Advanced Laser Interferometer Gravitational-Wave Research Articles

Intensity and anisotropies of the stochastic gravitational wave background from merging compact binaries in galaxies

We investigate the isotropic and anisotropic components of the Stochastic Gravitational Wave Background (SGWB) originated from unresolved merging compact binaries in galaxies. We base our analysis on an empirical approach to galactic astrophysics that allows to follow the evolution of individual systems. We then characterize the energy density of the SGWB as a tracer of the total matter density, in order to compute the angular power spectrum of anisotropies with the Cosmic Linear Anisotropy Solving System (CLASS) public code in full generality. We obtain predictions for the isotropic energy density and for the angular power spectrum of the SGWB anisotropies, and study the prospect for their observations with advanced Laser Interferometer Gravitational-Wave and Virgo Observatories and with the Einstein Telescope. We identify the contributions coming from different type of sources (binary black holes, binary neutron stars and black hole-neutron star) and from different redshifts. We examine in detail the spectral shape of the energy density for all types of sources, comparing the results for the two detectors. We find that the power spectrum of the SGWB anisotropies behaves like a power law on large angular scales and drops at small scales: we explain this behavior in terms of the redshift distribution of sources that contribute most to the signal, and of the sensitivities of the two detectors. Finally, we simulate a high resolution full sky map of the SGWB starting from the power spectra obtained with CLASS and including Poisson statistics and clustering properties.

Swift/UVOT follow-up of gravitational wave alerts in the O3 era

ABSTRACT In this paper, we report on the observational performance of the Swift Ultra-violet/Optical Telescope (UVOT) in response to the gravitational wave (GW) alerts announced by the Advanced Laser Interferometer Gravitational Wave Observatory and the Advanced Virgo detector during the O3 period. We provide the observational strategy for follow-up of GW alerts and provide an overview of the processing and analysis of candidate optical/UV sources. For the O3 period, we also provide a statistical overview and report on serendipitous sources discovered by Swift/UVOT. Swift followed 18 GW candidate alerts, with UVOT observing a total of 424 deg2. We found 27 sources that changed in magnitude at the 3σ level compared with archival u- or g-band catalogued values. Swift/UVOT also followed up a further 13 sources reported by other facilities during the O3 period. Using catalogue information, we divided these 40 sources into five initial classifications: 11 candidate active galactic nuclei (AGNs)/quasars, three cataclysmic variables (CVs), nine supernovae, 11 unidentified sources that had archival photometry, and six uncatalogued sources for which no archival photometry was available. We have no strong evidence to identify any of these transients as counterparts to the GW events. The 17 unclassified sources are likely a mix of AGN and a class of fast-evolving transient, and one source may be a CV.

Complexity analysis of gravitational waves

The recent observations of gravitational waves during the coalescence of black holes has confirmed various predictions of general relativity. However, some concerns have been raised that these putative waves are artifacts. We have analyzed the ten confident gravitational waves detected in Observation Run 1 (O1) and Observation Run 2 (O2) and the gravitational wave emitted by the single known example of a neutron star coalescence, all of which have been verified by the Advanced Laser Interferometer Gravitational Wave Observatory and/or the Advanced Virgo Collaboration. On three occasions both Advanced LIGO and Advanced Virgo detected the same event (Abbott et al., 2019).Whitening of the Hanford data (Gravitational Wave Open Science Center) was employed in this study to reduce colored non-transient noise, but template matching was not employed. In each of the ten events mentioned above we verified the presence of such waves by the application of non-stationary data analysis via the Morlet wavelet. We examined the strain data before, during and after each wave. In each case we employed seven measures of complexity or information before, and during each wave and analyzed these data using doubly multivariate MANOVA, the appropriate statistical test for repeated measures (pre-wave vs wave). In addition we compared the strain data before and after the putative event to see if there was persistence of any effect of the event. In each case the information content was significantly elevated during the wave compared to similar time samples taken before the wave. No persistent effects on the strain data were noted after the event. We conclude our analysis is consistent with the actual detection of gravitational waves by the LIGO and Virgo Collaboration. Our results suggest black hole coalescence generates mathematically complex gravitational waves which may elucidate aspects of such coalescence.

