GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence

Parameter Estimation for Gravitational-wave Bursts with the BayesWave Pipeline

We provide a comprehensive multi-aspect study of the performance of a pipeline used by the LIGO-Virgo Collaboration for estimating parameters of gravitational-wave bursts. We add simulated signals with four different morphologies (sine-Gaussians (SGs), Gaussians, white-noise bursts, and binary black hole signals) to simulated noise samples representing noise of the two Advanced LIGO detectors during their first observing run. We recover them with the BayesWave (BW) pipeline to study its accuracy in sky localization, waveform reconstruction, and estimation of model-independent waveform parameters. BW localizes sources with a level of accuracy comparable for all four morphologies, with the median separation of actual and estimated sky locations ranging from 25°.1 to 30°.3. This is a reasonable accuracy in the two-detector case, and is comparable to accuracies of other localization methods studied previously. As BW reconstructs generic transient signals with SG wavelets, it is unsurprising that BW performs best in reconstructing SG and Gaussian waveforms. The BW accuracy in waveform reconstruction increases steeply with the network signal-to-noise ratio (S/Nnet), reaching a 85% and 95% match between the reconstructed and actual waveform below S/Nnet ≈ 20 and S/Nnet ≈ 50, respectively, for all morphologies. The BW accuracy in estimating central moments of waveforms is only limited by statistical errors in the frequency domain, and is also affected by systematic errors in the time domain as BW cannot reconstruct low-amplitude parts of signals that are overwhelmed by noise. The figures of merit we introduce can be used in future characterizations of parameter estimation pipelines.

Metric Independence of Vacuum and Force-Free Electromagnetic Fields

Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well known to also be solutions in all spacetimes with conformally related metrics. This provides a sense in which electromagnetism alone cannot be used to measure certain aspects of geometry. We show that there is actually much more which cannot be so measured; relatively little of a spacetime's geometry is in fact imprinted in any particular electromagnetic field. This is demonstrated by finding a much larger class of metric transformations-involving five free functions-which preserve Maxwell solutions both in vacuum, without local currents, and also for the force-free electrodynamics associated with a tenuous plasma. One consequence of this is that many of the exact force-free fields which have previously been found around Schwarzschild and Kerr black holes are also solutions in appropriately identified flat backgrounds. As a more direct application, we use our metric transformations to write down a large class of electromagnetic waves which remain unchanged by a large class of gravitational waves propagating "in the same direction."

Formation of the first three gravitational-wave observations through isolated binary evolution

During its first four months of taking data, Advanced LIGO has detected gravitational waves from two binary black hole mergers, GW150914 and GW151226, along with the statistically less significant binary black hole merger candidate LVT151012. Here we use the rapid binary population synthesis code COMPAS to show that all three events can be explained by a single evolutionary channel-classical isolated binary evolution via mass transfer including a common envelope phase. We show all three events could have formed in low-metallicity environments (Z=0.001) from progenitor binaries with typical total masses ≳160M⊙, ≳60M⊙ and ≳90M⊙, for GW150914, GW151226 and LVT151012, respectively.

Detection methods for stochastic gravitational-wave backgrounds: a unified treatment

We review detection methods that are currently in use or have been proposed to search for a stochastic background of gravitational radiation. We consider both Bayesian and frequentist searches using ground-based and space-based laser interferometers, spacecraft Doppler tracking, and pulsar timing arrays; and we allow for anisotropy, non-Gaussianity, and non-standard polarization states. Our focus is on relevant data analysis issues, and not on the particular astrophysical or early Universe sources that might give rise to such backgrounds. We provide a unified treatment of these searches at the level of detector response functions, detection sensitivity curves, and, more generally, at the level of the likelihood function, since the choice of signal and noise models and prior probability distributions are actually what define the search. Pedagogical examples are given whenever possible to compare and contrast different approaches. We have tried to make the article as self-contained and comprehensive as possible, targeting graduate students and new researchers looking to enter this field.

