By now many gravitational wave (GW) signals have been detected by LIGO and Virgo, with the waves reaching earth directly from their respective sources. These waves will also travel to different pulsars and will cause (tiny) transient deformations in the pulsar shape. Some of us have recently shown that the resultant transient change in the pulsar moment of inertia may leave an observable imprint on the pulsar signals as detected on earth, especially at resonance. The pulsars may thus act as remotely stationed Weber gravitational wave detectors. This allows us to revisit the past GW events via pulsars. We give here a list of specific pulsars whose future signals will carry the imprints of past GW events, to be specific we constrain it within 50 years. Some interesting cases are, supernova SN1987A with earliest perturbed signals from pulsars J0709-5923 and B0559-57 expected to reach earth in 2023 and 2024 respectively, Crab supernova, with perturbed signal arrival date from pulsar J1856-3754 in 2057, and GW170814 event with its imprints on the signals on the pulsar J0437-4715 reaching earth between 2035-2043. Even the earliest recorded supernova SN185 event may become observable again via pulsar J0900-3144 with the perturbed pulsar signal reaching us sometime between 2033-2066. Importantly, even though the strength of the signal will depend on the interior properties of the pulsar, the expected dates of signal arrival are completely model independent, depending only on the locations of the source and the relevant pulsar.
A gravitational wave passing through a pulsar will lead to a variation in the moment of inertia of the pulsar affecting its rotation. This will affect the extremely accurately measured spin rate of the pulsar as well as its pulse profile (due to induced wobbling depending on the source direction). The effect will be most pronounced at resonance and should be detectable by accurate observations of the pulsar signal. The pulsar, in this sense, acts as a remotely stationed Weber detector of gravitational waves whose signal can be monitored on earth. With possible gravitational wave sources spread…
Neutron stars undergoing r-mode oscillation emit gravitational radiation that might be detected on earth. For known millisecond pulsars the observed spindown rate imposes an upper limit on the possible gravitational wave signal of these sources. Taking into account the physics of r-mode evolution, we show that only sources spinning at frequencies above a few hundred Hertz can be unstable to r-modes, and we derive a more stringent universal r-mode spindown limit on their gravitational wave signal, exploiting the fact that the r-mode saturation amplitude is insensitive to the structural properti…
The relationship between pulsar-like compact stars and gravitational waves is briefly reviewed. Due to regular spins, pulsars could be useful tools for us to detect ~nano-Hz low-frequency gravitational waves by pulsar-timing array technique; besides, they would also be ~kilo-Hz high-frequency gravitational wave radiators because of their compactness. The wave strain of an isolate pulsar depends on the equation state of cold matter at supra-nuclear densities. Therefore, a real detection of gravitational wave should be very meaningful in gravity physics, micro-theory of elementary strong interac…
We study the detectability of circular polarization in a stochastic gravitational wave background from various sources such as supermassive black hole binaries, cosmic strings, and inflation in the early universe with pulsar timing arrays. We calculate generalized overlap reduction functions for the circularly polarized stochastic gravitational wave background. We find that the circular polarization can not be detected for an isotropic background. However, there is a chance to observe the circular polarization for an anisotropic gravitational wave background. We also show how to separate polar…
Searches for continuous gravitational waves from known pulsars so far have been targeted at or near the spin frequency or double the spin frequency of each pulsar, appropriate for mass quadrupole emission. But some neutron stars might radiate strongly through current quadrupoles via $r$-modes, which oscillate at about four thirds the spin frequency. We show for the first time how to construct searches over appropriate ranges of frequencies and spin-down parameters to target $r$-modes from known pulsars. We estimate computational costs and sensitivities of realistic $r$-mode searches using the …
Several past searches for gravitational waves from a selection of known pulsars have been performed with data from the science runs of the Laser Inferometer Gravitational-wave Observatory (LIGO) gravitational wave detectors. So far these have lead to no detection, but upper limits on the gravitational wave amplitudes have been set. Here we study our intrinsic ability to detect, and estimate the gravitational wave amplitude for non-accreting pulsars. Using spin-down limits on emission as a guide we examine amplitudes that would be required to observe known pulsars with future detectors (Advance…
We study the putative emission of gravitational waves (GWs) in particular for pulsars with measured braking index. We show that the appropriate combination of both GW emission and magnetic dipole brakes can naturally explain the measured braking index, when the surface magnetic field and the angle between the magnetic dipole and rotation axes are time dependent. Then we discuss the detectability of these very pulsars by aLIGO and the Einstein Telescope. We call attention to the realistic possibility that aLIGO can detect the GWs generated by at least some of these pulsars, such as Vela, for ex…
I review some of the major developments in the theoretical background and experimental uses of binary pulsars to explore local Lorentz invariance in the gravitational sector and its possible violation.
