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 millisecond pulsars in the globular cluster Omega Centauri using data from the second Laser Interferometer Gravitational-Wave Observatory observing run. The computational cost is $17.2$ GPU-hours using the new implementation, compared to 1092 core-hours with the existing implementation.
Sufficient statistics are combinations of data in terms of which the likelihood function can be rewritten without loss of information. Depending on the data volume reduction, the use of sufficient statistics as a preliminary step in a Bayesian analysis can lead to significant increases in efficiency when sampling from posterior distributions of model parameters. Here we show that the frequency integrand of the cross-correlation statistic and its variance are approximate sufficient statistics for ground-based searches for stochastic gravitational-wave backgrounds. The sufficient statistics are …
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 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…
Matched filtering is a commonly used technique in gravitational wave searches for signals from compact binary systems and from rapidly rotating neutron stars. A common issue in these searches is dealing with four extrinsic parameters which do not affect the phase evolution of the system: the overall amplitude, initial phase, and two angles determining the overall orientation of the system. The F-statistic maximizes the likelihood function analytically over these parameters, while the B-statistic marginalizes over them. The B-statistic, while potentially more powerful and capable of incorporati…
We study an improved method for detecting gravitational wave (GW) signals from perturbed black holes by earth-based detectors in the quest for searching for intermediate-mass black holes (IMBHs). Such signals, called ringdowns, are damped sinusoids whose frequency and damping constant can be used to measure a black hole's mass and spin. Utilizing the output from a matched filter analysis pipeline, we present an improved statistic for the detection of a ringdown signal that is found to be coincident in multiple detectors. The statistic addresses the non-Gaussianity of the data without the use o…
In a blind search for continuous gravitational wave signals scanning a wide frequency band one looks for candidate events with significantly large values of the detection statistic. Unfortunately, a noise line in the data may also produce a moderately large detection statistic. In this paper, we describe how we can distinguish between noise line events and actual continuous wave (CW) signals, based on the shape of the detection statistic as a function of the signal's frequency. We will analyze the case of a particular detection statistic, the F statistic, proposed by Jaranowski, Krolak, and Sc…
Searches for gravitational waves produced by coalescing black hole binaries with total masses $\gtrsim25\,$M$_\odot$ use matched filtering with templates of short duration. Non-Gaussian noise bursts in gravitational wave detector data can mimic short signals and limit the sensitivity of these searches. Previous searches have relied on empirically designed statistics incorporating signal-to-noise ratio and signal-based vetoes to separate gravitational wave candidates from noise candidates. We report on sensitivity improvements achieved using a multivariate candidate ranking statistic derived fr…
We propose a graphical representation of detector sensitivity curves for stochastic gravitational-wave backgrounds that takes into account the increase in sensitivity that comes from integrating over frequency in addition to integrating over time. This method is valid for backgrounds that have a power-law spectrum in the analysis band. We call these graphs "power-law integrated curves." For simplicity, we consider cross-correlation searches for unpolarized and isotropic stochastic backgrounds using two or more detectors. We apply our method to construct power-law integrated sensitivity curves …
In this paper we study the use of cross-correlations between multiple gravitational wave (GW) data streams for detecting long-lived periodic signals. Cross-correlation searches between data from multiple detectors have traditionally been used to search for stochastic GW signals, but recently they have also been used in directed searches for periodic GWs. Here we further adapt the cross-correlation statistic for periodic GW searches by taking into account both the non-stationarity and the long term-phase coherence of the signal. We study the statistical properties and sensitivity of this search…
Statistics of time and frequency-averaged spectra in gravitational-wave background searches
Université Paris Cité（巴黎西岱大学）；CNRS, Astroparticule et Cosmologie（法国国家科学研究中心，强子与宇宙学）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）；IRFU, CEA, Université Paris-Saclay（法国原子能和替代能源署，萨克雷大学）
We propose a new method of gravitational wave detection using a modified form of higher criticism, a statistical technique introduced by Donoho & Jin (2004). Higher criticism is designed to detect a group of sparse, weak sources, none of which are strong enough to be reliably estimated or detected individually. We apply higher criticism as a second-pass method to synthetic F-statistic and C-statistic data for a monochromatic periodic source in a binary system and quantify the improvement relative to the first-pass methods. We find that higher criticism on C-statistic data is more sensitive by …
Joint ranking statistics are used to distinguish real from random coincidences, ideally considering whether shared parameters are consistent with each other as well as whether the individual candidates are distinguishable from noise. We expand on previous works to include additional shared parameters, we use galaxy catalogues aspriors for sky localization and distance, and avoid some approximations previously used. We develop methods to calculate this statistic both in low-latency using HEALPix sky maps, as well as with posterior samples. We show that these changes lead to a factor of one to t…
Generalized parameter-space metrics for continuous gravitational-wave searches
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）；Departament de Física, Universitat de les Illes Balears（巴利阿里群岛大学物理系）
We develop a new multi-detector signal-based discriminator to improve the sensitivity of searches for gravitational waves from compact binary coalescences. The new statistic is the traditional $χ^2$ computed on a null-stream synthesized from the gravitational-wave detector strain time-series of three detectors. This null-stream-$χ^2$ statistic can be extended to networks involving more than three detectors as well. The null-stream itself was proposed as a discriminator between correlated unmodeled signals in multiple detectors, such as arising from a common astrophysical source, and uncorrelat…
We present a heterogeneous search algorithm for broadband extended gravitational-wave emission (BEGE), expected from gamma-ray bursts and energetic core-collapse supernovae. It searches the $(f,\dot{f})$-plane for long duration bursts by inner engines slowly exhausting their energy reservoir by matched filtering on a {\em Graphics Processor Unit} (GPU) over a template bank of millions of one-second duration chirps. Parseval's Theorem is used to predict the standard deviation $σ$ of filter output, taking advantage of near-Gaussian noise in LIGO S6 data over 350-2000 Hz. Tails exceeding a mulitp…
The likelihood ratio for a continuous gravitational wave signal is viewed geometrically as a function of the orientation of two vectors; one representing the optimal signal-to-noise ratio, the other representing the maximised likelihood ratio or $\mathcal{F}$-statistic. Analytic marginalisation over the angle between the vectors yields a marginalised likelihood ratio which is a function of the $\mathcal{F}$-statistic. Further analytic marginalisation over the optimal signal-to-noise ratio is explored using different choices of prior. Monte-Carlo simulations show that the marginalised likelihoo…
Continuous gravitational waves from neutron stars could provide an invaluable resource to learn about their interior physics. A common search method involves matched filtering a modeled template against the noisy gravitational-wave data to find signals. This method suffers a mismatch (i.e., relative loss of the signal-to-noise ratio) if the signal deviates from the template. One possible instance in which this may occur is if the neutron star undergoes a glitch, a sudden rapid increase in the rotation frequency seen in the timing of many radio pulsars. In this work, we use a statistical charac…
The F-statistic is an established method to search for continuous gravitational waves from spinning neutron stars. Prix et al. (2011) introduced a variant for transient quasi-monochromatic signals. Possible astrophysical scenarios for such transients include glitching pulsars, newborn neutron stars and accreting systems. Here we present a new implementation of the transient F-statistic, using pyCUDA to leverage the power of modern graphics processing units (GPUs). The obtained speedup allows efficient searches over much wider parameter spaces, especially when using more realistic transient sig…
