Pulsar timing arrays (PTAs) will be sensitive to a finite number of gravitational wave (GW) "point" sources (e.g. supermassive black hole binaries). N quiet pulsars with accurately known distances d_{pulsar} can characterize up to 2N/7 distant chirping sources per frequency bin Δf_{gw}=1/T, and localize them with "diffraction limited" precision δθ\gtrsim (1/SNR)(λ_{gw}/d_{pulsar}). Even if the pulsar distances are poorly known, a PTA with F frequency bins can still characterize up to (2N/7)[1-(1/2F)] sources per bin, and the quasi-singular pattern of timing residuals in the vicinity of a GW source still allows the source to be localized quasi-topologically within roughly the smallest quadrilateral of quiet pulsars that encircles it on the sky, down to a limiting resolution δθ\gtrsim (1/SNR) \sqrt{λ_{gw}/d_{pulsar}}. PTAs may be unconfused, even at the lowest frequencies, with matched filtering always appropriate.
Pulsar timing experiments are currently searching for gravitational waves, and this dissertation focuses on the development and study of the pulsar timing residual models used for continuous wave searches. The first goal of this work is to re-present much of the fundamental physics and mathematics concepts behind the calculations and theory used in pulsar timing. While there exist many reference sources in the literature, I try to offer a fully self-contained explanation of the fundamentals of this research which I hope the reader will find helpful. The next goal broadly speaking has been to f…
We aim to resolve a misunderstanding about whether the so-called "Earth term" in the pulsar timing response to a gravitational wave is in phase among a set of pulsars. We note that the misunderstanding has potentially arisen from the statements that the Earth term is "coherent" or "builds up coherently" among the pulsars. We clarify what authors mean by "coherent" in these statements, pointing out that "coherent" does not indicate that the Earth terms are in phase among the pulsars. Using the pulsar timing residuals induced by a continuous gravitational wave, we show that the Earth term does n…
Gravitational waves provide a new probe of the Universe which can reveal a number of cosmological and astrophysical phenomena that cannot be observed by electromagnetic waves. Different frequencies of gravitational waves are detected by different means. Among them, precision measurements of pulsar timing provides a natural detector for gravitational waves with light-year scale wavelengths. In this review, first a basic framework to detect a stochastic gravitational wave background using pulsar timing array is introduced, and then possible interpretations of the latest observational result of 1…
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 a "pulsar timescale".
Pulsar timing provides a sensitive probe of small-scale structure. Gravitational perturbations arising from an inhomogeneous environment could manifest as detectable perturbations in the pulsation phase. Consequently, pulsar timing arrays have been proposed as a probe of dark matter substructure on mass scales as small as $10^{-11} M_\odot$. Since the small-scale mass distribution is connected to early-Universe physics, pulsar timing can therefore constrain the thermal history prior to Big Bang nucleosynthesis (BBN), a period that remains largely unprobed. We explore here the prospects for pul…
Highly precise pulsar timing is very important for understanding the nature of a neutron star, and it can even be used to detect gravitational waves. Unfortunately, the accuracy of the pulsar timing is seriously affected by the spin-down irregularities of pulsars.
We present a principal component analysis method which tracks and compensates for short-timescale variability in pulsar profiles, with a goal of improving pulsar timing precision. We couple this with a fast likelihood technique for determining pulse time of arrival, marginalizing over the principal component amplitudes. This allows accurate estimation of timing errors in the presence of pulsar variability. We apply the algorithm to the slow pulsar PSR J2139+0040 using an archived set of untargeted raster-scan observations at arbitrary epochs across four years, obtaining an improved timing solu…
A Realistic Pulsar -- Supermassive Black Hole Timing Model
Peking University（北京大学）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
From the basic concepts of general relativity, we investigate the rotation of the polarization angle by a moving gravitational lens. Particularly, we clarify the existing confusion in the literature by showing and explaining why such rotation must explicitly depend on the relative motion between the observer and the lens. We update the prediction of such effect on the double pulsar PSR J0737-3039 and estimate a rotation angle of $\sim 10^{-7}rad$. Despite its tiny signal, this is $10$ orders of magnitude larger than the previous prediction by Ruggiero and Tartaglia, which apparently was misgui…
Any unambiguous detection of a stochastic gravitational wave background by a pulsar timing array will rest on the measurement of a characteristic angular correlation between pulsars. The ability to measure this correlation will depend on the geometry of the array. However, spatially correlated sources of noise, such as errors in the planetary ephemeris or clock errors, can produce false-positive correlations. The severity of this contamination will also depend on the geometry of the array. This paper quantifies these geometric effects with a spherical harmonic analysis of the pulsar timing res…
Ultra-light Dark Matter (ULDM) models are suitable candidates for the cosmological Dark Matter that may leave characteristic imprints in many observables. Among other probes, signatures of ULDM can be searched for in pulsar timing data. In this work we describe the effects of spin-2 ULDM on pulsar timing arrays, extending previous results on lower spins. Spin-2 ULDM is universally coupled to standard matter with dimensionless strength $α$. We estimate that current data could constrain this coupling in the mass range $m\lesssim4\times10^{-22}$ eV at the $10^{-5}$ to $10^{-6}$ level, which is th…
A pulsar timing array (PTA) refers to a program of regular, high-precision timing observations of a widely distributed array of millisecond pulsars. Here we review the status of the three primary PTA projects and the joint International Pulsar Timing Array project. We discuss current results related to ultra-low-frequency gravitational wave searches and highlight opportunities for the near future.
