Among the potential gravitational wave (GW) sources for the upcoming space-based interferometer LISA are extreme- or intermediate-mass ratio inspirals (EMRI/IMRIs). These events involve the coalescence of supermassive black holes in the mass range $10^5M_{\odot}\lesssim M \lesssim 10^7M_{\odot}$ with companion BHs of much lower masses. A subset of E/IMRIs are expected to occur in the accretion discs of active galactic nuclei (AGN). Previous work has shown that torques exerted by the disc can interfere with the inspiral and cause a phase shift in the GW waveform detectable by LISA. Here we use a suite of two-dimensional hydrodynamical simulations with the moving-mesh code DISCO to present a systematic study of disc torques. We measure torques on an inspiraling BH and compute the corresponding waveform deviations as a function of the binary mass ratio $q\equiv M_2/M_1$, the disc viscosity ($\alpha$), and gas temperature (or equivalently Mach number; $\mathcal{M}$). We find that the absolute value of the gas torques is within an order of magnitude of previously determined planetary migration torques, but their precise value and sign depends non-trivially on the combination of these parameters, the inspiral rate, and the accretion rate onto the satellite BH. The gas imprint is generally detectable by LISA for binaries embedded in AGN discs with surface densities above $\Sigma_0\ge10^{4-6} \rm \, g \, cm^{-2}$, depending on $q$, $\alpha$ and $\mathcal{M}$. We find that the deviations are most pronounced in discs with higher viscosities, and for E/IMRIs detected at frequencies where LISA is most sensitive. Torques in colder discs exhibit a noticeable dependence on the GW-driven inspiral rate as well as strong fluctuations at late stages of the inspiral. Our results further suggest that LISA may be able to place constraints on AGN disc parameters and the physics of disc-satellite interaction.

中文翻译：

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LISA 波段中气体盘嵌入的中间质量比螺旋的演化

即将推出的天基干涉仪 LISA 的潜在引力波 (GW) 源包括极端或中等质量比螺旋 (EMRI/IMRI)。这些事件涉及质量范围为 $10^5M_{\odot}\lesssim M\lesssim 10^7M_{\odot}$ 的超大质量黑洞与质量低得多的伴生 BH 的合并。预计 E/IMRI 的一个子集将出现在活动星系核 (AGN) 的吸积盘中。先前的工作表明，圆盘施加的扭矩会干扰吸气并导致 LISA 可检测到的 GW 波形发生相移。在这里，我们使用一套带有移动网格代码 DISCO 的二维流体动力学模拟来系统地研究圆盘扭矩。我们测量激励 BH 上的扭矩并计算相应的波形偏差作为二元质量比 $q\equiv M_2/M_1$、圆盘粘度 ($\alpha$) 和气体温度（或等效的马赫数；$ \mathcal{M}$)。我们发现气体扭矩的绝对值在先前确定的行星迁移扭矩的一个数量级内，但它们的精确值和符号很大程度上取决于这些参数的组合、吸入率和吸积率卫星 BH。对于表面密度高于 $\Sigma_0\ge10^{4-6} \rm \, g \, cm^{-2}$（取决于 $q$， $\alpha$ 和 $\mathcal{M}$。我们发现偏差在具有较高粘度的圆盘中最为明显，以及在 LISA 最敏感的频率下检测到的 E/IMRI。较冷盘中的扭矩表现出对 GW 驱动的吸气率的显着依赖性以及吸气后期的强烈波动。我们的结果进一步表明，LISA 可能能够对 AGN 圆盘参数和圆盘-卫星相互作用的物理学施加限制。