Pulsar Time Scale Research Articles

An Improved Wiener Filtration Method for Constructing the Ensemble Pulsar Timescale

An improved Wiener filtration (WF) method for constructing the ensemble pulsar timescale (EPT) is proposed to solve the existing problems in the WF algorithm. The improvements consist of three parts: (i) adjusting the cross-power spectral density (PSD) and PSD estimated by the weighted average (WA) algorithm by the concept of the energy upper limit; (ii) combining the cross-PSD and WA PSD to form a different signal modulus for the filtration of residuals of different noise levels; and (iii) setting a weight for each residual by a more general algorithm based on the concept of effective power. We use this improved WF method to construct the EPT by both simulated data and observational data from the second data release of the International Pulsar Timing Array. The results from the simulated data indicate this improved WF can successfully suppress the noise level and reform the common signal. For observational data, this method also successfully detects the fluctuations of International Atomic Time (TAI) and local atomic time TA(NTSC). A stability analysis shows that an EPT will have the potential to reveal the instability of TAI on a scale longer than 7 yr. This improved WF method can also be used to detect and monitor the noise in pulsar timing residuals inversely, by using multiple atomic time standards, which can in turn improve the EPT.

Wiener Filtration Algorithm of an Ensemble Pulsar Timescale Based on a Power-law Model of Pulsar Power Spectrum

An ensemble pulsar timescale derived from the traditional Wiener filtration still contains some high level noise. To improve this situation we developed a Wiener filtration algorithm of the ensemble pulsar timescale based on a power-law model of power spectrum for pulsars. Our algorithm has three strengths: (1) mitigating spectral leakage between frequency bins for Fourier techniques; (2) using a power-law model for power spectrum; (3) signal realization in original residuals of data set by the power-law model. According to improved algorithm we constructed an ensemble pulsar timescale EPT−TAI using timing data with respect to International Atomic Time (TAI) about 16 yr time span of ten pulsars from International Pulsar Timing Array second data release (version A). The results show that EPT−TAI detected correctly the differences TT(BIPM2015)−TAI between terrestrial time TT(BIPM2015) and TAI. Fractional frequency stability σ z analysis shows that EPT−TAI does not indicate red noise for 16 yr time interval, and fractional frequency stability for 8 yr and longer time intervals is slightly better than that of TT(BIPM2015)−TAI. Stability for short time intervals of TT(BIPM2015)−TAI is better than that of EPT−TAI, but TT(BIPM2015)−TAI shows red noise for longer time intervals. Using the same algorithm we also derived an ensemble pulsar timescale EPT−TT(BIPM2015) with respect to TT(BIPM2015). The fractional frequency stability curve of EPT−TT(BIPM2015) shows similar characteristics as that of EPT−TAI but with slightly lower values.

Generalized Three-Cornered Hat Method and Its Application for the Construction of an Ensemble Pulsar Time Scale

Generalized Three-Cornered Hat Method and Its Application for the Construction of an Ensemble Pulsar Time Scale

Pulsar: physical generalization of the galactic time-space

The article considers a complex of geometric representations of space-time, based on general dynamic theories of celestial mechanics in close connection with pulsar astrometry as the physical basis of coordinate-time transformations within the solar system and galactic space as a whole. The pulsar time scale is considered as a certain material system with continuous and stable motion, representing a certain measurable parameter – the rotation period P, which changes as a function of the independent time variable – its derivative. The physical pulsar scale is a sequence of measured daily increments of the initial radiation period within any duration. According to observations at the BSA radio telescope (Pushchino) of the pulsar B0950+08, the time scale was determined with an initial period of P0=0.2530653211840410 s on the date MJD0 = 58971 (02.05.2020; 21h.58m.07s). A measured daily increment ΔP = 1.4441·10E-11 s corresponds to the measured value of the derivative P = 1.6759949886E-16, which is determined by the observational timing data. Measured ΔP are defined in the 25th decimal place. Up to 14-15 digits, Δ P there is a pulsar time scale with femtosecond resolution. From 15-16 to 25 digits Δ P is presumably sequential fixation of discrete states of microparticles during quantum-mechanical interactions of matter and electromagnetic radiation of a pulsar. According to our hypothesis, the diversity of the material world and physical processes occurring in celestial and quantum mechanics are finite and it can be generalized. This implies the inseparable unity of physical laws in four-dimensional space of celestial and quantum mechanics, detectable on pulsar time scales under the same conditions.

