Where post-Newtonian and numerical-relativity waveforms meet

Abstract

We analyze numerical-relativity (NR) waveforms that cover nine orbits (18 gravitational-wave cycles) before merger of an equal-mass system with low eccentricity, with numerical uncertainties of 0.25 radians in the phase and less than 2% in the amplitude; such accuracy allows a direct comparison with post-Newtonian (PN) waveforms. We focus on one of the PN approximants that has been proposed for use in gravitational-wave data analysis, the restricted 3.5PN ``TaylorT1'' waveforms, and compare these with a section of the numerical waveform from the second to the eighth orbit, which is about one and a half orbits before merger. This corresponds to a gravitational-wave frequency range of $M\omega =0.0455$ to 0.1. Depending on the method of matching PN and NR waveforms, the accumulated phase disagreement over this frequency range can be within numerical uncertainty. Similar results are found in comparisons with an alternative PN approximant, 3PN ``TaylorT3''. The amplitude disagreement, on the other hand, is around 6%, but roughly constant for all 13 cycles that are compared, suggesting that only 4.5 orbits need be simulated to match PN and NR waves with the same accuracy as is possible with nine orbits. If, however, we model the amplitude up to 2.5PN order, the amplitude disagreement is roughly within numerical uncertainty up to about 11 cycles before merger.

14 pages, 18 figures. Modifications resulting from bug fixes in LAL, and extended analysis of numerical errors and phase agreement with PN, now including the 3PN TaylorT3 approximant. No change to main conclusions

References in corpus (34)

• Evolution of Binary Black Hole Spacetimes
• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• Gravitational wave extraction from an inspiraling configuration of merging black holes
• On the Numerical Integration of Einstein's Field Equations
• Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects
• A simple construction of initial data for multiple black holes
• Inspiral, merger and ring-down of equal-mass black-hole binaries
• Inspiral, merger and ringdown of unequal mass black hole binaries: a multipolar analysis
• A single-domain spectral method for black hole puncture data
• Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order
• Phenomenological template family for black-hole coalescence waveforms
• A Comparison of search templates for gravitational waves from binary inspiral
• Toward faithful templates for non-spinning binary black holes using the effective-one-body approach
• Transition from inspiral to plunge in precessing binaries of spinning black holes
• Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order
• 3rd post-Newtonian higher order Hamilton dynamics for two-body point-mass systems
• Numerical simulation of orbiting black holes
• Binary black hole merger dynamics and waveforms
• Solving Einstein's Equations With Dual Coordinate Frames
• Reducing orbital eccentricity in binary black hole simulations
• Binary black-hole evolutions of excision and puncture data
• Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
• Detection template families for gravitational waves from the final stages of binary--black-hole inspirals: Nonspinning case
• The 2.5PN gravitational wave polarisations from inspiralling compact binaries in circular orbits
• Consistency of post-Newtonian waveforms with numerical relativity
• The last orbit of binary black holes
• Towards adiabatic waveforms for inspiral into Kerr black holes: I. A new model of the source for the time domain perturbation equation
• Spin-orbit interactions in black-hole binaries
• Binary black hole late inspiral: Simulations for gravitational wave observations
• Matched Filtering of Numerical Relativity Templates of Spinning Binary Black Holes
• A comparison of search templates for gravitational waves from binary inspiral - 3.5PN update
• Quasi-equilibrium binary black hole sequences for puncture data derived from helical Killing vector conditions
• Wave zone extraction of gravitational radiation in three-dimensional numerical relativity
• Quasi-Local Linear Momentum in Black-Hole Binaries

Cited by in corpus (130)