Chirp mass and spin of binary black holes from first star remnants

ABSTRACT We performed Population III (Pop III) binary evolution using population synthesis simulations for seven different models. We found that Pop III binaries tend to be binary black holes (BBHs) with chirp mass Mchirp ∼ 30 M⊙ and they can merge in the present day, due to a long merger time. The merger rate densities of Pop III BBHs at z = 0 are in the range 3.34–21.2 $\rm yr^{-1}\,Gpc^{-3}$ which is consistent with the Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO)/Advanced Virgo (aVIRGO) result of 9.7–101 $\rm yr^{-1}\,Gpc^{-3}$. These Pop III binaries might contribute some portion of the massive BBH gravitational wave (GW) sources detected by aLIGO/aVIRGO. We also calculated the redshift dependence of Pop III BBH mergers. We found that Pop III low-spin BBHs tend to merge at low redshift, while Pop III high-spin BBHs merge at high redshift, which can be confirmed by future GW detectors such as Einstein Telescope (ET), Cosmic Explorer (CE), and DECi-hertz Interferometer Gravitational wave Observatory (DECIGO). These detectors can also check the redshift dependence of the BBH merger rate and spin distribution. Our results show that, except for one model, the mean effective spin 〈χeff〉 at z = 0 lies in the range 0.02–0.3, while at z = 10 it is 0.16–0.64. Therefore, massive stellar-mass BBH detection by GWs will be key for stellar evolution study in the early Universe.

Application of hidden Markov model tracking to the search for long-duration transient gravitational waves from the remnant of the binary neutron star merger GW170817

The nature of the post-merger remnant of the first binary neutron star coalescence observed by the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO) and Advanced Virgo, GW170817, is unknown. Searches have been carried out for short ($\lesssim 1$ s), intermediate ($\lesssim 500$ s), and long ($\sim$ days) signals using various algorithms without yielding a detection. We describe an efficient frequency tracking scheme based on a hidden Markov model to search for long-duration transient signals from a neutron star remnant with spin-down time-scale in the range $\sim 10^2$s-$10^4$s. It was one of the methods used in the search for signals from a long-lived remnant of GW170817. We validate the method and estimate its sensitivity through Monte-Carlo simulations on the same data set as used in the GW170817 search. We describe the search configuration, procedure, and follow-up step by step. The methodology of the hidden Markov model is described fully to ensure that future analyses of this kind can be reproduced by an independent party.

Thermal noise of beam splitters in laser gravitational wave detectors

We present the calculation of thermal noise in interferometric gravitational-wave detectors due to the thermal fluctuations of the beam splitter (BS). This work makes use of a recently developed method of the analysis of thermal noise in mirrors from first principles, based on the fluctuation dissipation theorem. The evaluation of BS thermal noise is carried out for the two different grav- itational wave observatories, GEO600 and the Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO). The analysis evaluates thermal noise from both the substrate and the optical reflective and antireflective stacks located on the BS surface. We demonstrate that the fluctuations of both reflecting and anti-reflecting surfaces significantly contribute to the total thermal noise of the BS. The oscillating intensity pattern couples small-scale distortions of the surface to the overall phase readout, and therefore increases the overall thermal noise. In the case of aLIGO, the BS contribution is with $0.3\%$ negligibly small. At a frequency of 500Hz, the BS causes about $10\%$ of GEO600's sensitivity limit. BS noise impairs the feasible sensitivity of the GEO-HF design proposal by about $50\%$.