We estimate the gravitational wave amplitude as a function of frequency produced during the creation of pulsars from the gravitational collapse of a massive star. The three main quantities needed are the magnitude of the magnetic field producing pulsar kicks, the temperature which determines the velocity of the pulsar and the duration time for the gravitational radiation.res
We present the first searches for gravitational waves from r-modes of the Crab pulsar, coherently and separately integrating data from three stretches of the first two observing runs of Advanced LIGO using the F-statistic. The second run was divided in two by a glitch of the pulsar roughly halfway through. The frequencies and derivatives searched were based on radio measurements of the pulsar's spin-down parameters as described in Caride et al., Phys. Rev. D 100, 064013 (2019). We did not find any evidence of gravitational waves. Our best 90% confidence upper limits on gravitational wave intri…
We conduct searches for continuous gravitational waves from seven pulsars, that have not been targeted in continuous wave searches of Advanced LIGO data before. We target emission at exactly twice the rotation frequency of the pulsars and in a small band around such frequency. The former search assumes that the gravitational wave quadrupole is changing phase-locked with the rotation of the pulsar. The search over a range of frequencies allows for differential rotation between the component emitting the radio signal and the component emitting the gravitational waves, for example the crust or ma…
The sensitivity of pulsar timing arrays to gravitational waves is, at some level, limited by timing noise. Red timing noise - the stochastic wandering of pulse arrival times with a red spectrum - is prevalent in slow-spinning pulsars and has been identified in many millisecond pulsars. Phenomenological models of timing noise, such as from superfluid turbulence, suggest that the timing noise spectrum plateaus below some critical frequency, $f_c$, potentially aiding the hunt for gravitational waves. We examine this effect for individual pulsars by calculating minimum observation times, $T_{\rm m…
Pulsar timing arrays (PTAs) are being used to search for very low frequency gravitational waves. A gravitational wave signal appears in pulsar timing residuals through two components: one independent of and one dependent on the pulsar's distance, called the 'Earth term' (ET) and 'pulsar term' (PT), respectively. The signal of a burst (or transient) gravitational wave source in pulsars' residuals will in general have the Earth and pulsar terms separated by times of the order of the time of flight from the pulsar to the Earth. Therefore, both terms are not observable over a realistic observation…
Complementary to ground-based laser interferometers, pulsar timing array experiments are being carried out to search for nanohertz gravitational waves. Using the world's most powerful radio telescopes, three major international collaborations have collected $\sim$10-year high precision timing data for tens of millisecond pulsars. In this paper we give an overview on pulsar timing experiments, gravitational wave detection in the nanohertz regime, and recent results obtained by various timing array projects.
A rotating black hole can be clouded by light bosons via superradiance, and thus acquire an atom-like structure. If such a gravitational atom system is companioned with a pulsar, the pulsar can trigger transitions between energy levels of the gravitational atom, and these transitions can be detected by pulsar timing. We show that in such pulsar-black hole systems, fine and hyperfine structure transitions are more likely to be probed than the Bohr transition. Also, the calculation of these fine and hyperfine structure transitions are under better analytic control. Thus, these fine and hyperfine…
Pulsars, especially millisecond pulsars, are intrinsically very stable celestial clocks, and their great pulse period stability open up a wide range of potential applications to astronomical phenomena, such as a natural detector for very low frequency ($10^{-7}-10^{-9}$ Hz) gravitational waves (GWs) background from supermassive black hole binaries. Double neutron star (DNS) binary systems, containing one or two radio pulsars, lose orbital energy by gravitational radiation, which leads to the orbital shrink. As a result, two neutron stars get closer and closer, during which it contributes to th…
The search for gravitational waves using Pulsar Timing Arrays (PTAs) is a computationally expensive complex analysis that involves source-specific noise studies. As more pulsars are added to the arrays, this stage of PTA analysis will become increasingly challenging. Therefore, optimizing the number of included pulsars is crucial to reduce the computational burden of data analysis. Here, we present a suite of methods to rank pulsars for use within the scope of PTA analysis. First, we use the maximization of the signal-to-noise ratio as a proxy to select pulsars. With this method, we target the…
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…
The pulsar timing residuals induced by gravitational waves from non-evolving single binary sources with general elliptical orbits will be analyzed. For different orbital eccentricities, the timing residuals present different properties. The standard deviations of the timing residuals induced by a fixed gravitational wave source will be calculated for different values of the eccentricity. We will also analyze the timing residuals of PSR J0437-4715 induced by one of the best known single gravitational wave sources, the supermassive black hole binary in the blazar OJ287.
