Pulsar Timing with the Next Generation of Radio Telescopes

  • Xiaojin Liu

Student thesis: Phd


Pulsar timing, which tracks the rotational phase of pulsars over many years, has established pulsars as precise celestial clocks and enabled the tests of theories of gravity and the search for nano-Hz gravitational waves. For these applications, a higher timing precision can put a tighter bound on alternative theories of gravity or even detect the gravitational waves. The timing precision is expected to increase when a new generation of telescopes is rolling out, while an inspection on the method itself may further improve the precision. This thesis aims to improve the precision of pulsar timing arrays by inspecting the existing timing models, the correlations due to red noise, and the subtle variations of the pulsars per se. Firstly, the precision of the timing models in the Solar system is discussed, using the widely used software package \textsc{tempo2} as an example. \textsc{tempo2} was designed to achieve a precision of 1~ns over 20 years, but some components, especially wet delay and ionospheric delay, could induce errors above this level. The current atmospheric delay does not include the wet delay and could lead to an elevation-dependent error up to about 7~ns. Besides that, the existing atmospheric delay is also prone to errors around the horizon. Due to its strong dependence on the elevation and meteorological conditions, one may consider real-time observations of atmospheric delay via other means, like the global positioning systems. Also, there is no modelling of ionospheric delay although errors up to 100~ns could be induced, while the time delay of Solar wind is oversimplified and can lead to huge inaccuracy when the line-of-sight is close to the Sun. Secondly, the origin and detectability of the spin frequency second derivative are discussed. A comprehensive survey on the kinematic and dynamical origins was conducted for the pulsars in the International Pulsar Timing Array. It found that the contribution related to the radial velocity is dominant in most cases with a magnitude of $10^{-30}-10^{-29}$~s$^{-3}$. The measurement error of the spin frequency second derivative heavily depends on the noise in the timing residuals as well as the time span ($T$) of the data. In the case of white noise, the error decreases as $T^{-7/2}$, while if correlated noise exists, the error is proportional to $T^{-3.5+0.5\alpha}$ for power-law red noise with a power index of $\alpha \le4$. In addition to the power-law model, the possibility of using a squared exponential kernel to model the red noise was also discussed. Finally, I investigated potential shape variations of the pulse profile of PSR~B1937+21, using 637 observations spanning nearly 6 years. In this study, a Gaussian process was used to infer the shape variations between consecutive observations. Systematic variations with an amplitude of 1 per cent of the main peak were found near the shoulder of the main pulse and 0.5 per cent for those near the peak of the interpulse. The reason for such variations is not clear, but both polarisation impurities in the receiver and intrinsic shape changes are possible.
Date of Award1 Aug 2020
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorMichael Keith (Supervisor) & Benjamin Stappers (Supervisor)


  • pulsar
  • time
  • gravitational wave

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