Full-analytic frequency-domain gravitational wave forms from eccentric compact binaries to 2PN accuracy

Abstract

The article provides full-analytic gravitational wave (GW) forms for eccentric nonspinning compact binaries of arbitrary mass ratio in the time Fourier domain. The semi-analytical property of recent descriptions, i.e. the demand of inverting the higher-order Kepler equation numerically but keeping all other computations analytic, is avoided for the first time. The article is a completion of a previous one (Tessmer and Schäfer, Phys. Rev. D 82, 124064 (2010)) to second post-Newtonian (2PN) order in the harmonic GW amplitude and conservative orbital dynamics. A fully analytical inversion formula of the Kepler equation in harmonic coordinates is provided, as well as the analytic time Fourier expansion of trigonometric functions of the eccentric anomaly in terms of sines and cosines of the mean anomaly. Tail terms are not considered.

48 pages

References in corpus (7)

• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux
• Tail effects in the third post-Newtonian gravitational wave energy flux of compact binaries in quasi-elliptical orbits
• Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order
• Comparison between numerical relativity and a new class of post-Newtonian gravitational-wave phase evolutions: the non-spinning equal-mass case
• Full-analytic frequency-domain 1pN-accurate gravitational wave forms from eccentric compact binaries

Cited by in corpus (21)

• Accurate and efficient waveforms for compact binaries on eccentric orbits
• Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order
• An eccentric binary black hole inspiral-merger-ringdown gravitational waveform model from numerical relativity and post-Newtonian theory
• Frequency and time domain inspiral templates for comparable mass compact binaries in eccentric orbits
• Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians
• Third post-Newtonian gravitational waveforms for compact binary systems in general orbits: Instantaneous terms
• The gravitational-wave memory from eccentric binaries
• Eccentric black hole mergers and zoom-whirl behavior from elliptic inspirals to hyperbolic encounters
• Solving post-Newtonian accurate Kepler Equation
• Accuracy of Estimating Highly Eccentric Binary Black Hole Parameters with Gravitational-Wave Detections
• General relativistic spin-orbit and spin-spin effects on the motion of rotating particles in an external gravitational field
• Eccentric Gravitational Wave Bursts in the Post-Newtonian Formalism
• Hereditary Effects in Eccentric Compact Binary Inspirals to Third Post-Newtonian Order
• Residual eccentricity of inspiralling orbits at the gravitational-wave detection threshold: Accurate estimates using post-Newtonian theory
• Gravitational wave source localization for eccentric binary coalesce with a ground-based detector network
• Eccentric first post-Newtonian waveforms for compact binaries in frequency domain with Hansen coefficients
• Canonical Angles In A Compact Binary Star System With Spinning Components: Approximative Solution Through Next-To-Leading-Order Spin-Orbit Interaction for Circular Orbits
• Accuracy of source localization for eccentric inspiraling binary mergers using a ground-based detector network
• Pre-merger localization of eccentric compact binary coalescences with second-generation gravitational-wave detector networks
• Eccentric Motion of Spinning Compact Binaries
• Modeling Gravitational Wave Modes from the Inspiral of Binaries with Arbitrary Eccentricity