3000. We calculate the probability to exceed (PTE) this
value of χ2 for six degrees of freedom. The resulting PTE values should be uniformly distributed
between zero and one. We consider values >0.95 or <0.05 to be a jackknife failure.
4.1.7
Map Based Jackknives
We consider the map bundles (28 maps) the fundamental unit for our analysis, and perform jackknives of different sets of bundles, The metric used for dividing the bundles into sets to jackknife
is the average of the metric for individual observations.
We do five map based jackknife tests.
- 1st half/2nd half of observing season: The data is divided up in time. This test is for systematic effects with a temporal dependence. Power that would be temporally dependent could
be caused by a calibration drift, readout noise, or the sun being above the horizon at the end
of the season
- Left/Right: Difference maps made from left going scans and right going scans.
- Ground: Divide the maps up based on potential ground contamination. To do this jackknife
the actual polarized ground pickup versus azimuth for the 2012 season is computed. This is
65
Figure 4.7: A plot showing the results of a 1st half /2nd half jackknife test. Green: the raw
pseudo-Cl EE signal power spectrum. Blue: the raw jackknife (null) power spectrum. The χ2
comparing the raw jackknife power spectrum with a zero expectation is 316 for 661 degrees of
freedom. Typically the jackknife spectra are binned in Δ of 500, but this was binned more finely.
The result should be independent of bin size.
done by making maps in ground coordinates (AZ-EL) and then computing the RMS noise
fluctuations in these maps. The RMS noise fluctuation versus azimuth can be seen in Fig. 4.8.
This metric is then used to flag each observation, such that they can be ranked from least to
most ground contamination.
- Moon: A jackknife based on whether the moon is above the horizon. Bundles with the moon
above the horizon are subtracted from bundles with the moon below the horizon.
- Map RMS: RMS in the individual maps is used as a metric to rank maps. We difference
maps with the highest RMS from maps with the lowest RMS
An example jackknife power spectrum is shown in Fig. 4.7.
66
4.1.8
Systematic Effects from Detector Non-Idealities
In addition to having systematics associated with properties of the maps, there can also be systematics associated with detector properties. Doing detector based jackknives requires remaking
maps of the data with subsets of detectors. Non-linearity is a detector property that could cause
systematic bias.
A large fraction of the power (or loading) incident on the detectors is from the atmosphere.
Since the depth of the atmosphere seen by the telescope is larger when the telescope is pointing
at lower elevation the power observed changes with elevation. If the electrical response of the
detectors is not linear with the power incident on the detector it will induce a systematic in our
measurement. For a perfect detector the response of the detector changes linearly with loading.
For real TESs the linearity of a TES detector is a function of the shape of the superconducting
transition and the bias point of the detector. We use the internal calibrator source to measure how
the response of the detectors changes with elevation. Our metric for how non-linear the detector
is is the ratio of the response to the calibrator at 45 degrees to the response at 65 degrees. The
non-linearity of the 150 GHz detectors is plotted in Fig. 4.10. We do not present non-linearity
detector jackknife for this analysis, however we test using simulations that the non-linear detectors
at 150 GHz have a <0.5 percent effect on the EE power spectrum over our range.
4.1.9
Jackknife Results and Implications
For this analysis we do three different variations on this jackknife analysis. We refer to these
analyses as “naive,” “aggressive,” and “complete.” The results of these three analyses are shown in
tables 4.1, 4.2, 4.4. The power spectrum results in Chap. 5 use the complete analysis. We refer
to this as the complete analysis because we take into account expectations from simulations when
doing jackknife tests.
In the naive analysis we preform the jackknife tests as described above and for each test calculate a χ2 with respect to a model where we expect zero power in all bins. We show the results of
the jackknife tests for the naive analysis in Table 4.1. The left/right and RMS jackknife test fail for
67
Figure 4.8: Ground pickup measured versus telescope azimuth. This map was made by making
maps in ground centered coordinates, and then measuring the RMS of each map. This RMS is
plotted on the y axis versus the azimuth in degrees. The detectors see obvious ground signal but
a lead-trail analysis is not necessary because the signal is too small to cause a bias. We know this
because ground signal that would bias our measurement would show up in the ground jackknife
test. The large spike correspond to buildings near the South Pole Telescope, which are a different
temperature than the sky.
68
the EE power spectrum.
There are a few effects which might cause a left minus right jackknife failure and systematically
bias our power spectrum result. One such effect is caused by the movement of the telescope. When
observing the telescope scan across the sky in one direction, then scans back, and at the end of the
scan steps in elevation. There is a mechanical oscillation induced from the elevation step, such
that the telescope is actually moving a small amount in elevation during the beginning of a scan
across the sky. This change in elevation causes a change in the atmospheric signal measured by
the detectors.
