Continuous Gravitational Waves Research Articles

Search Methods for Continuous Gravitational-Wave Signals from Unknown Sources in the Advanced-Detector Era

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 signals. In this work, we review the current state of searches for continuous gravitational waves using ground-based interferometer data, focusing on searches for unknown sources. These searches typically consist of a main stage followed by several post-processing steps to rule out outliers produced by detector noise. So far, no continuous gravitational wave signal has been confidently detected, although tighter upper limits are placed as detectors and search methods are further developed.

Search for Continuous Gravitational-wave Signals in Pulsar Timing Residuals: A New Scalable Approach with Diffusive Nested Sampling

Abstract Detecting continuous nanohertz gravitational waves (GWs) generated by individual close binaries of supermassive black holes (CB-SMBHs) is one of the primary objectives of pulsar timing arrays (PTAs). The detection sensitivity is slated to increase significantly as the number of well-timed millisecond pulsars will increase by more than an order of magnitude with the advent of next-generation radio telescopes. Currently, the Bayesian analysis pipeline using parallel tempering Markov Chain Monte Carlo has been applied in multiple studies for CB-SMBH searches, but it may be challenged by the high dimensionality of the parameter space for future large-scale PTAs. One solution is to reduce the dimensionality by maximizing or marginalizing over uninformative parameters semianalytically, but it is not clear whether this approach can be extended to more complex signal models without making overly simplified assumptions. Recently, the method of diffusive nested (DNest) sampling has shown capability in coping with high dimensionality and multimodality effectively in Bayesian analysis. In this paper, we apply DNest to search for continuous GWs in simulated pulsar timing residuals and find that it performs well in terms of accuracy, robustness, and efficiency for a PTA including  ( 10 2 ) pulsars. DNest also allows a simultaneous search of multiple sources elegantly, which demonstrates its scalability and general applicability. Our results show that it is convenient and also highly beneficial to include DNest in current toolboxes of PTA analysis.

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.

Erratum: Directed searches for continuous gravitational waves from twelve supernova remnants in data from Advanced LIGO’s second observing run [Phys. Rev. D 101 , 083023 (2020)

Received 21 September 2021DOI:https://doi.org/10.1103/PhysRevD.104.109902© 2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGravitational wavesGravitation, Cosmology & Astrophysics

Gravitational waves from spinning neutron stars as not-quite-standard sirens

ABSTRACT As is well known, gravitational wave detections of coalescing binaries are standard sirens, allowing a measurement of source distance by gravitational wave means alone. In this paper we explore the analogue of this capability for continuous gravitational wave emission from individual spinning neutron stars, whose spin-down is driven purely by gravitational wave emission. We show that in this case, the distance measurement is always degenerate with one other parameter, which can be taken to be the moment of inertia of the star. We quantify the accuracy to which such degenerate measurements can be made. We also discuss the practical application of this method to scenarios where one or other of distance or moment of inertia is constrained, breaking this degeneracy and allowing a measurement of the remaining parameter. We consider a broad range of possible unknown parameters, as well as we present results for the aLIGO and Einstein Telescope sensitivities. Our results will be of use following the eventual detection of a neutron star spinning down through such gravitational wave emission.

Detectability of Continuous Gravitational Waves from Magnetically Deformed Neutron Stars

Neutron stars are known to contain extremely powerful magnetic fields. Their effect is to deform the shape of the star, leading to the potential emission of continuous gravitational waves. The magnetic deformation of neutron stars, however, depends on the geometry and strength of their internal magnetic field as well as 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 unknown, and assessing the detectability of continuous gravitational waves from neutron stars suffers from these uncertainties. Using our recent results relating the magnetic deformation of a neutron star to its mass and radius—based on models with realistic equations of state currently allowed by observational and nuclear physics constraints—and considering the Galactic pulsar population, we assess the detectability of continuous gravitational waves from pulsars in the galaxy by current and future gravitational waves detectors.

