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Register a new userMeasuring clock jumps using pulsar timing
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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 Students $t$-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.
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Pulsar timing is a technique that uses the highly stable spin periods of neutron stars to investigate a wide range of topics in physics and astrophysics. Pulsar timing arrays (PTAs) use sets of extremely well-timed pulsars as a Galaxy-scale detector with arms extending between Earth and each pulsar in the array. These challenging experiments look for correlated deviations in the pulsars timing that are caused by low-frequency gravitational waves (GWs) traversing our Galaxy. PTAs are particularly sensitive to GWs at nanohertz frequencies, which makes them complementary to other space- and ground-based detectors. In this chapter, we will describe the methodology behind pulsar timing; provide an overview of the potential uses of PTAs; and summarise where current PTA-based detection efforts stand. Most predictions expect PTAs to successfully detect a cosmological background of GWs emitted by supermassive black-hole binaries and also potentially detect continuous-wave emission from binary supermassive black holes, within the next several years.
The maximum frequency of gravitational waves (GWs) detectable with traditional pulsar timing methods is set by the Nyquist frequency ($f_{rm{Ny}}$) of the observation. Beyond this frequency, GWs leave no temporal-correlated signals; instead, they appear as white noise in the timing residuals. The variance of the GW-induced white noise is a function of the position of the pulsars relative to the GW source. By observing this unique functional form in the timing data, we propose that we can detect GWs of frequency $>$ $f_{rm{Ny}}$ (super-Nyquist frequency GWs; SNFGWs). We demonstrate the feasibility of the proposed method with simulated timing data. Using a selected dataset from the Parkes Pulsar Timing Array data release 1 and the North American Nanohertz Observatory for Gravitational Waves publicly available datasets, 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 pulsar timing array to single SNFGW sources is generated, and the position of the GW source where the selected pulsar timing array is most sensitive to is $lambda_{rm{s}}=-0.82$, $beta_{rm{s}}=-1.03$ (rad); the corresponding minimum GW strain is $h=6.31times10^{-11}$ at $f=1times10^{-5}$ Hz.
A pulsar timing array (PTA), in which observations of a large sample of pulsars spread across the celestial sphere are combined, allows investigation of global phenomena such as a background of gravitational waves or instabilities in atomic timescales that produce correlated timing residuals in the pulsars of the array. The Parkes Pulsar Timing Array (PPTA) is an implementation of the PTA concept based on observations with the Parkes 64-m radio telescope. A sample of 20 millisecond pulsars is being observed at three radio-frequency bands, 50cm (~700 MHz), 20cm (~1400 MHz) and 10cm (~3100 MHz), with observations at intervals of 2 - 3 weeks. Regular observations commenced in early 2005. This paper describes the systems used for the PPTA observations and data processing, including calibration and timing analysis. The strategy behind the choice of pulsars, observing parameters and analysis methods is discussed. Results are presented for PPTA data in the three bands taken between 2005 March and 2011 March. For ten of the 20 pulsars, rms timing residuals are less than 1 microsec for the best band after fitting for pulse frequency and its first time derivative. Significant red timing noise is detected in about half of the sample. We discuss the implications of these results on future projects including the International Pulsar Timing Array (IPTA) and a PTA based on the Square Kilometre Array. We also present an extended PPTA data set that combines PPTA data with earlier Parkes timing data for these pulsars.
We extend profile domain pulsar timing to incorporate wide-band effects such as frequency-dependent profile evolution and broadband shape variation in the pulse profile. We also incorporate models for temporal variations in both pulse width and in the separation in phase of the main pulse and interpulse. We perform the analysis with both nested sampling and Hamiltonian Monte Carlo methods. In the latter case we introduce a new parameterisation of the posterior that is extremely efficient in the low signal-to-noise regime and can be readily applied to a wide range of scientific problems. We apply this methodology to a series of simulations, and to between seven and nine yr of observations for PSRs J1713$+$0747, J1744$-$1134, and J1909$-$3744 with frequency coverage that spans 700-3600MHz. We use a smooth model for profile evolution across the full frequency range, and compare smooth and piecewise models for the temporal variations in DM. We find the profile domain framework consistently results in improved timing precision compared to the standard analysis paradigm by as much as 40% for timing parameters. Incorporating smoothness in the DM variations into the model further improves timing precision by as much as 30%. For PSR J1713+0747 we also detect pulse shape variation uncorrelated between epochs, which we attribute to variation intrinsic to the pulsar at a level consistent with previously published analyses. Not accounting for this shape variation biases the measured arrival times at the level of $sim$30ns, the same order of magnitude as the expected shift due to gravitational-waves in the pulsar timing band.
We describe the procedure, nuances, issues, and choices involved in creating times-of-arrival (TOAs), residuals and error bars from a set of radio pulsar timing data. We discuss the issue of mis-matched templates, the problem that wide- bandwidth backends introduce, possible solutions to that problem, and correcting for offsets introduced by various observing systems.
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