The gravitational-wave physics

The direct detection of gravitational wave by Laser Interferometer Gravitational-Wave Observatory indicates the coming of the era of gravitational-wave astronomy and gravitational-wave cosmology. It is expected that more and more gravitational-wave events will be detected by currently existing and planned gravitational-wave detectors. The gravitational waves open a new window to explore the Universe and various mysteries will be disclosed through the gravitational-wave detection, combined with other cosmological probes. The gravitational-wave physics is not only related to gravitation theory, but also is closely tied to fundamental physics, cosmology and astrophysics. In this review article, three kinds of sources of gravitational waves and relevant physics will be discussed, namely gravitational waves produced during the inflation and preheating phases of the Universe, the gravitational waves produced during the first-order phase transition as the Universe cools down and the gravitational waves from the three phases: inspiral, merger and ringdown of a compact binary system, respectively. We will also discuss the gravitational waves as a standard siren to explore the evolution of the Universe.

Basis-neutral Hilbert-space analyzers

Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert space spanned by spatial modes – a critical task for spatial-mode multiplexing and quantum communication – basis-specific principles are invoked that are altogether distinct from that of ‘delay’. Here, we extend the traditional concept of temporal delay to the spatial domain, thereby enabling the analysis of a beam in an arbitrary spatial-mode basis – exemplified using Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays correspond to optical implementations of fractional transforms; for example, the fractional Hankel transform is the generalized delay associated with the space of Laguerre-Gaussian modes, and an interferometer incorporating such a ‘delay’ obtains modal weights in the associated Hilbert space. By implementing an inherently stable, reconfigurable spatial-light-modulator-based polarization-interferometer, we have constructed a ‘Hilbert-space analyzer’ capable of projecting optical beams onto any modal basis.

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 (20-86 Hz). 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 20-1726 Hz 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 130-175 Hz. 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.

Design of a tuned mass damper for high quality factor suspension modes in Advanced LIGO

We discuss the requirements, design, and performance of a tuned mass damper which we have developed to damp the highest frequency pendulum modes of the quadruple suspensions which support the test masses in the two advanced detectors of the Laser Interferometric Gravitational-Wave Observatory. The design has to meet the requirements on mass, size, and level of damping to avoid unduly compromising the suspension thermal noise performance and to allow retrofitting of the dampers to the suspensions with minimal changes to the existing suspensions. We have produced a design satisfying our requirements which can reduce the quality factor of these modes from ∼500 000 to less than 10 000, reducing the time taken for the modes to damp down from several hours to a few minutes or less.

Gravity Spy: integrating advanced LIGO detector characterization, machine learning, and citizen science

With the first direct detection of gravitational waves, the advanced laser interferometer gravitational-wave observatory (LIGO) has initiated a new field of astronomy by providing an alternative means of sensing the universe. The extreme sensitivity required to make such detections is achieved through exquisite isolation of all sensitive components of LIGO from non-gravitational-wave disturbances. Nonetheless, LIGO is still susceptible to a variety of instrumental and environmental sources of noise that contaminate the data. Of particular concern are noise features known as glitches, which are transient and non-Gaussian in their nature, and occur at a high enough rate so that accidental coincidence between the two LIGO detectors is non-negligible. Glitches come in a wide range of time-frequency-amplitude morphologies, with new morphologies appearing as the detector evolves. Since they can obscure or mimic true gravitational-wave signals, a robust characterization of glitches is paramount in the effort to achieve the gravitational-wave detection rates that are predicted by the design sensitivity of LIGO. This proves a daunting task for members of the LIGO Scientific Collaboration alone due to the sheer amount of data. In this paper we describe an innovative project that combines crowdsourcing with machine learning to aid in the challenging task of categorizing all of the glitches recorded by the LIGO detectors. Through the Zooniverse platform, we engage and recruit volunteers from the public to categorize images of time-frequency representations of glitches into pre-identified morphological classes and to discover new classes that appear as the detectors evolve. In addition, machine learning algorithms are used to categorize images after being trained on human-classified examples of the morphological classes. Leveraging the strengths of both classification methods, we create a combined method with the aim of improving the efficiency and accuracy of each individual classifier. The resulting classification and characterization should help LIGO scientists to identify causes of glitches and subsequently eliminate them from the data or the detector entirely, thereby improving the rate and accuracy of gravitational-wave observations. We demonstrate these methods using a small subset of data from LIGO's first observing run.

