A comparison between best-fit eccentricity definitions and the standardized definition of eccentricity
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| Natura: | Preprint |
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2025
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| author | Chartier, Nicolas Shaikh, Md Arif Lee, Hyung Mok Kim, JeongCho |
| author_facet | Chartier, Nicolas Shaikh, Md Arif Lee, Hyung Mok Kim, JeongCho |
| contents | In the absence of a unique, gauge-independent definition of eccentricity in General Relativity, there have been efforts to standardize the definition for Gravitational-Wave astronomy. Recently, Shaikh et al. proposed a model-independent measurement of eccentricity $e_{\mathrm{gw}}$ from the phase evolution of the dominant mode. Many works use loss functions (LFs) to assign eccentricity to a reference waveform, for instance by fitting a Post-Newtonian expression to assign eccentricity to Numerical Relativity (NR) simulations. Therefore, we ask whether minimizing common LFs on gauge-dependent model parameters, such as the mismatch $\mathcal{M}$ or the $L_2$-norm of the dominant mode $h_{22}$ residuals, for non-precessing binaries, ensures a sufficient $e_{\mathrm{gw}}$ agreement. We use $10$ eccentric NR simulations and the eccentric waveform TEOBResumS-Dali as the parametric model to fit on eccentricity $e_0$ and reference frequency $f_0$. We first show that a minimized mismatch, the $\mathcal{M} \sim 10^{-3}- 10^{-2}$ results in better $e_{\mathrm{gw}}$ fractional differences ($\sim 1\%$) than with the minimized $h_{22}$ residuals. Nonetheless, for small eccentricity NR simulations $(e_{\mathrm{gw}} \lesssim 10^{-2}$), the mismatch can favor quasi-circular ($e_0=0$) best-fit models. Thus, with sufficiently long NR simulations, we can include $e_{\mathrm{gw}}$ in the LF. We explain why solely fitting with $e_{\mathrm{gw}}$ constitutes a degenerate problem. To circumvent these limitations, we propose to minimize a convex sum of $\mathcal{M}$ and the $e_{\mathrm{gw}}$ difference to both assign non-zero eccentric values to NR strains and to control the mismatch threshold. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_19538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A comparison between best-fit eccentricity definitions and the standardized definition of eccentricity Chartier, Nicolas Shaikh, Md Arif Lee, Hyung Mok Kim, JeongCho General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena In the absence of a unique, gauge-independent definition of eccentricity in General Relativity, there have been efforts to standardize the definition for Gravitational-Wave astronomy. Recently, Shaikh et al. proposed a model-independent measurement of eccentricity $e_{\mathrm{gw}}$ from the phase evolution of the dominant mode. Many works use loss functions (LFs) to assign eccentricity to a reference waveform, for instance by fitting a Post-Newtonian expression to assign eccentricity to Numerical Relativity (NR) simulations. Therefore, we ask whether minimizing common LFs on gauge-dependent model parameters, such as the mismatch $\mathcal{M}$ or the $L_2$-norm of the dominant mode $h_{22}$ residuals, for non-precessing binaries, ensures a sufficient $e_{\mathrm{gw}}$ agreement. We use $10$ eccentric NR simulations and the eccentric waveform TEOBResumS-Dali as the parametric model to fit on eccentricity $e_0$ and reference frequency $f_0$. We first show that a minimized mismatch, the $\mathcal{M} \sim 10^{-3}- 10^{-2}$ results in better $e_{\mathrm{gw}}$ fractional differences ($\sim 1\%$) than with the minimized $h_{22}$ residuals. Nonetheless, for small eccentricity NR simulations $(e_{\mathrm{gw}} \lesssim 10^{-2}$), the mismatch can favor quasi-circular ($e_0=0$) best-fit models. Thus, with sufficiently long NR simulations, we can include $e_{\mathrm{gw}}$ in the LF. We explain why solely fitting with $e_{\mathrm{gw}}$ constitutes a degenerate problem. To circumvent these limitations, we propose to minimize a convex sum of $\mathcal{M}$ and the $e_{\mathrm{gw}}$ difference to both assign non-zero eccentric values to NR strains and to control the mismatch threshold. |
| title | A comparison between best-fit eccentricity definitions and the standardized definition of eccentricity |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2503.19538 |