We present the results of an all-sky search for continuous gravitational wave signals with frequencies in the 1700-2000 Hz range from neutron stars with ellipticity of 1e-8. The search employs the Falcon analysis pipeline [citation 5] on LIGO O2 public data. Our results improve by a factor greater than 5 over [citation 11]. This is a huge leap forward: it takes an entirely new generation of gravitational wave detectors to achieve a 10-fold sensitivity increase over the previous generation [citation 12]. Within the probed frequency range and aside from the detected outliers, we can exclude neutron stars with ellipticity of 1e-8 within 65 pc of Earth. We set upper limits on the gravitational wave amplitude that hold even for worst-case signal parameters. New outliers are found, some of which we are unable to associate with any instrumental cause. If any were associated with a rotating neutron star, this would likely be the fastest neutron star today.
We present the results of an all-sky search for continuous gravitational wave signals with frequencies in the 500-1700 Hz range targeting neutron stars with ellipticity of 1e-8. The search is done on LIGO O2 data using the Falcon analysis pipeline. The results presented here double the sensitivity over any other result on the same data. The search is capable of detecting low ellipticity sources up to 170 pc. We establish strict upper limits which hold for worst-case signal parameters. We list outliers uncovered by the search, including several which we cannot associate with any known instrumen…
We present the results of an all-sky search for continuous gravitational wave signals with frequencies in the 20-500 Hz range from neutron stars with ellipticity of 1e-8. This frequency region is particularly hard to probe because of the quadratic dependence of signal strength on frequency. The search employs the Falcon analysis pipeline on LIGO O2 public data. Compared to previous Falcon analyses the coherence length has been quadrupled, with a corresponding increase in sensitivity. This enables us to search for small ellipticity neutron stars in this low frequency region up to 44 pc away. Th…
Neutron stars spin down over time due to a number of energy-loss processes. We provide tantalizing population-based evidence that millisecond pulsars (MSPs) have a minimum ellipticity of $ε\approx10^{-9}$ around their spin axis and that, consequently, some spin down mostly through gravitational-wave emission. We discuss the implications of such a minimum ellipticity in terms of the internal magnetic field strengths and nuclear matter composition of neutron stars and show it would result in the Advanced LIGO and Virgo gravitational-wave detectors, or their upgrades, detecting gravitational wave…
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.
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…
Galactic neutron stars are a promising source of gravitational waves in the analysis band of detectors such as LIGO and Virgo. Previous searches for gravitational waves from neutron stars have focused on the detection of individual neutron stars, which are either nearby or highly non-spherical. Here we consider the stochastic gravitational-wave signal arising from the ensemble of Galactic neutron stars. Using a population synthesis model, we estimate the single-sigma sensitivity of current and planned gravitational-wave observatories to average neutron star ellipticity $ε$ as a function of the…
X-ray observations of some short gamma-ray bursts indicate that a long-lived neutron star can form as a remnant of a binary neutron star merger. We develop a gravitational-wave detection pipeline for a long-lived binary neutron star merger remnant guided by these counterpart electromagnetic observations. We determine the distance out to which a gravitational-wave signal can be detected with Advanced LIGO at design sensitivity and the Einstein Telescope using this method, guided by X-ray data from GRB140903A as an example. Such gravitational waves can in principle be detected out to $\sim$ 20 M…
We consider a simulated population of isolated Galactic neutron stars. The rotational frequency of each neutron star evolves through a combination of electromagnetic and gravitational wave emission. The magnetic field strength dictates the dipolar emission, and the ellipticity (a measure of a neutron star's deformation) dictates the gravitational wave emission. Through both analytic and numerical means, we assess the detectability of the Galactic neutron star population and bound the magnetic field strength and ellipticity parameter space of Galactic neutron stars with or without a direct grav…
A millisecond pulsar having an ellipticity, that is an asymmetric mass distribution around its spin-axis, could emit continuous gravitational waves, which have not been detected so far. An indirect way to infer such waves is to estimate the contribution of the waves to the spin-down rate of the pulsar. The transitional pulsar PSR J1023+0038 is ideal and unique for this purpose, because this is the only millisecond pulsar for which the spin-down rate has been measured in both accreting and non-accreting states. Here we infer, from our formalism based on the complete torque budget equations and …
