AI 中文总结
本文通过相对论线性理论与数值格式，探究气体盘与极端质量比旋近（EMRIs）的相互作用，发现近25个史瓦西半径处相对论效应显著改变该相互作用，其框架可助力EMRI形成分析与波形模型构建。
AI 中文摘要
来自极端质量比旋近（EMRIs）的引力波是探测其环绕的超大质量黑洞（SMBHs）环境的精准探针。若超大质量黑洞正处于活跃吸积状态，其周围的气体盘可对EMRIs施加流体动力学力矩，并助力其在盘中形成。这类盘-EMRI相互作用会在激光干涉空间天线（LISA）的未来观测中留下可测量的印记，还可能为利用引力波观测约束气体盘属性提供途径。本文采用线性理论对这些流体动力学相互作用展开详细的相对论分析：首先推导了描述盘中螺旋密度波演化的拉格朗日量，并以此构建了EMRI与气体盘之间角动量转移的平衡定律；随后开发了一种稳定的数值格式，可处理共转共振并在薄盘中找到极大气周向数的模态解。利用该数值格式，我们探究了超大质量黑洞自旋、EMRI半长轴、盘标度高度、声速梯度及面密度梯度对吸积盘与圆轨道EMRIs相互作用的影响。结果表明，当次级天体轨道处于距超大质量黑洞约25个史瓦西半径以内时，相对论效应会显著改变盘-EMRI相互作用；将数值结果与近期分析模型对比后发现，有限厚度气体盘的压力梯度及引力势软化效应的影响十分重要，无法通过调整分析模型中的力矩截断参数来捕捉。本文提供的框架将有助于分析EMRIs的形成场景，并构建盘-EMRI相互作用的相对论精准波形模型。
英文摘要
Gravitational waves from extreme mass ratio inspirals (EMRIs) are precise probes of the environment of the supermassive black holes (SMBHs) they orbit. If an SMBH is actively accreting, the surrounding gaseous disk can impart hydrodynamic torques on and assist the formation of EMRIs within it. Such disk-EMRI interactions could leave measurable imprints on future observations by the Laser Interferometer Space Antenna (LISA), and potentially provide a route to constrain disk properties using gravitational wave observations. We present herein a detailed relativistic analysis of these hydrodynamic interactions using linear theory. We first derive a Lagrangian governing the evolution of spiral density waves in the disk and use it to formulate a balance law for the transfer of angular momentum between the EMRI and disk. We then develop a stable numerical scheme which can be used to treat corotation resonances and find modal solutions in thin disks up to very large azimuthal numbers. Using this numerical scheme, we explore how SMBH spins, EMRI semi-major axes, disk scale heights, sound speed gradients, and surface density gradients affect the interaction between accretion disks and circular EMRIs. Our results show that relativistic effects substantially alter disk-EMRI interactions once the secondary orbit is within $\mathcal{O}(25)$ Schwarzschild radii from the SMBH. Comparing our numerical results with recent analytical models suggests that the impact of pressure gradients and softening of the gravitational potential is important for disks with finite thickness and cannot be captured by tuning the torque cutoff parameters in the analytical models. The framework provided here will help analyze the formation scenarios of EMRIs and build relativistically accurate waveform models of disk-EMRI interactions.
Comments18 pages, 14 figures, supplementary mathematica notebook in the source file. Comments welcome!
