Post-Newtonian inspiral waveform model for eccentric precessing binaries with higher-order modes and matter effects
含高阶模与物质效应的偏心进动双星后牛顿旋近波形模型
We introduce pyEFPEHM, a post-Newtonian (PN) inspiral waveform model for eccentric and spin-precessing compact binaries that includes higher-order modes and matter effects. Accurate and efficient waveform models capturing these effects are essential for probing compact-binary formation channels and exploiting current and future gravitational-wave (GW) observations. pyEFPEHM extends pyEFPE, significantly improving its physical content and accuracy. In particular, we show that above 2.5PN order the quasicircular contributions to the orbital phasing dominate at each PN order, and we incorporate all available higher-order quasicircular PN corrections to the phasing, including adiabatic tidal effects. We generalize the multiple-scale analysis solution of the spin-precession equations, extending it to higher PN orders and including all available quasicircular corrections. Finally, we add eccentric corrections up to 1PN order in the waveform amplitudes, including the GW multipoles <inline-formula><mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mo>|</mml:mo><mml:mi>m</mml:mi><mml:mo>|</mml:mo><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mspace></mml:mspace><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mo>(</mml:mo><mml:mn>4</mml:mn><mml:mo>,</mml:mo><mml:mn>4</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mo>(</mml:mo><mml:mn>4</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mo>(</mml:mo><mml:mn>4</mml:mn><mml:mo>,</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. We validate pyEFPEHM against existing analytical waveform models and numerical relativity simulations, showing that it provides a robust and computationally efficient description of the inspiral, with good agreement across a broad region of parameter space and up to close to merger. The accuracy degrades in the late inspiral for systems with very unequal masses (<inline-formula><mml:math><mml:msub><mml:mi>m</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>≲</mml:mo><mml:mn>0.1</mml:mn></mml:math></inline-formula>), significant spins aligned with the orbital angular momentum (<inline-formula><mml:math><mml:mo>|</mml:mo><mml:msub><mml:mi>χ</mml:mi><mml:mi>eff</mml:mi></mml:msub><mml:mo>|</mml:mo><mml:mo>≳</mml:mo><mml:mn>0.5</mml:mn></mml:math></inline-formula>), and high eccentricities (<inline-formula><mml:math><mml:mi>e</mml:mi><mml:mo>≳</mml:mo><mml:mn>0.6</mml:mn></mml:math></inline-formula>), where the PN expansion is expected to break down. pyEFPEHM represents a significant step toward physically complete and efficient waveform modeling of eccentric and precessing binaries, providing a foundation for future extensions including higher-order corrections, calibration to numerical relativity, and merger-ringdown modeling.
展开 ▾在偏心进动框架中系统补齐 2.5PN 以上准圆相位贡献,将自旋进动多尺度解推广到 4PN,并加入 1PN 偏心高阶模;验证显示其兼具高计算效率与良好的数值相对论一致性。
pyEFPEHM 直接继承并扩展 EFPE 框架下的 pyEFPE 模型,后者已被用于 NSBH 偏心证据搜索和 LISA 数据挑战等场景。作者论证 2.5PN 以上准圆项逐阶主导相位,因而在原偏心底座上演化方程中加入 4.5PN 无自旋、4PN 自旋轨道/自旋-自旋、3.5PN 三次自旋及 7.5PN 潮汐相位修正;同时把此前进动方程的多尺度解推向更高 PN,并纳入十个 1PN 偏心高阶模。未来改进将围绕更高阶振幅与非线性记忆、自洽力信息、EOB/NR 校准,以及补全并合-铃宕模型,以更好覆盖极端质量比、大自旋和高偏心情形。
预印本 2026-04-13 · 刊出 2026-08-11 · 收录 2026-08-22