Gravitational waves from inspiraling compact binaries: Parameter estimation using second-post-Newtonian waveforms

Bayesian Inference for Gravitational Waves from Binary Neutron Star Mergers in Third Generation Observatories

Third generation (3G) gravitational-wave detectors will observe thousands of coalescing neutron star binaries with unprecedented fidelity. Extracting the highest precision science from these signals is expected to be challenging owing to both high signal-to-noise ratios and long-duration signals. We demonstrate that current Bayesian inference paradigms can be extended to the analysis of binary neutron star signals without breaking the computational bank. We construct reduced-order models for ∼90-min-long gravitational-wave signals covering the observing band (5-2048 Hz), speeding up inference by a factor of ∼1.3×10^{4} compared to the calculation times without reduced-order models. The reduced-order models incorporate key physics including the effects of tidal deformability, amplitude modulation due to Earth's rotation, and spin-induced orbital precession. We show how reduced-order modeling can accelerate inference on data containing multiple overlapping gravitational-wave signals, and determine the speedup as a function of the number of overlapping signals. Thus, we conclude that Bayesian inference is computationally tractable for the long-lived, overlapping, high signal-to-noise-ratio events present in 3G observatories.

Scope Out Multiband Gravitational-Wave Observations of GW190521-Like Binary Black Holes with Space Gravitational Wave Antenna B-DECIGO

The gravitational wave event, GW190521, is the most massive binary black hole merger observed by ground-based gravitational wave observatories LIGO/Virgo to date. While the observed gravitational wave signal is mainly in the merger and ringdown phases, the inspiral gravitational wave signal of the GW190521-like binary will be more visible to space-based detectors in the low-frequency band. In addition, the ringdown gravitational wave signal will be louder in the next generation (3G) of ground-based detectors in the high-frequency band, displaying the great potential of multiband gravitational wave observations. In this paper, we explore the scientific potential of multiband observations of GW190521-like binaries with a milli-Hz gravitational wave observatory: LISA; a deci-Hz observatory: B-DECIGO; and (next generation of) hecto-Hz observatories: aLIGO and ET. In the case of quasicircular evolution, the triple-band observations of LISA, B-DECIGO, and ET will provide parameter estimation errors of the masses and spin amplitudes of component black holes at the level of order of 1–10%. This would allow consistency tests of general relativity in the strong field at an unparalleled precision, particularly with the “B-DECIGO + ET” observation. In the case of eccentric evolution, the multiband signal-to-noise ratio found in “B-DECIGO + ET” observation would be larger than 100 for a five-year observation prior to coalescence, even with high final eccentricities.

Multiparameter Tests of General Relativity Using Multiband Gravitational-Wave Observations

In this Letter, we show that multiband observations of stellar-mass binary black holes by the next generation of ground-based observatories (3G) and the space-based Laser Interferometer Space Antenna (LISA) would facilitate a comprehensive test of general relativity by simultaneously measuring all the post-Newtonian coefficients. Multiband observations would measure most of the known post-Newtonian phasing coefficients to an accuracy below a few percent-2 orders-of-magnitude better than the best bounds achievable from even "golden" binaries in the 3G or LISA bands. Such multiparameter bounds would play a pivotal role in constraining the parameter space of modified theories of gravity beyond general relativity.

High-Accuracy Mass, Spin, and Recoil Predictions of Generic Black-Hole Merger Remnants

We present accurate fits for the remnant properties of generically precessing binary black holes, trained on large banks of numerical-relativity simulations. We use Gaussian process regression to interpolate the remnant mass, spin, and recoil velocity in the seven-dimensional parameter space of precessing black-hole binaries with mass ratios q≤2, and spin magnitudes χ_{1}, χ_{2}≤0.8. For precessing systems, our errors in estimating the remnant mass, spin magnitude, and kick magnitude are lower than those of existing fitting formulae by at least an order of magnitude (improvement is also reported in the extrapolated region at high mass ratios and spins). In addition, we also model the remnant spin and kick directions. Being trained directly on precessing simulations, our fits are free from ambiguities regarding the initial frequency at which precessing quantities are defined. We also construct a model for remnant properties of aligned-spin systems with mass ratios q≤8, and spin magnitudes χ_{1}, χ_{2}≤0.8. As a byproduct, we also provide error estimates for all fitted quantities, which can be consistently incorporated into current and future gravitational-wave parameter-estimation analyses. Our model(s) are made publicly available through a fast and easy-to-use Python module called surfinBH.

Forecasting Tidal Disruption Events for Binary Black Holes with an Outer Tertiary

We discuss the gravitational wave (GW) emission and the orbital evolution of a hierarchical triple system composed of an inner binary black hole (BBH) and an outer tertiary. Depending on the kick velocity at the merger, the merged BBH could tidally disrupt the tertiary. Even though the fraction of BBH mergers accompanied by such disruptions is expected to be much smaller than unity, the existence of a tertiary and its basic parameters (e.g., semimajor axis, projected mass) can be examined for more than 10^{3} BBHs with the follow-on missions to the space GW detector LISA. This allows us to efficiently prescreen the targets for the follow-up searches for the tidal disruption events (TDEs). The TDE probability would be significantly higher for triple systems with aligned orbital- and spin-angular momenta, compared with random configurations.

