We present a new measure for the comparison of unknown gravitational wave signals in two detectors, without recurring to an {\it a priori} template.
We apply this measure to the LIGO data of the GW150914 event and discover that Hanford and Livingston observatories have recorded two different components of the gravitational wave polarization signal.
This paper presents an algorithm for constructing matched-filter template banks in an arbitrary parameter space. The method places templates at random, then removes those which are "too close" together. The properties and optimality of stochastic template banks generated in this manner are investigated for some simple models. The effectiveness of these template banks for gravitational wave searches for binary inspiral waveforms is also examined. The properties of a stochastic template bank are then compared to the deterministically placed template banks that are currently used in gravitational…
Efficient multi-dimensional template placement is crucial in computationally intensive matched-filtering searches for Gravitational Waves (GWs). Here, we implement the Neighboring Cell Algorithm (NCA) to improve the detection volume of an existing Compact Binary Coalescence (CBC) template bank. This algorithm has already been successfully applied for a binary millisecond pulsar search in data from the Fermi satellite. It repositions templates from over-dense regions to under-dense regions and reduces the number of templates that would have been required by a stochastic method to achieve the sa…
Matched filtering is used to search for gravitational waves emitted by inspiralling compact binaries in data from ground-based interferometers. One of the key aspects of the detection process is the deployment of a set of templates, also called a template bank, to cover the astrophysically interesting region of the parameter space. In a companion paper, we described the template-bank algorithm used in the analysis of LIGO data to search for signals from non-spinning binaries made of neutron star and/or stellar-mass black holes; this template bank is based upon physical template families. In th…
Compact binaries inspiralling along quasi-circular orbits are the most plausible gravitational wave (GW) sources for the operational, planned and proposed laser interferometers. We provide new class of restricted post-Newtonian accurate GW templates for non-spinning compact binaries inspiralling along PN accurate quasi-circular orbits. Arguments based on data analysis, theoretical and astrophysical considerations are invoked to show why these time-domain Taylor approximants should be interesting to various GW data analysis communities.
An extreme mass ratio inspiral takes place when a compact stellar object is inspiraling into a supermassive black hole due to gravitational radiation reaction. Gravitational waves (GWs) from this system can be calculated using the Teukolsky equation (TE). In our case, we compute the asymptotic GW fluxes of a spinning body orbiting a Kerr black hole by solving numerically the TE both in time and frequency domain. Our ultimate goal is to produce GW templates for space-based detectors such as LISA.
We discuss a method to analyze data from interferometric gravitational wave detectors focusing on the technique of hierarchical search to detect gravitational waves from inspiraling binaries. For this purpose, we propose new coordinates to parameterize the template space. Using our new coordinates, we develop several new techniques for two step search, which would reduce the computation cost by large amount. These techniques become more important when we need to implement a $χ^2$-test as a detection criterion.
We study the parameter estimation of gravitational waves for aligned-spin binary black hole (BBH) signals and assess the impact of bias that can be produced by using nonspinning template waveforms. We employ simple methods to calculate the statistical uncertainty from an overlap distribution. For the fiducial waveform model, we use a phenomenological model, which is designed to generate the gravitational waveforms emitted from merging BBH systems. We show that the mass parameters recovered by nonspinning waveform templates can be significantly biased from the true values of aligned-spin signal…
Templates used in a search for binary black holes and neutron stars in gravitational wave interferometer data will have to be computed on-line since the computational storage and retrieval costs for the template bank are too expensive. The conventional dimensionless variable $T=(c^3/Gm)t,$ where $m$ is the total mass of a binary, in the time-domain and a not-so-conventional velocity-like variable $v=(πGm f)^{1/3}$ in the Fourier-domain, render the phasing of the waves independent of the total mass of the system enabling the construction of {\it mother templates} that depend only on the mass ra…