Aims. We estimate the number of pulsars, detectable as continuous gravitational wave sources with the current and future gravitational-wave detectors, assuming a simple phenomenological model of evolving non-axisymmetry of the rotating neutron star. Methods. We employ a numerical model of the Galactic neutron star population, with the properties established by comparison with radio observations of isolated Galactic pulsars. We generate an arbitrarily large synthetic population of neutron stars and evolve their period, magnetic field, and position in space. We use a gravitational wave emission …
When looking for gravitational wave signals from known pulsars, targets have been treated using independent searches. Here we use a hierarchical Bayesian framework to combine observations from individual sources for two purposes: to produce a detection statistic for the whole ensemble of sources within a search, and to estimate the hyperparameters of the underlying distribution of pulsar ellipticities. Both purposes require us to assume some functional form of the ellipticity distribution, and as a proof of principle we take two toy distributions. One is an exponential distribution, defined by…
We give the lens equation for light deflections caused by point mass condensations in an otherwise spatially homogeneous and flat universe. We assume the signal from a distant source is deflected by a single condensation before it reaches the observer. We call this deflector an embedded lens because the deflecting mass is part of the mean density. The embedded lens equation differs from the conventional lens equation because the deflector mass is not simply an addition to the cosmic mean. We prescribe an iteration scheme to solve this new lens equation and use it to compare our results with st…
Rotating neutron stars (NSs) are promising sources of gravitational waves (GWs) in the frequency band of ground-based detectors. They are expected to emit quasi-monochromatic, long-duration GW signals, called continuous waves (CWs), due to their deviations from spherical symmetry. The degree of such deformations, and hence the information about the internal structure of a NS, is encoded in a dimensionless parameter $\varepsilon$ called ellipticity. Searches for CW signals from isolated Galactic NSs have shown to be sensitive to ellipticities as low as $\varepsilon \sim \mathcal{O}(10^{-9})$. T…
Continuous gravitational waves from Galactic neutron stars: demography, detectability and prospects
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 Institute for Astronomy（马克斯·普朗克天文学研究所）；University of Utah（犹他大学）；California Institute of Technology（加州理工学院）；The University of Tokyo（东京大学）；University of Portsmouth（朴茨茅斯大学）
We describe a new method for extracting gravitational wave signals from pulsar timing data. We show that any gravitational wave signal can be decomposed into an orthogonal set of sky maps, with the number of maps equal to the number of pulsars in the timing array. These maps may be used as a basis to construct gravitational wave templates for any type of source, including collections of point sources. A variant of the standard Hellings-Downs correlation analysis is recovered for statistically isotropic signals. The template based approach allows us to probe potential anisotropies in the signal…
We study the prospects of detecting continuous gravitational waves (CGWs) from spinning neutron stars (NSs), gravitationally lensed by the galactic supermassive black hole. Assuming various astrophysically motivated spatial distributions of galactic NSs, we find that CGW signals from a few ($\sim 0-6$) neutron stars should be strongly lensed. Lensing will produce two copies of the signal (with time delays of seconds to minutes) that will interfere with each other. The relative motion of the NS with respect to the lensing optical axis will change the interference pattern, which will help us to …
Future observations of continuous gravitational waves from single neutron stars, apart from their monumental astrophysical significance, could also shed light on fundamental physics and exotic particle states. One such avenue is based on the fact that magnetic fields cause deformations of a neutron star, which results in a magnetic-field-induced quadrupole ellipticity. If the magnetic and rotation axes are different, this quadrupole ellipticity may generate continuous gravitational waves which may last decades, and may be observable in current or future detectors. Light, milli-magnetic monopol…
We introduce a fully-coherent method for searching for gravitational wave signals generated by the merger of black hole and/or neutron star binaries. This extends the coherent analysis previously developed and used for targeted gravitational wave searches to an all-sky, all-time search. We apply the search to one month of data taken during the fifth science run of the LIGO detectors. We demonstrate an increase in sensitivity of 25% over the coincidence search, which is commensurate with expectations. Finally, we discuss prospects for implementing and running a coherent search for gravitational…
The first detection of gravitational waves by LIGO from the merger of two compact objects has sparked new interest in detecting electromagnetic counterparts to these violent events. For mergers involving neutron stars, it is thought that prompt high-energy emission in gamma rays and x-rays will be followed days to weeks later by an afterglow in visible light, infrared and radio. Rapid sky localization using the data from a network of gravitational wave detectors is essential to maximize the chances of making a joint detection. Here I describe a new technique that is able to produce accurate, f…
