Extreme mass ratio inspirals (EMRIs), where a compact object orbits a massive black hole, are a key source of gravitational waves for the future Laser Interferometer Space Antenna (LISA). Due to their small mass ratio, ( ϵ∼10−4–10⁻⁷), the binary evolves slowly and EMRI signals will be in-band for years. Additionally, astrophysical EMRIs are expected to have complex dynamics featuring both spin-precession and eccentricity. A standard approach to modelling these inspirals is via the method of osculating geodesics (OG) which we employ along with a toy model for the gravitational self-force. Using this method requires resolving tens of thousands radial and polar orbital librations over the long duration of the signal which makes the inspiral trajectory expensive to compute. In this work we accelerate these calculations by employing Near-Identity (averaging) Transformations. However, this averaging technique breaks down at orbital resonances where the radial and polar frequencies are an integer ratio of each other. Thus, we switch to a partial averaging transformation in the vicinity of the resonance where the dynamics are characterised by the slow evolution of the so-called ‘resonant phase’. Additionally, we develop an optimal switching criterion to minimise the computation time while maximising accuracy. We find the error in the waveform phase is improved from O(ϵ−1/2) in the fully averaged scheme to O(ϵ4/7) in the switching scheme. At the same time, this scheme improves the scaling of the computation time from being inversely proportional to ϵ using OG, to a very weak scaling with ϵ. This results in a speed-up of at least two orders of magnitude for LISA EMRIs with room for further optimisation.

中文翻译：

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快速吸气和眼眶共振的治疗


极端质量比吸入式天线 （EMRI） 是指致密物体围绕大质量黑洞运行，是未来激光干涉仪空间天线 （LISA） 的关键引力波来源。由于它们的质量比小 （ ε∼10-4-10-7），双星演化缓慢，EMRI 信号将在带内持续数年。此外，预计天体物理 EMR 将具有复杂的动力学，同时具有自旋进动和偏心率。模拟这些引力的标准方法是通过振荡测地线 （OG） 的方法，我们将其与引力自力的玩具模型一起使用。使用这种方法需要在信号的较长持续时间内解析数以万计的径向和极坐标轨道天动，这使得螺旋轨迹的计算成本很高。在这项工作中，我们通过采用近等（平均）变换来加速这些计算。然而，这种平均技术在轨道共振处崩溃，其中径向频率和极坐标频率是彼此的整数比。因此，我们在共振附近切换到部分平均变换，其中动力学的特点是所谓的 “共振相 ”的缓慢演变。此外，我们开发了一个最佳开关标准，以最大限度地减少计算时间，同时最大限度地提高准确性。我们发现波形相位的误差从全平均方案中的 O（ε−1/2） 改善到开关方案中的 O（ε4/7）。同时，该方案将计算时间的缩放从使用 OG 的 ε 成反比，提高到使用 ε 的非常弱的缩放。这使得 LISA EMR 的加速至少提高了两个数量级，并有进一步优化的空间。