Parametrized tests of the strong-field dynamics of general relativity using gravitational wave signals from coalescing binary black holes: Fast likelihood calculations and sensitivity of the method

Thanks to the recent discoveries of gravitational wave signals from binary black hole mergers by Advanced Laser Interferometer Gravitational Wave Observatory and Advanced Virgo, the genuinely strong-field dynamics of spacetime can now be probed, allowing for stringent tests of general relativity (GR). One set of tests consists of allowing for parametrized deformations away from GR in the template waveform models and then constraining the size of the deviations, as was done for the detected signals in previous work. In this paper, we construct reduced-order quadratures so as to speed up likelihood calculations for parameter estimation on future events. Next, we explicitly demonstrate the robustness of the parametrized tests by showing that they will correctly indicate consistency with GR if the theory is valid. We also check to what extent deviations from GR can be constrained as information from an increasing number of detections is combined. Finally, we evaluate the sensitivity of the method to possible violations of GR.

Hidden Markov model tracking of continuous gravitational waves from young supernova remnants

Searches for persistent gravitational radiation from nonpulsating neutron stars in young supernova remnants (SNRs) are computationally challenging because of rapid stellar braking. We describe a practical, efficient, semi-coherent search based on a hidden Markov model (HMM) tracking scheme, solved by the Viterbi algorithm, combined with a maximum likelihood matched filter, the $\mathcal{F}$-statistic. The scheme is well suited to analyzing data from advanced detectors like the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO). It can track rapid phase evolution from secular stellar braking and stochastic timing noise torques simultaneously without searching second- and higher-order derivatives of the signal frequency, providing an economical alternative to stack-slide-based semi-coherent algorithms. One implementation tracks the signal frequency alone. A second implementation tracks the signal frequency and its first time derivative. It improves the sensitivity by a factor of a few upon the first implementation, but the cost increases by two to three orders of magnitude.

Gravitational lensing of gravitational waves: a statistical perspective

In this paper, we study the strong gravitational lensing of gravitational waves (GWs) from a statistical perspective, with particular focus on the high frequency GWs from stellar binary black hole coalescences. These are most promising targets for ground-based detectors such as Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) and the proposed Einstein Telescope (ET) and can be safely treated under the geometrical optics limit for GW propagation. We perform a thorough calculation of the lensing rate, by taking account of effects caused by the ellipticity of lensing galaxies, lens environments, and magnification bias. We find that in certain GW source rate scenarios, we should be able to observe strongly lensed GW events once per year ($\sim1~\text{yr}^{-1}$) in the aLIGO survey at its design sensitivity; for the proposed ET survey, the rate could be as high as $\sim80~\text{yr}^{-1}$. These results depend on the estimate of GW source abundance, and hence can be correspondingly modified with an improvement in our understanding of the merger rate of stellar binary black holes. We also compute the fraction of four-image lens systems in each survey, predicting it to be $\sim30$ per cent for the aLIGO survey and $\sim6$ per cent for the ET survey. Finally, we evaluate the possibility of missing some images due to the finite survey duration, by presenting the probability distribution of lensing time delays. We predict that this selection bias will be insignificant in future GW surveys, as most of the lens systems ($\sim90$ per cent) will have time delays less than $\sim1$ month, which will be far shorter than survey durations.

The First Detection of Gravitational Waves

This article deals with the first detection of gravitational waves by the advanced Laser Interferometer Gravitational Wave Observatory (LIGO) detectors on 14 September 2015, where the signal was generated by two stellar mass black holes with masses 36 M ⊙ and 29 M ⊙ that merged to form a 62 M ⊙ black hole, releasing 3 M ⊙ energy in gravitational waves, almost 1.3 billion years ago. We begin by providing a brief overview of gravitational waves, their sources and the gravitational wave detectors. We then describe in detail the first detection of gravitational waves from a binary black hole merger. We then comment on the electromagnetic follow up of the detection event with various telescopes. Finally, we conclude with the discussion on the tests of gravity and fundamental physics with the first gravitational wave detection event.

Enhanced Gravitational Wave Science with LISA and gLISA.