Properties of the Binary Black Hole Merger GW150914

On September 14, 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected a gravitational-wave transient (GW150914); we characterize the properties of the source and its parameters. The data around the time of the event were analyzed coherently across the LIGO network using a suite of accurate waveform models that describe gravitational waves from a compact binary system in general relativity. GW150914 was produced by a nearly equal mass binary black hole of masses 36_{-4}^{+5}M_{⊙} and 29_{-4}^{+4}M_{⊙}; for each parameter we report the median value and the range of the 90% credible interval. The dimensionless spin magnitude of the more massive black hole is bound to be <0.7 (at 90% probability). The luminosity distance to the source is 410_{-180}^{+160}  Mpc, corresponding to a redshift 0.09_{-0.04}^{+0.03} assuming standard cosmology. The source location is constrained to an annulus section of 610  deg^{2}, primarily in the southern hemisphere. The binary merges into a black hole of mass 62_{-4}^{+4}M_{⊙} and spin 0.67_{-0.07}^{+0.05}. This black hole is significantly more massive than any other inferred from electromagnetic observations in the stellar-mass regime.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

Systematic parameter errors in inspiraling neutron star binaries

The coalescence of two neutron stars is an important gravitational wave source for LIGO and other detectors. Numerous studies have considered the precision with which binary parameters (masses, spins, Love numbers) can be measured. Here I consider the accuracy with which these parameters can be determined in the presence of systematic errors due to waveform approximations. These approximations include truncation of the post-Newtonian (PN) series and neglect of neutron star (NS) spin, tidal deformation, or orbital eccentricity. All of these effects can yield systematic errors that exceed statistical errors for plausible parameter values. In particular, neglecting spin, eccentricity, or high-order PN terms causes a significant bias in the NS Love number. Tidal effects will not be measurable with PN inspiral waveforms if these systematic errors are not controlled.

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (eLISA, etc.), inspiralling compact binaries - binary star systems composed of neutron stars and/or black holes in their late stage of evolution - require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary's orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries - moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.

Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays

This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review ends with a discussion of gravitational-wave tests for compact binary systems.

Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case

The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter estimation are presented. Several tools needed for both theoretical evaluation of the optimal data analysis methods and for their practical implementation are introduced. They include optimal signal-to-noise ratio, Fisher matrix, false alarm and detection probabilities, [Formula: see text]-statistic, template placement, and fitting factor. These tools apply to the case of signals buried in a stationary and Gaussian noise. Algorithms to efficiently implement the optimal data analysis techniques are discussed. Formulas are given for a general gravitational-wave signal that includes as special cases most of the deterministic signals of interest.

Imprint of accretion disk-induced migration on gravitational waves from extreme mass ratio inspirals

We study the effects of a thin gaseous accretion disk on the inspiral of a stellar-mass black hole into a supermassive black hole. We construct a phenomenological angular momentum transport equation that reproduces known disk effects. Disk torques modify the gravitational wave phase evolution to detectable levels with LISA for reasonable disk parameters. The Fourier transform of disk-modified waveforms acquires a correction with a different frequency trend than post-Newtonian vacuum terms. Such inspirals could be used to detect accretion disks with LISA and to probe their physical parameters.

Physics, Astrophysics and Cosmology with Gravitational Waves

Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.

Calculation of the first nonlinear contribution to the general-relativistic spin-spin interaction for binary systems

We use recently developed effective field theory techniques to calculate the third order post-Newtonian correction to the spin-spin potential between two spinning objects. This correction represents the first contribution to the spin-spin interaction due to the nonlinear nature of general relativity and will play an important role in forthcoming gravity wave experiments.

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary's orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and other binary pulsar systems have yielded other tests, especially of strong-field effects. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.

Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case

The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter estimation are presented. Several tools needed for both theoretical evaluation of the optimal data analysis methods and for their practical implementation are introduced. They include optimal signal-to-noise ratio, Fisher matrix, false alarm and detection probabilities, [Formula: see text]-statistic, template placement, and fitting factor. These tools apply to the case of signals buried in a stationary and Gaussian noise. Algorithms to efficiently implement the optimal data analysis techniques are discussed. Formulas are given for a general gravitational-wave signal that includes as special cases most of the deterministic signals of interest.

Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order

The gravitational radiation from point particle binaries is computed at the third post-Newtonian (3PN) approximation of general relativity. Three previously introduced ambiguity parameters, coming from the Hadamard self-field regularization of the 3PN source-type mass quadrupole moment, are consistently determined by means of dimensional regularization, and proved to have the values xi=-9871/9240, kappa=0, and zeta=-7/33. These results complete the derivation of the general relativistic prediction for compact binary inspiral up to 3.5PN order, and should be of use for searching and deciphering the signals in the current network of gravitational wave detectors.

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the post-Newtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail effects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary's orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP and of the inverse square law will search for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light defl ection the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to half a percent using the Hulse-Taylor binary pulsar, and new binary pulsar systems may yield further improvements. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.