Modeling the Galactic Neutron Star Population for Use in Continuous Gravitational-wave Searches

Abstract Searches for continuous gravitational waves (GW) from unknown Galactic neutron stars provide limits on the shapes of neutron stars. A rotating neutron star will produce GW if asymmetric deformations exist in its structure that are characterized by the star’s ellipticity. In this study, we use a simple model of the spatial and spin distribution of Galactic neutron stars to estimate the total number of neutron stars probed, using GW, to a given upper limit on the ellipticity. This may help optimize future searches with improved sensitivity. The improved sensitivity of third-generation GW detectors may increase the number of neutron stars probed, to a given ellipticity, by factors of 100 to 1000.

Searches for Continuous Gravitational Waves from Young Supernova Remnants in the Early Third Observing Run of Advanced LIGO and Virgo

Abstract We present results of three wide-band directed searches for continuous gravitational waves from 15 young supernova remnants in the first half of the third Advanced LIGO and Virgo observing run. We use three search pipelines with distinct signal models and methods of identifying noise artifacts. Without ephemerides of these sources, the searches are conducted over a fRequency band spanning from 10 to 2 kHz. We find no evidence of continuous gravitational radiation from these sources. We set upper limits on the intrinsic signal strain at 95% confidence level in sample subbands, estimate the sensitivity in the full band, and derive the corresponding constraints on the fiducial neutron star ellipticity and r-mode amplitude. The best 95% confidence constraints placed on the signal strain are 7.7 × 10−26 and 7.8 × 10−26 near 200 Hz for the supernova remnants G39.2–0.3 and G65.7+1.2, respectively. The most stringent constraints on the ellipticity and r-mode amplitude reach ≲10−7 and ≲ 10−5, respectively, at frequencies above ∼400 Hz for the closest supernova remnant G266.2–1.2/Vela Jr.

Deep searches for X-ray pulsations from Scorpius X-1 and Cygnus X-2 in support of continuous gravitational wave searches

ABSTRACT Neutron stars in low mass X-ray binaries (LMXBs) are hypothesised to emit continuous gravitational waves that may be detectable by ground-based observatories. The torque balance model predicts that a higher accretion rate produces larger-amplitude gravitational waves, hence LMXBs with high X-ray flux are promising targets for gravitational wave searches. The detection of X-ray pulsations would identify the spin frequency of these neutron stars, and thereby improve the sensitivity of continuous gravitational-wave searches by reducing the volume of the search parameter space. We perform a semi-coherent search for pulsations in the two LMXBs Scorpius X-1 (Sco X-1) and Cygnus X-2 (Cyg X-2) using X-ray data from the Rossi X-ray Timing Explorer Proportional Counter Array. We find no clear evidence for pulsations, and obtain upper limits (at 90 per cent confidence) on the fractional pulse amplitude, with the most stringent being 0.034 per cent for Sco X-1 and 0.23 per cent for Cyg X-2. These upper limits improve upon those in previous work by factors of ∼8.2 and ∼1.6, respectively.

Poisson-Arago spot for gravitational waves

For the observer at infinity, a Schwarzschild black hole serves as an attractive opaque disk with a radius of $$3\,\sqrt 3 M$$ that will produce the diffraction pattern of gravitational waves (GWs). In this study, we demonstrate that a bright spot, which is a diffraction effect analogous to the Poisson-Arago spot in optics, will appear when an ingoing (quasi-)plane GW is diffracted by a Schwarzschild black hole. Here, we propose the diffraction effect of the GWs described by the exact diffraction solution of the GWs using the Heun function. For the first time, the Fresnel half-wave zone method is proposed to calculate the angular part of the GW scattering stripes for the observer at infinity. The prospect of observing the diffraction bright spot is discussed with an eikonal approximation. For normal incidence (quasi)-plane waves with 100 Hz (0.1 Hz) frequency diffracted by the central black hole of the Milky Way, the time delay between the Earth bathed in a bright spot and the minimum of the first dark stripe is 3.86 (3860) d. We will witness the second bright fringe (40% amplitude of the central bright spot) after 6.2 (6200) d. This new diffraction pattern involving the early phase of inspirals and pulsars as continuous gravitational wave sources is a potential scientific target for future space-and ground-based gravitational wave detectors, respectively.

