Tests of General Relativity with GW170817.

The recent discovery by Advanced LIGO and Advanced Virgo of a gravitational wave signal from a binary neutron star inspiral has enabled tests of general relativity (GR) with this new type of source. This source, for the first time, permits tests of strong-field dynamics of compact binaries in the presence of matter. In this Letter, we place constraints on the dipole radiation and possible deviations from GR in the post-Newtonian coefficients that govern the inspiral regime. Bounds on modified dispersion of gravitational waves are obtained; in combination with information from the observed electromagnetic counterpart we can also constrain effects due to large extra dimensions. Finally, the polarization content of the gravitational wave signal is studied. The results of all tests performed here show good agreement with GR.

Constraining the p-Mode-g-Mode Tidal Instability with GW170817.

We analyze the impact of a proposed tidal instability coupling p modes and g modes within neutron stars on GW170817. This nonresonant instability transfers energy from the orbit of the binary to internal modes of the stars, accelerating the gravitational-wave driven inspiral. We model the impact of this instability on the phasing of the gravitational wave signal using three parameters per star: an overall amplitude, a saturation frequency, and a spectral index. Incorporating these additional parameters, we compute the Bayes factor (lnB_{!pg}^{pg}) comparing our p-g model to a standard one. We find that the observed signal is consistent with waveform models that neglect p-g effects, with lnB_{!pg}^{pg}=0.03_{-0.58}^{+0.70} (maximum a posteriori and 90% credible region). By injecting simulated signals that do not include p-g effects and recovering them with the p-g model, we show that there is a ≃50% probability of obtaining similar lnB_{!pg}^{pg} even when p-g effects are absent. We find that the p-g amplitude for 1.4 M_{⊙} neutron stars is constrained to less than a few tenths of the theoretical maximum, with maxima a posteriori near one-tenth this maximum and p-g saturation frequency ∼70 Hz. This suggests that there are less than a few hundred excited modes, assuming they all saturate by wave breaking. For comparison, theoretical upper bounds suggest ≲10^{3} modes saturate by wave breaking. Thus, the measured constraints only rule out extreme values of the p-g parameters. They also imply that the instability dissipates ≲10^{51} erg over the entire inspiral, i.e., less than a few percent of the energy radiated as gravitational waves.

Search for Subsolar-Mass Ultracompact Binaries in Advanced LIGO's First Observing Run.

We present the first Advanced LIGO and Advanced Virgo search for ultracompact binary systems with component masses between 0.2 M_{⊙}-1.0 M_{⊙} using data taken between September 12, 2015 and January 19, 2016. We find no viable gravitational wave candidates. Our null result constrains the coalescence rate of monochromatic (delta function) distributions of nonspinning (0.2 M_{⊙}, 0.2 M_{⊙}) ultracompact binaries to be less than 1.0×10^{6} Gpc^{-3} yr^{-1} and the coalescence rate of a similar distribution of (1.0 M_{⊙}, 1.0 M_{⊙}) ultracompact binaries to be less than 1.9×10^{4} Gpc^{-3} yr^{-1} (at 90% confidence). Neither black holes nor neutron stars are expected to form below ∼1 M_{⊙} through conventional stellar evolution, though it has been proposed that similarly low mass black holes could be formed primordially through density fluctuations in the early Universe and contribute to the dark matter density. The interpretation of our constraints in the primordial black hole dark matter paradigm is highly model dependent; however, under a particular primordial black hole binary formation scenario we constrain monochromatic primordial black hole populations of 0.2 M_{⊙} to be less than 33% of the total dark matter density and monochromatic populations of 1.0 M_{⊙} to be less than 5% of the dark matter density. The latter strengthens the presently placed bounds from microlensing surveys of massive compact halo objects (MACHOs) provided by the MACHO and EROS Collaborations.

GW170817: Measurements of Neutron Star Radii and Equation of State.