Space/ground based pulsar timescale for comprehensive PNT system

The comprehensive positioning navigation timing (PNT) system in China is a multi-source information fusion system with BeiDou navigation satellite system (BDS) as a core. The high-precision millisecond pulsar timing can enhance the long-term stability of the BDS time benchmark and maintain a space-time benchmark for future deep-space users. In this paper, a ground-based pulsar time service system is proposed for detecting and improving the time benchmark of BDS. The preliminary designs and functions of the system are outlined. At the same time, the method of establishing space and ground-based pulsar time is studied. The ground radio timing data from the international pulsar timing array (IPTA), the X-ray timing data from the neutron star interior composition explorer (NICER) in space, and the simulation data from the 500-meter spherical radio telescope (five-hundred-meter aperture spherical radio telescope, FAST) for three millisecond pulsars are used to analyze the stability of ground/space-based pulsar time. The research results are as follows. The annual stability of the PSR J0437-4715 ground-based pulsar time based on IPTA data is 3.30 × 10<sup>–14</sup>, and the 10-year stability is 1.23 × 10<sup>–15</sup>, respectively. The existence of pulsar red noise can reduce the time stability of the pulsar. The annual stability of the PSR J1939+2134 ground-based pulsar time is 6.51 × 10<sup>–12</sup>. We find that the accuracy of the pulse time of Arrival(TOA) is an important factor that restricts the stability of space-based pulsar time. Based on NICER space X-ray timing data, the stability of the pulsar time for PSR J1824-2452A is 1.36 × 10<sup>–13</sup> in one year. Finally, the simulation analysis of the FAST’s data without considering the influence of red noise is completed, and we find that the PSR J1939+2134 ground-based pulsar time based on the FAST has an annual stability of 2.55 × 10<sup>–15</sup>, a 10-year stability of 1.39 × 10<sup>–16</sup>, and a 20-year stability of 5.08 × 10<sup>–17</sup>. It demonstrates that the powerful pulsar observation capability of FAST will help to improve the accuracy of ground-based pulsar time and enhance the long-term stability of the comprehensive PNT system time benchmark in China.

Space-Time: from Indefinite at the Locality to Generality at the Infinity

The article presents physical and theoretical generalizations of the space-time metrics, based on invariant coordinate time transformations over the intervals of the observed periodic emission of pulsars. Synchronization of spatial reference systems by the observed passage of the wave front of the coherent radiation of a pulsar corresponds to the axiomatic matching of coordinate time scales defined by the observed rotation parameters of the pulsar with the initial coordinates of spatial reference frames within the homogeneous Galileo space of the Galaxy. As a result, all physical processes in such coordinates systems, including the observed coherent radiation of a pulsar, are indistinguishable from each of them. The estimated span of minimum recognizable on the pulsar time scale is 10−12–10−14 s in the extent from several years to several decades and then gradually decreases, reaching limit values of the order of 10−16–10−17 s in the extent compared to the lifetime of a pulsar. The relative size of the resolved interval is within approximately 10−19–10−29.

A pulsar-based time-scale from the International Pulsar Timing Array

ABSTRACT We have constructed a new time-scale, TT(IPTA16), based on observations of radio pulsars presented in the first data release from the International Pulsar Timing Array (IPTA). We used two analysis techniques with independent estimates of the noise models for the pulsar observations and different algorithms for obtaining the pulsar time-scale. The two analyses agree within the estimated uncertainties and both agree with TT(BIPM17), a post-corrected time-scale produced by the Bureau International des Poids et Mesures (BIPM). We show that both methods could detect significant errors in TT(BIPM17) if they were present. We estimate the stability of the atomic clocks from which TT(BIPM17) is derived using observations of four rubidium fountain clocks at the US Naval Observatory. Comparing the power spectrum of TT(IPTA16) with that of these fountain clocks suggests that pulsar-based time-scales are unlikely to contribute to the stability of the best time-scales over the next decade, but they will remain a valuable independent check on atomic time-scales. We also find that the stability of the pulsar-based time-scale is likely to be limited by our knowledge of solar-system dynamics, and that errors in TT(BIPM17) will not be a limiting factor for the primary goal of the IPTA, which is to search for the signatures of nano-Hertz gravitational waves.