The geosynchronous Laser Interferometer Space Antenna (gLISA) is a space-based gravitational wave (GW) mission that, for the past five years, has been under joint study at the Jet Propulsion Laboratory, Stanford University, the National Institute for Space Research (I.N.P.E., Brazil), and Space Systems Loral. With an arm length of 73,000 km, gLISA will display optimal sensitivity over a frequency region that is exactly in between those accessible by LISA and LIGO. Such a GW frequency band is characterized by the presence of a very large ensemble of coalescing black-hole binaries (BHBs) similar to those first observed by LIGO and with masses that are 10 to 100 times the mass of the Sun. gLISA will detect thousands of such signals with good signal-to-noise ratio (SNR) and enhance the LIGO science by measuring with high precision the parameters characterizing such signals (source direction, chirp parameter, time to coalescence, etc.) well before they will enter the LIGO band. This valuable information will improve LIGO’s ability to detect these signals and facilitate its study of the merger and ring-down phases not observable by space-based detectors. If flown at the same time as the LISA mission, the two arrays will deliver a joint sensitivity that accounts for the best performance of both missions in their respective parts of the milliHertz band. This simultaneous operation will result in an optimally combined sensitivity curve that is “white” from about 3 × 10−3 Hz to 1 Hz, making the two antennas capable of detecting, with high signal-to-noise ratios (SNRs), BHBs with masses in the range (10 − 107)M⊙. Their ability of jointly tracking, with enhanced SNR, signals similar to that observed by the Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) on September 14, 2015 (the GW150914 event) will result in a larger number of observable small-mass binary black-holes and an improved precision of the parameters characterizing these sources. Together, LISA, gLISA and aLIGO will cover, with good sensitivity, the (10−4 − 103) Hz frequency band.

Quantum correlation measurements in interferometric gravitational-wave detectors

Quantum fluctuations in the phase and amplitude quadratures of light set limitations on the sensitivity of modern optical instruments. The sensitivity of the interferometric gravitational wave detectors, such as the Advanced Laser Interferometer Gravitational wave Observatory (LIGO), is limited by quantum shot noise, quantum radiation pressure noise, and a set of classical noises. We show how the quantum properties of light can be used to distinguish these noises using correlation techniques. Particularly, in the first part of the paper we show estimations of the coating thermal noise and gas phase noise, hidden below the quantum shot noise in the Advanced LIGO sensitivity curve. We also make projections on the observatory sensitivity during the next science runs. In the second part of the paper we discuss the correlation technique that reveals the quantum radiation pressure noise from the background of classical noises and shot noise. We apply this technique to the Advanced LIGO data, collected during the first science run, and experimentally estimate the quantum correlations and quantum radiation pressure noise in the interferometer for the first time.

Upper Limits on the Stochastic Gravitational-Wave Background from Advanced LIGO's First Observing Run.

A wide variety of astrophysical and cosmological sources are expected to contribute to a stochastic gravitational-wave background. Following the observations of GW150914 and GW151226, the rate and mass of coalescing binary black holes appear to be greater than many previous expectations. As a result, the stochastic background from unresolved compact binary coalescences is expected to be particularly loud. We perform a search for the isotropic stochastic gravitational-wave background using data from Advanced Laser Interferometer Gravitational Wave Observatory's (aLIGO) first observing run. The data display no evidence of a stochastic gravitational-wave signal. We constrain the dimensionless energy density of gravitational waves to be Ω_{0}<1.7×10^{-7} with 95%confidence, assuming a flat energy density spectrum in the most sensitive part of the LIGO band (20-86Hz). This is a factor of ∼33 times more sensitive than previous measurements. We also constrain arbitrary power-law spectra. Finally, we investigate the implications of this search for the background of binary black holes using an astrophysical model for the background.

Directional Limits on Persistent Gravitational Waves from Advanced LIGO's First Observing Run.