On 17 August 2017, the LIGO and Virgo observatories made the first direct detection of gravitational waves from the coalescence of a neutron star binary system. The detection of this gravitational-wave signal, GW170817, offers a novel opportunity to directly probe the properties of matter at the extreme conditions found in the interior of these stars. The initial, minimal-assumption analysis of the LIGO and Virgo data placed constraints on the tidal effects of the coalescing bodies, which were then translated to constraints on neutron star radii. Here, we expand upon previous analyses by working under the hypothesis that both bodies were neutron stars that are described by the same equation of state and have spins within the range observed in Galactic binary neutron stars. Our analysis employs two methods: the use of equation-of-state-insensitive relations between various macroscopic properties of the neutron stars and the use of an efficient parametrization of the defining function p(ρ) of the equation of state itself. From the LIGO and Virgo data alone and the first method, we measure the two neutron star radii as R_{1}=10.8_{-1.7}^{+2.0} km for the heavier star and R_{2}=10.7_{-1.5}^{+2.1} km for the lighter star at the 90% credible level. If we additionally require that the equation of state supports neutron stars with masses larger than 1.97 M_{⊙} as required from electromagnetic observations and employ the equation-of-state parametrization, we further constrain R_{1}=11.9_{-1.4}^{+1.4} km and R_{2}=11.9_{-1.4}^{+1.4} km at the 90% credible level. Finally, we obtain constraints on p(ρ) at supranuclear densities, with pressure at twice nuclear saturation density measured at 3.5_{-1.7}^{+2.7}×10^{34} dyn cm^{-2} at the 90% level.

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background.

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω_{0}^{T}<5.58×10^{-8}, Ω_{0}^{V}<6.35×10^{-8}, and Ω_{0}^{S}<1.08×10^{-7} at a reference frequency f_{0}=25 Hz.

Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA.

We present possible observing scenarios for the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We estimate the sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron star systems, which are the most promising targets for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and [Formula: see text] credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5-[Formula: see text] requires at least three detectors of sensitivity within a factor of [Formula: see text] of each other and with a broad frequency bandwidth. When all detectors, including KAGRA and the third LIGO detector in India, reach design sensitivity, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.

GW170817: Implications for the Stochastic Gravitational-Wave Background from Compact Binary Coalescences.

The LIGO Scientific and Virgo Collaborations have announced the event GW170817, the first detection of gravitational waves from the coalescence of two neutron stars. The merger rate of binary neutron stars estimated from this event suggests that distant, unresolvable binary neutron stars create a significant astrophysical stochastic gravitational-wave background. The binary neutron star component will add to the contribution from binary black holes, increasing the amplitude of the total astrophysical background relative to previous expectations. In the Advanced LIGO-Virgo frequency band most sensitive to stochastic backgrounds (near 25 Hz), we predict a total astrophysical background with amplitude Ω_{GW}(f=25 Hz)=1.8_{-1.3}^{+2.7}×10^{-9} with 90% confidence, compared with Ω_{GW}(f=25 Hz)=1.1_{-0.7}^{+1.2}×10^{-9} from binary black holes alone. Assuming the most probable rate for compact binary mergers, we find that the total background may be detectable with a signal-to-noise-ratio of 3 after 40 months of total observation time, based on the expected timeline for Advanced LIGO and Virgo to reach their design sensitivity.

First Search for Nontensorial Gravitational Waves from Known Pulsars.

We present results from the first directed search for nontensorial gravitational waves. While general relativity allows for tensorial (plus and cross) modes only, a generic metric theory may, in principle, predict waves with up to six different polarizations. This analysis is sensitive to continuous signals of scalar, vector, or tensor polarizations, and does not rely on any specific theory of gravity. After searching data from the first observation run of the advanced LIGO detectors for signals at twice the rotational frequency of 200 known pulsars, we find no evidence of gravitational waves of any polarization. We report the first upper limits for scalar and vector strains, finding values comparable in magnitude to previously published limits for tensor strain. Our results may be translated into constraints on specific alternative theories of gravity.

GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral.