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 feasib…
The smooth spin-down of young pulsars is perturbed by two non-deterministic phenomenon, glitches and timing noise. Although the timing noise provides insights into nuclear and plasma physics at extreme densities, it acts as a barrier to high-precision pulsar timing experiments. An improved methodology based on Bayesian inference is developed to simultaneously model the stochastic and deterministic parameters for a sample of 85 high-$\dot{E}$ radio pulsars observed for $\sim$ 10 years with the 64-m Parkes radio telescope. Timing noise is known to be a red process and we develop a parametrizatio…
While pulsars possess exceptional rotational stability, large scale timing studies have revealed at least two distinct types of irregularities in their rotation: red timing noise and glitches. Using modern Bayesian techniques, we investigated the timing noise properties of 300 bright southern-sky radio pulsars that have been observed over 1.0-4.8 years by the upgraded Molonglo Observatory Synthesis Telescope (MOST). We reanalysed the spin and spin-down changes associated with nine previously reported pulsar glitches, report the discovery of three new glitches and four unusual glitch-like event…
We investigate the impact of intrinsic, kinematic and gravitational effects on high precision pulsar timing. We present an analytical derivation and a numerical computation of the impact of these effects on the first and second derivative of the pulsar spin frequency. In addition, in the presence of white noise, we derive an expression to determine the expected measurement uncertainty of a second derivative of the spin frequency for a given timing precision, observing cadence and timing baseline and find that it strongly depends on the latter ($\propto t^{-7/2}$). We show that for pulsars with…
Young pulsars deviate from a perfectly regular spin-down by two non-deterministic phenomena: impulsive glitches and timing noise. Both phenomena are interesting per se, and may provide insights into the superfluid properties of neutron stars, but they also act as a barrier to high-precision pulsar timing and gravitational wave experiments. We study a minimal stochastic model to describe the spin-down of a multicomponent neutron star, with fluctuations in both the internal and external torques. The power spectral density and timing noise strength of this kind of model can be obtained analytical…
Radio pulsars are often used as clocks in a wide variety of experiments. Imperfections in the clock, known as timing noise, have the potential to reduce the significance of, or even thwart e.g. the attempt to find a stochastic gravitational wave (GW) background. We measure the timing noise in a group of 129 mostly middle-aged pulsars (i.e. characterstic ages near 1~Myr) observed with the Parkes radio telescope on a monthly basis since 2014. We examine four different metrics for timing noise, but it remains unclear which, if any, provides the best determination. In spite of this, it is evident …
The main goal of pulsar timing array experiments is to detect correlated signals such as nanohertz-frequency gravitational waves. Pulsar timing data collected in dense monitoring campaigns can also be used to study the stars themselves, their binary companions, and the intervening ionised interstellar medium. Timing observations are extraordinarily sensitive to changes in path length between the pulsar and the Earth, enabling precise measurements of the pulsar positions, distances and velocities, and the shapes of their orbits. Here we present a timing analysis of 25 pulsars observed as part o…
Efforts are underway to use high-precision timing of pulsars in order to detect low-frequency gravitational waves. A limit to this technique is the timing noise generated by dispersion in the plasma along the line of sight to the pulsar, including the solar wind. The effects due to the solar wind vary with time, influenced by the change in solar activity on different time scales, ranging up to $\sim 11$ years for a solar cycle. The solar wind contribution depends strongly on the angle between the pulsar line of sight and the solar disk, and is a dominant effect at small separations. Although s…
There are two types of timing irregularities seen in pulsars: glitches and timing noise. Both of these phenomena can help us probe the interior of such exotic objects. This article presents a brief overview of the observational and theoretical aspects of pulsar timing irregularities and the main results from the investigations of these phenomena in India. The relevance of such Indian programs for monitoring of young pulsars with the Square Kilometer Array (SKA) is presented, highlighting possible contributions of the Indian neutron star community to the upcoming SKA endeavour.