We employ gravitational-wave radiometry to map the stochastic gravitational wave background expected from a variety of contributing mechanisms and test the assumption of isotropy using data from the Advanced Laser Interferometer Gravitational Wave Observatory's (aLIGO) first observing run. We also search for persistent gravitational waves from point sources with only minimal assumptions over the 20-1726Hz frequency band. Finding no evidence of gravitational waves from either point sources or a stochastic background, we set limits at 90%confidence. For broadband point sources, we report upper limits on the gravitational wave energy flux per unit frequency in the range F_{α,Θ}(f)<(0.1-56)×10^{-8} erg cm^{-2} s^{-1} Hz^{-1}(f/25 Hz)^{α-1} depending on the sky location Θ and the spectral power index α. For extended sources, we report upper limits on the fractional gravitational wave energy density required to close the Universe of Ω(f,Θ)<(0.39-7.6)×10^{-8} sr^{-1}(f/25 Hz)^{α} depending on Θ and α. Directed searches for narrowband gravitational waves from astrophysically interesting objects (Scorpius X-1, Supernova 1987 A, and the Galactic Center) yield median frequency-dependent limits on strain amplitude of h_{0}<(6.7,5.5, and 7.0)×10^{-25}, respectively, at the most sensitive detector frequencies between 130-175Hz. This represents a mean improvement of a factor of 2 across the band compared to previous searches of this kind for these sky locations, considering the different quantities of strain constrained in each case.

Higher-order Laguerre-Gauss modes in (non-) planar four-mirror cavities for future gravitational wave detectors.

One of the limiting noise sources in the current generation of gravitational wave detectors, such as the advanced laser interferometer gravitational wave observatory (aLIGO), is the thermal noise in the interferometer's test mass coatings. One proposed method to reduce the coupling of this noise source to the gravitational wave readout is using a laser beam in the higher-order spatial LG33 mode within the interferometer. Here we show that the current four-mirror cavities of aLIGO are not compatible with Laguerre-Gauss modes due to astigmatism. A non-degeneracy of modes of the same order could be observed in experiment and simulation. We demonstrate that a non-planar cavity could be used instead as it compensates for the astigmatism and transmits the LG33 mode undisturbed.

Coherent observations of gravitational radiation with LISA and gLISA

The geosynchronous Laser Interferometer Space Antenna (gLISA) is a space-based gravitational wave (GW) mission that, for the past five years, has been under joint study at the Jet Propulsion Laboratory, Stanford University, the National Institute for Space Research (I.N.P.E., Brazil), and Space Systems Loral. If flown at the same time as the LISA mission, the two arrays will deliver a joint sensitivity that accounts for the best performance of both missions in their respective parts of the mHz band. This simultaneous operation will result in an optimally combined sensitivity curve that is "white" from a few mHz to 1 Hz, making the two antennas capable of detecting, with high signal-to-noise ratios (SNRs), coalescing black-hole binaries (BHBs) with masses in the range (10 - 100 million) solar masses. Their ability of jointly tracking, with enhanced SNR, signals similar to that observed by the Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) on September 14, 2015 (the GW150914 event) will result in a larger number of observable small-mass binary black-holes and an improved precision of the parameters characterizing these sources. Together, LISA, gLISA and aLIGO will cover, with good sensitivity, a frequency band from a tenth of a mHz to a kHz frequency band.

The basic physics of the binary black hole merger GW150914

The first direct gravitational‐wave detection was made by the Advanced Laser Interferometer Gravitational Wave Observatory on September 14, 2015. The GW150914 signal was strong enough to be apparent, without using any waveform model, in the filtered detector strain data. Here, features of the signal visible in the data are analyzed using concepts from Newtonian physics and general relativity, accessible to anyone with a general physics background. The simple analysis presented here is consistent with the fully general‐relativistic analyses published elsewhere, in showing that the signal was produced by the inspiral and subsequent merger of two black holes. The black holes were each of approximately , still orbited each other as close as ∼350 km apart and subsequently merged to form a single black hole. Similar reasoning, directly from the data, is used to roughly estimate how far these black holes were from the Earth, and the energy that they radiated in gravitational waves.