• The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics
• Matching post-Newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries
• A template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries
• High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
• Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: Ready-to-use gravitational waveforms
• High-accuracy waveforms for binary black hole inspiral, merger, and ringdown
• Closed-form tidal approximants for binary neutron star gravitational waveforms constructed from high-resolution numerical relativity simulations
• The third post-Newtonian gravitational wave polarisations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits
• Black-hole binaries, gravitational waves, and numerical relativity
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-spinning, equal-mass black holes
• Simulating coalescing compact binaries by a new code SACRA
• Exploring black hole superkicks
• Simulations of Binary Black Hole Mergers Using Spectral Methods
• Post-Newtonian corrections to the gravitational-wave memory for quasicircular, inspiralling compact binaries
• Tracking the precession of compact binaries from their gravitational-wave signal
• Addressing the spin question in gravitational-wave searches: Waveform templates for inspiralling compact binaries with nonprecessing spins
• Accurate Effective-One-Body waveforms of inspiralling and coalescing black-hole binaries
• Longterm general relativistic simulation of binary neutron stars collapsing to a black hole
• Hyperboloidal foliations and scri-fixing
• Numerical relativity simulations of binary neutron stars
• High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants
• Black-hole hair loss: learning about binary progenitors from ringdown signals
• High accuracy binary black hole simulations with an extended wave zone
• Reducing phase error in long numerical binary black hole evolutions with sixth order finite differencing
• The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries
• Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration
• On the unreasonable effectiveness of the post-Newtonian approximation in gravitational physics
• Third post-Newtonian angular momentum flux and the secular evolution of orbital elements for inspiralling compact binaries in quasi-elliptical orbits
• Testing gravitational-wave searches with numerical relativity waveforms: Results from the first Numerical INJection Analysis (NINJA) project
• Merger of black hole and neutron star in general relativity: Tidal disruption, torus mass, and gravitational waves
• Search for Gravitational Waves from Compact Binary Coalescence in LIGO and Virgo Data from S5 and VSR1
• Circularization and Final Spin in Eccentric Binary Black Hole Inspirals
• Extrapolating gravitational-wave data from numerical simulations
• Search for Gravitational Waves from Low Mass Compact Binary Coalescence in 186 Days of LIGO's fifth Science Run
• Comparisons of eccentric binary black hole simulations with post-Newtonian models
• Comparison between numerical-relativity and post-Newtonian waveforms from spinning binaries: the orbital hang-up case
• Search for Gravitational Waves from Binary Black Hole Inspiral, Merger and Ringdown in LIGO-Virgo Data from 2009-2010
• Comparison of Numerical and Post-Newtonian Waveforms for Generic Precessing Black-Hole Binaries
• The RIT binary black hole simulations catalog
• Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity
• Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order
• Wormholes and trumpets: the Schwarzschild spacetime for the moving-puncture generation
• Reducing eccentricity in black-hole binary evolutions with initial parameters from post-Newtonian inspiral
• Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• Binary black hole merger in the extreme-mass-ratio limit: a multipolar analysis
• Extra-Large Remnant Recoil Velocities and Spins from Near-Extremal-Bowen-York-Spin Black-Hole Binaries
• Black-hole binary simulations: the mass ratio 10:1
• Detectability of gravitational waves from binary black holes: Impact of precession and higher modes
• A Parameter Estimation Method that Directly Compares Gravitational Wave Observations to Numerical Relativity
• The Samurai Project: verifying the consistency of black-hole-binary waveforms for gravitational-wave detection
• High accuracy simulations of black hole binaries:spins anti-aligned with the orbital angular momentum
• Numerical Relativity of Compact Binaries in the 21st Century
• Effects of nonquadrupole modes in the detection and parameter estimation of black hole binaries with nonprecessing spins
• Observing mergers of non-spinning black-hole binaries
• Third post-Newtonian gravitational waveforms for compact binary systems in general orbits: Instantaneous terms
• Simulations of black-hole binaries with unequal masses or non-precessing spins: accuracy, physical properties, and comparison with post-Newtonian results
• The Current Status of Binary Black Hole Simulations in Numerical Relativity
• Gravitational-wave data analysis using binary black-hole waveforms
• Reducing orbital eccentricity in initial data of binary neutron stars
• Conservative self-force correction to the innermost stable circular orbit: comparison with multiple post-Newtonian-based methods
• The NINJA-2 project: Detecting and characterizing gravitational waveforms modelled using numerical binary black hole simulations
• Perturbative extraction of gravitational waveforms generated with Numerical Relativity
