Modeling of extreme mass ratio inspiral for testing gravity theories

该研究项目的重点是极端质量比激励物遇到的潮汐共振。极端质量比激发源是空间干涉仪(如LISA)最令人兴奋和最有希望的目标来源之一，它将为广义相对论提供严格的测试。它们还可能通过发射引力波，提供有关银河系中心致密环境的丰富信息。我们在2022财年的工作(已经发表)是2021年发表的工作的延伸。现在，我们放松了之前的假设，准备了一个现实的模型。我们广泛地探索了带有附加共振组合的潮汐微扰器的更一般的模型，以研究共振强度与固有轨道和潮汐参数的依赖关系。为了分析共振信号，需要准确的模板来正确地结合潮汐磁场的影响。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内插来计算的。我们通过将我们的近似方法与数值进化进行比较来对这一过程进行基准测试。此外，我们还利用Fisher矩阵研究了参数的测量精度和由于建模不准确而引起的系统偏差。还可以使用本研究中提出的实现对自力共振进行建模，这将是EMRI波形建模的关键。

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.