All-sky search for continuous gravitational waves from isolated neutron stars in the early O3 LIGO data

We report on an all-sky search for continuous gravitational waves in the frequency band 20-2000\,Hz and with a frequency time derivative in the range of $[-1.0, +0.1]\times10^{-8}$\,Hz/s. Such a signal could be produced by a nearby, spinning and slightly non-axisymmetric isolated neutron star in our galaxy. This search uses the LIGO data from the first six months of Advanced LIGO's and Advanced Virgo's third observational run, O3. No periodic gravitational wave signals are observed, and 95\%\ confidence-level (CL) frequentist upper limits are placed on their strengths. The lowest upper limits on worst-case (linearly polarized) strain amplitude $h_0$ are $~1.7\times10^{-25}$ near 200\,Hz. For a circularly polarized source (most favorable orientation), the lowest upper limits are $\sim6.3\times10^{-26}$. These strict frequentist upper limits refer to all sky locations and the entire range of frequency derivative values. For a population-averaged ensemble of sky locations and stellar orientations, the lowest 95\%\ CL upper limits on the strain amplitude are $\sim1.\times10^{-25}$. These upper limits improve upon our previously published all-sky results, with the greatest improvement (factor of $\sim$2) seen at higher frequencies, in part because quantum squeezing has dramatically improved the detector noise level relative to the second observational run, O2. These limits are the most constraining to date over most of the parameter space searched.

Prototype superfluid gravitational wave detector

We study a cross-shaped cavity filled with superfluid $^4$He as a prototype resonant-mass gravitational wave detector. Using a membrane and a re-entrant microwave cavity as a sensitive optomechanical transducer, we were able to observe the thermally excited high-$Q$ acoustic modes of the helium at 20 mK temperature and achieved a strain sensitivity of $8 \times 10^{-19}$ Hz$^{-1/2}$ to gravitational waves. To facilitate the broadband detection of continuous gravitational waves, we tune the kilohertz-scale mechanical resonance frequencies up to 173 Hz/bar by pressurizing the helium. With reasonable improvements, this architecture will enable the search for GWs in the 1-30 kHz range, relevant for a number of astrophysical sources both within and beyond the Standard Model.

Quasi-universality of the magnetic deformation of neutron stars in general relativity and beyond

Neutron stars are known to host extremely powerful magnetic fields. Among its effects, one of the consequences of harbouring such fields is the deformation of the neutron star structure, leading, together with rotation, to the emission of continuous gravitational waves. On the one hand, the details of their internal magnetic fields are mostly unknown. Likewise, their internal structure, encoded by the equation of state, is highly uncertain. Here, we present a study of axisymmetric models of isolated magnetised neutron stars for various realistic equations of state considered viable by observations and nuclear physics constraints. We show that it is possible to find simple relations between the magnetic deformation of a neutron star, its Komar mass, and its circumferential radius in the case of purely poloidal and purely toroidal magnetic configurations that satisfy the criterion for equilibrium in the Bernoulli formalism. Such relations are quasi-universal, meaning that they are mostly independent from the equation of state of the neutron star. Thanks to their formulation in terms of potentially observable quantities, as we discuss, our results could help to constrain the magnetic properties of the neutron star interior and to better assess the detectability of continuous gravitational waves by isolated neutron stars, without knowing their equation of state. Our results are derived both in general relativity and in scalar-tensor theories (one of the most promising extensions of general relativity), in this case by also considering the scalar charge. We show that even in this case, general relations that account for deviations from general relativity still hold, which could potentially be used to set constraints on the gravitational theory.

