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Measuring the Gravitational Wave Background Using Precision Pulsar Timing by Paul B. Demorest BA

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Measuring the Gravitational Wave Background Using Precision Pulsar Timing by Paul B. Demorest BA Measuring the Gravitational Wave Background using Precision Pulsar Timing by Paul B. Demorest B.A. (University of California, Berkeley) 2000 M.A. (University of California, Berkeley) 2002 A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the GRADUATE DIVISION of the UNIVERSITY OF CALIFORNIA, BERKELEY Committee in charge: Professor Donald Backer, Co-chair Professor Steven Boggs, Co-chair Professor William Holzapfel Professor Carl Heiles Spring 2007 The dissertation of Paul B. Demorest is approved: Co-chair Date Co-chair Date Date Date University of California, Berkeley Spring 2007 Measuring the Gravitational Wave Background using Precision Pulsar Timing Copyright 2007 by Paul B. Demorest 1 Abstract Measuring the Gravitational Wave Background using Precision Pulsar Timing by Paul B. Demorest Doctor of Philosophy in Physics University of California, Berkeley Professor Donald Backer, Co-chair Professor Steven Boggs, Co-chair We investigate the possibility of using high precision timing measurements of radio pulsars to constrain or detect the stochastic gravitational wave background (GWB). Improved algorithms are presented for more accurately determining the pulse times of arrival at Earth and characterizing pulse profile shape variation. Next, we describe the design and construction of a new set of pulsar backends based on clusters of standard personal computers. These machines, the Astronomy Signal Processors (ASPs), coherently correct the pulse broadening caused by interstellar plasma dispersion. Since they are based in software, they are inherently more flexible than previous generations of pulsar data recorders. In addition, they provide increased bandwidth and quantization accuracy. We apply these methods to 2.5 years worth 2 of millisecond pulsar data recorded with the ASP systems at the Arecibo and Green Bank Telescopes, and present pulse profiles, dispersion measure variation, and timing model parameters derived from this data. We then develop the theory of gravitational wave detection using pulsar timing, and show how data from several pulsars can be combined into a pulsar timing array for this purpose. In particular, a new method of accounting for the effect of the tim- ing model fit on the gravitational wave signal is presented. This method incorporates the exact timing model basis functions without relying on Monte Carlo simulation. We apply this method to the 2.5 year dataset previously mentioned and derive a −1 −14 gravitational wave limit of hc(1 yr ) < 2.46 × 10 . Finally, we study the 20-year timing record of PSR B1937+21 and obtain information on how severely interstellar medium effects will compromise future GWB detection. We predict that these devel- opments, in conjunction with historical data, could provide the first successful direct gravitational wave detection on a 5–10 year timescale. Professor Donald Backer Dissertation Committee Co-chair Professor Steven Boggs Dissertation Committee Co-chair i Dedicated to Sara, for her love, support, and especially, patience. ii Contents List of Figures v List of Tables viii 1 Introduction 1 1.1 Introduction . 1 1.2 Pulsar Basics . 2 1.3 Gravitational Radiation Basics . 4 1.4 Overview . 7 2 Methods for Determining Pulse Times of Arrival 10 2.1 Introduction . 10 2.2 Basic TOA Fit Procedure . 12 2.3 Effect of Profile Shape Errors on Timing . 14 2.4 Template Determination . 16 2.5 Principal Components Analysis . 19 2.6 Application to Simulated Data . 25 2.7 Polarization Calibration . 28 3 New Instrumentation for Precision Pulsar Timing: The Astronomy Signal Processors 33 3.1 Introduction . 33 3.2 Coherent Dedispersion . 34 3.2.1 Implementation as a Digital Filter . 38 3.3 System Architecture . 41 3.3.1 Analog Front End . 43 3.3.2 SERENDIP5 Spectrometer . 