The phase parameters of matched-filtering searches for continuous gravitational-wave signals are sky position, frequency and frequency time-derivatives. The space of these parameters features strong global correlations in the optimal detection statistic. For observation times smaller than one year, the orbital motion of the Earth leads to a family of global-correlation equations which describes the "global maximum structure" of the detection statistic. The solution to each of these equations is a different hypersurface in parameter space. The expected detection statistic is maximal at the intersection of these hypersurfaces. The global maximum structure of the detection statistic from stationary instrumental-noise artifacts is also described by the global-correlation equations. This permits the construction of a veto method which excludes false candidate events.
We present the Fourier Transform of continuous gravitational wave for arbitrary location of detector and source and for any duration of observation time in which both rotational motion of earth about its spin axis and orbital motion around sun has been taken into account. We also give the method to account the spin down of continuous gravitational wave.
We determine the transfer functions of two kinds of filters that can be used in the detection of continuous gravitational radiation. The first one optimizes the signal-to-noise ratio, and the second reproduces the wave with minimum error. We analyse the behaviour of these filters in connection with actual detection schemes.
$χ^2$ vetoes are commonly used in searching for gravitational waves, in particular for broad-band signals, but they can also be applied to narrow-band continuous wave signals, such as those expected from rapidly rotating neutron stars. In this paper we present a $χ^2$ veto adapted to the Hough transform searches for continuous gravitational wave signals; we characterize the $χ^2$-significance plane for different frequency bands; and discuss the expected performance of this veto in LIGO analysis.
We analyze the computational costs of searches for continuous monochromatic gravitational waves emitted by rotating neutron stars orbiting a companion object. As a function of the relevant orbital parameters, we address the computational load involved in targeted searches, where the position of the source is known; the results are applied to known binary radio pulsars and Sco-X1.
The main problem that we will face in the data analysis for continuous gravitational-wave sources is processing of a very long time series and a very large parameter space. We present a number of analytic and numerical tools that can be useful in such a data analysis. These consist of methods to calculate false alarm probabilities, use of probabilistic algorithms, application of signal splitting, and accurate estimation of parameters by means of optimization algorithms.
Detection of continuous gravitational waves from rapidly-spinning neutron stars opens up the possibility of examining their internal physics. We develop a framework that leverages a future continuous gravitational wave detection to infer a neutron star's moment of inertia, equatorial ellipticity, and the component of the magnetic dipole moment perpendicular to its rotation axis. We assume that the neutron star loses rotational kinetic energy through both gravitational wave and electromagnetic radiation, and that the distance to the neutron star can be measured, but do not assume electromagneti…
Continuous gravitational waves are long-lasting forms of gravitational radiation produced by persistent quadrupolar variations of matter. Standard expected sources for ground-based interferometric detectors are neutron stars presenting non-axisymmetries such as crustal deformations, r-modes or free precession. More exotic sources could include decaying ultralight boson clouds around spinning black holes. A rich suite of data-analysis methods spanning a wide bracket of thresholds between sensitivity and computational efficiency has been developed during the last decades to search for these sign…
We describe an efficient method of matched filtering over long (greater than 1 day) time baselines starting from Fourier transforms of short durations (roughly 30 minutes) of the data stream. This method plays a crucial role in the search algorithm developed by Schutz and Papa for the detection of continuous gravitational waves from pulsars. Also, we discuss the computational cost--saving approximations used in this method, and the resultant performance of the search algorithm.
We derive a simple algebraic criterion to select the optimal detector network for a coherent wide parameter-space (all-sky) search for continuous gravitational waves. Optimality in this context is defined as providing the highest (average) sensitivity per computing cost. This criterion is a direct consequence of the properties of the multi-detector F-statistic metric, which has been derived recently. Interestingly, the choice of the optimal network only depends on the noise-levels and duty-cycles of the respective detectors, and not on the available computing power.
We analyze a bifurcation phenomenon associated with critical gravitational collapse in a family of self-gravitating SU(2) $σ$-models. As the dimensionless coupling constant decreases, the critical solution changes from discretely self-similar (DSS) to continuously self-similar (CSS). Numerical results provide evidence for a bifurcation which is analogous to a heteroclinic loop bifurcation in dynamical systems, where two fixed points (CSS) collide with a limit cycle (DSS) in phase space as the coupling constant tends to a critical value.