We ascertain the effectiveness of the second post-Newtonian approximation to the gravitational waves emitted during the adiabatic inspiral of a compact binary system as templates for signal searches with kilometer-scale interferometric detectors. The reference signal is obtained by solving the Teukolsky equation for a small mass moving on a circular orbit around a large nonrotating black hole. Fitting factors computed from this signal and these templates, for various types of binary systems, are all above the 90% mark. According to Apostolatos' criterion, second post-Newtonian waveforms should…
We extend the description of gravitational waves emitted by binary black holes during the final stages of inspiral and merger by introducing in the third post-Newtonian (3PN) effective-one-body (EOB) templates seven new ``flexibility'' parameters that affect the two-body dynamics and gravitational radiation emission. The plausible ranges of these flexibility parameters, notably the parameter characterising the fourth post-Newtonian effects in the dynamics, are estimated. Using these estimates, we show that the currently available standard 3PN bank of EOB templates does ``span'' the space of si…
The construction of optimal template banks for matched-filtering searches is an example of the sphere covering problem. For parameter spaces with constant-coefficient metrics a (near-) optimal template bank is achieved by the A_n* lattice, which is the best lattice-covering in dimensions n <= 5, and is close to the best covering known for dimensions n <= 16. Generally this provides a substantially more efficient covering than the simpler hyper-cubic lattice. We present an algorithm for generating lattice template banks for constant-coefficient metrics and we illustrate its implementation by ge…
All-sky, broadband, coherent searches for gravitational-wave pulsars are restricted by limited computational resources. Minimizing the number of templates required to cover the search parameter space, of sky position and frequency evolution, is one important way to reduce the computational cost of a search. We demonstrate a practical algorithm which, for the first time, achieves template placement with a minimal number of templates for an all-sky search, using the reduced supersky parameter-space metric of Wette and Prix [Phys. Rev. D 88, 123005 (2013)]. The metric prescribes a constant templa…
We present further evidence that the second post-Newtonian (pN) approximation to the gravitational waves emitted by inspiraling compact binaries is sufficient for the detection of these systems. This is established by comparing the 2-pN wave forms to signals calculated from black hole perturbation theory. Results are presented for different detector noise curves. We also discuss the validity of this type of analysis.
Phasing formulas in a recent paper of ours' (Phys. Rev. D 63, 044023-1 (2001) are updated taking into account the recent 3.5PN results. Some misprints in the published version of the recent paper are also corrected.
Observations by laser interferometric detectors of gravitational waves from inspiraling compact binary systems can be used to search for a dependence of the waves' propagation speed on wavelength, and thereby to bound the mass or Compton wavelength of a putative graviton. We study the effect of including higher harmonics, as well as their post-Newtonian amplitude corrections, in the template gravitational waveforms employed in the process of parameter estimation using matched filtering. We consider the bounds that could be achieved using advanced LIGO, a proposed third generation instrument ca…
Gravitational waves from coalescing compact binaries are one of the most promising sources for detectors such as LIGO, Virgo and GEO600. If the components of the binary posess significant angular momentum (spin), as is likely to be the case if one component is a black hole, spin-induced precession of a binary's orbital plane causes modulation of the gravitational-wave amplitude and phase. If the templates used in a matched-filter search do not accurately model these effects then the sensitivity, and hence the detection rate, will be reduced. We investigate the ability of several search pipelin…
We construct efficient banks of templates suitable for all-sky narrow-band searches of almost monochromatic gravitational waves originating from spinning neutron stars in our Galaxy in data collected by interferometric detectors. We consider waves with one spindown parameter included and we assume that both the position of the gravitational-wave source in the sky and the wave's frequency together with spindown parameter are unknown. In the construction we employ simplified model of the signal with constant amplitude and phase which is a linear function of unknown parameters. Our template banks…
The prior knowledge of the gravitational waveform from compact binary systems makes matched filtering an attractive detection strategy. This detection method involves the filtering of the detector output with a set of theoretical waveforms or templates. One of the most important factors in this strategy is knowing how many templates are needed in order to reduce the loss of possible signals. In this study we calculate the number of templates and computational power needed for a one-step search for gravitational waves from inspiralling binary systems. We build on previous works by firstly expan…
