Search For Continuous Waves Research Articles

Searches for continuous gravitational waves from neutron stars: A twenty-year retrospective

Seven years after the first direct detection of gravitational waves, from the collision of two black holes, the field of gravitational wave astronomy is firmly established. A first detection of continuous gravitational waves from rapidly-spinning neutron stars could be the field’s next big discovery. I review the last twenty years of efforts to detect continuous gravitational waves using the LIGO and Virgo gravitational wave detectors. I summarise the model of a continuous gravitational wave signal, the challenges to finding such signals in noisy data, and the data analysis algorithms that have been developed to address those challenges. I present a quantitative analysis of 297 continuous wave searches from 80 papers, published from 2003 to 2022, and compare their sensitivities and coverage of the signal model parameter space.

Precision Ephemerides for Gravitational-wave Searches – IV. Corrected and refined ephemeris for Scorpius X-1

ABSTRACTLow-mass X-ray binaries have long been theorized as potential sources of continuous gravitational-wave radiation, yet there is no observational evidence from recent LIGO/Virgo observing runs. Even for the theoretically ‘loudest’ source, Sco X-1, the upper limit on gravitational-wave strain has been pushed ever lower. Such searches require precise measurements of the source properties for sufficient sensitivity and computational feasibility. Collating over 20 yr of high-quality spectroscopic observations of the system, we present a precise and comprehensive ephemeris for Sco X-1 through radial velocity measurements, performing a full homogeneous re-analysis of all relevant data sets and correcting previous analyses. Our Bayesian approach accounts for observational systematics and maximizes not only precision, but also the fidelity of uncertainty estimates – crucial for informing principled continuous-wave searches. Our extensive data set and analysis also enables us to construct the highest signal-to-noise ratio, highest resolution phase-averaged spectrum of a low-mass X-ray binary to date. Doppler tomography reveals intriguing transient structures present in the accretion disc and flow driven by modulation of the accretion rate, necessitating further characterization of the system at high temporal and spectral resolution. Our ephemeris corrects and supersedes previous ephemerides, and provides a factor three reduction in the number of templates in the search space, facilitating precision searches for continuous gravitational-wave emission from Sco X-1 throughout the upcoming LIGO/Virgo/KAGRA O4 observing run and beyond.

Continuous gravitational waves in the lab: Recovering audio signals with a table-top optical microphone

Gravitational-wave observatories around the world are searching for continuous waves: persistent signals from sources, such as spinning neutron stars. These searches use sophisticated statistical techniques to look for weak signals in noisy data. In this paper, we demonstrate these techniques using a table-top model gravitational-wave detector: a Michelson interferometer where sound is used as an analog for gravitational waves. Using signal processing techniques from continuous-wave searches, we demonstrate the recovery of tones with constant and wandering frequencies. We also explore the use of the interferometer as a teaching tool for educators in physics and electrical engineering by using it as an “optical microphone” to capture music and speech. A range of filtering techniques used to recover signals from noisy data are detailed in the supplementary material of this article. Here, we present the highlights of our results using a combined notch plus Wiener filter and the statistical log minimum mean-square error (logMMSE) estimator. Using these techniques, we easily recover recordings of simple chords and drums, but complex music and speech are more challenging. This demonstration can be used by educators in undergraduate laboratories and can be adapted for communicating gravitational-wave and signal-processing topics to nonspecialist audiences.

