Detecting gravitational lensing in hierarchical triples in galactic nuclei with space-borne gravitational-wave observatories
Detecting gravitational lensing in hierarchical triples in galactic nuclei with space-borne gravitational-wave observatories
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DOI：
10.1103/physrevd.104.103011
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发表时间：
2021-07
影响因子：
5
通讯作者：
Hang Yu;Yijun Wang;Brian C Seymour;Yanbei Chen
中科院分区：
文献类型：
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作者：
Hang Yu;Yijun Wang;Brian C Seymour;Yanbei Chen
恒星质量双黑洞（BBH）可能会在超大质量黑洞（SMBH）附近合并。这表明，如果BBH围绕SMBH的轨道（即，外层轨道）的周期不到一年，短于星载GW观测站对BBH的观测持续时间。对于这样的BBH + SMBH三重系统，BBH轨道平面的德西特岁差也很重要。在这项工作中，我们因此研究GW波形发射的BBH，然后调制的SMBH由于影响，包括多普勒频移，德西特进动，引力透镜。我们特别指出，对于0.1年的外轨道周期和10^7 M_odot$的SMBH质量，标准的强透镜特征有3%-10%的机会被星载GW探测器（如丽莎和/或TianGO）探测到。对于更大质量的透镜（$\gtrsim 10^8 M_\odot$）和周期<0.1年的更紧凑的外轨道，SMBH的逆透镜也可能有1%的检测机会。此外，通过结合透镜效应和外轨道的动力学，我们发现中心SMBH的质量可以准确地确定与一个分数误差为$\sim 10^{-4}$。这比静态透镜的情况好得多，因为透镜的质量和源的角位置之间的简并被外轨道运动提升。包括透镜效应还允许在比没有透镜效应的情况长3倍的进动周期处可检测到德西特进动。最后，我们证明，可以检查SMBH的质量之间的一致性确定的轨道动力学和一个推断引力透镜，这作为一个测试这两种现象背后的理论。偏差的统计误差可以限制在1%的水平。
Stellar-mass binary black holes (BBHs) may merge in the vicinity of a supermassive black hole (SMBH). It is suggested that the gravitational-wave (GW) emitted by a BBH has a high probability to be lensed by the SMBH if the BBH's orbit around the SMBH (i.e., the outer orbit) has a period of less than a year and is less than the duration of observation of the BBH by a space-borne GW observatory. For such a BBH + SMBH triple system, the de Sitter precession of the BBH's orbital plane is also significant. In this work, we thus study GW waveforms emitted by the BBH and then modulated by the SMBH due to effects including Doppler shift, de Sitter precession, and gravitational lensing. We show specifically that for an outer orbital period of 0.1 yr and an SMBH mass of $10^7 M_\odot$, there is a 3%-10% chance for the standard, strong lensing signatures to be detectable by space-borne GW detectors such as LISA and/or TianGO. For more massive lenses ($\gtrsim 10^8 M_\odot$) and more compact outer orbits with periods <0.1 yr, retro-lensing of the SMBH might also have a 1%-level chance of detection. Furthermore, by combining the lensing effects and the dynamics of the outer orbit, we find the mass of the central SMBH can be accurately determined with a fraction error of $\sim 10^{-4}$. This is much better than the case of static lensing because the degeneracy between the lens' mass and the source's angular position is lifted by the outer orbital motion. Including lensing effects also allows the de Sitter precession to be detectable at a precession period 3 times longer than the case without lensing. Lastly, we demonstrate that one can check the consistency between the SMBH's mass determined from the orbital dynamics and the one inferred from gravitational lensing, which serves as a test on theories behind both phenomena. The statistical error on the deviation can be constrained to a 1% level.