We compare the performances of the templates defined by three different types of approaches: traditional post-Newtonian templates (Taylor-approximants), ``resummed'' post-Newtonian templates assuming the adiabatic approximation and stopping before the plunge (P-approximants), and further ``resummed'' post-Newtonian templates going beyond the adiabatic approximation and incorporating the plunge with its transition from the inspiral (Effective-one-body approximants). The signal to noise ratio is significantly enhanced (mainly because of the inclusion of the plunge signal) by using these new effe…
Gravitational waves from coalescing compact binaries are searched using the matched filtering technique. As the model waveform depends on a number of parameters, it is necessary to filter the data through a template bank covering the astrophysically interesting region of the parameter space. The choice of templates is defined by the maximum allowed drop in signal-to-noise ratio due to the discreteness of the template bank. In this paper we describe the template-bank algorithm that was used in the analysis of data from the Laser Interferometer Gravitational Wave Observatory (LIGO) and GEO 600 d…
We study the performance of various analytical frequency-domain templates for detection and parameter estimation of gravitational waves from spin-precessing, quasi-circular, compact binary inspirals. We begin by assessing the extent to which non-spinning, spin-aligned, and the new (analytical, frequency-domain, small-spin) double-precessing frequency-domain templates can be used to detect signals from such systems. For effective, dimensionless spin values above $0.2$, the use of non-spinning or spin-aligned templates for detection purposes will result in a loss of up to $30%$ of all events, wh…
We investigate the problem of detecting gravitational waves from binaries of nonspinning black holes with masses m = 5--20 Msun, moving on quasicircular orbits, which are arguably the most promising sources for first-generation ground-based detectors. We analyze and compare all the currently available post--Newtonian approximations for the relativistic two-body dynamics; for these binaries, different approximations predict different waveforms. We then construct examples of detection template families that embed all the approximate models, and that could be used to detect the true gravitational…
We probe the ability of various types of post-Newtonian(PN)-accurate circular templates to capture inspiral gravitational-wave (GW) signals from compact binaries having tiny orbital eccentricities. The GW signals are constructed by adapting the phasing formalism, available in T. Damour, A. Gopakumar, and B. R. Iyer, [Phys. Rev. D 70, 064028 (2004)], employing the orbital energy and the time-eccentricity to describe the orbital evolution. Using the fitting factor estimates, relevant for the initial LIGO, we show that circular templates, based on the adiabatic TaylorT1, complete adiabatic Taylor…
It has long been known that the search for gravitational waves from inspiraling binaries must be aided by signal processing methods, and that the technique of matched filtering is the most likely to be used for the detection of inspiral ``chirps''. This means that the output of an interferometer must be cross- correlated with many waveform templates to dig out faint signals buried in the noise. The templates are characterized by several parameters which vary continuously over some finite range; but because the amount of computing power available to perform the cross-correlations of the search …
We study gravitational wave searches for merging binary neutron stars (NSs). We use nonspinning template waveforms towards the signals emitted from aligned-spin NS-NS binaries, in which the spins of the NSs are aligned with the orbital angular momentum. We use the TaylorF2 waveform model, which can generate inspiral waveforms emitted from aligned-spin compact binaries. We employ the single effective spin parameter $χ_{\rm eff}$ to represent the effect of two component spins ($χ_1, χ_2$) on the wave function. For a target system, we choose a binary consisting of the same component masses of $1.…
Matched filtering is used to search for gravitational waves emitted by inspiralling compact binaries in data from the ground-based interferometers. One of the key aspects of the detection process is the design of a template bank that covers the astrophysically pertinent parameter space. In an earlier paper, we described a template bank that is based on a square lattice. Although robust, we showed that the square placement is over-efficient, with the implication that it is computationally more demanding than required. In this paper, we present a template bank based on an hexagonal lattice, whic…