To test that this center region or edge of the maps could be a source of the left-right jackknife
failure we repeated the entire jackknife analysis but used a sky window function that removed
the data in the center strip of the field and cut aggressively on the edge of the maps. This is the
“aggressive” jackknife analysis. This more restrictive sky window function is shown in Fig. ??.
This more restrictive mask cuts the area of sky analyzed down to 76.02 deg2 to 100.36 deg2 . which
would increase the sample variance error bars by 15 % if used in the final analysis.
Table 4.2 shows the jackknife results for this alternate analysis with the more restrictive window
function. We pass all jackknife test when doing the alternate analysis which confirms that it is this
center or edge region causing the jackknife failure.
Another effect that could cause a left-right jackknife failure (but not result in a biased power
spectrum) is different pixel weighting in the left and right maps. This is likely to be a strongest
effect at the edge and center stripe of the map so would also be mitigated by the above restrictive
sky window test. In the analysis it is assumed that the maps used to make the power spectrum have
uniform noise and full coverage of the field. We tested this by looking at the difference between
the left and right simulated maps. Fig. 4.9 shows a left minus right maps from the simulated data.
Qualitatively it looks like there is a residual in the simulated left-right maps.
To correct for this effect, we perform the jackknife tests on simulated maps in the same way
that is was done on the data maps. Our jackknife results are now the χ2 of the data with respect
to the simulated jackknife results, this is what we refer to as our “complete” analysis, as this is the
69
TT
Left/Right
3.43e-09
1st half/2nd half 1.14e-4
Ground
0.81
Moon
0.04
Map RMS
0.0
TE
0.69
0.5
0.95
0.41
0.35
EE
0.01
0.81
0.88
0.62
0.02
Table 4.1: The results of the jackknife tests are quoted as the probability to exceed (PTE) the χ2
per dof for each test. Results are highlighted if the TE or EE jackknife fails. The sun jackknife is
not reported because it is the same as the 1st half/ 2nd half test.
TT
Left/Right
1.05e-4
1st half/2nd half
0.04
Ground
0.61
Moon
0.22
Map RMS
8.96e-7
TE
0.33
0.56
0.93
0.35
0.48
EE
0.27
0.93
0.65
0.58
0.18
Table 4.2: The results of the jackknife tests are quoted as the probability to exceed (PTE) the χ2
per dof for each test. A more restrictive sky window function is used for this analysis. Results are
highlighted if the TE or EE jackknife fails.
correct spectrum we should be comparing our jackknifes to given the non-uniform weighting of
the maps.
The conclusion from the jackknife tests using the complete analysis is that we see no systematic
biases in our measurement from ground contamination or moon contamination. There also do not
seem to be any temporal effects that bias our polarization data. We also pass the left-right test. We
do not pass the map RMS test, but do not yet understand the source of this failure. The results for
the complete analysis are shown in Table 4.4. The TT spectra show significant non-zero power in
most tests, but we do not consider a failure in TT a problem for our polarization spectra since we
do not report TT bandpowers.
70
TT
Left/Right
0.01
1st half/2nd half 6.26e-4
Ground
0.81
Moon
0.04
Map RMS
0.0
TE
0.64
0.49
0.95
0.41
0.36
EE
0.06
0.82
0.88
0.63
0.04
Table 4.3: The results of the jackknife tests are quoted as the probability to exceed (PTE) the
χ2 per dof for each test. The results of the test are compared to the results of the test done on
simulated . Results are highlighted if the TE or EE jackknife fails.
Left/Right
1st half/2nd half
Ground
Moon
Map RMS
TE
0.64
0.49
0.95
0.41
0.36
EE
0.06
0.82
0.88
0.63
0.04
Table 4.4: The results of the jackknife tests are quoted as the probability to exceed (PTE) the
χ2 per dof for each test. The results of the test are compared to the results of the test done on
simulated . Results are highlighted if the TE or EE jackknife fails.
Figure 4.9: A left minus right difference map made from simulated data. This shows an area of
non-uniform noise in the center of the field.
71
Figure 4.10: The non-linearity of the 150 GHz detectors. The red line shows the detectors with
high non-linearity which were excluded when making maps.
72
CHAPTER 5
RESULTS
5.1
TE and EE Polarized Power Spectra
The data products resulting from this measurement and analysis are T, Q, and U maps at both
90 and 150 GHz (shown in Fig. 3.9 - Fig. 3.14) and TE and EE bandpowers at 150 GHz. The
bandpowers are reported for the range 500-3000. The 150 GHz maps have 0.5 arcminute resolution and the 90 GHz maps have 1.0 arcminute resolution. For this result, we report EE and TE
bandpowers in terms of Dell , which is defined as
D =
( + 1)
C
2π
(5.1)
where C is the measured bandpowers corrected for the beam, transfer function, and mixing between modes. We report bandpowers in bins of δ = 50 between 500 < < 3000. These are
shown in Fig. 5.1 and Fig. 5.2. We have a clear measurement of the peaks in the EE power spectrum out to of 2000. The results are plotted on top of a fiducial Planck determined cosmology.