Revisiting neutron starquakes caused by spin-down

Context. Pulsars show a steady decrease in their rotational frequency, occasionally interrupted by sudden spin-ups called glitches, whose physical origin is still a mystery. One suggested explanation for at least the small glitches are starquakes, that is, failures of the solid neutron star crust, in which the progressive reduction in the centrifugal force deforms the star, stressing the solid until it breaks. This produces a spin-up, dissipating energy inside the star. Aims. We explore this suggestion by analyzing a mostly analytical model in order to understand the possible consequences of starquakes, particularly whether they can explain at least the small glitches. Methods. We analyze the deformations and strains produced by the decreasing centrifugal force, modeling the neutron star with a fluid core and a solid crust, each with uniform density and with the core possibly denser than the crust, as a simple approximation to the strong density gradient present in real neutron stars. Results. The deformation of a star with very different densities in the core and crust is qualitatively different from the previously studied case of equal densities. The former more closely resembles the behavior of a fluid star, in which the core-crust interface is a surface of constant gravitational plus centrifugal potential. Conclusions. Regardless of the uncertain breaking strain, the glitch activity in this model is several orders of magnitude smaller than observed, even if only small glitches are considered. For a large breaking strain, suggested by simulations, glitches due to starquakes could be roughly of the correct size but much less frequent than observed glitches. The energy released in each such glitch is much larger than in the standard model of angular momentum transfer from a faster rotating superfluid in the inner crust. On the other hand, we cannot rule out that the heating produced by small starquakes could trigger glitches by allowing neutron superfluid vortices to move. We also confirm that stresses in the neutron star crust can in principle support an ellipticity much larger than some observational upper limits from pulsar timing and continuous gravitational wave searches.

Resolving dichotomy in compact objects through continuous gravitational waves observation

ABSTRACT More than two dozen soft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs) have been detected so far. These are isolated compact objects. Many of them are either found to be associated with supernova remnants or their surface magnetic fields are directly measured, confirming that they are neutron stars (NSs). However, it has been argued that some SGRs and AXPs are highly magnetized white dwarfs (WDs). Meanwhile, the existence of super-Chandrasekhar WDs has remained to be a puzzle. However, not even a single such massive WD has been observed directly. Moreover, some WD pulsars are detected in electromagnetic surveys and some of their masses are still not confirmed. Here, we calculate the signal-to-noise ratio for all these objects, considering different magnetic field configurations and thereby estimate the required time for their detection by various gravitational wave (GW) detectors. For SGRs and AXPs, we show that, if these are NSs, they can hardly be detected by any of the GW detectors, while if they are WDs, big bang Observer (BBO), DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) and Advanced Laser Interferometer Antenna (ALIA) would be able to detect them within a few days to a year of integration, depending on the magnetic field strength and its configuration. Similarly, if a super-Chandrasekhar WD has a dominant toroidal field, we show that even Laser Interferometer Space Antenna (LISA) and TianQin would be able to detect it within one year of integration. We also discuss how GWs can confirm the masses of the WD pulsars.

Erratum: “Searches for Continuous Gravitational Waves from 15 Supernova Remnants and Fomalhaut b with Advanced LIGO” (2019, ApJ, 875, 122) *

Equation (5) of the published article?(Abbott et al. 2019) is in error; it should read (Formula Presented) The upper limits on o presented in the published article are unaffected by this error.

Erratum: “Searches for Continuous Gravitational Waves from Nine Young Supernova Remnants” (2015, ApJ, 813, 39) *

Equation (7) of the published article (Aasi et al. 2015) is in error; it should read (Equation presented). The upper limits on o presented in the published article are unaffected by this error. Equation (8) of the published article is in error; it should read (Equation presented) The upper limits on α presented in Figure 3 and Table 4 of the published article were computed incorrectly. The revised Figure 3 (bottom) shows the corrected upper limits on α for the G266.2-1.2 (Vela Jr.) wide search. The revised Table 4 is provided here. The correct lowest upper limit on α (quoted in the Abstract of the published article) is 3 × 10-6. Figure 4 shows the incorrect and corrected upper limits on α for the G266.2-1.2 (Vela Jr.) wide search, which have been surpassed by upper limits from Abbott et al. (2019).

