Eccentric first post-Newtonian waveforms for compact binaries in frequency domain with Hansen coefficients

Abstract

The inspiral and merger of supermassive black hole binary systems with high orbital eccentricity are among the promising sources of the advanced gravitational wave observatories. In this paper we derive analytic ready-to-use first post-Newtonian eccentric waveform in Fourier domain with the use of Hansen coefficients. Introducing generic perturbations of celestial mechanics we have generalized the Hansen expansion to the first post-Newtonian order which are then used to express the waveforms. Taking into account the high eccentricity of the orbit leads to the appearance of secular terms in the waveform which are eliminated with the introduction of a phase shift. The waveforms have a systematic structure and as our main result these are expressed in a tabular form.

19 pages, 3 figures

References in corpus (14)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Robust parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library
• Gravitational waves from scattering of stellar-mass black holes in galactic nuclei
• Massive black hole binary mergers within sub-pc scale gas discs
• Dynamics of triple black hole systems in hierarchically merging massive galaxies
• Self consistent model for the evolution of eccentric massive black hole binaries in stellar environments: implications for gravitational wave observations
• Accurate and efficient waveforms for compact binaries on eccentric orbits
• A novel scheme for rapid parallel parameter estimation of gravitational waves from compact binary coalescences
• Third post-Newtonian gravitational waveforms for compact binary systems in general orbits: Instantaneous terms
• Tracing intermediate-mass black holes in the Galactic Centre
• Detecting gravitational waves from highly eccentric compact binaries
• The detectability of eccentric compact binary coalescences with advanced gravitational-wave detectors
• Full-analytic frequency-domain 1pN-accurate gravitational wave forms from eccentric compact binaries
• Detecting compact binary coalescences with seedless clustering

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• Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order
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• High Eccentricities and High Masses Characterize Gravitational-wave Captures in Galactic Nuclei as Seen by Earth-based Detectors
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• Combining Post-Circular and Padé approximations to compute Fourier domain templates for eccentric inspirals
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• Neutron Stars in the Effective Fly-By Framework: $f$-Mode Re-summation
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