We discuss some aspects of de Araujo, Coelho & Costa (2016, 2017) concerning the role of a time dependent magnetic ellipticity on the pulsars' braking indices and on the putative gravitational waves (GWs) these objects can emit. Since only nine of more than 2000 known pulsars have accurately measured braking indices, it is of interest to extend this study to all known pulsars, in particular as regards GW generation. In summary, our results show a pessimistic prospect for the detection of GWs generated by these pulsars, even for advanced detectors such as aLIGO and AdVirgo, and the planned Eins…
We have earlier proposed a fourth order gravity model as a possible explanation for late time cosmic acceleration, and for flattened galaxy rotation curves. The model has a free length parameter whose value depends on the scale of the system under study (e.g. the whole Universe, a galaxy, or a compact binary pulsar). In the present work, we investigate the constraints imposed on the free model parameter by Hulse-Taylor binary pulsar data: periastron advance; and emission of gravitational waves and consequent period decay. It is shown that the model is consistent with these observations, provid…
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…
Recently, a braking index for the pulsar PSR J1640-4631 has been measured. With a braking index of $n = 3.15 \pm 0.03$, this pulsar has the highest braking index ever measured. As it is well known, a pure magnetic dipole brake yields $n = 3$, whereas a pure gravitational wave brake yields $n = 5$. Therefore, each of these mechanisms alone can not account for the braking index found for PSR J1640-4631. Here we show that such a braking index can be accounted for if the spindown model combines magnetic dipole and gravitational wave brakes. Then, we briefly discuss the detectability of this pulsar…
We study the role of time dependent magnetic ellipticities ($ε_{B}$) on the calculation of the braking index of pulsars. Moreover, we study the consequences of such a $ε_{B}$ on the amplitude of gravitational waves (GWs) generated by pulsars with measured braking indices. We show that, since the ellipticity generated by the magnetic dipole is extremely small, the corresponding amplitude of GWs is much smaller than the amplitude obtained via the spindown limit.
The present work is devoted to the detection of monochromatic gravitational wave signals emitted by pulsars using ALLEGRO's data detector. We will present the region (in frequency) of millisecond pulsars of the globular cluster 47 Tucanae (NGC 104) in the band of detector. With this result it was possible to analyse the data in the frequency ranges of the pulsars J1748-2446L and J1342+2822c, searching for annual Doppler variations using power spectrum estimates for the year 1999. We tested this method injecting a simulated signal in real data and we were able to detect it.
Pulsars are precision celestial clocks. When being put in a binary, the ticking conveys the secret of underlying spacetime geometrodynamics. We use pulsars to test if the gravitational interaction possesses a tiny deviation from Einstein's General Relativity (GR). In the framework of Standard-Model Extension (SME), we systematically search for Lorentz-violating operators cataloged by (a) the minimal couplings of mass dimension 4, (b) the CPT symmetry of mass dimension 5, and (c) the gravitational weak equivalence principle (GWEP) of mass dimension 8. No deviation from GR was found yet.
We propose to use pulsar-black hole binaries as a probe of gravitational collider physics. Induced by the gravitation of the pulsar, the atomic transitions of the boson cloud around the black hole back-react on the orbital motion. This leads to the deviation of binary period decrease from that predicted by general relativity, which can be directly probed by the Rømer delay of pulsar time-of-arrivals. The sensitivity and accuracy of this approach is estimated for two typical atomic transitions. It is shown that once the transitions happen within the observable window, the pulsar-timing accuracy…
We describe several new techniques which accelerate Bayesian searches for continuous gravitational-wave emission from supermassive black-hole binaries using pulsar timing arrays. These techniques mitigate the problematic increase of search-dimensionality with the size of the pulsar array which arises from having to include an extra parameter per pulsar as the array is expanded. This extra parameter corresponds to searching over the phase of the gravitational-wave as it propagates past each pulsar so that we can coherently include the pulsar-term in our search strategies. Our techniques make th…
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 f…
Pulsar timing arrays (PTAs) are used to search for long-wavelength gravitational waves (GWs) by monitoring a set of spin-stable millisecond pulsars. Most theoretical analyses assume that the relevant GW sources are much more distant from Earth than the pulsars comprising the array. Unlike ground- or solar system-based GW detectors, PTAs might well contain embedded GW sources. We derive the PTA response from sources at any distance, with a specific focus on GW bursts with memory (BWMs). We consider supernovae and compact binary mergers as potential Galactic BWM sources and evaluate the signatur…
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.
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…
Gravitational wave bursts produced by supermassive binary black hole mergers will leave a persistent imprint on the space-time metric. Such gravitational wave memory signals are detectable by pulsar timing arrays as a glitch event that would seem to occur simultaneously for all pulsars. In this paper, we describe an initial algorithm which can be used to search for gravitational wave memory signals. We apply this algorithm to the Parkes Pulsar Timing Array data set. No significant gravitational wave memory signal is founded in the data set.