Hidden Markov model tracking of continuous gravitational waves from a binary neutron star with wandering spin. III. Rotational phase tracking

A hidden Markov model (HMM) solved recursively by the Viterbi algorithm can be configured to search for persistent, quasimonochromatic gravitational radiation from an isolated or accreting neutron star, whose rotational frequency is unknown and wanders stochastically. Here an existing HMM analysis pipeline is generalized to track rotational phase and frequency simultaneously, by modeling the intra-step rotational evolution according to a phase-wrapped Ornstein-Uhlenbeck process, and by calculating the emission probability using a phase-sensitive version of the Bayesian matched filter known as the $\mathcal{B}$-statistic. The generalized algorithm tracks signals from isolated and binary sources with characteristic wave strain $h_0 \geq 1.3\times 10^{-26}$ in Gaussian noise with amplitude spectral density $4\times 10^{-24}\,{\rm Hz^{-1/2}}$, for a simulated observation composed of $N_T=37$ data segments, each $T_{\rm drift}=10\,{\rm days}$ long, the typical duration of a search for the low-mass X-ray binary (LMXB) Sco X$-$1 with the Laser Interferometer Gravitational Wave Observatory (LIGO). It is equally sensitive to isolated and binary sources and $\approx 1.5$ times more sensitive than the previous pipeline. Receiver operating characteristic curves and errors in the recovered parameters are presented for a range of practical $h_0$ and $N_T$ values. The generalized algorithm successfully detects every available synthetic signal in Stage I of the Sco X$-$1 Mock Data Challenge convened by the LIGO Scientific Collaboration, recovering the frequency and orbital semimajor axis with accuracies of better than $9.5\times 10^{-7}\,{\rm Hz}$ and $1.6\times 10^{-3}\,{\rm lt\,s}$ respectively. The Viterbi solver runs in $\approx 2\times 10^3$ CPU-hr for an isolated source and $\sim 10^5$ CPU-hr for a LMXB source in a typical, broadband ($0.5$-${\rm kHz}$) search.

Search for continuous gravitational waves from small-ellipticity sources at low frequencies

We present the results of an all-sky search for continuous gravitational wave signals with frequencies in the 20-500 Hz range from neutron stars with ellipticity of 1e-8. This frequency region is particularly hard to probe because of the quadratic dependence of signal strength on frequency. The search employs the Falcon analysis pipeline on LIGO O2 public data. Compared to previous Falcon analyses the coherence length has been quadrupled, with a corresponding increase in sensitivity. This enables us to search for small ellipticity neutron stars in this low frequency region up to 44 pc away. The frequency derivative range is up to 3e-13 Hz/s easily accommodating sources with ellipticities of 1e-7 and a corresponding factor of 10 increase in reach. New outliers are found, many of which we are unable to associate with any instrumental cause.

Frame-dragging effects in obliquely rotating magnetars

Magnetars are highly magnetized neutron stars. For a slowly rotating magnetar, the strong magnetic field deforms the star, making it axisymmetric with respect to the magnetic axis (the body symmetry axis). In magnetars, the rotation axis is tilted to the magnetic axis, and we have an oblique rotator. General relativistic treatment of the obliquely rotating magnetar gives rise to frame-dragging velocities both in the azimuthal and polar direction. Solving the Einstein equation up to first-order perturbation in rotation and second-order perturbation in the magnetic field, we calculate the geodesic of a particle near the star's surface. The polar frame-dragging velocity makes the particle orbit non-planar, and the particle moves both along the azimuthal and polar direction for a fixed radial distance. The extent of particle deviation from planar orbit depends on the magnetic field strength and the misalignment angle. We find that the continuous gravitational wave emitted from such obliquely rotating axisymmetric star is non zero, and for small misalignment angle, the gravitational wave amplitude depends more on the azimuthal frame-dragging velocity. In contrast, for a large misalignment angle, the polar frame-dragging velocity dominates. The energy loss from such a misaligned rotator depends more significantly on the polar frame-dragging velocity and therefore, can significantly affect the magnetosphere around a magnetar.