Determination of the refractive index and thickness of a hydroxide-catalysis bond between fused silica from reflectivity measurements

Hydroxide-catalysis bonding is a high precision jointing technique producing strong, transparent and thin bonds, the use of which in the delicate fused silica mirror suspensions of aLIGO have been instrumental in the first detections of gravitational radiation. More sensitive future gravitational wave detectors will require more accurate (ideally in situ) measurements of properties such as bond thickness. Here a non-destructive technique is presented in which the thickness and refractive index of a bond are determined from measurements of optical reflectivity. The reflectivity of a bond made between two fused silica discs using sodium silicate solution is less than 1⋅10^-3 after 3 months. The thickness decreases to a constant value of around 140 nm at its minimum and the refractive index increases from 1.36 to 1.45. This proves that as well as determination of bond thickness in situ this bonding technique is highly interesting for optical applications.

Interferometer techniques for gravitational-wave detection

Several km-scale gravitational-wave detectors have been constructed worldwide. These instruments combine a number of advanced technologies to push the limits of precision length measurement. The core devices are laser interferometers of a new kind; developed from the classical Michelson topology these interferometers integrate additional optical elements, which significantly change the properties of the optical system. Much of the design and analysis of these laser interferometers can be performed using well-known classical optical techniques; however, the complex optical layouts provide a new challenge. In this review, we give a textbook-style introduction to the optical science required for the understanding of modern gravitational wave detectors, as well as other high-precision laser interferometers. In addition, we provide a number of examples for a freely available interferometer simulation software and encourage the reader to use these examples to gain hands-on experience with the discussed optical methods.

Stochastic Gravitational-Wave Background due to Primordial Binary Black Hole Mergers

Recent Advanced LIGO detections of binary black hole mergers have prompted multiple studies investigating the possibility that the heavy GW150914 binary system was of primordial origin, and hence could be evidence for dark matter in the form of black holes. We compute the stochastic background arising from the incoherent superposition of such primordial binary black hole systems in the Universe and compare it to the similar background spectrum due to binary black hole systems of stellar origin. We investigate the possibility of detecting this background with future gravitational-wave detectors, and conclude that constraining the dark matter component in the form of black holes using stochastic gravitational-wave background measurements will be very challenging.

Redshift Factor and the First Law of Binary Black Hole Mechanics in Numerical Simulations

The redshift factor z is an invariant quantity of fundamental interest in post-Newtonian and self-force descriptions of compact binaries. It connects different approximation schemes, and plays a central role in the first law of binary black hole mechanics, which links local quantities to asymptotic measures of energy and angular momentum in these systems. Through this law, the redshift factor is conjectured to have a close relation to the surface gravity of the event horizons of black holes in circular orbits. We propose and implement a novel method for extracting the redshift factor on apparent horizons in numerical simulations of quasicircular binary inspirals. Our results confirm the conjectured relationship between z and the surface gravity of the holes and that the first law holds to a remarkable degree for binary inspirals. The redshift factor enables tests of analytic predictions for z in spacetimes where the binary is only approximately circular, giving a new connection between analytic approximations and numerical simulations.

