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arXiv 2302.04015astro-ph.HEgr-qc
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非常接近旋转的超大质量黑洞的合并双星黑洞的出现

The appearance of a merging binary black hole very close to a spinning supermassive black hole

Xiaoyue Zhang, Xian Chen

摘要:

双黑洞的质量和距离是引力波天文学测量的基本参数。众所周知,测量结果会受到宇宙学红移的影响,最近的工作也表明,如果BBH靠近超大质量黑洞(SMBH)并合,多普勒和引力红移会进一步影响测量结果。在这里,我们考虑的额外的透镜效应引起的附近SMBH的测量。我们计算了克尔SMBH的$10$引力半径内的零测地线,以确定由BBH发射的GW的红移和放大率。我们发现红移和缩小率之间存在正相关,这导致探测器框架中BBH的质量和距离之间存在正相关。更重要的是,我们发现信号出现红移和缩小到远处观察者的概率更高,而不是蓝移和放大。基于这些结果,我们证明了宇宙学红移为$z_{\rm cos}=(10^{-2}-10^{-1})$,由$(10-20)M_\odot$的BH组成的双星可以伪装成红移为$z_{\rm cos}\sim1$,含有$(44-110)M_\odot$大小的BH的BBH。在极度缩小的情况下,我们也发现同样的黑洞可能出现在$z_{\rm cos}>10$上,并且包含亚太阳质量的黑洞。如果不考虑这种效应,可能会使我们对通过GWs检测到的BH的起源的理解产生偏差。

英文摘要:

The mass and distance of a binary black hole (BBH) are fundamental parameters to measure in gravitational-wave (GW) astronomy. It is well-known that the measurement is affected by cosmological redshift, and recent works also showed that Doppler and gravitational redshifts could further affect the result if the BBH coalesces close to a supermassive black hole (SMBH). Here we consider the additional lensing effect induced by the nearby SMBH on the measurement. We compute the null geodesics originating within $10$ gravitational radii of a Kerr SMBH to determine the redshift and magnification of the GWs emitted by the BBH. We find a positive correlation between redshift and demagnification, which results in a positive correlation between the mass and distance of the BBH in the detector frame. More importantly, we find a higher probability for the signal to appear redshifted and demagnified to a distant observer, rather than blueshifted and magnified. Based on these results, we show that a binary at a cosmological redshift of $z_{\rm cos}=(10^{-2}-10^{-1})$ and composed of BHs of $(10-20)M_\odot$ could masquerade as a BBH at a redshift of $z_{\rm cos}\sim1$ and containing BHs as large as $(44-110)M_\odot$. In the case of extreme demagnification, we also find that the same BBH could appear to be at $z_{\rm cos}>10$ and contain subsolar-mass BHs. Such an effect, if not accounted for, could bias our understanding of the origin of the BHs detected via GWs.

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