[en] The pulsar timing residuals induced by gravitational waves from non-evolving single binary sources are affected by many parameters related to the relative positions of the pulsar and the gravitational wave sources. We will analyze the various effects due to different parameters. The standard deviations of the timing residuals will be calculated with a variable parameter fixing a set of other parameters. The orbits of the binary sources will be generally assumed to be elliptical. The influences of different eccentricities on the pulsar timing residuals will also be studied in detail. We find that the effects of the related parameters are quite different, and some of them display certain regularities

[en] Employing multiple pulsars and using an appropriate algorithm to establish ensemble pulsar timescale can reduce the influences of various noises on the long-term stability of pulsar timescale, compared to a single pulsar. However, due to the low timing precision and significant red noises of some pulsars, their participation in the construction of ensemble pulsar timescale is often limited. Inspired by the principle of solving non-stationary sequence modeling using co-integration theory, we put forward an algorithm based on co-integration theory to establish an ensemble pulsar timescale. It is found that this algorithm can effectively suppress some noise sources if a co-integration relationship between different pulsar data exists. Different from the classical weighted average algorithm, the co-integration method provides the chance for a pulsar with significant red noises to be included in the establishment of an ensemble pulsar timescale. Based on data from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), we found that the co-integration algorithm can successfully reduce several timing noises and improve the long-term stability of the ensemble pulsar timescale. (paper)

[en] Relic gravitational waves (RGWs), a background originating during inflation, would leave imprints on pulsar timing residuals. This makes RGWs an important source for detection of RGWs using the method of pulsar timing. In this paper, we discuss the effects of RGWs on single pulsar timing, and quantitatively analyze the timing residuals caused by RGWs with different model parameters. In principle, if the RGWs are strong enough today, they can be detected by timing a single millisecond pulsar with high precision after the intrinsic red noises in pulsar timing residuals are understood, even though simultaneously observing multiple millisecond pulsars is a more powerful technique for extracting gravitational wave signals. We correct the normalization of RGWs using observations of the cosmic microwave background (CMB), which leads to the amplitudes of RGWs being reduced by two orders of magnitude or so compared to our previous works. We obtained new constraints on RGWs using recent observations from the Parkes Pulsar Timing Array, employing the tensor-to-scalar ratio r = 0.2 due to the tensor-type polarization observations of CMB by BICEP2 as a reference value, even though its reliability has been brought into question. Moreover, the constraints on RGWs from CMB and Big Bang nucleosynthesis will also be discussed for comparison. (paper)

[en] The pulsar timing residuals induced by gravitational waves from non-evolving single binary sources with general elliptical orbits are analyzed. For different orbital eccentricities, the timing residuals present different properties. The standard deviations of the timing residuals induced by a fixed gravitational wave source are calculated for different values of the eccentricity. We also analyze the timing residuals of PSR J0437-4715 induced by one of the best known single gravitational wave sources, the supermassive black hole binary in the blazar OJ287

[en] Pulsars are very stable spinning stars, which have the potential to application in the work of time-keeping and autonomous navigation in deep space. For time application, an individual pulsar can be regarded as a clock. The accuracy and stability of a pulsar clock are mainly determined by various timing noises and the measurement errors; however, they would be affected by the concrete observational strategy. Taking four millisecond pulsars from the first data released by International Pulsar Timing Array (IPTA) as an example, we investigated the influences of different observational strategies on the properties of pulsar clocks by removing some data in various ways. We find that the long-term stabilities of pulsar clocks are nearly not affected by increasing the observational cadence with a fixed time span. It is also found that the capabilities of prediction by pulsar clocks are also hardly affected by different observational strategies, which is reflected by both the stable weighted root-mean-square (wrms) and the stability of the resulting pre-fit timing residuals, unless the data span is too short or the data period is too far from the start of prediction. (paper)

[en] We report pulsar timing observations carried out in L-band with NTSC’s 40-meter Haoping Radio Telescope (HRT), which was constructed in 2014. These observations were carried out using the pulsar machine we developed. Timing observations toward millisecond pulsar J0437–4715 obtain a timing residual (r.m.s.) of 397 ns in the time span of 284 days. Our observations successfully detected Crab pulsar’s glitch that happened on 2019 July 23. (paper)