On August 17, 2017 at 12∶41:04 UTC the Advanced LIGO and Advanced Virgo gravitational-wave detectors made their first observation of a binary neutron star inspiral. The signal, GW170817, was detected with a combined signal-to-noise ratio of 32.4 and a false-alarm-rate estimate of less than one per 8.0×10^{4} years. We infer the component masses of the binary to be between 0.86 and 2.26 M_{⊙}, in agreement with masses of known neutron stars. Restricting the component spins to the range inferred in binary neutron stars, we find the component masses to be in the range 1.17-1.60 M_{⊙}, with the total mass of the system 2.74_{-0.01}^{+0.04}M_{⊙}. The source was localized within a sky region of 28 deg^{2} (90% probability) and had a luminosity distance of 40_{-14}^{+8} Mpc, the closest and most precisely localized gravitational-wave signal yet. The association with the γ-ray burst GRB 170817A, detected by Fermi-GBM 1.7 s after the coalescence, corroborates the hypothesis of a neutron star merger and provides the first direct evidence of a link between these mergers and short γ-ray bursts. Subsequent identification of transient counterparts across the electromagnetic spectrum in the same location further supports the interpretation of this event as a neutron star merger. This unprecedented joint gravitational and electromagnetic observation provides insight into astrophysics, dense matter, gravitation, and cosmology.

GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence.

On August 14, 2017 at 10∶30:43 UTC, the Advanced Virgo detector and the two Advanced LIGO detectors coherently observed a transient gravitational-wave signal produced by the coalescence of two stellar mass black holes, with a false-alarm rate of ≲1 in 27 000 years. The signal was observed with a three-detector network matched-filter signal-to-noise ratio of 18. The inferred masses of the initial black holes are 30.5_{-3.0}^{+5.7}M_{⊙} and 25.3_{-4.2}^{+2.8}M_{⊙} (at the 90% credible level). The luminosity distance of the source is 540_{-210}^{+130} Mpc, corresponding to a redshift of z=0.11_{-0.04}^{+0.03}. A network of three detectors improves the sky localization of the source, reducing the area of the 90% credible region from 1160 deg^{2} using only the two LIGO detectors to 60 deg^{2} using all three detectors. For the first time, we can test the nature of gravitational-wave polarizations from the antenna response of the LIGO-Virgo network, thus enabling a new class of phenomenological tests of gravity.

GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2.

We describe the observation of GW170104, a gravitational-wave signal produced by the coalescence of a pair of stellar-mass black holes. The signal was measured on January 4, 2017 at 10∶11:58.6 UTC by the twin advanced detectors of the Laser Interferometer Gravitational-Wave Observatory during their second observing run, with a network signal-to-noise ratio of 13 and a false alarm rate less than 1 in 70 000 years. The inferred component black hole masses are 31.2_{-6.0}^{+8.4}M_{⊙} and 19.4_{-5.9}^{+5.3}M_{⊙} (at the 90% credible level). The black hole spins are best constrained through measurement of the effective inspiral spin parameter, a mass-weighted combination of the spin components perpendicular to the orbital plane, χ_{eff}=-0.12_{-0.30}^{+0.21}. This result implies that spin configurations with both component spins positively aligned with the orbital angular momentum are disfavored. The source luminosity distance is 880_{-390}^{+450} Mpc corresponding to a redshift of z=0.18_{-0.07}^{+0.08}. We constrain the magnitude of modifications to the gravitational-wave dispersion relation and perform null tests of general relativity. Assuming that gravitons are dispersed in vacuum like massive particles, we bound the graviton mass to m_{g}≤7.7×10^{-23} eV/c^{2}. In all cases, we find that GW170104 is consistent with general relativity.

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.

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.

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

We report the observation of a gravitational-wave signal produced by the coalescence of two stellar-mass black holes. The signal, GW151226, was observed by the twin detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) on December 26, 2015 at 03:38:53 UTC. The signal was initially identified within 70 s by an online matched-filter search targeting binary coalescences. Subsequent off-line analyses recovered GW151226 with a network signal-to-noise ratio of 13 and a significance greater than 5σ. The signal persisted in the LIGO frequency band for approximately 1 s, increasing in frequency and amplitude over about 55 cycles from 35 to 450 Hz, and reached a peak gravitational strain of 3.4_{-0.9}^{+0.7}×10^{-22}. The inferred source-frame initial black hole masses are 14.2_{-3.7}^{+8.3}M_{⊙} and 7.5_{-2.3}^{+2.3}M_{⊙}, and the final black hole mass is 20.8_{-1.7}^{+6.1}M_{⊙}. We find that at least one of the component black holes has spin greater than 0.2. This source is located at a luminosity distance of 440_{-190}^{+180} Mpc corresponding to a redshift of 0.09_{-0.04}^{+0.03}. All uncertainties define a 90% credible interval. This second gravitational-wave observation provides improved constraints on stellar populations and on deviations from general relativity.