• Suitability of post-Newtonian/numerical-relativity hybrid waveforms for gravitational wave detectors
• Multipolar analysis of spinning binaries
• Introductory lectures on the Effective One Body formalism
• Status of black-hole-binary simulations for gravitational-wave detection
• Status of NINJA: the Numerical INJection Analysis project
• Reducing spurious gravitational radiation in binary-black-hole simulations by using conformally curved initial data
• Modeling maximum astrophysical gravitational recoil velocities
• Comparison of high-accuracy numerical simulations of black-hole binaries with stationary phase post-Newtonian template waveforms for Initial and Advanced LIGO
• Close encounters of three black holes
• Comparing Post-Newtonian and Numerical-Relativity Precession Dynamics
• Length requirements for numerical-relativity waveforms
• Comparison between numerical relativity and a new class of post-Newtonian gravitational-wave phase evolutions: the non-spinning equal-mass case
• Non-conformally flat initial data for binary compact objects
• Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
• Bowen-York trumpet data and black-hole simulations
• Template banks to search for compact binaries with spinning components in gravitational wave data
• A Reinvestigation of Moving Punctured Black Holes with a New Code
• An efficient iterative method to reduce eccentricity in numerical-relativity simulations of compact binary inspiral
• A hyperboloidal study of tail decay rates for scalar and Yang-Mills fields
• Numerical simulations with a first order BSSN formulation of Einstein's field equations
• The General Relativistic Two Body Problem and the Effective One Body Formalism
• The slicing dependence of non-spherically symmetric quasi-local horizons in Vaidya Spacetimes
• Transformation of the multipolar components of gravitational radiation under rotations and boosts
• Modelling gravitational waves from precessing black-hole binaries: Progress, challenges and prospects
• Numerical-relativity simulations of the quasi-circular inspiral and merger of non-spinning, charged black holes: methods and comparison with approximate approaches
• Quasiequilibrium states of black hole-neutron star binaries in the moving-puncture framework
• Regression methods in waveform modeling: a comparative study
• Tidal interaction in compact binaries: a post-Newtonian affine framework
• Modeling Gravitational Recoil Using Numerical Relativity
• Full 3D Numerical Relativity Simulations of Neutron Star -- Boson Star Collisions with BAM
• Hyperboloidal evolution of test fields in three spatial dimensions
• Gravitational wave burst search in the Virgo C7 data
• Is J enough? Comparison of gravitational waves emitted along the total angular momentum direction with other preferred orientations
• The Final Merger of Black-Hole Binaries
• Ineffectiveness of Padé resummation techniques in post-Newtonian approximations
• The Close-Limit Approximation for Black Hole Binaries with Post-Newtonian Initial Conditions
• Likelihood-ratio ranking of gravitational-wave candidates in a non-Gaussian background
• Method to estimate ISCO and ring-down frequencies in binary systems and consequences for gravitational wave data analysis
• Advances in Simulations of Generic Black-Hole Binaries
• Hybrid black-hole binary initial data
• A note on gravitational wave extraction from binary simulations
• Including realistic tidal deformations in binary black-hole initial data
• Numerical modeling of black holes as sources of gravitational waves in a nutshell
• Detecting transient gravitational waves in non-Gaussian noise with partially redundant analysis methods
• Binary black hole evolutions of approximate puncture initial data
• Perturbational Treatment of the Gravitational Potential Effect on Binary Black Hole Evolution
• A joint approach for reducing eccentricity and spurious gravitational radiation in binary black hole initial data construction
• Seeking for toroidal event horizons from initially stationary BH configurations
• Searching for binary coalescences with inspiral templates: Detection and parameter estimation
• Parameter estimation using a complete signal and inspiral templates for low mass binary black holes with Advanced LIGO sensitivity
• Searching for numerically-simulated signals of black hole binaries with a phenomenological template family
• A Numerical Study of Boson Star Binaries
• Hybrid waveforms for generic precessing binaries for gravitational-wave data analysis
• Enhancing gravitational waveform models through dynamic calibration
• Binary Black Hole Coalescence in Semi-Analytic Puncture Evolution
• Numerical relativity simulations in the era of the Einstein Telescope
• Analytic Approximations in GR and Gravitational Waves
• The Effective One Body description of the Two-Body problem
• On the approximate relation between black-hole perturbation theory and numerical relativity
• Modeling Gravitational Wave Modes from the Inspiral of Binaries with Arbitrary Eccentricity
• Ninja data analysis with a detection pipeline based on the Hilbert-Huang Transform
• Influence of gravitational waves on circular moving particles
• Un-modeled search for black hole binary systems in the NINJA project
• Eccentric Pairs: Analytic Gravitational Waves from Binary Black Holes in Elliptic Orbits
• A comprehensive look into the accuracy of SpEC binary black hole waveforms
• Search for gravitational waves from binary black hole inspiral, merger and ringdown
• Gravitational waves from black-hole mergers