Continuous gravitational waves represent one of the long-sought types of signals that have yet to be detected. Due to their small amplitude, long observational datasets (months-years) have to be analyzed together, thereby vastly increasing the computational cost of these searches. All-sky searches face the most severe computational obstacles, especially searches for sources in unknown binary systems, which need to break the data into very short segments in order to be computationally feasible. In this paper, we present a new detection statistic that improves sensitivity by up to 19% compared t…
We derive two different methods to compute the minimal required integration time of a fully coherent follow-up of candidates produced in wide parameter space semi-coherent searches, such as global correlation StackSlide searches using Einstein@Home. We numerically compare these methods in terms of integration duration and computing cost. In a Monte Carlo study we confirm that we can achieve the required detection probability.
We pursue a novel strategy towards a first detection of continuous gravitational waves from rapidly-rotating deformed neutron stars. Computational power is focused on a narrow region of signal parameter space selected by a strategically-chosen benchmark. We search data from the 2nd observing run of the LIGO Observatory with an optimised analysis run on graphics processing units. While no continuous waves are detected, the search achieves a sensitivity to gravitational wave strain of $h_0 = 1.01{\times}10^{-25}$ at 90% confidence, 24% to 69% better than past searches of the same parameter space…
This paper describes an incoherent method to search for continuous gravitational waves based on the Hough transform, a well known technique used for detecting patterns in digital images. We apply the Hough transform to detect patterns in the time-frequency plane of the data produced by an earth-based gravitational wave detector. Two different flavors of searches will be considered, depending on the type of input to the Hough transform: either Fourier transforms of the detector data or the output of a coherent matched-filtering type search. We present the technical details for implementing the …
We present a search for continuous gravitational waves emitted by neutron stars in binary systems conducted on data from the early third observing run of the Advanced LIGO and Advanced Virgo detectors using the semicoherent, GPU-accelerated, BinarySkyHough pipeline. The search analyzes the most sensitive frequency band of the LIGO detectors, 50 - 300 Hz. Binary orbital parameters are split into four regions, comprising orbital periods of 3 - 45 days and projected semimajor axes of 2 - 40 light-seconds. No detections are reported. We estimate the sensitivity of the search using simulated contin…
The direct detection of continuous gravitational waves from pulsars is a much anticipated discovery in the emerging field of multi-messenger gravitational wave (GW) astronomy. Because putative pulsar signals are exceedingly weak large amounts of data need to be integrated to achieve desired sensitivity. Contemporary searches use ingenious ad-hoc methods to reduce computational complexity. In this paper we provide analytical expressions for the Fourier transform of realistic pulsar signals. This provides description of the manifold of pulsar signals in the Fourier domain, used by many search me…
The birth of gravitational wave astronomy was triggered by the first detection of a signal produced by the merger of two compact objects (also known as a compact binary coalescence event). The following detections made by the Earth-based network of advanced interferometers had a significant impact in many fields of science: astrophysics, cosmology, nuclear physics and fundamental physics. However, compact binary coalescence signals are not the only type of gravitational waves potentially detectable by LIGO, Virgo, and KAGRA. An interesting family of still undetected signals, and the ones that …
Fully coherent searches (over realistic ranges of parameter space and year-long observation times) for unknown sources of continuous gravitational waves are computationally prohibitive. Less expensive hierarchical searches divide the data into shorter segments which are analyzed coherently, then detection statistics from different segments are combined incoherently. The novel method presented here solves the long-standing problem of how best to do the incoherent combination. The optimal solution exploits large-scale parameter-space correlations in the coherent detection statistic. Application …
Periodic (almost monochromatic) gravitational waves emitted by rotating, asymmetric neutron stars are intriguing potential signals in the sensitivity band of Advanced LIGO and Advanced Virgo detectors. These signals are related to elastic and magnetic stresses in the neutron-star interior, as well as to various possible instabilities, and thus are interesting from the point of view of the largely-unknown neutron star structure. I will describe the main challenges related to these searches, the current state of the data-analysis methods and plans for the future.