Astrophysical compact binary systems consisting of neutron stars and blackholes are an important class of gravitational wave (GW) sources for advanced LIGO detectors. Accurate theoretical waveform models from the inspiral, merger and ringdown phases of such systems, are used to filter detector data under the template based matched filtering paradigm. An efficient grid over the parameter space at a fixed minimal match has a direct impact on the overall time taken by these searches. We present a new hybrid geometric-random template placement algorithm for signals described by two masses and one …
In order to improve the phasing of the comparable-mass waveform as we approach the last stable orbit for a system, various re-summation methods have been used to improve the standard post-Newtonian waveforms. In this work we present a new family of templates for the detection of gravitational waves from the inspiral of two comparable-mass black hole binaries. These new adiabatic templates are based on re-expressing the derivative of the binding energy and the gravitational wave flux functions in terms of shifted Chebyshev polynomials. The Chebyshev polynomials are a useful tool in numerical me…
Gravitational Wave (GW) burst detection algorithms typically rely on the hypothesis that the burst signal is "locally stationary", that is it changes slowly with frequency. Under this assumption, the signal can be decomposed into a small number of wavelets with constant frequency. This justifies the use of a family of sine-Gaussian templates in the Omega pipeline, one of the algorithms used in LIGO-Virgo burst searches. However there are plausible scenarios where the burst frequency evolves rapidly, such as in the merger phase of a binary black hole and/or neutron star coalescence. In those ca…
We estimate the number of templates, computational power, and storage required for a one-step matched filtering search for gravitational waves from inspiraling compact binaries. These estimates should serve as benchmarks for the evaluation of more sophisticated strategies such as hierarchical searches. We use waveform templates based on the second post-Newtonian approximation for binaries composed of nonspinning compact bodies in circular orbits. We present estimates for six noise curves: LIGO (three configurations), VIRGO, GEO600, and TAMA. To search for binaries with components more massive …
We construct efficient banks of templates suitable for directed searches of almost monochromatic gravitational waves originating from spinning nuetron stars in our Galaxy in data being collected by currently operating interferometric detectors. We thus assume that the position of the gravitational-wave source in the sky is known, but we do not assume that the wave's frequency and its derivatives are a priori known. In the construction we employ simplified model of the signal with constant amplitude and phase which is a polynomial function of time. All our template banks enable usage of the fas…
Recent discoveries of gravitational wave (GW) signals from astrophysical compact binary systems of neutron stars and black holes have firmly established them as prime sources for advanced GW detectors. Theoretical templates of expected signals from such systems have been used to filter the detector data using the \emph{matched filtering} technique. An efficient grid over the parameter space at a fixed minimal match has a direct impact on improving the computational efficiency of these searches. We present the construction of three-dimensional template banks (in component masses and an effectiv…
We introduce a new template for the detection of gravitational waves from compact binary systems which is based on Chebyshev polynomials of the first kind. As well as having excellent convergence properties, these polynomials are also very closely related to the elusive minimax polynomial. In this study we have limited ourselves to the test-mass regime, where we model a test particle in a circular equatorial orbit around a Schwarzschild black hole. Our objective is to model the numerical gravitational wave flux function, starting with the post-Newtonian expansion from Black Hole Perturbation T…
Parameter estimation on gravitational wave signals from compact binary coalescence (CBC) requires the evaluation of computationally intensive waveform models, typically the bottleneck in the analysis. This cost will increase further as low frequency sensitivity in later second and third generation detectors motivates the use of longer waveforms. We describe a method for accelerating parameter estimation by exploiting the chirping behaviour of the signals to sample the waveform sparsely for portions where the full frequency resolution is not required. We demonstrate that the method can reproduc…
Most of the inspiralling compact binaries are expected to be circularized by the time their gravitational-wave signals enter the frequency band of ground-based detectors such as LIGO or VIRGO. However, it is not excluded that some of these binaries might still possess a significant eccentricity at a few tens of hertz. Despite this possibility, current search pipelines based on matched filtering techniques consider only non-eccentric templates. The effect of such an approximation on the loss of signal-to-noise ratio (SNR) has been investigated by Martel and Poisson (1999 Phys. Rev. D 60 124008)…