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 grou…
Gravitational scattering events, in which the path of an interstellar object is deflected by a pulsar or the solar system, give rise to reflex motion which can potentially be detected using pulsar timing. We determine the form of the timing signal expected from a gravitational scattering event, which is ramp-like and resembles the signal produced by a glitch or a gravitational wave burst with memory (BWM), and investigate the prospects for detecting such a signal using a pulsar timing array. The level of timing precision currently achieved for some millisecond pulsars makes it possible to dete…
We have used the Nanshan 25-m Radio Telescope at Xinjiang Astronomical Observatory to obtain timing observations of 87 pulsars from 2002 July to 2014 March. Using the "Cholesky" timing analysis method we have determined positions and proper motions for 48 pulsars, 24 of which are improved positions compared to previously published values. We also present the first published proper motions for nine pulsars and improved proper motions for 21 pulsars using pulsar timing and position comparison method. The pulsar rotation parameters are derived and are more accurate than previously published value…
Radio timing observations of a millisecond pulsar in orbit around the Galactic centre black hole (BH) or a BH at the centre of globular clusters could answer foundational questions in astrophysics and fundamental physics. Pulsar radio astronomy typically employs the post-Keplerian approximation to determine the system parameters. However, in the strong gravitational field around the central BH, higher order relativistic effects may become important. We compare the pulsar timing delays given by the post-Keplerian approximation with those given by a relativistic timing model. We find significant…
Pulsar's position, proper motion and parallax are important parameters in timing equations. It is a really challenging work to fit astrometric parameters accurately through pulsar timing, especially for pulsars that show irregular timing properties. As the fast development of related techniques, it is possible to measure astrometric parameters of more and more pulsars in a model$\textrm{-}$independent manner with the Very Long Baseline Interferometry (VLBI). In this work, we select 16 normal pulsars, whose parallax and proper motion have not been successfully fitted with timing observations or…
We investigate the impact of noise processes on high-precision pulsar timing. Our analysis focuses on the measurability of the second spin frequency derivative $\ddotν$. This $\ddotν$ can be induced by several factors including the radial velocity of a pulsar. We use Bayesian methods to model the pulsar times-of-arrival in the presence of red timing noise and dispersion measure variations, modelling the noise processes as power laws. Using simulated times-of-arrival that both include red noise, dispersion measure variations and non-zero $\ddotν$ values, we find that we are able to recover the …
We study the timing stability of three black widow pulsars, both in terms of their long-term spin evolution and their shorter-term orbital stability. The erratic timing behaviour and radio eclipses of the first two black widow pulsar systems discovered (PSRs B1957+20 and J2051$-$0827) was assumed to be representative for this class of pulsars. With several new black widow systems added to this population in the last decade, there are now several systems known that do not show these typical orbital variations or radio eclipses. We present timing solutions using 7$-$8 yrs of observations from fo…
Pulsar positions can be measured with high precision using both pulsar timing methods and very-long-baseline interferometry (VLBI). Pulsar timing positions are referenced to a solar-system ephemeris, whereas VLBI positions are referenced to distant quasars. Here we compare pulsar positions from published VLBI measurements with those obtained from pulsar timing data from the Nanshan and Parkes radio telescopes in order to relate the two reference frames. We find that the timing positions differ significantly from the VLBI positions (and also differ between different ephemerides). A statisticall…
Modeling of frequency-dependent effects, contributed by the turbulence in the free electron density of interstellar plasma, is required to enable the detection of the expected imprints from the stochastic gravitational-wave (GW) background in pulsar timing data. In this work, we present an investigation of temporal variations of interstellar medium for a set of millisecond pulsars (MSPs) with the upgraded GMRT aided by large fractional bandwidth at lower observing frequencies. Contrary to the conventional narrow-band analysis using a frequency invariant template profile, we applied $PulsePortr…
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；Max-Planck-Institut für Radioastronomie（马克斯·普朗克射电天文研究所）