In this work we present the results of a search for continuous gravitational waves from the Galactic Center using LIGO O2 data. The search uses the Band-Sampled-Data directed search pipeline, which performs a semi-coherent wide-parameter-space search, exploiting the robustness of the FrequencyHough transform algorithm. The search targets signals emitted by isolated asymmetric spinning neutron stars, located within 25-150 parsecs from the Galactic Center. The frequencies covered in this search range between 10 and 710 Hz with a spin-down range from $-1.8\times10^{-9}$ to $3.7\times10^{-11}$ Hz/…
The $\mathcal{F}$-statistic is a detection statistic used widely in searches for continuous gravitational waves with terrestrial, long-baseline interferometers. A new implementation of the $\mathcal{F}$-statistic is presented which accelerates the existing "resampling" algorithm using graphics processing units (GPUs). The new implementation runs between 10 and 100 times faster than the existing implementation on central processing units without sacrificing numerical accuracy. The utility of the GPU implementation is demonstrated on a pilot narrowband search for four newly discovered millisecon…
We report results of a search for continuous gravitational waves from a region covering the globular cluster Terzan 5 and the galactic center. Continuous gravitational waves are expected from fast-spinning, slightly non-axisymmetric isolated neutron stars as well as more exotic objects. The regions that we target are believed to be unusually abundant in neutron stars. We use a new loosely coherent search method that allows to reach unprecedented levels of sensitivity for this type of search. The search covers the frequency band 475-1500 Hz and frequency time derivatives in the range of [-3e-8,…
Rapidly spinning neutron stars with non-axisymmetric mass distributions are expected to generate quasi-monochromatic continuous gravitational waves. While many searches for unknown, isolated spinning neutron stars have been carried out, there have been no previous searches for unknown sources in binary systems. Since current search methods for unknown, isolated neutron stars are already computationally limited, expanding the parameter space searched to include binary systems is a formidable challenge. We present a new hierarchical binary search method called TwoSpect, which exploits the period…
We derive explicit expressions for the multi-detector F-statistic metric applied to short-duration non-precessing inspiral signals. This is required for template bank production associated with coherent searches for short-duration non-precessing inspiral signals in gravitational-wave data from a network of detectors. We compare the metric's performance with explicit overlap calculations for all relevant dimensions of parameter space and find the metric accurately predicts the loss of detection statistic above overlaps of 95%. We also show the effect that neglecting the variations of the detect…
We investigate the Bayesian framework for detection of continuous gravitational waves (GWs) in the context of targeted searches, where the phase evolution of the GW signal is assumed to be known, while the four amplitude parameters are unknown. We show that the orthodox maximum-likelihood statistic (known as F-statistic) can be rediscovered as a Bayes factor with an unphysical prior in amplitude parameter space. We introduce an alternative detection statistic ("B-statistic") using the Bayes factor with a more natural amplitude prior, namely an isotropic probability distribution for the orienta…
It is well known that matched filtering techniques cannot be applied for searching extensive parameter space volumes for continuous gravitational wave signals. This is the reason why alternative strategies are being pursued. Hierarchical strategies are best at investigating a large parameter space when there exist computational power constraints. Algorithms of this kind are being implemented by all the groups that are developing software for analyzing the data of the gravitational wave detectors that will come online in the next years. In this talk we will report about the hierarchical Hough t…
The search for continuous gravitational waves from unknown isolated sources is computationally limited due to the enormous parameter space that needs to be covered and the weakness of the expected signals. Therefore semi-coherent search strategies have been developed and applied in distributed computing environments such as Einstein@Home, in order to narrow down the parameter space and identify interesting candidates. However, in order to optimally confirm or dismiss a candidate as a possible gravitational-wave signal, a fully-coherent follow-up using all the available data is required. We pre…
We characterize and present the details of the follow-up method used on the most significant outliers of the Hough Einstein@Home all-sky search for continuous gravitational waves arXiv:1207.7176. This follow-up method is based on the two-stage approach introduced in arXiv:1303.2471, consisting of a semicoherent refinement followed by a fully coherent zoom. We quantify the efficiency of the follow-up pipeline using simulated signals in Gaussian noise. This pipeline does not search beyond first-order frequency spindown, and therefore we also evaluate its robustness against second-order spindown.…