Searching for a signal depending on unknown parameters in a noisy background with matched filtering techniques always requires an analysis of the data with several templates in parallel in order to ensure a proper match between the filter and the real waveform. The key feature of such an implementation is the design of the filter bank which must be small to limit the computational cost while keeping the detection efficiency as high as possible. This paper presents a geometrical method which allows one to cover the corresponding physical parameter space by a set of ellipses, each of them being …
We report the construction of a three-dimensional template bank for the search for gravitational waves from inspiralling binaries consisting of spinning compact objects. The parameter space consists of two dimensions describing the mass parameters and one "reduced-spin" parameter, which describes the secular (non-precessing) spin effects in the waveform. The template placement is based on an efficient stochastic algorithm and makes use of the semi-analytical computation of a metric in the parameter space. We demonstrate that for "low-mass" ($m_1 + m_2 \lesssim 12\,M_\odot$) binaries, this temp…
Coalescence of two massive black holes is the strongest and most promising source for LISA. In fact, gravitational signal from the end of inspiral and merger will be detectable throughout the Universe. In this article we describe the first step in the two-step hierarchical search for gravitational wave signal from the inspiraling massive BH binaries. It is based on the routinely used in the ground base gravitational wave astronomy method of filtering the data through the bank of templates. However we use a novel Monte-Carlo based (stochastic) method to lay a grid in the parameter space, and we…
Accurate waveform models describing the complete evolution of compact binaries are crucial for the maximum likelihood detection framework, testing the predictions of General Relativity (GR) and investigating the possibility of an alternative theory of gravity. Deviations from GR could manifest in subtle variations of the numerical value of the GW signal's post-Newtonian (PN) phasing coefficients. Once the search pipelines confirm an unambiguous signal detection, deviations of the signal phasing coefficients at various PN orders are routinely measured and reported. As the search templates thems…
A type of gravitational-wave signals in the LIGO-Virgo sensitivity band are expected to be emitted by spinning asymmetric neutron stars, with rotational frequencies that could plausibly emit continuous gravitational radiation in the most sensitive band of the LIGO-Virgo detectors. The most important feature of such kind of signals is in their phase evolution, which is stable over a long observation run. When using analysis based on matched filtering, the phase evolution of long-coherent signals is needed to define how to build a proper template grid in order to gain the best signal-to-noise ra…
In this study we apply post-Newtonian (T-approximants) and resummed post-Newtonian (P-approximants) to the case of a test-particle in equatorial orbit around a Kerr black hole. We compare the two approximants by measuring their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, T-approximant templates obtain an effectualness of ~0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-ap…
The final inspiral phase in the evolution of a compact binary consisting of black holes and/or neutron stars is among the most probable events that a network of ground-based interferometric gravitational wave detectors is likely to observe. Gravitational radiation emitted during this phase will have to be dug out of noise by matched-filtering (correlating) the detector output with a bank of several $10^5$ templates, making the computational resources required quite demanding, though not formidable. We propose an interpolation method for evaluating the correlation between template waveforms and…
We compute the overlap function between Post-Newtonian (PN) templates and gravitational signals emitted by binary systems composed of one neutron star and one point mass, obtained by a perturbative approach. The calculations are performed for different stellar models and for different detectors, to estimate how effectual and faithful the PN templates are, and to establish whether effects related to the internal structure of neutron stars may possibly be extracted by the matched filtering technique.
We present a unified description of gravitational-wave data analysis that unites the template-based analysis used to detect deterministic signals from well-modeled sources, such as binary-black-hole mergers, with the cross-correlation analysis used to detect stochastic gravitational-wave backgrounds. We also discuss the connection between template-based analyses and those that target poorly-modeled bursts of gravitational waves, and suggest a new approach for detecting burst signals.