Constraints on planetary and asteroid-mass primordial black holes from continuous gravitational-wave searches

We present new constraints on the merging rates of planetary-mass and asteroid-mass primordial black hole binaries using limits on continuous waves(quasi-monochromatic, quasi-infinite duration signals) derived from an all-sky search for isolated compact objects in the first six months of the third observing run (O3a) of LIGO/Virgo. We calculate the merging rates of these binaries in a model-independent way, and convert them to constraints on the primordial black hole abundance with minimal modelling assumptions. Our results show that we are sensitive to sources at most $\mathcal{O}(10$ pc) away for systems with chirp masses of $\mathcal{O}(10^{-5}M_\odot)$ at gravitational-wave frequencies around 30-40 Hz. These results also show that continuous-wave searches could in the future directly probe the existence of planetary-mass and asteroid-mass primordial black holes, especially those in binaries with asymmetric mass ratios. Furthermore, they demonstrate that new methods accounting for the full nonlinear gravitational-wave frequency evolution are needed to improve constraints on primordial black holes.

Empirically estimating the distribution of the loudest candidate from a gravitational-wave search

Searches for gravitational-wave signals are often based on maximizing a detection statistic over a bank of waveform templates, covering a given parameter space with a variable level of correlation. Results are often evaluated using a noise-hypothesis test, where the background is characterized by the sampling distribution of the loudest template. In the context of continuous gravitational-wave searches, properly describing said distribution is an open problem: current approaches focus on a particular detection statistic and neglect template-bank correlations. We introduce a new approach using extreme value theory to describe the distribution of the loudest template's detection statistic in an arbitrary template bank. Our new proposal automatically generalizes to a wider class of detection statistics, including (but not limited to) line-robust statistics and transient continuous-wave signal hypotheses, and improves the estimation of the expected maximum detection statistic at a negligible computing cost. The performance of our proposal is demonstrated on simulated data as well as by applying it to different kinds of (transient) continuous-wave searches using O2 Advanced LIGO data. We release an accompanying python software package, distromax, implementing our new developments.

New Searches for Continuous Gravitational Waves from Seven Fast Pulsars

Abstract We conduct searches for continuous gravitational waves from seven pulsars that have not been targeted in continuous wave searches of Advanced LIGO data before. We target emission at exactly twice the rotation frequency of the pulsars and in a small band around such a frequency. The former search assumes that the gravitational-wave quadrupole is changing in a phase-locked manner with the rotation of the pulsar. The latter search over a range of frequencies allows for differential rotation between the component emitting the radio signal and the component emitting the gravitational waves, for example the crust or magnetosphere versus the core. Timing solutions derived from the Arecibo 327 MHz Drift-Scan Pulsar Survey observations are used. No evidence of a signal is found and upper limits are set on the gravitational-wave amplitude. For one of the pulsars we probe gravitational-wave intrinsic amplitudes just a factor of 3.8 higher than the spin-down limit, assuming a canonical moment of inertia of 1038 kg m2. Our tightest ellipticity constraint is 1.5 × 10−8, which is a value well within the range of what a neutron star crust could support.

Application of a hierarchical MCMC follow-up to Advanced LIGO continuous gravitational-wave candidates

We present the first application of a hierarchical Markov Chain Monte Carlo (MCMC) follow-up on continuous gravitational-wave candidates from real-data searches. The follow-up uses an MCMC sampler to draw parameter-space points from the posterior distribution, constructed using the matched-filter as a log-likelihood. As outliers are narrowed down, coherence time increases, imposing more restrictive phase-evolution templates. We introduce a novel Bayes factor to compare results from different stages: The signal hypothesis is derived from first principles, while the noise hypothesis uses extreme value theory to derive a background model. The effectiveness of our proposal is evaluated on fake Gaussian data and applied to a set of 30 outliers produced by different continuous wave searches on O2 Advanced LIGO data. The results of our analysis suggest all but five outliers are inconsistent with an astrophysical origin under the standard continuous wave signal model. We successfully ascribe four of the surviving outliers to instrumental artifacts and a strong hardware injection present in the data. The behavior of the fifth outlier suggests an instrumental origin as well, but we could not relate it to any known instrumental cause.

