Cheng-Shi Zhao’s research while affiliated with Chinese Academy of Sciences and other places

The establishment of pulsar space–time reference frame is of great significance for X‐ray pulsar deep space navigation. To demonstrate that the pulsar parameters are accurate enough to be used as a spatial reference, the transformation parameters, that is, α, β, and γ, of different reference frames determined based on pulsar timing are shown and compared with that of the heliocentric coordinates of Earth‐Moon barycenter. The JPL ephemerides such as DE421, DE200 and INPOP series, are mainly selected for conversion parameter calculation. For the best‐determined parameter γ, the discrepancy between the two different data is 0.38 mas/1.33σ. The timing positions of pulsars clearly show the frame‐tie of different ephemerides, indicating that MSPs have the potential to be a candidate for constructing time–space standard. It is also found that the rotation angles change linearly with time, and PSR J0437 − 4715 plays a critical role in the fitting of α. By employing a few high‐quality MSPs, the transformation precision of the right ascension is evaluated to be on the order of sub‐milliarcsecond, which is an order of magnitude higher than that of the declination.

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.

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.

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.

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 the 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 puts forward an algorithm based on the co-integration theory to establish ensemble pulsar timescale. It is found that this algorithm can effectively suppress some noise sources if a co-integration relationship between different pulsar data exist. Different from the classical weighted average algorithm, the co-integration method provides the chances of the pulsar with significant red noises to attend the establishment of ensemble pulsar timescale. Based on the data from the North American Nanohertz Observatory for Gravitational Waves, we found that the co-integration algorithm can successfully reduce several timing noises and improve the long-term stability of the ensemble pulsar timescale.

Millisecond pulsars have a very high rotation stability, which can be applied to many research fields, such as the establishment of the pulsar time standard, the detection of gravitational wave, the spacecraft navigation by using X-ray pulsars and so on. In this paper, we employ two millisecond pulsars PSR J0437-4715 and J1713+0743, which are observed by the International Pulsar Timing Array (IPTA), to analyze the precision of pulsar clock parameter and the prediction accuracy of pulse time of arrival (TOA). It is found that the uncertainty of spin frequency is 10⁻¹⁵ Hz, the uncertainty of the first derivative of spin frequency is 10⁻²³ s⁻², and the precision of measured rotational parameters increases by one order of magnitude with the accumulated observational data every 4∼5 years. In addition, the errors of TOAs within 4.8 yr which are predicted by the clock model established by the 10 yr data of J0437-4715 are less than 1 μs. Therefore, one can use the pulsar time standard to calibrate the atomic clock, and make the atomic time deviate from the TT (Terrestrial Time) less than 1 μs within 4.8 yr.

Relic gravitational waves (RGWs) , a background originated during inflation, would give imprints on the pulsar timing residuals. This makes RGWs be one of important sources for detection using the method of pulsar timing. In this paper, we discuss the effects of RGWs on the single pulsar timing, and give quantitively 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 noise in pulsar timing residuals were understood, even though observing simultaneously multiple millisecond pulsars is a more powerful technique in extracting gravitational wave signals. We corrected 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 made new constraints on RGWs using the 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 referenced value even though it has been denied. Moreover, the constraints on RGWs from CMB and BBN (Big Bang nucleosynthesis) will also be discussed for comparison.

In the non-standard model of relic gravitational waves (RGWs) generated in the early universe, the theoretical spectrum of is mainly described by an amplitude r and a spectral index $\beta$, the latter usually being determined by the slope of the inflation potential. Pulsar timing arrays (PTAs) data have imposed constraints on the amplitude of strain spectrum for a power-law form as a phenomenological model. Applying these constraints to a generic, theoretical spectrum with r and $\beta$ as independent parameters, we convert the PTAs constraint into an upper bound on the index $\beta$, which turns out to be less stringent than those upper bounds from BBN, CMB, and LIGO/VIRGO, respectively. Moreover, it is found that PTAs constrain the non-standard RGWs more stringent than the standard RGWs. If the condition of the quantum normalization is imposed upon a theoretical spectrum of RGWs, r and $\beta$ become related. With this condition, a minimum requirement of the horizon size during inflation is greater than the Planck length results in an upper bound on $\beta$, which is comparable in magnitude to that by PTAs. When both PTAs and the quantum normalization are applied to a theoretical spectrum of RGWs, constraints can be obtained for other cosmic processes of the early universe, such as the reheating, a process less understood observationally so far. The resulting constraint is consistent with the slow-roll, massive scalar inflation model. The future SKA will be able to constrain RGWs further and might even detect RGWs, rendering an important probe to the very early universe.

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 fully analyze the effects due to different parameters one by one. 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 studied in detail. We find that effects of the related parameters are quite different, and some of them present certain regularities.