The gravitational wave measurements of spin-induced multipole moment coefficients of a binary black hole system can be used to distinguish black holes from other compact objects [N. V. Krishnendu et al., PRL 119, 091101 (2017)]. Here, we apply the idea proposed in [N. V. Krishnendu et al., PRL 119, 091101 (2017)] to binary systems composed of intermediate-mass and supermassive black holes and derive the expected bounds on their Kerr nature using future space-based gravitational wave detectors. We demonstrate this method for an astrophysical population of binary black holes distributed uniformly in the comoving volume and show that the space-based gravitational wave detectors LISA and DECIGO would be able to measure both spin-induced quadrupole and octupole moment parameters with errors smaller than $\leq1$ for $13\%$ and $89\%$, respectively, of the total population. If we consider basic DECIGO (DECIGO-B) configuration with a more conservative lower cut-off frequency, $8\%$ of the total population gives errors on both spin-induced quadrupole and octupole moment parameters $\leq1$. We also discuss how the bounds on spin-induced quadrupole moment coefficients of intermediate-mass ratio inspiraling compact binaries may be translated to certain theoretical models which describe parametric deviations from Kerr black holes using space-based gravitational wave detectors.

中文翻译：

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使用自旋诱导多极矩测量测试超大质量和中等质量黑洞双星的克尔性质

双黑洞系统自旋诱导多极矩系数的引力波测量可用于区分黑洞与其他致密物体 [NV Krishnendu et al., PRL 119, 091101 (2017)]。在这里，我们将 [NV Krishnendu et al., PRL 119, 091101 (2017)] 中提出的想法应用于由中等质量和超大质量黑洞组成的双星系统，并使用未来的空间引力推导出其克尔性质的预期界限波探测器。我们针对在联动体积中均匀分布的双黑洞的天体物理群体演示了这种方法，并表明天基引力波探测器 LISA 和 DECIGO 将能够测量自旋诱导的四极矩和八极矩参数，误差小于 $ \leq1$ 分别为 $13\%$ 和 $89\%$，的总人口。如果我们考虑具有更保守的较低截止频率的基本 DECIGO (DECIGO-B) 配置，则总群体的 $8\%$ 在自旋诱导的四极杆和八极矩参数 $\leq1$ 上都会产生误差。我们还讨论了如何将中等质量比激励紧凑双星的自旋诱导四极矩系数的界限转化为某些理论模型，这些模型描述了使用天基引力波探测器与克尔黑洞的参数偏差。