The Advanced LIGO photon calibrators

The two interferometers of the Laser Interferometry Gravitational-wave Observatory (LIGO) recently detected gravitational waves from the mergers of binary black hole systems. Accurate calibration of the output of these detectors was crucial for the observation of these events and the extraction of parameters of the sources. The principal tools used to calibrate the responses of the second-generation (Advanced) LIGO detectors to gravitational waves are systems based on radiation pressure and referred to as photon calibrators. These systems, which were completely redesigned for Advanced LIGO, include several significant upgrades that enable them to meet the calibration requirements of second-generation gravitational wave detectors in the new era of gravitational-wave astronomy. We report on the design, implementation, and operation of these Advanced LIGO photon calibrators that are currently providing fiducial displacements on the order of 10^-18m/Hz with accuracy and precision of better than 1%.

Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency

Squeezed states of light belong to the most prominent nonclassical resources. They have compelling applications in metrology, which has been demonstrated by their routine exploitation for improving the sensitivity of a gravitational-wave detector since 2010. Here, we report on the direct measurement of 15 dB squeezed vacuum states of light and their application to calibrate the quantum efficiency of photoelectric detection. The object of calibration is a customized InGaAs positive intrinsic negative (p-i-n) photodiode optimized for high external quantum efficiency. The calibration yields a value of 99.5% with a 0.5% (k=2) uncertainty for a photon flux of the order 10^{17}  s^{-1} at a wavelength of 1064 nm. The calibration neither requires any standard nor knowledge of the incident light power and thus represents a valuable application of squeezed states of light in quantum metrology.

Spectroscopy of Kerr Black Holes with Earth- and Space-Based Interferometers

We estimate the potential of present and future interferometric gravitational-wave detectors to test the Kerr nature of black holes through "gravitational spectroscopy," i.e., the measurement of multiple quasinormal mode frequencies from the remnant of a black hole merger. Using population synthesis models of the formation and evolution of stellar-mass black hole binaries, we find that Voyager-class interferometers will be necessary to perform these tests. Gravitational spectroscopy in the local Universe may become routine with the Einstein Telescope, but a 40-km facility like Cosmic Explorer is necessary to go beyond z∼3. In contrast, detectors like eLISA (evolved Laser Interferometer Space Antenna) should carry out a few-or even hundreds-of these tests every year, depending on uncertainties in massive black hole formation models. Many space-based spectroscopical measurements will occur at high redshift, testing the strong gravity dynamics of Kerr black holes in domains where cosmological corrections to general relativity (if they occur in nature) must be significant.

Distributed state machine supervision for long-baseline gravitational-wave detectors

The Laser Interferometer Gravitational-wave Observatory (LIGO) consists of two identical yet independent, widely separated, long-baseline gravitational-wave detectors. Each Advanced LIGO detector consists of complex optical-mechanical systems isolated from the ground by multiple layers of active seismic isolation, all controlled by hundreds of fast, digital, feedback control systems. This article describes a novel state machine-based automation platform developed to handle the automation and supervisory control challenges of these detectors. The platform, called Guardian, consists of distributed, independent, state machine automaton nodes organized hierarchically for full detector control. User code is written in standard Python and the platform is designed to facilitate the fast-paced development process associated with commissioning the complicated Advanced LIGO instruments. While developed specifically for the Advanced LIGO detectors, Guardian is a generic state machine automation platform that is useful for experimental control at all levels, from simple table-top setups to large-scale multi-million dollar facilities.

Detecting Gravitational-Wave Memory with LIGO: Implications of GW150914

It may soon be possible for Advanced LIGO to detect hundreds of binary black hole mergers per year. We show how the accumulation of many such measurements will allow for the detection of gravitational-wave memory: a permanent displacement of spacetime that comes from strong-field, general relativistic effects. We estimate that Advanced LIGO operating at design sensitivity may be able to make a signal-to-noise ratio 3 (5) detection of memory with ∼35 (90) events with masses and distance similar to GW150914. We highlight the importance of incorporating higher-order gravitational-wave modes for parameter estimation of binary black hole mergers, and describe how our methods can also be used to detect higher-order modes themselves before Advanced LIGO reaches design sensitivity.