Modeling of extreme mass ratio inspiral for testing gravity theories

该研究项目的重点是极端质量比螺旋遇到的潮汐共振。极端质量比螺旋是天基干涉仪（例如 LISA）最令人兴奋和最有前途的目标源之一，它将为广义相对论提供严格的测试。它们还可能通过引力波的发射提供有关银河系中心密集环境的大量信息。我们在 2022 财年的工作（已经发布）是 2021 年发布的工作的延伸。现在，我们放松了之前的假设并准备了一个现实的模型。我们广泛探索了具有附加共振组合的潮汐扰动器的更通用模型，以研究共振强度对固有轨道和潮汐参数的依赖性。 为了分析共振信号，需要正确结合潮汐场影响的精确模板。通过共振的演化是使用阶跃函数获得的，其幅度是使用共振跳跃的解析插值来计算的。我们通过将近似方法与数值演化进行比较来对这个过程进行基准测试。此外，我们使用 Fisher 矩阵来研究参数的测量精度以及由于建模不准确而导致的系统偏差。自力共振的建模也可以使用本研究中提出的实现来进行，这对于 EMRI 波形建模至关重要。

The research project was focused on tidal resonances encountered by extreme-mass-ratio inspirals. Extreme mass ratio inspirals are one of the most exciting and promising target sources for space-based interferometers (such as LISA) that will offer stringent tests on the general theory of relativity. They might also provide a wealth of information about the dense environment in galactic centers via the emission of gravitational waves. Our work (already published) in the fiscal year 2022 is an extension of the work published in 2021. Now, we have relaxed previous assumptions and prepared a realistic model. We extensively explore a more generic model for the tidal perturber with additional resonance combinations, to study the dependence of resonance strength on the intrinsic orbital and tidal parameters. To analyze the resonant signals, accurate templates that correctly incorporate the effects of the tidal field are required. The evolution through resonances is obtained using a step function, whose amplitude is calculated using an analytic interpolation of the resonance jumps. We benchmark this procedure by comparing our approximate method to a numerical evolution. Further, we use Fisher matrices to study both the measurement precision of parameters and the systematic bias due to inaccurate modeling. Modeling of self-force resonances can also be carried out using the implementation presented in this study, which will be crucial for EMRI waveform modeling.