Hidden Markov model tracking of continuous gravitational waves from a neutron star with wandering spin

Gravitational wave searches for continuous-wave signals from neutron stars are especially challenging when the star's spin frequency is unknown a priori from electromagnetic observations and wanders stochastically under the action of internal (e.g. superfluid or magnetospheric) or external (e.g. accretion) torques. It is shown that frequency tracking by hidden Markov model (HMM) methods can be combined with existing maximum likelihood coherent matched filters like the F-statistic to surmount some of the challenges raised by spin wandering. Specifically it is found that, for an isolated, biaxial rotor whose spin frequency walks randomly, HMM tracking of the F-statistic output from coherent segments with duration T_drift = 10d over a total observation time of T_obs = 1yr can detect signals with wave strains h0 > 2e-26 at a noise level characteristic of the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO). For a biaxial rotor with randomly walking spin in a binary orbit, whose orbital period and semi-major axis are known approximately from electromagnetic observations, HMM tracking of the Bessel-weighted F-statistic output can detect signals with h0 > 8e-26. An efficient, recursive, HMM solver based on the Viterbi algorithm is demonstrated, which requires ~10^3 CPU-hours for a typical, broadband (0.5-kHz) search for the low-mass X-ray binary Scorpius X-1, including generation of the relevant F-statistic input. In a "realistic" observational scenario, Viterbi tracking successfully detects 41 out of 50 synthetic signals without spin wandering in Stage I of the Scorpius X-1 Mock Data Challenge convened by the LIGO Scientific Collaboration down to a wave strain of h0 = 1.1e-25, recovering the frequency with a root-mean-square accuracy of <= 4.3e-3 Hz.

A step-wise steerable source of illumination for low-noise "Violin-Mode" shadow sensors, intended for use in interferometric gravitational wave detectors.

A steerable low-noise source of illumination is described for shadow-sensors having a displacement sensitivity of ∼100 pm (rms)/√Hz, at 500 Hz, over a measuring span of at least ±0.5 mm. These sensors were designed to detect lateral "Violin-Mode" resonances in the highly tensioned fused-silica suspension fibres of the test-masses/mirrors for the Advanced Laser Interferometer Gravitational Wave Observatory gravitational wave detectors. The shadow sensors-one intended for each of the four fibres in a suspension-comprised a source of Near InfraRed (NIR) radiation (emitter) and a differential shadow-displacement sensor (detector), these bracketing the fibre under test. The suspension fibres themselves were approximately 600 mm long by 0.4 mm in diameter, and when illuminated from the side, they cast narrow, vertical, shadows onto their respective detectors-these being located at an effective distance of 50 fibre diameters behind the axes of the fibres themselves. The emitter described here was designed to compensate for a significant degree of mechanical drift or creep over time in the mean position of its suspension fibre. This was achieved by employing five adjacent columns of 8 × miniature NIR LEDs (Light Emitting Diodes, λ = 890 nm), with one column being activated at a time. When used in conjunction with a "reverse Galilean" telescope, the LED sources allowed the collimated beam from the emitter to be steered azimuthally in fine angular increments (0.65°), causing the fibre's shadow to move laterally, in a step-wise manner, across the plane of its facing detector. Each step in shadow position was approximately 0.23 mm in size, and this allowed the fibre's shadow to be re-centred, so as to bridge once again both elements of its photodiode detector-even if the fibre was off-centred by as much as ±0.5 mm. Re-centring allowed Violin-Mode vibrations of the fibre to be sensed once again as differential AC photocurrents, these flowing in anti-phase in the two elements of the "split-photodiode" detector.

Technology for the next gravitational wave detectors

This paper reviews some of the key enabling technologies for advanced and future laser interferometer gravitational wave detectors, which must combine test masses with the lowest possible optical and acoustic losses, with high stability lasers and various techniques for suppressing noise. Sect. 1 of this paper presents a review of the acoustic properties of test masses. Sect. 2 reviews the technology of the amorphous dielectric coatings which are currently universally used for the mirrors in advanced laser interferometers, but for which lower acoustic loss would be very advantageous. In sect. 3 a new generation of crystalline optical coatings that offer a substantial reduction in thermal noise is reviewed. The optical properties of test masses are reviewed in sect. 4, with special focus on the properties of silicon, an important candidate material for future detectors. Sect. 5 of this paper presents the very low noise, high stability laser technology that underpins all advanced and next generation laser interferometers.