Observations of short gamma-ray bursts indicate ongoing energy injection following the prompt emission, with the most likely candidate being the birth of a rapidly rotating, highly magnetised neutron star. We utilise X-ray observations of the burst remnant to constrain properties of the nascent neutron star, including its magnetic field-induced ellipticity and the saturation amplitude of various oscillation modes. Moreover, we derive strict upper limits on the gravitational wave emission from these objects by looking only at the X-ray light curve, showing the burst remnants are unlikely to be …
We report the results of a directed search for continuous gravitational-wave emission in a broad frequency range (between 50 and 1000 Hz) from the central compact object of the supernova remnant Cassiopeia A (Cas A). The data comes from the sixth science run of LIGO and the search is performed on the volunteer distributed computing network Einstein@Home. We find no significant signal candidate, and set the most constraining upper limits to date on the gravitational-wave emission from Cas A, which beat the indirect age-based upper limit across the entire search range. At around 170 Hz (the most…
A theoretical description of electromagnetic waves in the background of a (weak) gravitational wave is presented. Explicit expressions are obtained for the Stokes parameters during the passage of a plane-fronted gravitational wave described by the Ehlers-Kundt metric. In particular, it is shown that the axis of the polarization ellipse oscillates, its ellipticity remaining constant.
Localization estimates for GW150914, the first binary black hole detected by the LIGO instruments, were shared with partner facilities for electromagnetic follow-up. While the source was a compact binary coalescence (CBC), it was first identified by algorithms that search for unmodeled signals, which produced the skymaps that directed electromagnetic observations. Later on, CBC specific algorithms produced refined versions, which showed significant differences. In this paper we show that those differences were not accidental and that CBC and unmodeled skymaps for binary black holes will freque…
We present the results of an all-sky search for continuous gravitational wave signals with frequencies in the 200-600 Hz range and frequency derivative (spindown) from -1e-8 through 1.11e-9 Hz/s. Together with the results from [1], this search completes the all-sky survey for frequencies between 20 to 600 Hz on O1 data. It also demonstrates the scalability of our search on a parameter space 26 times larger than previously considered. The results presented here complement the LIGO O2 data results [2,3] with comparable when not better sensitivity and do not rely on data with irregularities in th…
We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50--1100 Hz and with the frequency's time derivative in the range -5.0E-9 Hz/s to zero. Data from the first eight months of the fifth LIGO science run (S5) have been used in this search, which is based on a semi-coherent method (PowerFlux) of summing strain power. Observing no evidence of periodic gravitational radiation, we report 95% confidence-level upper limits on radiation emitted by any unknown isolated rotating neutron stars within the search range. Strain limits below 1.E-24 a…
We estimate the maximum equatorial ellipticity sustainable by compact stars composed of crystalline color-superconducting quark matter. For the theoretically allowed range of the gap parameter $Δ$, the maximum ellipticity could be as large as $10^{-2}$, which is about 4 orders of magnitude larger than the tightest upper limit obtained by the recent science runs of the LIGO and GEO600 gravitational wave detectors based on the data from 78 radio pulsars. We point out that the current gravitational-wave strain upper limit already has some implications for the gap parameter. In particular, the upp…
We provide analysis to determine the effects of gravitational waves on electromagnetic waves, using perturbation theory in general relativity. Our analysis is performed in a completely covariant manner without invoking any coordinates. For a given observer, in the geometrical-optics approximation, we work out the perturbations of the phase, amplitude, frequency and polarization properties--axes of ellipse and ellipticity of light, due to gravitational waves. With regard to the observation of gravitational waves, we discuss the measurement of Stokes parameters, through which the antenna pattern…
Binary millisecond pulsars (MSPs) are detached binary systems consisting of a MSP and a He white dwarf. If the initial orbital periods of binary MSPs are less than 0.3 day, they would evolve toward ultra-compact binary pulsars due to the rapid orbital shrinkage by the gravitational wave (GW) radiation. During the orbital decay, the MSP with an ellipticity would spin down by the GW radiation and the magnetic dipole radiation. Our calculations indicate that the angular momentum loss is dominated by the GW radiation when the ellipticities of the neutron stars (NSs) are in the range of $(1-50)\tim…
We formulate deformation of relativistic stars due to the magnetic stress, considering the magnetic fields to be perturbations from spherical stars. The ellipticity for the dipole magnetic field is calculated for some stellar models. We have found that the ellipticity becomes large with increase of a relativistic factor for the models with the same energy ratio of the magnetic energy to the gravitational energy.
