Large-Eccentricity Asymptotics and Fast Analytic Approximation for Fourier modes of Post-Newtonian Eccentric Waveforms
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917443464593408 |
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| author | Liu, Xiaolin Cao, Zhoujian |
| author_facet | Liu, Xiaolin Cao, Zhoujian |
| contents | In this work, we developed analytic asymptotic methods for computing the Fourier modes of gravitational waves from post-Newtonian binary systems in the quasi-Keplerian parametrization in the high eccentricity regime. We have also derived the large-eccentricity asymptotic expansion of the eccentricity enhancement function appearing in the tail contributions to the radiation. Furthermore, based on these results, we constructed an endpoint-constrained analytic approximation that significantly accelerate the computation of the Fourier modes at large eccentricity.The overall error of this analytic approximation is controlled within $10^{-3}$, and it remains valid for Fourier modes with $p\le200$. This approach provides an analytic building blocks for modeling frequency-domain gravitational wave from highly eccentric binaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25536 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large-Eccentricity Asymptotics and Fast Analytic Approximation for Fourier modes of Post-Newtonian Eccentric Waveforms Liu, Xiaolin Cao, Zhoujian General Relativity and Quantum Cosmology In this work, we developed analytic asymptotic methods for computing the Fourier modes of gravitational waves from post-Newtonian binary systems in the quasi-Keplerian parametrization in the high eccentricity regime. We have also derived the large-eccentricity asymptotic expansion of the eccentricity enhancement function appearing in the tail contributions to the radiation. Furthermore, based on these results, we constructed an endpoint-constrained analytic approximation that significantly accelerate the computation of the Fourier modes at large eccentricity.The overall error of this analytic approximation is controlled within $10^{-3}$, and it remains valid for Fourier modes with $p\le200$. This approach provides an analytic building blocks for modeling frequency-domain gravitational wave from highly eccentric binaries. |
| title | Large-Eccentricity Asymptotics and Fast Analytic Approximation for Fourier modes of Post-Newtonian Eccentric Waveforms |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.25536 |