Time-frequency track distance for comparing continuous gravitational wave signals

Searches for continuous gravitational waves from unknown sources attempt to detect long-lasting gravitational radiation by identifying Doppler-modulated signatures in the data. Semicoherent methods allow for wide parameter space surveys, identifying interesting regions to be followed up using more sensitive (and computationally expensive) tools. Thus, it is required to properly understand the parameter space structure under study, as failing to do so could significantly affect the effectiveness of said strategies. We introduce a new measure for distances in parameter space suited for semicoherent continuous wave searches. This novel approach, based on comparing time-frequency tracks, can be applied to any kind of quasi-monochromatic continuous wave signals and adapts itself to the underlying structure of the parameter space under study. In a first application to the post-processing stage of an all-sky search for continuous waves from neutron stars in binary systems, we demonstrate a search sensitivity improvement by solely replacing previous ad hoc distance measures in the candidate clustering procedure by the new proposal.

Effects of proper motion of neutron stars on continuous gravitational-wave searches

ABSTRACT All-sky and directed continuous gravitational-wave searches look for signals from unknown asymmetric rotating neutron stars or from neutron stars of unknown rotational frequency. These searches do not take into account the proper motion of the neutron star, assuming that the loss of signal-to-noise ratio caused by this is negligible and that no biases in parameter estimation are introduced. In this paper, we study the effect that proper motion has on continuous wave searches, and we show for what regions of parameter space (frequency, proper motion, sky position) and observation times this assumption may not be valid. We also calculate the relative uncertainty on the proper motion parameter estimation that these searches can achieve.

Modelling neutron star mountains

ABSTRACT As the era of gravitational-wave astronomy has well and truly begun, gravitational radiation from rotating neutron stars remains elusive. Rapidly spinning neutron stars are the main targets for continuous-wave searches since, according to general relativity, provided they are asymmetrically deformed, they will emit gravitational waves. It is believed that detecting such radiation will unlock the answer to why no pulsars have been observed to spin close to the break-up frequency. We review existing studies on the maximum mountain that a neutron star crust can support, critique the key assumptions and identify issues relating to boundary conditions that need to be resolved. In light of this discussion, we present a new scheme for modelling neutron star mountains. The crucial ingredient for this scheme is a description of the fiducial force which takes the star away from sphericity. We consider three examples: a source potential which is a solution to Laplace’s equation, another solution which does not act in the core of the star and a thermal pressure perturbation. For all the cases, we find that the largest quadrupoles are between a factor of a few to two orders of magnitude below previous estimates of the maximum-mountain size.

Core collapse in massive scalar-tensor gravity

This paper provides an extended exploration of the inverse-chirp gravitational-wave signals from stellar collapse in massive scalar-tensor gravity reported in [Phys. Rev. Lett. {\bf 119}, 201103]. We systematically explore the parameter space that characterizes the progenitor stars, the equation of state and the scalar-tensor theory of the core collapse events. We identify a remarkably simple and straightforward classification scheme of the resulting collapse events. For any given set of parameters, the collapse leads to one of three end states, a weakly scalarized neutron star, a strongly scalarized neutron star or a black hole, possibly formed in multiple stages. The latter two end states can lead to strong gravitational-wave signals that may be detectable in present continuous-wave searches with ground-based detectors. We identify a very sharp boundary in the parameter space that separates events with strong gravitational-wave emission from those with negligible radiation.

Search strategies for long gravitational-wave transients: Hidden Markov model tracking and seedless clustering

A number of detections have been made in the past few years of gravitational waves from compact binary coalescences. While there exist well-understood waveform models for signals from compact binary coalescences, many sources of gravitational waves are not well modeled, including potential long-transient signals from a binary neutron star post-merger remnant. Searching for these sources requires robust detection algorithms that make minimal assumptions about any potential signals. In this paper, we compare two unmodeled search schemes for long-transient gravitational waves, operating on cross-power spectrograms. One is an efficient algorithm first implemented for continuous wave searches, based on a hidden Markov model. The other is a seedless clustering method, which has been used in transient gravitational wave analysis in the past. We quantify the performance of both algorithms, including sensitivity and computational cost, by simulating synthetic signals with a special focus on sources like binary neutron star post-merger remnants. We demonstrate that the hidden Markov model tracking is a good option in model-agnostic searches for low signal-to-noise ratio signals. We also show that it can outperform the seedless method for certain categories of signals while also being computationally more efficient.