The uncertainty on the EE power spectrum presented is dominated by sample variance out to of
2000. Above 2000 the measurement uncertainty is dominant.
5.2
Lensing B-Mode Detection
The Q and U polarization maps described in Chap. 3 were also used to make the first detection of
a lensing B-mode signal (Hanson et al., 2013). Despite the fact that there may still be some unaccounted for systematics in the EE and TE power spectrum results, the polarization maps from this
thesis were used in a cross-correlation study whose results are not susceptible to systematic contamination. The CMB polarization maps along with Hershel-SPIRE cosmic infrared background
(CIB) data in the SPTpol 23h30 field were used to make measurement. The data used for this
measurement are shown in Fig. 5.3. This measurement was made by constructing a template for
73
Figure 5.1: The 150 GHz EE power spectrum measured by SPTpol. Error bars are the square root
of the diagonal elements of the covariance matrix and include measurement uncertainty as well as
sample variance from measuring a fraction of the sky.
Figure 5.2: The 150 GHz TE power spectrum measured by SPTpol. Error bars are the square root
of the diagonal elements of the covariance matrix and include measurement uncertainty as well as
sample variance from measuring a fraction of the sky.
74
Figure 5.3: Left: E-mode polarization map measured by SPTpol at 150 GHz. Center: CMB
lensing potential inferred from CIB fluctuations measured by Herschel. Right panel: Gravitational
lensing B-mode estimate from the E-mode and lensing potential map. SOURCE: Hanson et al.
(2013).
the lensing B-mode signal by combining E-mode polarization measured by SPTpol with estimates
of the lensing potential from the CIB map. This template was then cross-correlated with the B
modes measured directly in the SPTpol polarization maps giving a ∼ 7 sigma detection of B-mode
lensing (Fig. 5.4).
5.3
Discussion
The EE and TE power spectra are roughly consistent with current cosmology, however there could
be unaccounted for systematics, especially at low angular scales, which will be examined in future
work. Some other possible but unlikely sources of systematic error are the mode mixing matrix and
the transfer function that are used to go from estimated pseudo-Cls to measured Cls as discussed
in Sec. 4.1. Additionally, the sample variance error bars could be misestimated due to the small
number of simulations used to calculate these errors.
The mode mixing matrix for this result is measured in coarsely defined bins for computational
reasons. This binning may have some effect on the result if the function is varying quickly within
a bin. The mode mixing matrix can be calculated analytically which will be used as a cross-check.
The resolution of the simulations could also be doubled to see if that gives consistent results. The
75
12
lClBB [μK2 ×104 ]
) × B̂
CIB
) × B̂
CIB
) × B̂χ
φ̂
95
φ̂
150
φ̂
(Ê
8
CIB
150
(Ê
10
(Ê
150
150
150
6
4
2
0
500
1000
1500
l
2000
2500
Figure 5.4: Black points: Cross-correlation of the lensing B modes measured by SPTpol at 150
GHz with lensing B modes from combining CIB fluctuations measured by Herschel and E modes
measured by SPTpol at 150 GHz. A null test is shown in gray. SOURCE: Hanson et al. (2013).
uncertainty on the transfer function is difficult to estimate at large angular scales. Additionally,
since the transfer function is measured using simulations, consistency tests should be done using
simulations with a few different cosmological models to assure that the resulting transfer function
is not dependent on the input model. Beam errors that are unaccounted for could also effect the
power spectrum at large scales. We also do not optimally weight the fourier modes, to downweight
noisy modes which will increase the size of the error bars, not cause a systematic effect, but this
has not been investigated.
5.4
Conclusions and Future Work
In this thesis we have described the design and construction of SPTpol, a CMB polarimeter with
high sensitivity capable of measuring modes from degree scales out to of 10,000. It is a state
of the art instrument that will be used for a wide range of science, from its primary goals of constraining cosmological models with CMB data, to finding galaxy clusters and measuring polarized
foregrounds. We have presented here the first EE and TE power spectrum results from SPTpol.
76
This is one of the first high signal to noise measurement of the EE power spectrum between of
1500 and 3000. While the measurement of the EE and TE power spectra alone will provide only
a few percent improvement on ΛCDM cosmological parameter constraints, they will be used in
combination with other data sets to constrain extensions to ΛCDM. The work in this thesis to
understand and control the systematics affecting the SPTpol power spectrum measurement is a
vitally important step on the path to directly measuring the B mode polarization power spectrum
from gravitational lensing and for eventually constraining the B mode signal from inflationary
gravitational waves.