All-sky, broadband, coherent searches for gravitational-wave pulsars are computationally limited. It is therefore important to make efficient use of available computational resources, notably by minimizing the number of templates used to cover the signal parameter space of sky position and frequency evolution. For searches over the sky, however, the required template density (determined by the parameter-space metric) is different at each sky position, which makes it difficult in practice to achieve an efficient covering. Previous work on this problem has found various choices of sky and freque…
The gravitational wave detectors currently in operation perform the analysis of their scientific data jointly. Concerning the search for bursting sources, coherent data analysis methods have been shown to be more efficient. In the coherent approach, the data collected by the detectors are time-shifted and linearly combined so that the signatures received by each detector add up constructively (thus improving the resulting signal-to-noise ratio). This operation has to be performed over a sky grid (which determines the sky locations to be searched). A limitation of those pipelines is their large…
We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1000 Hz and having a negative frequency time derivative with magnitude between zero and $10^{-8}$ Hz/s. Data from the fourth LIGO science run have been used in this search. Three different semi-coherent methods of summing strain power were applied. Observing no evidence for periodic gravitational radiation, we report upper limits on strain amplitude and interpret these limits to constrain radiation from rotating neutron stars.
We perform a wide parameter space search for continuous gravitational waves over the whole sky and over a large range of values of the frequency and the first spin-down parameter. Our search method is based on the Hough transform, which is a semi-coherent, computationally efficient, and robust pattern recognition technique. We apply this technique to data from the second science run of the LIGO detectors and our final results are all-sky upper limits on the strength of gravitational waves emitted by unknown isolated spinning neutron stars on a set of narrow frequency bands in the range 200-$40…
Data collected by the GEO600 and LIGO interferometric gravitational wave detectors during their first observational science run were searched for continuous gravitational waves from the pulsar J1939+2134 at twice its rotation frequency. Two independent analysis methods were used and are demonstrated in this paper: a frequency domain method and a time domain method. Both achieve consistent null results, placing new upper limits on the strength of the pulsar's gravitational wave emission. A model emission mechanism is used to interpret the limits as a constraint on the pulsar's equatorial ellipt…
We develop a set of data analysis tools for a realistic all-sky search for continuous gravitational-wave signals. The methods that we present apply to data from both the resonant bar detectors that are currently in operation and the laser interferometric detectors that are in the final stages of construction and commissioning. We show that with our techniques we shall be able to perform an all-sky 2-day long coherent search of the narrow-band data from the resonant bar EXPLORER with no loss of signals with the dimensionless amplitude greater than $2.8\times10^{-23}$.