The space of phase-parameters (sky-position, frequency, spindowns) of a coherent matched-filtering search for continuous gravitational waves from isolated neutron stars shows strong global correlations (``circles in the sky''). In the local limit this can be analysed in terms of a parameter-space metric, but the global properties are less well studied. In this work we report on our recent progress in understanding these global correlations analytically for short to intermediate (less than a month, say) observation times and neglecting spindowns. The location of these correlation-circles in par…
The direct detection of gravitational waves provides the opportunity to measure fundamental aspects of gravity which have never been directly probed before, including the polarization of gravitational waves. In the context of searches for continuous waves from known pulsars, we present novel methods to detect signals of any polarization content, measure the modes present and place upper-limits on the amplitude of non-tensorial components. This will allow us to obtain new model-independent, dynamical constraints on deviations from general relativity. We test this framework on multiple potential…
We consider the Bayesian detection statistic for a targeted search for continuous gravitational waves, known as the $\mathcal{B}$-statistic. This is a Bayes factor between signal and noise hypotheses, produced by marginalizing over the four amplitude parameters of the signal. We show that by Taylor-expanding to first order in certain averaged combinations of antenna patterns (elements of the parameter space metric), the marginalization integral can be performed analytically, producing a closed-form approximation in terms of confluent hypergeometric functions. We demonstrate using Monte Carlo s…
It is expected that interferometric gravitational wave detectors such as LIGO \cite{Barish99} will be eventually limited by fundamental noise sources like shot noise and Brownian motion, as well as by seismic noise. In the commissioning process, other technical noise sources (electronics noise, alignment fluctuations) limit the sensitivity and are eliminated one by one. We propose here a way to correlate the noise in the output of the gravitational wave detector with other detector and environmental signals not through their linear transfer functions (often unknown), but through their statisti…
Continuous Bogoliubov formalism for gravitational-wave generation in a unified dark sector warm inflation
University of Camerino（卡梅里诺大学）；INAF - Osservatorio Astronomico di Brera（国家天体物理研究所-布雷拉天文台）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Perugia（国家核物理研究所-佩鲁贾分部）
We present the foundations of a new solution technique for the characteristic initial value problem (IVP) of colliding plane gravitational waves. It has extensive similarities to the approach of Alekseev and Griffiths in 2001, but we use an inverse scattering method with a Riemann-Hilbert problem (RHP), which allows for a transformation to a continuous RHP with a solution given in terms of integral equations for non-singular functions. Ambiguities in this procedure lead to the construction of a family of spacetimes containing the solution to the IVP. Therefore the described technique also serv…
The population properties of intermediate mass black holes remain largely unknown, and understanding their distribution could provide a missing link in the formation of supermassive black holes and galaxies. Gravitational wave observations can help fill in the gap from stellar mass black holes to supermassive black holes. In our work, we propose a new method for probing lens populations through lensing statistics of gravitational waves, here focusing on inferring the number density of intermediate mass black holes. Using hierarchical Bayesian inference of injected lensed gravitational waves, w…
Coherent wide parameter-space searches for continuous gravitational waves are typically limited in sensitivity by their prohibitive computing cost. Therefore semi-coherent methods (such as StackSlide) can often achieve a better sensitivity. We develop an analytical method for finding optimal StackSlide parameters at fixed computing cost under ideal conditions of gapless data with Gaussian stationary noise. This solution separates two regimes: an unbounded regime, where it is always optimal to use all the data, and a bounded regime with a finite optimal observation time. Our analysis of the sen…
Rotating neutron stars can emit continuous gravitational waves, which have not yet been detected. We present a search for continuous gravitational waves from unknown neutron stars in binary systems with orbital period between 15 and 45 days. This is the first time that Advanced LIGO data and the recently developed BinarySkyHough pipeline have been used in a search of this kind. No detections are reported, and upper limits on the gravitational wave amplitude are calculated, which improve the previous results by a factor of 17.
We show that the gravitational magnification factor averaged over all configurations of lenses in a locally inhomogeneous universe satisfy a second order differential equation with redshift $z$ by taking the continuous limit of multi-plane gravitational lens equation (the number $N$ of lenses $\to\infty$) and that the gravitationally magnified Dyer-Roeder distance in a clumpy universe becomes to that of the Friedmann-Lema\^ıtre universe for arbitrary values of the density parameter $Ω_{0}$ and of a mass fraction $\barα$ (smoothness parameter).