Tracking continuous gravitational waves from a neutron star at once and twice the spin frequency with a hidden Markov model

Searches for continuous gravitational waves from rapidly spinning neutron stars normally assume that the star rotates about one of its principal axes of moment of inertia, and hence the gravitational radiation emits only at twice the spin frequency of the star, $2f_*$. The superfluid interior of a star pinned to the crust along an axis nonaligned with any of its principal axes allows the star to emit gravitational waves at both $f_*$ and $2f_*$, even without free precession, a phenomenon not clearly observed in known pulsars. The dual-harmonic emission mechanism motivates searches combining the two frequency components of a signal to improve signal-to-noise ratio. We describe an economical, semicoherent, dual-harmonic search method, combined with a maximum likelihood coherent matched filter, F-statistic, and improved from an existing hidden Markov model (HMM) tracking scheme to track two frequency components simultaneously. We validate the method and demonstrate its performance through Monte Carlo simulations. We find that for sources emitting gravitational waves at both $f_*$ and $2f_*$, the rate of correctly recovering synthetic signals (i.e., detection efficiency), at a given false alarm probability, can be improved by $\sim 10$%-70% by tracking two frequencies simultaneously compared to tracking a single component only. For sources emitting at $2f_*$ only, dual-harmonic tracking only leads to minor sensitivity loss, producing $\lesssim 10\%$ lower detection efficiency than tracking a single component. In directed continuous-wave searches where $f_*$ is unknown and hence the full frequency band is searched, the computationally efficient HMM tracking algorithm provides an option of conducting both the dual-harmonic search and the conventional single frequency tracking to obtain optimal sensitivity, with a typical run time of $\sim 10^3$ core-hr for one year's observation.

Efficient estimation of barycentered relative time delays for distant gravitational wave sources

Accurate determination of gravitational wave source parameters relies on transforming between the source and detector frames. All-sky searches for continuous wave sources are computationally expensive, in part, because of barycentering transformation of time delays to a solar system frame. This expense is exacerbated by the complicated modulation induced in signal templates. We investigate approximations for determining time delays of signals received by a gravitational wave detector with respect to the solar system barycenter. A highly non-linear conventional computation is transformed into one that has a pure linear sum in its innermost loop. We discuss application of these results to determination of the maximal useful integration time of continuous wave searches.

Faster search for long gravitational-wave transients: GPU implementation of the transient -statistic

The -statistic is an established method to search for continuous gravitational waves from spinning neutron stars. Prix et al (2011 Phys. Rev. D 84 023007) introduced a variant for transient, hours–months long, 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 -statistic, using 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 signal models including time-varying (e.g. exponentially decaying) amplitudes. Hence, it can enable comprehensive coverage of glitches in known nearby pulsars, improve the follow-up of outliers from continuous-wave searches, and might be an important ingredient for future blind all-sky searches for unknown neutron stars.

All-sky radiometer for narrowband gravitational waves using folded data

We demonstrate an all-sky search for persistent, narrowband gravitational waves using mock data. The search employs radiometry to sidereal-folded data in order to uncover persistent sources of gravitational waves with minimal assumptions about the signal model. The method complements continuous-wave searches, which are finely tuned to search for gravitational waves from rotating neutron stars while providing a means of detecting more exotic sources that might be missed by dedicated continuous-wave techniques. We apply the algorithm to simulated Gaussian noise at the level of LIGO design sensitivity. We project the strain amplitude sensitivity for the algorithm for a LIGO network in the first observing run to be $h_0 \approx 1.2 \times 10^{-24}$ ($1\%$ false alarm probability, $10\%$ false dismissal probability). We include treatment of instrumental lines and detector artifacts using time-shifted LIGO data from the first observing run.