Measuring clock jumps using pulsar timing

In this paper, we investigate the statistical signal-processing algorithm to measure the instant local clock jump from the timing data of multiple pulsars. Our algorithm is based on the framework of Bayesian statistics. In order to make the Bayesian algorithm applicable with limited computational resources, we dedicated our efforts to the analytic marginalization of irrelevant parameters. We found that the widely used parameter for pulsar timing systematics, the `Efac' parameter, can be analytically marginalized. This reduces the Gaussian likelihood to a function very similar to the Student's $t$-distribution. Our iterative method to solve the maximum likelihood estimator is also explained in the paper. Using pulsar timing data from the Yunnan Kunming 40m radio telescope, we demonstrate the application of the method, where 80-ns level precision for the clock jump can be achieved. Such a precision is comparable to that of current commercial time transferring service using satellites. We expect that the current method could help developing the autonomous pulsar time scale.

The application of co-integration theory in ensemble pulsar timescale algorithm

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.

A Pulsar Time Scale

A pulsar time scale is considered, including possibilities for its realization and possible applications to fundamental problems in astronomy and physics.

The relativistic inertial coordinate reference frames, synchronized the observed radio emission of pulsar

We obtain the es – as series of simultaneous and joint rotational motions of the planets. Copernicus (1473-1543 analytical coordinate-independent pulsar time scales, which are determined by the observed rotation parameters of pulsar. The scales extent into barycentric and any topocentric coordinate systems, providing simultaneity of the observed physical phenomena, including the periodic radiation of a pulsar as well, in any point of the three-dimensional space.

A Pulsar Time Scale Based on Parkes Observations in 1995–2010

Timing of highly stable millisecond pulsars provides the possibility of independently verifying terrestrial time scales on intervals longer than a year. An ensemble pulsar time scale is constructed based on pulsar timing data obtained on the 64-m Parkes telescope (Australia) in 1995--2010. Optimal Wiener filters were applied to enhance the accuracy of the ensemble time scale. The run of the time--scale difference PT$_{ens}$ $-$ TT(BIPM2011) does not exceed $0.8 {\pm} 0.4$ $\mu s$ over the entire studied time interval. The fractional instability of the difference $_{ens}$ $-$ TT(BIPM2011) over 15 years is ${\sigma_z} = (0.6\pm 1.6){\cdot}10^{-15}$, which corresponds to an upper limit for the energy density of the gravitational--wave background ${\Omega_g}h^2 {\sim} 10^{-10}$ and variations in the gravitational potential ${\sim} 10^{-15}$ Hz at the frequency $2{\cdot}10^{-9}$.

Pulsar timing and its applications

Pulsars are remarkably precise “celestial clocks” that can be used to explore many different aspects of physics and astrophysics. In this article I give a brief summary of pulsar properties and describe some of the applications of pulsar timing, including tests of theories of gravitation, efforts to detect low-frequency gravitational waves using pulsar timing arrays and establishment of a “pulsar timescale”.