77
REFERENCES
Araki, T., Eguchi, K., Enomoto, S., et al. 2005, Physical Review Letters, 94, 081801
Battistelli, E. S., Amico, G., Baù, A., et al. 2012, MNRAS, 3009
Bhatia, R., Chase, S., Edgington, S., et al. 2000, Cryogenics, 40, 685
Bleem, L., Ade, P., Aird, K., et al. 2012, Journal of Low Temperature Physics, 196
Carlstrom, J. E., Ade, P. A. R., Aird, K. A., et al. 2011, PASP, 123, 568
Clarke, J. 1996, 1
Crites, A. T., Benson, B. A., Bleem, L., et al. 2011, IEEE Transactions on Applied Superconductivity, 21, 184
Das, S., Sherwin, B. D., Aguirre, P., et al. 2011, Physical Review Letters, 107, 021301
de Bernardis, P., Ade, P. A. R., Bock, J. J., et al. 2000, Nature, 404, 955, astro-ph/0004404
de Haan, T., Smecher, G., & Dobbs, M. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8452, Society of Photo-Optical Instrumentation Engineers
(SPIE) Conference Series
Dobbs, M., Bissonnette, E., & Spieler, H. 2008, IEEE Transactions on Nuclear Science, 55, 21
George, E. M., Ade, P., Aird, K. A., et al. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8452, Society of Photo-Optical Instrumentation Engineers
(SPIE) Conference Series
Guth, A. H. 1981, Phys. Rev. D, 23, 347
Halverson, N. W., Leitch, E. M., Pryke, C., et al. 2002, ApJ, 568, 38, astro-ph/0104489
Hanany, S., Ade, P., Balbi, A., et al. 2000, ApJ, 545, L5, astro-ph/0005123
Hanson, D., Hoover, S., Crites, A., et al. 2013, ArXiv e-prints, arXiv:1307.5830 [astro-ph.CO]
Henning, J. W., Ade, P., Aird, K. A., et al. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8452, Society of Photo-Optical Instrumentation Engineers
(SPIE) Conference Series
Hivon, E., Górski, K. M., Netterfield, C. B., et al. 2002, ApJ, 567, 2
Hou, Z., Reichardt, C. L., Story, K. T., et al. 2012, ArXiv e-prints, arXiv:1212.6267 [astroph.CO]
Hu, W., & Dodelson, S. 2002, ARA&A, 40, 171
Keisler, R., Reichardt, C. L., Aird, K. A., et al. 2011, ApJ, 743, 28
78
Komatsu, E., Smith, K. M., Dunkley, J., et al. 2011, ApJS, 192, 18
Kovac, J. M., Leitch, E. M., Pryke, C., et al. 2002, Nature, 420, 772
Lee, A. T., Richards, P. L., Nam, S. W., Cabrera, B., & Irwin, K. D. 1996, Applied Physics Letters,
69, 1801
Lesgourgues, J., Perotto, L., Pastor, S., & Piat, M. 2006, Phys. Rev. D, 73, 045021
Lueker, M., Reichardt, C. L., Schaffer, K. K., et al. 2010, ApJ, 719, 1045
Mather, J. C. 1982, Appl. Opt., 21, 1125
Mather, J. C., Cheng, E. S., Cottingham, D. A., et al. 1994, ApJ, 420, 439
McMahon, J., Appel, J. W., Austermann, J. E., et al. 2009, in American Institute of Physics Conference Series, Vol. 1185, American Institute of Physics Conference Series, ed. B. Young, B. Cabrera, & A. Miller, 490
Padin, S., Staniszewski, Z., Keisler, R., et al. 2008, Appl. Opt., 47, 4418
Penzias, A. A., & Wilson, R. W. 1965, ApJ, 142, 419
Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2013, ArXiv e-prints, arXiv:1303.5076
[astro-ph.CO]
Polenta, G., Marinucci, D., Balbi, A., et al. 2005, Journal of Cosmology and Astro-Particle Physics,
11, 1
Pryke, C., Ade, P., Bock, J., et al. 2009, ApJ, 692, 1247
Quiet Collaboration. 2012, ApJ
Reichardt, C. L., Shaw, L., Zahn, O., et al. 2012, ApJ, 755, 70
Sayre, J. T., Ade, P., Aird, K. A., et al. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8452, Society of Photo-Optical Instrumentation Engineers
(SPIE) Conference Series
Smoot, G. F., et al. 1992, ApJ, 396, L1
Story, K. T., Reichardt, C. L., Hou, Z., et al. 2012, ArXiv e-prints, arXiv:1210.7231 [astroph.CO]
Tristram, M., Macı́as-Pérez, J. F., Renault, C., & Santos, D. 2005, MNRAS, 358, 833
Yefremenko, V., Datesman, A., Wang, G., et al. 2009, AIP Conference Proceedings, 1185, 359
79
Документ
Категория
Без категории
Просмотров
0
Размер файла
3 049 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа