Imprints of relic gravitational waves on pulsar timing

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.     

Pulsar timing residuals due to individual non-evolving gravitational wave sources

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 or- bits 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.     

Effect of weak gravitational microlensing on pulsar timing

The effect of weak gravitational microlensing on the pulsar timing is considered. The residuals of the times of arrival due to this effect for the pulsar B1937+21 will be ～10 ns if the time span of observations is about 20 years. It has also been shown that the residuals due to this effect will be several microseconds in the same 20 years in future SKA (Square Kilometer Array) observations of pulsars located behind the bulge.     

The role of FAST in pulsar timing arrays

The Five-hundred-meter Aperture Spherical radio Telescope(FAST) will become one of the world-leading telescopes for pulsar timing array(PTA) research. The primary goals for PTAs are to detect(and subsequently study) ultra-low-frequency gravitational waves, to develop a pulsar-based time standard and to improve solar system planetary ephemerides. FAST will have the sensitivity to observe known pulsars with significantly improved signal-to-noise ratios and will discover a large number of currently unknown pulsars. We describe how FAST will contribute to PTA research and show that jitter-and timing-noise will be the limiting noise processes for FAST data sets. Jitter noise will limit the timing precision achievable over data spans of a few years while timing noise will limit the precision achievable over many years.     

四种综合脉冲星时算法比较

由单颗脉冲星定义的脉冲星时受多种噪声源的影响,其短期和长期稳定度都不够好.为了削弱这些噪声源对单脉冲星时的影响,可以采取合适的算法对多个单脉冲星时进行综合得到综合脉冲星时,从而提高综合脉冲星时的长期稳定度.文中介绍4种综合脉冲星时算法:经典加权算法、小波分析算法、维纳滤波算法和小波域中的维纳滤波算法,将这4种算法分别应用于Arecibo天文台对两颗毫秒脉冲星PSR B1855+09和PSRB1937+21观测得到的计时残差并作出比较.     

Shapiro effect as a possible cause of the low-frequency pulsar timing noise in globular clusters

A prolonged timing of millisecond pulsars has revealed low-frequency uncorrelated (infrared) noise, presumably of astrophysical origin, in the pulse arrival time (PAT) residuals for some of them. Currently available pulsar timing methods allow the statistical parameters of this noise to be reliably measured by decomposing the PAT residual function into orthogonal Fourier harmonics. In most cases, pulsars in globular clusters show a low-frequency modulation of their rotational phase and spin rate. The relativistic time delay of the pulsar signal in the curved spacetime of randomly distributed and moving globular cluster stars (the Shapiro effect) is suggested as a possible cause of this modulation. Extremely important (from an astrophysical point of view) information about the structure of the globular cluster core, which is inaccessible to study by other observational methods, could be obtained by analyzing the spectral parameters of the low-frequency noise caused by the Shapiro effect and attributable to the random passages of stars near the line of sight to the pulsar. Given the smallness of the aberration corrections that arise from the nonstationarity of the gravitational field of the randomly distributed ensemble of stars under consideration, a formula is derived for the Shapiro effect for a pulsar in a globular cluster. The derived formula is used to calculate the autocorrelation function of the low-frequency pulsar noise, the slope of its power spectrum, and the behavior of the σ_z statistic that characterizes the spectral properties of this noise in the form of a time function. The Shapiro effect under discussion is shown to manifest itself for large impact parameters as a low-frequency noise of the pulsar spin rate with a spectral index of n = −1.8 that depends weakly on the specific model distribution of stars in the globular cluster. For small impact parameters, the spectral index of the noise is n = −1.5.     

Application of ‘CLEAN’ in the power spectral analysis of non-uniformly sampled pulsar timing data

Spectral analysis of the residual pulsearrival times of pulsars is a useful tool in understanding the nature of the underlying processes that may be responsible for the timing noise observed from pulsars. Power spectra of pulsar timing residuals may be described by one or a combination of powerlaws. As these spectra are expected to be very steep, it is important to ensure a high dynamic range in the estimation of the spectrum. This is difficult in practice since one is, in general, dealing with timing measurements made at unevenly placed epochs. In this paper, we present a technique based on, ‘CLEAN’ to obtain high dynamic range spectra from unevenly sampled data. We compare the performance of this technique with other techniques including some that were used earlier for estimation of power spectra of pulsar timing residuals.     

A Comparison of the Four Algorithms of Ensemble Pulsar Time

The pulsar time defined by a single pulsar is affected by many kinds of noise sources. Its short-term and long-term degrees of stability are both not good enough. In order to weaken the influence of these noise sources on the single pulsar time, an appropriate algorithm can be adopted to make a synthesis of many single pulsar times, then the ensemble pulsar time is obtained, thereby increasing the long-term degree of stability of the ensemble pulsar time. In this article four kinds of algorithms of the ensemble pulsar time are introduced, i.e., the classical weighting algorithm, wavelet analysis algorithm, Wiener filtering algorithm and Wiener filtering algorithm in wavelet domain. These four algorithms are respectively applied to the timing residuals obtained from the observation of two millisecond pulsars, PSR B1855+09 and PSR B1937+21 made at the Arecibo Astronomical Observatory, and comparisons are carried out.     

tempo2: a new pulsar timing package – III. Gravitational wave simulation

Analysis of pulsar timing data sets may provide the first direct detection of gravitational waves. This paper, the third in a series describing the mathematical framework implemented into the tempo2 pulsar timing package, reports on using tempo2 to simulate the timing residuals induced by gravitational waves. The tempo2 simulations can be used to provide upper bounds on the amplitude of an isotropic, stochastic, gravitational wave background in our Galaxy and to determine the sensitivity of a given pulsar timing experiment to individual, supermassive, binary black hole systems.     

On measuring the gravitational-wave background using Pulsar Timing Arrays

The long-term precise timing of Galactic millisecond pulsars holds great promise for measuring the long-period (months to years) astrophysical gravitational waves. Several gravitational-wave observational programs, called Pulsar Timing Arrays (PTA), are being pursued around the world.
Here, we develop a Bayesian algorithm for measuring the stochastic gravitational-wave background (GWB) from the PTA data. Our algorithm has several strengths: (i) it analyses the data without any loss of information; (ii) it trivially removes systematic errors of known functional form, including quadratic pulsar spin-down, annual modulations and jumps due to a change of equipment; (iii) it measures simultaneously both the amplitude and the slope of the GWB spectrum and (iv) it can deal with unevenly sampled data and coloured pulsar noise spectra. We sample the likelihood function using Markov Chain Monte Carlo simulations. We extensively test our approach on mock PTA data sets and find that the algorithm has significant benefits over currently proposed counterparts. We show the importance of characterizing all red noise components in pulsar timing noise by demonstrating that the presence of a red component would significantly hinder the detection of the GWB.
Lastly, we explore the dependence of the signal-to-noise ratio on the duration of the experiment, number of monitored pulsars and the magnitude of the pulsar timing noise. These parameter studies will help formulate observing strategies for the PTA experiments.     

Precession of the isolated neutron star PSR B1828−11

Stairs, Lyne & Shemar have found that the arrival-time residuals from PSR B1828−11 vary periodically with a period ≈500 d. This behaviour can be accounted for by precession of the radio pulsar, an interpretation that is reinforced by the detection of variations in its pulse profile on the same time-scale. Here, we model the period residuals from PSR B1828−11 in terms of precession of a triaxial rigid body. We include two contributions to the residuals: (i) the geometric effect, which arises because the times at which the pulsar emission beam points towards the observer varies with precession phase; and (ii) the spin-down contribution, which arises from any dependence of the spin-down torque acting on the pulsar on the angle between its spin     and magnetic     axes. We use the data to probe numerous properties of the pulsar, most notably its shape, and the dependence of its spin-down torque on     , for which we assume the sum of a spin-aligned component (with a weight  1 − a   ) and a dipolar component perpendicular to the magnetic beam axis (weight a ), rather than the vacuum dipole torque  ( a = 1)  . We find that a variety of shapes are consistent with the residuals, with a slight statistical preference for a prolate star. Moreover, a range of torque possibilities fit the data equally well, with no strong preference for the vacuum model. In the case of a prolate star, we find evidence for an angle-dependent spin-down torque. Our results show that the combination of geometrical and spin-down effects associated with precession can account for the principal features of the timing behaviour of PSR B1828−11, without fine tuning of the parameters.     

Precision pulsar timing with the ORT and the GMRT and its applications in pulsar astrophysics

Radio pulsars show remarkable clock-like stability, which make them useful astronomy tools in experiments to test equation of state of neutron stars and detecting gravitational waves using pulsar timing techniques. A brief review of relevant astrophysical experiments is provided in this paper highlighting the current state-of-the-art of these experiments. A program to monitor frequently glitching pulsars with Indian radio telescopes using high cadence observations is presented, with illustrations of glitches detected in this program, including the largest ever glitch in PSR B0531+21. An Indian initiative to discover sub-\(\mu \)Hz gravitational waves, called Indian Pulsar Timing Array (InPTA), is also described briefly, where time-of-arrival uncertainties and post-fit residuals of the order of \(\mu \)s are already achievable, comparable to other international pulsar timing array experiments. While timing the glitches and their recoveries are likely to provide constraints on the structure of neutron stars, InPTA will provide upper limits on sub-\(\mu \)Hz gravitational waves apart from auxiliary pulsar science. Future directions for these experiments are outlined.     

