[论文解读] Extreme mass ratio inspirals in galaxies with dark matter halos

Ning Dai, Yungui Gong+2 more|arXiv (Cornell University)|Jan 12, 2023

Astrophysical Phenomena and Observations被引用 10

一句话总结

论文推导了在 Schwarzschild 黑洞内嵌入 Hernquist 型暗物质晕时空中的 EMRI 轨道动力学与引力波信号的解析表达，显示 DM 晕会在 LISA 波段信号中留下可检测的相位偏移与失配。

ABSTRACT

Using an analytic, static, and spherically symmetric metric for a Schwarzschild black hole immersed in a dark matter (DM) halo with the Hernquist-type profile, we derive analytic expressions for the orbital period and precession of eccentric extreme mass ratio inspirals (EMRIs) surrounded by DM halos, and we show how the precession rates decrease and even undergo a prograde-to-retrograde precession transition if the density of DM halo is large enough. The presence of local DM halos also retards the decrease of the semi-latus rectum and the eccentricity. The orbital evolution of EMRIs immersed in DM halos is then calculated numerically by considering the combined effects of gravitational radiation reaction, dynamical friction, and accretion. Comparing the number of orbital cycles accumulated over a one-year evolution for EMRIs with and without DM halos, we find that DM halos with compactness as small as $10^{-5}$ can be detected. From the mismatch between gravitational waveforms of EMRIs with and without DM halos, we show that EMRIs in galaxies can be used to probe the existence of DM halos and detect the compactness of DM halos as small as $10^{-5}$. Employing the Fisher information matrix method, we find that larger compactness and density values of DM halos help to reduce the estimation error of parameters and further break the degeneracy between the parameters.

研究动机与目标

• 评估围绕大型黑洞的暗物质晕如何影响 EMRI 的轨道和 GW 信号。
• 推导 DM 环境中的轨道周期与进动的解析公式。
• 量化 DM 晕导致的 GW 相位偏移与波形失配对 LISA 可检测性的影响。

提出的方法

• 对 Schwarzschild 黑洞内的 Hernquist 型 DM 晕使用静态、球对称度量。
• 由测地线运动推导轨道元（p、e）与进动的解析表达式。
• 计算包含环境修正的初步 GW 通量（dE/dt、dL/dt）。
• 通过能量和角动量平衡及 GW 发射来演化 p(t) 与 e(t)。
• 计算时域 GW 波形及相对于真空情形的相位偏移。
• 通过轨道圈数与波形失配来评价 LISA 的可检测性。

Figure 1: The orbits of EMRIs in galaxies with and without DM halos. The mass of MBHs is set as $M_{\text{BH}}=10^{6}M_{\odot}$ , the eccentricity $e=0.6$ , and the semi-latus rectum $p=20R_{s}$ . We take the compactness $M/r_{0}$ as $10^{-2}$ and $10^{-3}$ , and the total mass $M$ as $10^{2}M_{\tex

实验结果

研究问题

• RQ1 Hernquist DM 晕如何改变围绕中心 Schwarzschild BH 的测地线轨道？
• RQ2 DM 晕对轨道周期、进动与轨道元演化的解析修正是什么？
• RQ3 DM 晕是否会在如 LISA 的太空基观测中对 EMRI 信号产生可测的相位偏移或波形失配？
• RQ4 通过 GW 观测可检测的 DM 晕致密度与 M/r0 的阈值是多少？
• RQ5 偏心轨道如何影响在 EMRI 中检测 DM 晕的能力？

主要发现

• DM 晕会降低轨道进动，且对于足够致密的晕可产生逆向进动。
• DM 晕在 GW 发射下减缓半短半径圆点(p) 与离心率的减小速率。
• 在合并前一年内，紧致度仅为 10^-4 的 DM 晕就可通过循环计数相偏检测到。
• 在 LISA 条件下，DM-嵌入的波形与真空 EMRI 之间的失配可探测到紧致度低至 ~10^-5 的 DM 晕。
• 偏心轨道比圆轨道更有利于探测较小的 DM 晕紧致度。
• 研究给出包含 DM 晕修正的 T（轨道周期）与 Δφ（近心进动）解析表达式（文中 Eq. 23–24）。

Figure 2: The results of orbital period and precession for EMRIs in galaxies with and without DM. The mass of central MBHs is set as $M_{\text{BH}}=10^{6}M_{\odot}$ and the eccentricity $e=0.6$ . We take the compactness $M/r_{0}$ as $10^{-2}$ and $10^{-3}$ , and the total mass $M$ as $10^{2}M_{\text