Ensemble Pulsar Time Scale

Millisecond pulsars can generate another type of time scale that is totally independent of the atomic time scale, because the physical mechanisms of the pulsar time scale and the atomic time scale are quite different from each other. Usually the pulsar timing observations are not evenly sampled, and the internals between two data points range from several hours to more than half a month. Further more, these data sets are sparse. All this makes it difficult to generate an ensemble pulsar time scale. Hence, a new algorithm to calculate the ensemble pulsar time scale is proposed. Firstly, a cubic spline interpolation is used to densify the data set, and make the intervals between data points uniform. Then, the Vondrak filter is employed to smooth the data set, and get rid of the high-frequency noises, and finally the weighted average method is adopted to generate the ensemble pulsar time scale. The newly released NANOGRAV (North American Nanohertz Observatory for Gravitational Waves) 9-year data set is used to generate the ensemble pulsar time scale. This data set includes the 9-year observational data of 37 millisecond pulsars observed by the 100-meter Green Bank telescope and the 305-meter Arecibo telescope. It is found that the algorithm used in this paper can reduce effectively the influence caused by the noises in pulsar timing residuals, and improve the long-term stability of the ensemble pulsar time scale. Results indicate that the long-term (> 1 yr) stability of the ensemble pulsar time scale is better than 3.4 × 10−15.

DIVISION A COMMISSION 31: TIME

Time is an essential element of fundamental astronomy. In recent years there have been many time-related issues, in scientific and technological aspects as well as in conventions and definitions. At the Commission 31 (Time) business meeting at the XXIX General Assembly, recent progress and many topics, including Pulsar Time Scales WG and Future UTC WG activities, were reviewed and discussed. In this report, we will review the progress of these topics in the past three years. There are many remarkable topics, such as Time scales, Atomic clock development, Time transfer, Future UTC and future redefinition of the second. Among them, scientific highlights are the progress of pulsar time scales and the optical frequency standards. On the other hand, as the social convention, change in the definition of UTC and the second is important.

Development of a pulsar-based time-scale

Using observations of pulsars from the Parkes Pulsar Timing Array (PPTA) project we develop the first pulsar-based timescale that has a precision comparable to the uncertainties in international atomic timescales. Our ensemble of pulsars provides an Ensemble Pulsar Scale (EPS) analogous to the free atomic timescale Echelle Atomique Libre (EAL). The EPS can be used to detect fluctuations in atomic timescales and therefore can lead to a new realisation of Terrestrial Time, TT(PPTA11). We successfully follow features known to affect the frequency of the International Atomic Timescale (TAI) and we find marginally significant differences between TT(PPTA11) and TT(BIPM11). We discuss the various phenomena that lead to a correlated signal in the pulsar timing residuals and therefore limit the stability of the pulsar timescale.

Pulsar time scale and its future application

AbstractAn Ensemble Pulsar Time Scale (EPT) is derived based on the Pulsar Timing Array. It is interesting to compare the EPT with the TT terrestrial time scale, and get many new realization on the pulsar time scale and the algorithm. Some future interesting applications of the EPT are described and discussed.

Research on Ensemble Pulsar Time Based on Observed Data

The applications of pulsar timing to several important aspects are introduced and a skeletal definition of the pulsar time scale is given. By taking advantage of the observational timing data of millisecond pulsars obtained at the Parkes Astronomical Observatory, Australia, the ensemble pulsar time based on 4 millisecond pulsars is built up, the comparison of its stability σz, with that of the atomic time is made, and finally a few of important factors which affect the ensemble pulsar time, as well as their influences on the pulsar timing accuracy and application are analyzed.

Pulsar timing array

AbstractSimultaneous timing of several pulsars distributed over the sky, so called Pulsar Timing Array (PTA), is used for a variety of metrological and astronomical applications. Three examples of PTA application are presented: link between celestial reference frames, ensemble pulsar time scale and detection of gravitational waves.

Stability of pulsar rotational and orbital periods

AbstractMillisecond and binary pulsars are the most stable astronomical standards of frequency. They can be applied to solving a number of problems in astronomy and time-keeping metrology including the search for a stochastic gravitational wave background in the early universe, testing general relativity, and establishing a new time-scale. The full exploration of pulsar properties requires that proper unbiased estimates of spin and orbital parameters of the pulsar be obtained. These estimates depend essentially on the random noise components present in pulsar timing residuals. The instrumental white noise has predictable statistical properties and makes no harm for interpretation of timing observations, while the astrophysical/geophyeical low-frequency noise corrupts them, thus, reducing the quality of tests of general relativity and decreasing the stability of the pulsar time scale.