从合流Heun方程到圆化、无自旋致密双星的新分解和重求和的引力波形
From the confluent Heun equation to a new factorized and resummed gravitational waveform for circularized, nonspinning, compact binaries
AI总结：
通过将Teukolsky方程映射为合流Heun方程，提出一种新的分解和重求和波形，完全吸收所有测试质量对数项和超越数，得到多项式形式的残余修正，在测试质量极限下比标准方法更精确。
摘要：
我们引入了一种新的分解和重求和波形，用于圆化、无自旋致密双星，该波形利用了Teukolsky方程映射为合流Heun方程后的解。解的结构允许我们识别出新的重求和因子，这些因子通过指数函数和$\Gamma$函数在任何后牛顿（PN）阶完全吸收所有测试质量对数项和超越数。相应的残余相对论修正和相位修正是具有有理系数的多项式，实际上是PN截断的超几何函数。我们的方法补充了Ivanov等人[Phys. Rev. Lett. 135 (2025) 14, 141401]的最新提议，特别地从第一原理恢复了相应的多极矩重整化群标度，并确定了标度常数。在测试质量极限下，我们的方法（推进到10PN）产生的波形和通量在全局上比使用Damour等人[Phys. Rev. D 79 (2009), 064004]的标准分解方法更准确。该方法通过实现多极矩的通用反常维数新概念，直接推广到质量相当的双星，并可能最终有助于改进当前最先进的有效单体波形模型用于并合双星。
英文摘要：
We introduce a new factorized and resummed waveform for circularized, nonspinning, compact binaries that leverages on the solution of the Teukolsky equation once mapped into a confluent Heun equation. The structure of the solution allows one to identify new resummed factors that completely absorb all test-mass logarithms and transcendental numbers via exponentials and $Γ$-functions at any post-Newtonian (PN) order. The corresponding residual relativistic and phase corrections are thus polynomial with rational coefficients, that are in fact PN-truncated hypergeometric functions. Our approach complements the recent proposal of Ivanov et al. [Phys. Rev. Lett. 135 (2025) 14, 141401], notably recovering the corresponding renormalization group scaling of multipole moments from first principles and fixing the scaling constant. In the test mass limit, our approach (pushed up to 10PN) yields waveforms and fluxes that are globally more accurate than those obtained using the standard factorized approach of Damour et al. [Phys. Rev. D 79 (2009), 064004]. The method generalizes straightforwardly to comparable mass binaries implementing the new concept of universal anomalous dimension of multipole moments and might be eventually useful to improve current state of the art effective-one-body waveform models for coalescing binaries.
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