This paper presents an efficient numerical sensitivity-estimation method and implementation for continuous-gravitational-wave searches, extending and generalizing an earlier analytic approach by Wette [1]. This estimation framework applies to a broad class of F-statistic-based search meth- ods, namely (i) semi-coherent StackSlide F-statistic (single-stage and hierarchical multi-stage), (ii) Hough number count on F-statistics, as well as (iii) Bayesian upper limits on (coherent or semi-coherent) F-statistic search results. We test this estimate against results from Monte-Carlo simulations assum…
Continuous gravitational-wave signals from isolated non-axisymmetric rotating neutron stars may undergo episodic spin-up events known as glitches. If unmodelled by a search, these can result in missed or misidentified detections. We outline a semicoherent glitch-robust search method that allows identification of glitching signal candidates and inference about the model parameters.
Continuous gravitational wave signals, like those expected by asymmetric spinning neutron stars, are among the most promising targets for LIGO and Virgo detectors. The development of fast and robust data analysis methods is crucial to increase the chances of a detection. We have developed a new and flexible general data analysis framework for the search of this kind of signals, which allows to reduce the computational cost of the analysis by about two orders of magnitude with respect to current procedures. This can correspond, at fixed computing cost, to a sensitivity gain of up to 10%-20%, de…
We present the Fourier Transform of a continuous gravitational wave. We have analysed the data set for one day observation time and our analysis is applicable for arbitrary location of detector and source. We have taken into account the effects arising due to rotational as well as orbital motions of the earth.
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）
Searches for continuous gravitational waves from neutron stars: A twenty-year retrospective
Australian National University（澳大利亚国立大学）；Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav)（澳大利亚研究委员会引力波发现卓越中心）
Gravitational wave predicted by General Relativity is the transverse wave of spatial strain. Several gravitational waveform signals from binary black holes and from a binary neutron star system accompanied by electromagnetic counterparts have been recorded by advanced LIGO and advanced Virgo. In analogy to light, the spatial fringes of diffraction and interference should also exist as the important features of gravitational waves. We propose that observational detection of such fringes could be achieved through gravitational lensing of continuous gravitational waves. The lenses would play the …
Extremely powerful magnetic fields are contained inside neutron stars. Their effect is to deform the shape of the star, leading to the emission of continuous gravitational waves. The magnetic deformation of neutron stars depends on the details of their magnetic field, that is its geometry and strength. Moreover, it depends on their composition, described by the equation of state. Unfortunately, both the configuration of the magnetic field and the equation of state of neutron stars are unkown, and assessing the detectability of continuous gravitational waves from neutron stars suffers from thes…
The direct detection of gravitational waves with the next generation detectors, like Advanced LIGO, provides the opportunity to measure deviations from the predictions of General Relativity. One such departure would be the existence of alternative polarizations. To measure these, we study a single detector measurement of a continuous gravitational wave from a triaxial pulsar source. We develop methods to detect signals of any polarization content and distinguish between them in a model independent way. We present LIGO S5 sensitivity estimates for 115 pulsars.
Gravitational wave astronomy opened dramatically in September 2015 with the LIGO discovery of a distant and massive binary black hole coalescence. The more recent discovery of a binary neutron star merger, followed by a gamma ray burst and a kilonova, reinforces the excitement of this new era, in which we may soon see other sources of gravitational waves, including continuous, nearly monochromatic signals. Potential continuous wave (CW) sources include rapidly spinning galactic neutron stars and more exotic possibilities, such as emission from axion Bose Einstein "clouds" surrounding black hol…
Continuous gravitational waves are analogous to monochromatic light and therefore could be used to detect wave effects like interference or diffraction. This would be possible with strongly lensed gravitational waves. This article reviews and summaries the theory of gravitational lensing in the context of gravitational waves in two different regimes: geometric optics and wave optics, for two widely used lens models such as point mass lens and Singular Isothermal Sphere (SIS). Observable effects due to wave nature of gravitational waves are discussed. As a consequence of interference GWs produc…