Fully-coherent all-sky search for gravitational wave (GW) signals from the coalescence of compact object binaries is a computationally expensive task. Approximations, such as semi-coherent coincidence searches, are currently used to circumvent the computational barrier with a concomitant loss in sensitivity. We explore the effectiveness of Particle Swarm Optimization (PSO) in addressing this problem. Our results, using a simulated network of detectors with initial LIGO design sensitivities and a realistic signal strength, show that PSO can successfully deliver a fully-coherent all-sky search w…
For a uniform population of neutron stars whose spin-down is dominated by the emission of gravitational radiation, an old argument of Blandford states that the expected gravitational-wave amplitude of the nearest source is independent of the deformation and rotation frequency of the objects. Recent work has improved and extended this argument to set upper limits on the expected amplitude from neutron stars that also emit electromagnetic radiation. We restate these arguments in a more general framework, and simulate the evolution of such a population of stars in the gravitational potential of o…
Detection of gravitational waves(GW) involves using the network of GW telescopes to observe a large sky region. However, owing to the arrangement of the GW telescopes, even with aLIGO- aVirgo-KAGRA network,parameter estimation accuracy deteriorates depending on the sky region of the GW source due to the ill-posed nature of the inverse operator. A regularization-based method is proposed herein to improve parameter estimation accuracy. Although conventional regularization methods cannot optimize all regulator parameters completely, the proposed method archives full optimization by applying an a-…
Probing magnetic fields of compact objects with continuous gravitational waves
Inter University Centre for Astronomy and Astrophysics（大学天文与天体物理中心）；Universitat de les Illes Balears（巴利阿里群岛大学）；Department of Physics, Indian Institute of Technology Gandhinagar（印度理工学院甘地纳加尔物理系）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究院国际理论科学中心）
Localizing the sky position of the gravitational wave source is a key scientific goal for gravitational wave observations. Employing the Fisher information matrix approximation, we compute the angular resolutions of LISA and TianQin, two planned space-based gravitational wave detectors and examine how detectors' configuration properties, such as the orientation change of the detector plane, heliocentric or geocentric motion and the arm length etc. affect the accuracy of source localization. We find that the amplitude modulation due to the annual changing orientation of the detector plane helps…
We present results of the all-sky search for gravitational-wave signals from spinning neutron stars in the data of the EXPLORER resonant bar detector. Our data analysis technique was based on the maximum likelihood detection method. We briefly describe the theoretical methods that we used in our search. The main result of our analysis is an upper limit of ${\bf 2\times10^{-23}}$ for the dimensionless amplitude of the continuous gravitational-wave signals coming from any direction in the sky and in the narrow frequency band from 921.00 Hz to 921.76 Hz.
We revisit the gravitational lensing phenomenon using a new visualization technique. It consists in projecting the observers sky into the source plane, what gives rise to a folded and stretched surface. This provides a clear graphical tool to visualize some interesting well-known effects, such as the development of multiple images of a source, the structure of the caustic curves, the parity of the images and their magnification as a function of the source position.
Our understanding of observed Gravitational Waves (GWs) comes from matching data to known signal models describing General Relativity (GR). These models, expressed in the post-Newtonian formalism, contain the mathematical constant $π$. Allowing $π$ to vary thus enables a strong, universal and generalisable null test of GR. From a population of 22 GW observations, we make an astrophysical measurement of $π=3.115^{+0.048}_{-0.088}$, and prefer GR as the correct theory of gravity with a Bayes factor of 321. We find the variable $π$ test robust against simulated beyond-GR effects.
We investigate the independent points in the sky require to search the periodic gravitational wave, assuming the noise power spectral density to be flat. We have made an analysis with different initial azimuth of the Earth for a week data set. The analysis shows significant difference in the independent points in the sky for the search. We numerically obtain an approximate relation to make trade-off between computational cost and sensitivities. We also discuss the feasibility of the coherent search in small frequency band in reference to advanced LIGO.
We report a new pulsar population synthesis based on Monte Carlo techniques, aiming to estimate the contribution of galactic radio pulsars to the continuous gravitational wave emission. Assuming that the rotation periods of pulsars at birth have a Gaussian distribution, we find that the average initial period is 290 ms. The number of objects with periods equal to or less than 0.4 s, and therefore capable of being detected by an interferometric gravitational antenna like VIRGO, is of the order of 5100-7800. With integration times lasting between 2 and 3 yr, our simulations suggest that about tw…
