This thesis includes my work during my Ph.D study. The main focus of the thesis is on three aspects of applications of pulsar timing, namely: 1) Gravitational Waves (GWs) searching; 2) To explain the long term red timing noise of pulsar via the evolution of the inclination angle of neutron star; 3) Set up a novel method to detect gravitational wave whose frequency is higher than the Nyquist frequency by pulsar timing array.
On the first aspect, we present the results of a search for gravitational waves (GWs) from individual sources using high cadence observations of PSR B1937+21. The data were acquired from an intensive observation campaign with the Lovell telescope at Jodrell Bank, between June 2011 and May 2013. The almost daily observations allow us to probe GWs with frequencies up to 4.98 × 10^−6 Hz, extending the upper bound of the typical frequency range probed by Pulsar Timing Arrays (PTA). We used observations taken at three different radio frequency bands with the Westerbork Synthesis Radio Telescope in order to correct for dispersion measure effects and scattering variances. The corrected timing residuals exhibit an unmodeled periodic noise with an amplitude ~150 ns and a frequency of 3.4 yr^−1. As the signal is present not in the entire data set, we attribute it to the rotational behaviour of the pulsar, ruling out the possibilities of it being either due to a GW or an asteroid as the cause. After removing this noise component, we place limits on the GW strain of individual sources equaling to h_s = 1.53 × 10^−11 and h_s = 4.99 × 10^−14 at 10^−7 MHz for random and optimal sources locations respectively.
On the second aspect, we study the possibility that the long term red timing-noise in pulsars originates from the evolution of the magnetic inclination angle \chi. The braking torque under consideration is a combination of the dipole radiation and the current loss. We find that the evolution of \chi can give rise to extra cubic and fourth-order polynomial terms in the timing residuals. These two terms are determined by the efficiency of the dipole radiation, the relative electric-current density in the pulsar tube and \chi. The following observation facts can be explained with this model: a) young pulsars have positive \dot{\nu}; b) old pulsars can have both positive and negative \ddot{\nu}; c) the absolute values of \ddot{\nu} are proportional to −\dot{\nu}; d) the absolute values of the braking indices are proportional to the characteristic ages of pulsars. If the evolution of \chi is purely due to rotation kinematics, then it can not explain the pulsars with braking index less than 3, and thus the intrinsic change of the magnetic field is needed in this case. Comparing the model with observations, we conclude that the drift direction of χ might oscillate many times during the lifetime of a pulsar. The evolution of \chi is not sufficient to explain the rotation behavior of the Crab pulsar, because the observed \chi and \dot{\chi} are inconsistent with the values indicated from the timing residuals using this model.
In the third part, we try to find a method to solve the following limitation of the tra- ditional pulsar timing methods of Gravitational Waves (GW) detecting: The detectable gravitational waves (GWs) with traditional pulsar timing methods have a maximum fre- quency which is set by the Nyquist frequency of the observation. Beyond this frequency, GWs leave no temporal-correlated signals but instead white noise in the timing residuals. The variance of the GW-induced white noise is a function of the position of pulsars rela- tive to the GW source. We propose that by observing this unique functional form in the timing data, we can detect the GWs, the frequency of which is higher than the Nyquist frequency (Super-Nyquist Frequency GW, or SNFGW). We demonstrate the feasibility of the proposed method with simulated timing data. Using the selected dataset from the PPTA DR1 and NANOGrav publicly available data sets, we try to detect the signals from single SNFGW sources. The result is consistent with no GW detection with 65.5% probability. An all-sky map of the sensitivity of the selected PTA to single SNFGW sources is gener- ated and the position of the GW source where the selected PTA is most sensitivity to is \lambda_s = −0.82, \beta_s = −1.03 (rad); the corresponding minimum GW strain is h = 6.31x10^−11 at f = 1x10^−5 Hz.
Besides the main topic, this thesis includes also my other work during my Ph.D study, i.e., the study of the Birkhoff theorem in General Relativity (GR). In this work we point out a common misunderstanding of the theorem, i.e., a spherically symmetric distribution of mass does not affect the gravitational field inside. By solving the Einstein equation an- alytically, we show that the spherically symmetric matter can also affect the inside metric. A specific case is given to illustrate the difference between the results from the common misunderstanding and the correct one.
For full text of my thesis (in Chinese), click here
To download the powerpoints lides of the thesis defense (in Chinese), click here