发表机构
Shanghai University; Kyoto University（上海大学; 京都大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过数值近似方法计算自旋次级天体在旋转毛状黑洞周围的偏心轨道引力波，发现自旋和毛形变通过累积相位失谐留下主要印刻，并影响捕获阈值与信噪比，为区分毛状黑洞与Kerr黑洞提供可能。
AI 中文摘要
我们研究了致密次级天体的自旋以及引力解耦对Kerr几何的形变如何印刻在围绕旋转黑洞的强场偏心运动所产生的引力波上。轨道在Tulczyjew自旋补充条件下，由Mathisson-Papapetrou-Dixon方程演化，辐射则采用数值近似（numerical-kludge）方法计算。该形变仅在两个毛参数平面中的临界曲线以下描述一个黑洞。次级天体的自旋将近心点向内拉动，并在超过临界值时，将粒子带入黑洞。毛（hair）提高了这一捕获阈值，从Kerr中的$S\simeq0.66$提升到接近视界边界时的0.9及以上，因为它降低了黑洞附近的等效质量。发射的信号仍保持为轨道谐波的离散梳状结构：自旋增强了近心点爆发，并将功率向更高谐波转移，而自旋和毛的主要印刻则通过累积的相位失谐（dephasing）体现。毛的印刻由决定形变径向范围的参数控制，在族类的Kerr极限中消失，并受到次级天体自旋的放大。对于距离为$2$ Gpc、$M=10^6M_\odot$和$\mu=10M_\odot$的源，信号的$6.8$小时片段在LISA中携带的信噪比约为$1.4$，在Taiji中为$2.7$，在天琴（TianQin）中为$0.9$。在同一片段内，更扩展的形变变得可与Kerr区分，首先在Taiji中实现；由于这适用于无自旋的次级天体，因此直接适用于天体物理极端质量比旋进（EMRI）。自旋引起的频移与自旋呈线性关系，因此这里使用的大自旋是相位失谐的放大示例，对于现实中的次级天体，该失谐在旋进过程中累积到约一弧度的相位。
英文摘要
We study how the spin of a compact secondary and a gravitational-decoupling deformation of the Kerr geometry are imprinted on gravitational waves from strong-field eccentric motion around a rotating black hole. The orbit is evolved with the Mathisson--Papapetrou--Dixon equations under the Tulczyjew spin supplementary condition, and the radiation is computed with the numerical-kludge method. The deformation describes a black hole only below a critical curve in the plane of the two hair parameters. The spin of the secondary pulls the pericenter inward and, above a critical value, carries the particle into the black hole. The hair raises this capture threshold, from $S\simeq0.66$ in Kerr to $0.9$ and above close to the horizon boundary, because it reduces the effective mass near the black hole. The emitted signal remains a discrete comb of orbital harmonics: the spin strengthens the pericenter bursts and shifts power toward higher harmonics, while both the spin and the hair leave their main imprint through an accumulated dephasing. The imprint of the hair is controlled by the parameter that sets the radial reach of the deformation, disappears in the Kerr-like limit of the family, and is amplified by the spin of the secondary. For a source at $2$ Gpc with $M=10^6M_\odot$ and $μ=10M_\odot$, a $6.8$ h segment of the signal carries a signal-to-noise ratio of about $1.4$ in LISA, $2.7$ in Taiji and $0.9$ in TianQin. Within the same segment the more extended deformations become distinguishable from Kerr, first in Taiji; since this holds for a nonspinning secondary, it applies directly to astrophysical EMRIs. The spin-induced frequency shifts are linear in the spin, so the large spins used here are a magnified illustration of a dephasing that, for realistic secondaries, accumulates to a phase of order a radian over an inspiral.
Comments15 pages, 7 figures
