EXPLORING PULSAR{BLACK HOLE BINARIES USING THE NEXT GENERATION OF RADIO TELESCOPES A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences 2012 By Kuo Liu Jodrell Bank Centre for Astrophysics School of Physics and Astronomy Contents Contents 2 List of Figures 8 List of Tables 11 Abstract 13 Declaration 15 Copyright 17 The author 19 Publications 21 Acknowledgements 23 1 Introduction 25 1.1 Pulsars . 26 1.2 Dipole model . 27 1.2.1 Spin evolution and braking index . 28 1.2.2 Characteristic age . 30 1.2.3 Magnetic ¯eld strength . 30 1.3 Population and the P -P_ diagram . 31 1.4 Propagation through the ISM . 32 2 1.4.1 Dispersion delay . 32 1.4.2 Scattering and scintillation . 34 1.5 Binary systems . 35 1.6 Rotational stability . 39 1.7 Celestial laboratory in relativity test . 41 1.7.1 Double neutron star binaries . 41 1.7.2 Neutron star-white dwarf binaries . 42 1.7.3 Neutron star-black hole binaries . 44 1.8 Searching for binary pulsars . 44 1.8.1 Constant acceleration search . 44 1.8.2 Phase modulation search . 46 1.8.3 Additional tools . 46 1.9 Thesis structure . 47 2 Pulsar Timing analysis 49 2.1 Introduction . 49 2.2 Instrumentation . 50 2.3 TOA measurement . 53 2.3.1 Algorithm . 54 2.3.2 Limitation . 55 2.4 Interpreting TOAs . 58 2.4.1 Time standard . 59 2.4.2 Timing model . 60 2.4.3 Binary correction . 62 2.4.4 Further corrections . 65 2.4.5 Methodology . 67 2.5 Improvement with future telescopes . 68 2.5.1 Design goals . 68 2.5.2 Bene¯t . 69 3 3 Prospects for High-Precision Pulsar Timing 73 3.1 Introduction . 73 3.2 Observations . 75 3.3 Issues a®ecting pro¯le stability . 75 3.3.1 Dispersion changes . 76 3.3.1.1 Theory . 76 3.3.1.2 Discussion . 77 3.3.2 ISM Scattering and scintillation . 78 3.3.2.1 Theory . 78 3.3.2.2 Data investigation . 79 3.3.3 Signal digitisation e®ects . 80 3.3.3.1 Phenomena . 80 3.3.3.2 Correction . 81 3.3.4 Polarimetric calibration imperfections . 82 3.3.4.1 Theory . 82 3.3.4.2 Calibration . 83 3.3.5 Interference and unknown observing system instabilities . 85 3.3.5.1 Diagnostic theory . 85 3.3.5.2 Data analysis . 86 3.3.6 Pulse jitter . 89 3.3.6.1 Theoretical model . 89 3.3.6.2 Data analysis . 91 3.3.6.3 Conclusions . 94 3.4 Discussion and consequences for future telescopes . 95 3.4.1 Summary . 95 3.4.2 Timing in the new millennium . 96 3.4.3 Limits and future work . 98 4 Pulse jitter analyses of MSPs 101 4.1 Introduction . 101 4 4.2 Pro¯le shape and phase jitter analysis . 103 4.2.1 Stability Analysis . 103 4.2.2 Phase Jitter . 104 4.3 Observations . 106 4.4 Results . 108 4.4.1 Measurement of shape constant . 108 4.4.2 Fit of phase jitter . 110 4.5 Conclusions and Discussions . 118 4.5.1 Summary of the results . 118 4.5.2 Future telescopes . 118 5 Pulsar{black hole investigation 121 5.1 Overview . 121 5.1.1 Black hole properties and testing General Relativity . 121 5.1.2 Measurement approach . 123 5.1.3 Formation scenario of a PSR-BH system . 124 5.1.4 Birthrate and population synthesis . 126 5.1.5 Discovery strategy . 127 5.1.6 Further application . 129 5.1.7 Structure and symbols . 130 5.2 Frame dragging and Cosmic Censorship Conjecture . 131 5.2.1 Precession of the orbit . 132 5.2.2 Long-term evolution of observable quantities . 135 5.2.3 Spin extraction and geometry determination . 137 5.2.3.1 Pulsar with stellar mass black hole . 137 5.2.3.2 Pulsar around Sgr A* . 140 5.3 Quadrupole measurement and no-hair theorem . 142 5.3.1 The Hamiltonian . 143 5.3.2 The orbital motion . 144 5.3.3 The RÄomerdelay . 148 5 5.4 Timing precision and scheme of simulations . 149 5.4.1 Timing precisions . 150 5.4.2 Simulation schemes . 152 5.5 Simulations for PSR-SBH system . 154 5.5.1 Mass measurement . 155 5.5.2 Spin measurement . 156 5.5.2.1 Normal pulsar{stellar mass black hole systems . 156 5.5.2.2 Millisecond pulsar{stellar mass black hole systems 156 5.5.3 Quadrupole measurement . 164 5.6 Simulations for PSR-Sgr A*system . 168 5.6.1 Mass measurement . 171 5.6.2 Spin measurement . 171 5.6.3 Quadrupole measurement . 175 5.7 Conclusions and discussions . 177 5.7.1 Summary . 177 5.7.1.1 Pulsar{stellar mass black hole . 179 5.7.1.2 Pulsar around Sgr A* . 180 5.7.2 Measurement pipeline . 181 5.7.3 Other e®ects . 182 5.7.4 Discussions . 184 6 Conclusions and future work 187 6.1 Summary . 187 6.1.1 Limits on precision timing . 187 6.1.2 Timing of a pulsar{black hole binary . 188 6.2 Further research . 189 A E®ective pulse number 193 B Uncertainty in arrival time 195 B.1 Radiometer noise . 195 6 B.2 Phase jitter . 196 C Correlation-coe±cient scaling 199 C.1 Additive noise . 199 C.2 Phase jitter . 201 D Spin and geometry solution for pulsar{Sgr A* system 205 D.1 Use of! Äs ................................ 206 D.2 Use ofx Äs ................................ 207 Bibliography 210 (Final word count: 40,021) 7 List of Figures 1.1 Pulsar dipole emission model . 29 1.2 P -P_ diagram . 33 1.3 Thin screen model of scattering . 36 1.4 Formation procedure of binary pulsars . 37 1.5 Comparison of clocks . 40 1.6 Test of GR with accumulated changing of periastron . 42 1.7 Mass-mass diagram of the double pulsar system . 43 2.1 Data path of pulsar timing . 50 2.2 Cross correlation with noisy template . 55 2.3 PSR J0437¡4715 pro¯le ¯t with Guassians . 56 2.4 Corrupted template matching . 58 2.5 Reliability of template matching with low S/N pro¯le . 59 2.6 SKA con¯guration . 69 2.7 FAST con¯guration . 70 3.1 E®ects changing pro¯le shape . 76 3.2 Sub-band template matching . 80 3.3 2-bit digitisation scattered power correction . 82 3.4 Comparison of polarimetric calibration models . 84 3.5 Correlation of sharpness and 2-bit distortion . 87 3.6 S/N versus σTOA ........................... 88 8 3.7 Correlation.