Core-collapse supernovae emit on the order of 3x10^53 ergs in high-energy neutrinos over a time of order 10 seconds, and so decrease their mass by about 0.2 solar mass. If the explosion is nearly spherically symmetric, there will be little gravitational wave emission. Nevertheless, the sudden decrease of mass of the progenitor may cause a change in the gravitational time delay of signals from a nearby pulsar. We calculate the change in arrival times as successive pulses pass through the neutrino shell at different times, and find that the effect may be detectable in ideal circumstances.
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…
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 so…
Pulsar timing array experiments have recently reported strong evidence for a common-spectrum stochastic process with a strain spectral index consistent with that expected of a nanohertz-frequency gravitational-wave background, but with negligible yet non-zero evidence for spatial correlations required for a definitive detection. However, it was pointed out by the Parkes Pulsar Timing Array (PPTA) collaboration that the same models used in recent analyses resulted in strong evidence for a common-spectrum process in simulations where none is present. In this work, we introduce a methodology to d…
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…
The phenomenal rotational stability of millisecond pulsars allows them to be used as precise celestial clocks. An array of these pulsars can be exploited to search for correlated perturbations in their pulse times of arrival due to gravitational waves. Here, I describe the observations and analysis necessary to accomplish this goal and present an overview of the efforts of the worldwide pulsar timing community. Due to a growing number of millisecond pulsar discoveries, improved instrumentation, and growing timespans of observation, the sensitivity of our pulsar timing array experiments is expe…
Until recently, the only way to observe the Universe was from light received by telescopes. But we are now able to measure gravitational waves, which are ripples in the fabric of the Universe predicted by Albert Einstein. If two very dense objects (like black holes) orbit each other closely, they warp space and send out gravitational waves. For black holes that are similar in mass to the Sun, scientists use the LIGO detector on Earth. But for the biggest black holes in the Universe (billions of times more massive than the Sun), scientists monitor a net of rapidly-spinning neutron stars (called…
In one of our previous articles we have considered the role of a time dependent magnetic ellipticity on pulsars' braking indices and on the putative gravitational waves these objects can emit. Since only nine of more than 2000 known pulsars have accurately measured braking indices, it is of interest to extend this study to all known pulsars, in particular to what concerns the gravitational waves generation. To do so, as shown in our previous article, we need to know some pulsars' observable quantities such as: periods and their time derivatives, and estimated distances to the Earth. Moreover, …
Pulsar Timing Array (PTA) experiments exploit the clock-like behaviour of an array of millisecond pulsars, with the goal of detecting low-frequency gravitational waves. PTA experiments have been in operation over the last decade, led by groups in Europe, Australia, and North America. These experiments use the most sensitive radio telescopes in the world, extremely precise pulsar timing models and sophisticated detection algorithms to increase the sensitivity of PTAs. No detection of gravitational waves has been made to date with this technique, but PTA upper limits already contributed to rule …
Pulsars (PSRs) orbiting intermediate or supermassive black holes at the centre of galaxies and globular clusters are known as Extreme Mass Ratio Binaries (EMRBs) and have been identified as precision probes of strong-field GR. For appropriate orbital parameters, some of these systems may also emit gravitational radiation in a `burst-like' pattern. The observation of this burst radiation in conjunction with the electromagnetic radio timing signal would allow for multimessenger astronomy in strong-field gravitational regimes. In this work we investigate gravitational radiation from these PSR-EMR…
Observations of low-frequency gravitational waves will require the highest possible timing precision from an array of the most spin-stable pulsars. We can improve the sensitivity of a pulsar timing array (PTA) to different gravitational-wave sources by observing pulsars with low timing noise over years to decades and distributed across the sky. We discuss observing strategies for a PTA focused on a stochastic gravitational-wave background such as from unresolved supermassive black hole binaries as well as focused on single continuous-wave sources. First we describe the method to calculate a PT…
Two-Dimensional Pulsar Distance Inference from Nanohertz Gravitational Waves
College of Sciences, Northeastern University（东北大学理学院）；Liaoning Normal University（辽宁师范大学）；Hainan University（海南大学）；MOE Key Laboratory of Data Analytics and Optimization for Smart Industry, Northeastern University（东北大学工业智能与系统优化教育部重点实验室）；National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Northeastern University（东北大学工业智能与系统优化前沿科学中心）
Observations of short-duration gamma-ray bursts and their afterglows show that a good fraction (perhaps $\gtrsim50\%$) of binary neutron star mergers lead to strongly magnetized, rapidly rotating pulsars (including millisecond magnetars), no matter whether the pulsar remnants are short- or long-lived. Such compact objects are very likely to have significant radial oscillations and high interior temperatures, as indicated in recent numerical simulations. In this paper, we have investigated rotation-induced gravitational radiation from possibly existing, radially oscillating pulsars after binary…
This review is focused on tests of Einstein's theory of General Relativity with gravitational waves that are detectable by ground-based interferometers and pulsar timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent th…