Tests of General Relativity with GW150914.

The LIGO detection of GW150914 provides an unprecedented opportunity to study the two-body motion of a compact-object binary in the large-velocity, highly nonlinear regime, and to witness the final merger of the binary and the excitation of uniquely relativistic modes of the gravitational field. We carry out several investigations to determine whether GW150914 is consistent with a binary black-hole merger in general relativity. We find that the final remnant's mass and spin, as determined from the low-frequency (inspiral) and high-frequency (postinspiral) phases of the signal, are mutually consistent with the binary black-hole solution in general relativity. Furthermore, the data following the peak of GW150914 are consistent with the least-damped quasinormal mode inferred from the mass and spin of the remnant black hole. By using waveform models that allow for parametrized general-relativity violations during the inspiral and merger phases, we perform quantitative tests on the gravitational-wave phase in the dynamical regime and we determine the first empirical bounds on several high-order post-Newtonian coefficients. We constrain the graviton Compton wavelength, assuming that gravitons are dispersed in vacuum in the same way as particles with mass, obtaining a 90%-confidence lower bound of 10^{13} km. In conclusion, within our statistical uncertainties, we find no evidence for violations of general relativity in the genuinely strong-field regime of gravity.

GW150914: The Advanced LIGO Detectors in the Era of First Discoveries.

Following a major upgrade, the two advanced detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) held their first observation run between September 2015 and January 2016. With a strain sensitivity of 10^{-23}/sqrt[Hz] at 100 Hz, the product of observable volume and measurement time exceeded that of all previous runs within the first 16 days of coincident observation. On September 14, 2015, the Advanced LIGO detectors observed a transient gravitational-wave signal determined to be the coalescence of two black holes [B. P. Abbott et al., Phys. Rev. Lett. 116, 061102 (2016)], launching the era of gravitational-wave astronomy. The event, GW150914, was observed with a combined signal-to-noise ratio of 24 in coincidence by the two detectors. Here, we present the main features of the detectors that enabled this observation. At full sensitivity, the Advanced LIGO detectors are designed to deliver another factor of 3 improvement in the signal-to-noise ratio for binary black hole systems similar in mass to GW150914.

GW150914: Implications for the Stochastic Gravitational-Wave Background from Binary Black Holes.

The LIGO detection of the gravitational wave transient GW150914, from the inspiral and merger of two black holes with masses ≳30M_{⊙}, suggests a population of binary black holes with relatively high mass. This observation implies that the stochastic gravitational-wave background from binary black holes, created from the incoherent superposition of all the merging binaries in the Universe, could be higher than previously expected. Using the properties of GW150914, we estimate the energy density of such a background from binary black holes. In the most sensitive part of the Advanced LIGO and Advanced Virgo band for stochastic backgrounds (near 25 Hz), we predict Ω_{GW}(f=25 Hz)=1.1_{-0.9}^{+2.7}×10^{-9} with 90% confidence. This prediction is robustly demonstrated for a variety of formation scenarios with different parameters. The differences between models are small compared to the statistical uncertainty arising from the currently poorly constrained local coalescence rate. We conclude that this background is potentially measurable by the Advanced LIGO and Advanced Virgo detectors operating at their projected final sensitivity.

Observation of Gravitational Waves from a Binary Black Hole Merger.

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160) Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

GW150914: First results from the search for binary black hole coalescence with Advanced LIGO.

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) simultaneously observed the binary black hole merger GW150914. We report the results of a matched-filter search using relativistic models of compact-object binaries that recovered GW150914 as the most significant event during the coincident observations between the two LIGO detectors from September 12 to October 20, 2015. GW150914 was observed with a matched filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203000 years, equivalent to a significance greater than 5.1 σ.