Probing dynamical gravity with the polarization of continuous gravitational waves

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 nontensorial components. This will allow us to obtain new model-independent, dynamical constraints on deviations from general relativity. We test this framework on multiple potential sources using simulated data from three advanced-era detectors at design sensitivity. We find that signals of any polarization will become detectable and distinguishable for characteristic strains $h\ensuremath{\gtrsim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}\sqrt{1\text{ }\text{ }\mathrm{yr}/T}$, for an observation time $T$. We also find that our ability to detect nontensorial components depends only on the power present in those modes, irrespective of the strength of the tensorial strain.

Distinguishing transient signals and instrumental disturbances in semi-coherent searches for continuous gravitational waves with line-robust statistics

Non-axisymmetries in rotating neutron stars emit quasi-monochromatic gravitational waves. These long-duration ‘continuous wave’ signals are among the main search targets of ground-based interferometric detectors. However, standard detection methods are susceptible to false alarms from instrumental artefacts that resemble a continuous-wave signal. Past work [Keitel, Prix, Papa, Leaci and Siddiqi 2014, Phys. Rev. D 89 064023] showed that a Bayesian approach, based on an explicit model of persistent single-detector disturbances, improves robustness against such artefacts. Since many strong outliers in semi-coherent searches of LIGO data are caused by transient disturbances that last only a few hours or days, I describe in a recent paper [Keitel D 2015, LIGO-P1500159] how to extend this approach to cover transient disturbances, and demonstrate increased sensitivity in realistic simulated data. Additionally, neutron stars could emit transient signals which, for a limited time, also follow the continuous-wave signal model. As a pragmatic alternative to specialized transient searches, I demonstrate how to make standard semi-coherent continuous-wave searches more sensitive to transient signals. Focusing on the time-scale of a single segment in the semi-coherent search, Bayesian model selection yields a simple detection statistic without a significant increase in computational cost. This proceedings contribution gives a brief overview of both works.

Methods to filter out spurious disturbances in continuous-wave searches from gravitational-wave detectors

Semicoherent all-sky searches over year-long observation times for continuous gravitational wave signals produce various thousands of potential periodic source candidates. Efficient methods able to discard false candidate events are crucial in order to put all the efforts into a computationally intensive follow-up analysis for the remaining most promising candidates (Shaltev et al 2014 Phys. Rev. D 89 124030). In this paper we present a set of techniques able to fulfill such requirements, identifying and eliminating false candidate events, reducing thus the bulk of candidate sets that need to be further investigated. Some of these techniques were also used to streamline the candidate sets returned by the Einstein@Home hierarchical searches presented in (Aasi J et al (The LIGO Scientific Collaboration and the Virgo Collaboration) 2013 Phys. Rev. D 87 042001). These powerful methods and the benefits originating from their application to both simulated and on detector data from the fifth LIGO science run are illustrated and discussed.

Method for narrow-band search of continuous gravitational wave signals

Targeted searches of continuous waves from spinning neutron stars normally assume that the frequency of the gravitational wave signal is at a given known ratio with respect to the rotational frequency of the source, e.g. twice for an asymmetric neutron star rotating around a principal axis of inertia. In fact this assumption may well be invalid if, for instance, the gravitational wave signal is due to a solid core rotating at a slightly different rate with respect to the star crust. In this paper we present a method for {\it narrow-band} searches of continuous gravitational wave signals from known pulsars in the data of interferometric detectors. This method assumes source position is known to high accuracy, while a small frequency and spin-down range around the electromagnetic-inferred values is explored. Barycentric and spin-down corrections are done with an efficient time-domain procedure. Sensitivity and computational efficiency estimates are given and results of tests done using simulated data are also discussed.