Inspiral signals from binary black holes, in particular those with masses in the range $10M_\odot \lsim M \lsim 1000 M_\odot,$ may last for only a few cycles within a detector's most sensitive frequency band. The spectrum of a square-windowed time-domain signal could contain unwanted power that can cause problems in gravitational wave data analysis, particularly when the waveforms are of short duration. There may be leakage of power into frequency bins where no such power is expected, causing an excess of false alarms. We present a method of tapering the time-domain waveforms that significantl…
We study the efficiency of nonspinning waveform templates in gravitational wave searches for aligned-spin binary black holes (BBHs). We use PhenomD, which is the most recent phenomenological waveform model designed to generate the full inspiral-merger-ringdown waveforms emitted from BBHs with the spins aligned with the orbital angular momentum. Here, we treat the effect of aligned-spins with a single spin parameter $χ$. We consider the BBH signals with moderately small spins in the range of $-0.4\leq χ\leq 0.4$. Using nonspinning templates, we calculate fitting factors of the aligned-spin sign…
One strategy for reducing the online computational cost of matched-filter searches for gravitational waves is to introduce a compressed basis for the waveform template bank in a grid-based search. In this paper, we propose and investigate several tunable compression schemes for a general template bank. Through offline compression, such schemes are shown to yield faster detection and localisation of signals, along with moderately improved sensitivity and accuracy over coarsened banks at the same level of computational cost. This is potentially useful for any search involving template banks, and…
All-sky surveys for isolated continuous gravitational waves present a significant data-analysis challenge. Semicoherent search methods are commonly used to efficiently perform the computationally-intensive task of searching for these weak signals in the noisy data of gravitational-wave detectors such as LIGO and Virgo. We present a new implementation of a semicoherent search method, Weave, that for the first time makes full use of a parameter-space metric to generate banks of search templates at the correct resolution, combined with optimal lattices to minimize the required number of templates…
The spin-free binary-inspiral parameter-space introduced by Tanaka and Tagoshi to construct a uniformly-spaced lattice of templates at (and possibly beyond) $2.5PN$ order is shown to work for all first generation interferometric gravitational wave antennas. This allows to extend the minimum-redundant cardinal interpolation techniques of the correlator bank developed by the Authors to the highest available order PN templates. The total number of 2PN templates to be computed for a minimal match $Γ=0.97$ is reduced by a factor 4, as in the 1PN case.
We have studied the problem of all sky search in reference to continuous gravitational wave particularly for such sources whose wave-form are known in advance. We have made an analysis of the number of templates required for matched filter analysis as applicable to these sources. We have employed the concept of {\it fitting factor} {\it (FF)}; treating the source location as the parameters of the signal manifold and have studied the matching of the signal with templates corresponding to different source locations. We have investigated the variation of FF with source location and have noticed a…
Matched-filtering for the identification of compact object mergers in gravitational-wave antenna data involves the comparison of the data stream to a bank of template gravitational waveforms. Typically the template bank is constructed from phenomenological waveform models since these can be evaluated for an arbitrary choice of physical parameters. Recently it has been proposed that singular value decomposition (SVD) can be used to reduce the number of templates required for detection. As we show here, another benefit of SVD is its removal of biases from the phenomenological templates along wit…
Gravitational-wave searches for signals from inspiralling compact binaries have relied on matched filtering banks of waveforms (called template banks) to try to extract the signal waveforms from the detector data. These template banks have been constructed using four main considerations, the region of parameter space of interest, the sensitivity of the detector, the matched filtering bandwidth, and the sensitivity one is willing to lose due to the granularity of template placement, the latter of which is governed by the minimal match. In this work we describe how the choice of the lower freque…
The ringdown of the gravitational-wave signal from a merger of two black holes has been suggested as a probe of the structure of the remnant compact object, which may be more exotic than a black hole. It has been pointed out that there will be a train of echoes in the late-time ringdown stage for different types of exotic compact objects. In this paper, we present a template-based search methodology using Bayesian statistics to search for echoes of gravitational waves. Evidence for the presence or absence of echoes in gravitational-wave events can be established by performing Bayesian model se…
We calculate the signal-to-noise ratio (SNR) of the stochastic gravitational-wave background in an extreme case that its spectrum has a sharp falloff with its amplitude close to the detection threshold. Such a spectral feature is a characteristic imprint of the change in the number of relativistic degrees of freedom on the stochastic background generated during inflation in the early Universe. We find that, although SNR is maximal with the correct template which is proportional to the assumed real spectrum, its sensitivity to the shape of template is fairly weak indicating that a simple power-…
