Development and Initial Operation of AMiBA

CBI and ACBAR reported in the CMB power spectrum ${it l}>2000$, they detected power excess to the primary signal. Secondary signal, mainly unresolved SZ effect of fainter objects, has been proposed to explain the result. AMiBA intends to measure this band power to higher accuracy, and put a tighter constraint on $sigma_{8}$, which is directly related to the amplitude of primordial density fluctuation. A second goal of AMiBA is to measure the number count of high redshift galaxy clusters, thereby probing the evolution of structure formation history using the most massive bound objects. To conduct numerical simulation on the expected science output, we report an instantaneous heating scheme, for which gases in dense regions receive a temperature increment of several keV at $z=2$ whereas those in rarefied regions remain intact, that can produce bound objects obeying the observed mass-temperature and luminosity-temperature relations. Based on these simulations and AMiBA sensitivity, we expect to measure the $it{l}sim3000$ band to $5-sigma$ in one month with 60cm dish. Upgrading to 1.2m dish, and we may measure the SZ power in $it{l}=4000--6000$ band in 1.5 months. And for blind surveys, we expect to find $sim$10 clusters/$deg^2$ with deep exposures ($sim$0.8 $deg^2$/month). Detailed testing of AMiBA a two-element prototype has been conducted on site. The 7-element system was recently installed and is being commissioned. Initial test shows a promising white spectrum of noise. The important tasks of ground pickup and delay measurement has been performed or planned. And a sweeping CW source is being designed and tested to be the main calibrator of AMiBA.Acknowledge 1 Abstract 3 1 Introduction 15 1.1 Galaxy Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.2 CMB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.3 AMiBA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.4 Contributions and Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 Numerical Simulation 22 2.1 Simulations, M - T and L - T Relations . . . . . . . . . . . . . . . . . . . . 22 2.2 SZ and CMB Power Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3 Prototype Testing 30 3.1 Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 Prototype system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3 DC Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3.1 Impurity in LO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3.2 Curing the LO Impurity . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3.3 Phase Switch Level Imbalance . . . . . . . . . . . . . . . . . . . . . . 39 3.3.4 Reducing the LO Amplitude Modulation . . . . . . . . . . . . . . . . 40 3.4 Phase Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4 7-element System 46 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.2 Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.3 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.4 IF/LO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.5 Correlator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.6 Platform and Mount . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.7 Lag-to-Visibility Transformation . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.7.1 Basic Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.7.2 SVD Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.7.3 Natural Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.7.4 The Frequency Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5 Calibration 83 5.1 System Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.1.1 Pointing Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.1.2 Phase Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.1.3 Gain Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.1.4 Spectral Response Change . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.2 Calibration on Astronomical Source . . . . . . . . . . . . . . . . . . . . . . . 90 5.2.1 Phase Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.2.2 Flux Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.3 CW Calibration System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.3.1 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.3.2 CW Signal Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.3.3 Lab Testing Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3.4 Control Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.3.5 Further Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.4 Platform Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.4.1 Photogrammetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.4.2 Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6 Commissioning of AMiBA 109 6.1 Delay Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.1.1 Translation Stage Measurements . . . . . . . . . . . . . . . . . . . . . 110 6.1.2 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.1.3 Sources of Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.1.4 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6.1.5 Solving Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.1.6 Systematic Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6.2 Drift Scan of Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.3 Noise Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 6.4 Ground Pickup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.4.1 Total Power Pickup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.4.2 Correlation Pickup and Scanning Strategy . . . . . . . . . . . . . . . . 129 7 Conclusion and Future Work 131 A Information in the Fringe 133 A.1 Basic Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 A.2 Fringe Envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 A.3 Asymmetric Fringe Envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 A.3.1 flat response, parabolic phase deviation . . . . . . . . . . . . . . . . . 138 A.3.2 2-band response, parabolic phase deviation . . . . . . . . . . . . . . . 138 A.3.3 flat response, cubic phase deviation . . . . . . . . . . . . . . . . . . . . 138 A.3.4 2-band response, sine phase deviation . . . . . . . . . . . . . . . . . . 139 A.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 B Angles in Astronomy 14