Two-frequency timing of the pulsar B1937+21 in Kalyazin and Kashima in 1997–2002

We present the results from our timing of the millisecond pulsar B1937+21, performed jointly since 1997 on two radio telescopes: the RT-64 in Kalyazin (Russia) at a frequency of 0.6GHz and RT-34 in Kashima (Japan) at a frequency of 2.15 GHz. The rms value of the pulse time of arrival (TOA) residuals for the pulsar at the barycenter of the Solar system is 1.8 μs (the relative variation is ≈10^?14 over the observing period). The TOA residuals are shown to be dominated by white phase noise, which allows this pulsar to be used as an independent time scale keeper. The upper limit for the gravitational background energy density Ω_gh² at frequencies ≈6.5 × 10^?9 Hz is estimated to be no higher than 10^?6. Based on the long-term timing of the pulsar, we have improved its parameters and accurately determined the dispersion measure and its time variation over the period 1984–2002, which was, on average, ?0.00114(3) pc cm^?3 yr^?1.     

A high-significance detection of non-Gaussianity in the Wilkinson Microwave Anisotropy Probe 1-yr data using directional spherical wavelets

A directional spherical wavelet analysis is performed to examine the Gaussianity of the Wilkinson Microwave Anisotropy Probe ( WMAP ) 1-yr data. Such an analysis is facilitated by the introduction of a fast directional continuous spherical wavelet transform. The directional nature of the analysis allows us to probe orientated structure in the data. Significant deviations from Gaussianity are detected in the skewness and kurtosis of spherical elliptical Mexican hat and real Morlet wavelet coefficients for both the WMAP and Tegmark, de Oliveira-Costa & Hamilton foreground-removed maps. The previous non-Gaussianity detection made by Vielva et al. using the spherical symmetric Mexican hat wavelet is confirmed, although their detection at the 99.9 per cent significance level is only made at the 95.3 per cent significance level using our most conservative statistical test. Furthermore, deviations from Gaussianity in the skewness of spherical real Morlet wavelet coefficients on a wavelet scale of 550 arcmin (corresponding to an effective global size on the sky of ∼26° and an internal size of ∼3°) at an azimuthal orientation of 72°, are made at the 98.3 per cent significance level, using the same conservative method. The wavelet analysis inherently allows us to localize on the sky those regions that introduce skewness and those that introduce kurtosis. Preliminary noise analysis indicates that these detected deviation regions are not atypical and have average noise dispersion. Further analysis is required to ascertain whether these detected regions correspond to secondary or instrumental effects, or whether in fact the non-Gaussianity detected is due to intrinsic primordial fluctuations in the cosmic microwave background.     

小行星(469219) Kamo`oalewa轨道的确定与误差分析

作为一颗与地球共轨道的小行星,(469219)Kamo'oalewa是一个具有很高研究价值的近地小天体,也是中国首次小行星探测计划的目标天体之一.针对其轨道特性,建立了兼顾太阳、地球和月球非球形引力作用的小行星动力学模型.并在该模型的基础上,利用国际小行星中心(Minor Planet Center,MPC)提供的2004|2018年间的光学观测数据对该小行星的轨道进行确定.拟合后观测残差的均方根误差约为0:2″(与美国喷气推进实验室的Horizons在线历表系统相当),其中2004年期间数据的观测残差有所改进.最后,对小行星(469219)Kamo'oalewa的轨道误差进行了详细分析,并预报了2020-2025年期间该小行星的轨道误差.     

Spacecraft Doppler tracking with possible violations of LLI and LPI:upper bounds from one-way measurements on MEX

We analyze the post-fit residuals of one-way Doppler tracking data from the Mars Express(MEX) spacecraft to test possible violations of local Lorentz invariance(LLI) and local position invariance(LPI).These one-way Doppler observations were carried out on 2011 August 7 for about 20 minutes at Sheshan Station of Shanghai Astronomical Observatory in China.These downlink signals were sent by MEX for telemetry at X-band.Because we are not able to decode the data in the form of telemetry and separate them from the carrier frequency,this makes the post-fit residuals of the Doppler data degrade to the level of 0.1 m s~(-1).Even so,the residuals can still impose upper bounds on LLI and LPI at 10~(-1),which is consistent with the prediction based on our analysis of the detectability.Although the upper bounds given by three-way Doppler tracking of MEX are better than those obtained in the present work,one-way Doppler measurements still provide a unique chance to test possible violations of LLI and LPI far from the ground stations.     

