Data-driven extraction and phenomenology of eccentric harmonics in eccentric spinning binary black hole mergers
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916968142995456 |
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| author | Islam, Tousif Venumadhav, Tejaswi Mehta, Ajit Kumar Wadekar, Digvijay Roulet, Javier Anantpurkar, Isha Mushkin, Jonathan Zackay, Barak Zaldarriaga, Matias |
| author_facet | Islam, Tousif Venumadhav, Tejaswi Mehta, Ajit Kumar Wadekar, Digvijay Roulet, Javier Anantpurkar, Isha Mushkin, Jonathan Zackay, Barak Zaldarriaga, Matias |
| contents | Newtonian and post-Newtonian (PN) calculations indicate that the phenomenology of eccentric binary black hole (BBH) merger waveforms is significantly more complex than that of their quasi-circular counterparts. Each spherical harmonic mode of the radiation can be further decomposed into several eccentricity-induced components, referred to as eccentric harmonics. Unlike the (cumulative) spherical harmonic modes, these constituent eccentric harmonics exhibit monotonically time-varying amplitudes and frequencies. However, these eccentric harmonics are not directly accessible in numerical relativity (NR) simulations or current eccentric waveform models. Using the recently developed data-driven framework gwMiner, which combines singular value decomposition, input from post-Newtonian theory, and signal processing techniques, we extract eccentric harmonics from eccentric, aligned-spin waveforms for six different spherical harmonic modes: (2,1), (2,2), (3,2), (3,3), (4,3), (4,4). We demonstrate that the phase (frequency) of each eccentric harmonic takes the form $j\,ϕ_{\ell,m,λ} + ϕ_{\ell,m,\rm ecc}$ ($j\,f_{\ell,m,λ} + f_{\ell,m,\rm ecc}$), where $ϕ_{\ell,m,λ}$ ($f_{\ell,m,λ}$) corresponds to the secular orbital phase (frequency), and $ϕ_{\ell,m,\rm ecc}$ ($f_{\ell,m,\rm ecc}$) is an additional contribution that depends solely on the eccentricity. We further find that $ϕ_{\ell,m,λ}$ is the same across different spherical harmonic modes $(\ell, m)$, whereas the eccentric correction term $ϕ_{\ell,m,\rm ecc}$ scales with $\ell$. Using effective-one-body dynamics, we further show that $ϕ_{\ell,m,λ}$ is nothing but the relativistic anomaly and $ϕ_{\ell,m,\rm ecc}$ is related to the precession advances. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_20556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data-driven extraction and phenomenology of eccentric harmonics in eccentric spinning binary black hole mergers Islam, Tousif Venumadhav, Tejaswi Mehta, Ajit Kumar Wadekar, Digvijay Roulet, Javier Anantpurkar, Isha Mushkin, Jonathan Zackay, Barak Zaldarriaga, Matias General Relativity and Quantum Cosmology Newtonian and post-Newtonian (PN) calculations indicate that the phenomenology of eccentric binary black hole (BBH) merger waveforms is significantly more complex than that of their quasi-circular counterparts. Each spherical harmonic mode of the radiation can be further decomposed into several eccentricity-induced components, referred to as eccentric harmonics. Unlike the (cumulative) spherical harmonic modes, these constituent eccentric harmonics exhibit monotonically time-varying amplitudes and frequencies. However, these eccentric harmonics are not directly accessible in numerical relativity (NR) simulations or current eccentric waveform models. Using the recently developed data-driven framework gwMiner, which combines singular value decomposition, input from post-Newtonian theory, and signal processing techniques, we extract eccentric harmonics from eccentric, aligned-spin waveforms for six different spherical harmonic modes: (2,1), (2,2), (3,2), (3,3), (4,3), (4,4). We demonstrate that the phase (frequency) of each eccentric harmonic takes the form $j\,ϕ_{\ell,m,λ} + ϕ_{\ell,m,\rm ecc}$ ($j\,f_{\ell,m,λ} + f_{\ell,m,\rm ecc}$), where $ϕ_{\ell,m,λ}$ ($f_{\ell,m,λ}$) corresponds to the secular orbital phase (frequency), and $ϕ_{\ell,m,\rm ecc}$ ($f_{\ell,m,\rm ecc}$) is an additional contribution that depends solely on the eccentricity. We further find that $ϕ_{\ell,m,λ}$ is the same across different spherical harmonic modes $(\ell, m)$, whereas the eccentric correction term $ϕ_{\ell,m,\rm ecc}$ scales with $\ell$. Using effective-one-body dynamics, we further show that $ϕ_{\ell,m,λ}$ is nothing but the relativistic anomaly and $ϕ_{\ell,m,\rm ecc}$ is related to the precession advances. |
| title | Data-driven extraction and phenomenology of eccentric harmonics in eccentric spinning binary black hole mergers |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2509.20556 |