47 3.4 Software Components . 51 3.4.1 Data Servers . 53 3.4.2 Processing Nodes . 55 iii 3.4.3 Master Node . 58 3.5 Systematic Profile Shape Errors . 59 3.5.1 Effect of Quantization . 60 3.5.2 Quadrature Downconversion . 62 4 Timing Analysis of 16 Millisecond Pulsars 66 4.1 Introduction . 66 4.2 Description of Observations . 67 4.3 Timing Analysis Procedure . 72 4.4 Summary of Results . 78 4.4.1 Profile Variation . 83 4.4.2 Dispersion Measure Variation . 83 4.4.3 Plots . 95 5 Gravitational Radiation Data Analysis 131 5.1 Introduction . 131 5.2 Detecting GW Using Pulsar Timing . 135 5.3 Effect of the Timing Model . 138 5.4 Stochastic Background . 141 5.4.1 Measurement using a Single Pulsar . 147 5.4.2 Measurement using Several Pulsars . 148 5.5 Analysis of Timing Data . 151 5.5.1 Incoherent Analysis . 152 5.5.2 Coherent Analysis . 157 5.6 Discussion . 160 6 A Long-Term Timing Study of PSR B1937+21 164 6.1 Introduction . 164 6.2 Observations . 168 6.3 Basic Analysis . 170 6.4 Distribution of Scattering Material Along the Line of Sight . 177 6.5 Refractive Scintillation . 183 6.5.1 Parameter Estimation . 183 6.5.2 Nature of the Spectrum: Inner Scale Cutoff . 187 6.6 DM Variations . 190 6.7 Frequency Dependence of DM . 198 6.8 Achievable Timing Accuracy . 201 6.8.1 Fluctuation of Apparent Angular Size . 201 6.8.2 Image Wandering . 202 6.8.3 Barycentric Position Errors . 204 6.8.4 Frequency Dependent DM . 204 6.9 Concluding Remarks . 206 iv Bibliography 208 A Effect of the Timing Model Fit 220 A.1 Properties of Residuals . 220 A.2 Frequency Domain Analysis . 222 A.3 Optimal Basis . 224 A.3.1 Note on Units . 227 A.4 Cross-correlation . 231 v List of Figures 2.1 Template profile and power spectrum for PSR J1713+0747 at 1400 MHz. 20 2.2 Template profile determined from the simulated dataset. 26 2.3 Principal component eigenvalues from the simulated data. 27 2.4 First principal component of the simulated data. 28 2.5 Measured principal component value versus true Gaussian amplitude. 29 2.6 Timing residual versus measured component value. 30 2.7 Effect of polarization calibration on timing . 32 3.1 Coherent dedispersion computational cost . 40 3.2 ASP System architecture overview . 42 3.3 Example GPS time correction . 49 3.4 ARTS Software block diagram . 52 3.5 ASP bandwidth versus dispersion length . 57 3.6 Effect of quantization on profile shape . 60 3.7 Effect of quadrature downconversion on timing . 64 4.1 Principal component profile decomposition for J2145−0750 . 84 4.2 Dispersion measure variation as a function of DM . 86 4.3 J0030+0451 Template profiles . 96 4.4 J0218+4232 Template profiles . 97 4.5 J0613−0200 Template profiles . 98 4.6 J1012+5307 Template profiles . 99 4.7 J1455−3330 Template profiles . 100 4.8 J1640+2224 Template profiles . 101 4.9 J1643−1224 Template profiles . 102 4.10 J1713+0747 Template profiles . 103 4.11 J1744−1134 Template profiles . 104 4.12 B1855+09 Template profiles . 105 4.13 J1909−3744 Template profiles . 106 4.14 J1918−0642 Template profiles . 107 vi 4.15 B1937+21 Template profiles . 108 4.16 B1937+21 Template profiles . 109 4.17 J2019+2425 Template profiles . 110 4.18 J2145−0750 Template profiles . 111 4.19 J2317+1439 Template profiles . 112 4.20 J0030+0451 Dispersion measure . 113 4.21 J0218+4232 Dispersion measure . 114 4.22 J0613−0200 Dispersion measure . 114 4.23 J1012+5307 Dispersion measure . 115 4.24 J1455−3330 Dispersion measure . 115 4.25 J1640+2224 Dispersion measure . 116 4.26 J1643−1224 Dispersion measure . 116 4.27 J1713+0747 Dispersion measure . 117 4.28 J1744−1134 Dispersion measure . 117 4.29 B1855+09 Dispersion measure . 118 4.30 J1909−3744 Dispersion measure . 118 4.31 J1918−0642 Dispersion measure . 119 4.32 B1937+21 Dispersion measure . 119 4.33 J2019+2425 Dispersion measure . 120 4.34 J2145−0750 Dispersion measure . 120 4.35 J2317+1439 Dispersion measure . 121 4.36 J0030+0451 Timing residuals . 122 4.37 J0218+4232 Timing residuals . 123 4.38 J0613−0200 Timing residuals . 123 4.39 J1012+5307 Timing.
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