Spherical harmonic modes of 5.5 post-Newtonian gravitational wave polarizations and associated factorized resummed waveforms for a particle in circular orbit around a Schwarzschild black hol

Abstract

Recent breakthroughs in numerical relativity enable one to examine the validity of the post-Newtonian expansion in the late stages of inspiral. For the comparison between post-Newtonian (PN) expansion and numerical simulations, the waveforms in terms of the spin-weighted spherical harmonics are more useful than the plus and cross polarizations, which are used for data analysis of gravitational waves. Factorized resummed waveforms achieve better agreement with numerical results than the conventional Taylor expanded post-Newtonian waveforms. In this paper, we revisit the post-Newtonian expansion of gravitational waves for a test-particle of mass $\m$ in circular orbit of radius $r_0$ around a Schwarzschild black hole of mass $M$ and derive the spherical harmonic components associated with the gravitational wave polarizations up to order $v^{11}$ beyond Newtonian. Using the more accurate $h_{\ell m}$'s computed in this work, we provide the more complete set of associated ${\rho }_{\ell m}$'s and ${\delta }_{\ell m}$'s that form important bricks in the factorized resummation of waveforms with potential applications for the construction of further improved waveforms for prototypical compact binary sources in the future. We also provide ready-to-use expressions of the 5.5PN gravitational waves polarizations $h_{+}$ and $h_{\times }$ in the test-particle limit for gravitational wave data analysis applications. Additionally, we provide closed analytical expressions for 2.5PN $h_{\ell m}$, 2PN ${\rho }_{\ell m}$ and 3PN ${\delta }_{\ell m}$, for general multipolar orders $\ell$ and $m$ in the test-particle limit. Finally, we also examine the implications of the present analysis for compact binary sources in Laser Interferometer Space Antenna.

42 pages, 2 figures, match with accepted version by PRD

References in corpus (13)

• Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors
• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Faithful Effective-One-Body waveforms of small-mass-ratio coalescing black-hole binaries
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-spinning, equal-mass black holes
• An improved analytical description of inspiralling and coalescing black-hole binaries
• Comparing Effective-One-Body gravitational waveforms to accurate numerical data
• Using Full Information When Computing Modes of Post-Newtonian Waveforms From Inspiralling Compact Binaries in Circular Orbit
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-precessing, spinning, equal-mass black holes
• Modeling Extreme Mass Ratio Inspirals within the Effective-One-Body Approach
• An Efficient Numerical Method for Computing Gravitational Waves Induced by a Particle Moving on Eccentric Inclined Orbits around a Kerr Black Hole
• The Current Status of Binary Black Hole Simulations in Numerical Relativity
• New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation II. Solutions of the Continued Fraction Equation
• Status of black-hole-binary simulations for gravitational-wave detection

Cited by in corpus (39)

• Measurability of the tidal polarizability of neutron stars in late-inspiral gravitational-wave signals
• Inspiral-merger-ringdown multipolar waveforms of nonspinning black-hole binaries using the effective-one-body formalism
• Prototype effective-one-body model for nonprecessing spinning inspiral-merger-ringdown waveforms
• Improved effective-one-body description of coalescing nonspinning black-hole binaries and its numerical-relativity completion
• Gravitational Waves from Quasicircular Extreme Mass-Ratio Inspirals as Probes of Scalar-Tensor Theories
• Post-Newtonian factorized multipolar waveforms for spinning, non-precessing black-hole binaries
• The complete non-spinning effective-one-body metric at linear order in the mass ratio
• Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration
• The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries
• Accurate numerical simulations of inspiralling binary neutron stars and their comparison with effective-one-body analytical models
• Extreme Mass-Ratio Inspirals in the Effective-One-Body Approach: Quasi-Circular, Equatorial Orbits around a Spinning Black Hole
• A new gravitational wave generation algorithm for particle perturbations of the Kerr spacetime
• The Science of the Einstein Telescope
• Modeling multipolar gravitational-wave emission from small mass-ratio mergers
• The Effect of Massive Perturbers on Extreme Mass-Ratio Inspiral Waveforms
• Binary black hole coalescence in the extreme-mass-ratio limit: testing and improving the effective-one-body multipolar waveform
• Binary black hole coalescence in the large-mass-ratio limit: the hyperboloidal layer method and waveforms at null infinity
• Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole to the 11th Post-Newtonian Order
• Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order
• Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order
• Modeling the horizon-absorbed gravitational flux for equatorial-circular orbits in Kerr spacetime
• Horizon-absorption effects in coalescing black-hole binaries: An effective-one-body study of the non-spinning case
• Towards a gravitational self force-informed effective-one-body waveform model for nonprecessing, eccentric, large-mass-ratio inspirals
• Horizon-absorbed energy flux in circularized, nonspinning black-hole binaries and its effective-one-body representation
• The General Relativistic Two Body Problem and the Effective One Body Formalism
• Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter
• Impact of the second order self-forces on the dephasing of the gravitational waves from quasi-circular extreme mass-ratio inspirals
• Constructing EOB dynamics with numerical energy flux for intermediate-mass-ratio inspirals
• Complete gravitational-waveform amplitude modes for quasi-circular compact binaries to the 3.5PN order
• Exploring the Outer Limits of Numerical Relativity
• Observables from classical black hole scattering in Scalar-Tensor theory of gravity from worldline quantum field theory
• Accuracy of the Post-Newtonian Approximation for Extreme-Mass Ratio Inspirals from Black-hole Perturbation Approach
• Taming the post-Newtonian expansion: Simplifying the modes of the gravitational wave energy flux at infinity for a point particle in a circular orbit around a Schwarzschild black hole
• Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions
• Comparison of post-Newtonian templates for extreme mass ratio inspirals
• Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order
• Observable Signatures of EMRI Black Hole Binaries Embedded in Thin Accretion Disks
• The general relativistic two body problem
• Waveform models for the gravitational-wave memory effect: Extreme mass-ratio limit and final memory offset