Bayesian joint analysis of cluster weak lensing and Sunyaev–Zel'dovich effect data

As the quality of the available galaxy cluster data improves, the models fitted to these data might be expected to become increasingly complex. Here we present the Bayesian approach to the problem of cluster data modelling: starting from simple, physically motivated parametrized functions to describe the cluster's gas density, gravitational potential and temperature, we explore the high-dimensional parameter spaces with a Markov-Chain Monte Carlo sampler, and compute the Bayesian evidence in order to make probabilistic statements about the models tested. In this way sufficiently good data will enable the models to be distinguished, enhancing our astrophysical understanding; in any case the models may be marginalized over in the correct way when estimating global, perhaps cosmological, parameters. In this work we apply this methodology to two sets of simulated interferometric Sunyaev–Zel'dovich effect and gravitational weak lensing data, corresponding to current and next-generation telescopes. We calculate the expected precision on the measurement of the cluster gas fraction from such experiments, and investigate the effect of the primordial cosmic microwave background (CMB) fluctuations on their accuracy. We find that data from instruments such as the Arcminute Microkelvin Imager (AMI), when combined with wide-field ground-based weak lensing data, should allow both cluster model selection and estimation of gas fractions to a precision of better than 30 per cent for a given cluster.     

Orbit Determination of the Asteroid (469219) Kamoòalewa and Its Error Analysis

As an Earth co-orbital asteroid, (469219) Kamoòalewa is a near earth object (NEO) with high value of research, and one of the targets explored by the first Chinese asteroid exploration mission. Given its orbit characteristics, we build a refined dynamical model for this asteroid, in which the effects induced by nonspherical gravitational fields of the Sun, the Earth, and the Moon are combined. On the basis of the dynamical model of the asteroid (469219) Kamoòalewa, its orbit is determined with optical data from 2004 to 2018 available on the Minor Planet Center (MPC) database. The root mean square error of post-fit residuals is about 0.2 arc second (comparable with that of the Jet Propulsion Laboratory (JPL)/Horizons), and the post-fit residuals of optical observations in 2004 are decreased. At the end, we implement error analysis on the asteroid (469219) Kamoòalewa's orbit in detail, and also predict its orbit error at the time interval between 2020 and 2025.     

Correcting for the solar wind in pulsar timing observations: the role of simultaneous and low-frequency observations

The primary goal of pulsar timing array projects is to detect ultra-low-frequency gravitational waves. Pulsar data sets are affected by numerous noise processes including varying dispersive delays in the interstellar medium and from the solar wind. The solar wind can lead to rapidly changing variations that, with existing telescopes, can be hard to measure and then remove. In this paper we study the possibility of using a low frequency telescope to aid in such correction for the Parkes Pulsar Timing Array(PPTA) and also discuss whether the ultra-wide-bandwidth receiver for the FAST telescope is sufficient to model solar wind variations. Our key result is that a single wide-bandwidth receiver can be used to model and remove the effect of the solar wind. However, for pulsars that pass close to the Sun such as PSR J1022+1022, the solar wind is so variable that observations at two telescopes separated by a day are insufficient to correct the solar wind effect.     

Non-Gaussian distribution and clustering of hot and cold pixels in the five-year WMAP sky

We present measurements of the clustering of hot and cold patches in the microwave background sky as measured from the Wilkinson Microwave Anisotropy Probe 5-year data. These measurements are compared with theoretical predictions which assume that the cosmological signal obeys Gaussian statistics. We find significant differences from the simplest Gaussian-based prediction. However, the measurements are sensitive to the fact that the noise is spatially inhomogeneous (e.g. because different parts of the sky were observed for different lengths of time). We show how to account for this spatial inhomogeneity when making predictions. Differences from the Gaussian-based expectation remain even after this more careful accounting of the noise. In particular, we note that hot and cold pixels cluster differently within the same temperature thresholds at few-degree scales. While these findings may indicate primordial non-Gaussianity, we discuss other plausible explanations for these discrepancies. In addition, we find some deviations from Gaussianity at sub-degree scales, especially in the W band, whose origin may be associated with extragalactic dust emission.