未建模偏心率对潮汐形变度测量的影响及对引力波物理推断的启示
Impact of unmodeled eccentricity on the tidal deformability measurement and implications for gravitational wave physics inference
AI总结：
本文评估未建模残余偏心率对第三代探测器测量双中子星潮汐形变度的系统影响，发现其会偏置 EoS、红移及黑洞 Kerr 检验，并强调采用偏心波形模型。
摘要：
随着预期将通过引力波（GW）观测到大量双中子星（BNS）系统，第三代引力波探测器 Cosmic Explorer（CE）和 Einstein Telescope（ET）将能够以极高精度约束潮汐形变度，进而约束中子星（NS）的状态方程（EoS）。一部分被探测到的 BNS 系统在探测器频段内可能仍保留残余偏心率。我们研究了潮汐形变度测量中因未建模偏心率导致的系统误差，及其对中子星 EoS 和通过 Love siren 方法进行红移测量的影响。我们发现，在以 10 Hz 为参考引力波频率时，对于 CE（ET），当偏心率约为 10^-3（约 3×10^-4）时，潮汐形变度参数的系统误差会超过统计误差。我们表明，这些对潮汐形变度参数的偏置会显著偏置中子星 EoS 推断。此外，潮汐形变度的误差会传播到源参考系下的中子星质量，进而偏置红移推断。对于 CE，在偏心率约为 10^-3（参考频率为 10 Hz）时，红移推断会受到显著偏置。我们还研究了潮汐形变度偏置在检验黑洞 Kerr 性质方面的影响。潮汐形变度参数的系统误差会使双黑洞的潮汐形变度出现非零值，从而错误地指示其偏离 Kerr 性质。最后，我们表明，在波形模型中纳入偏心率会使潮汐形变度测量的统计误差增加不超过约 2 倍。因此，我们的研究强调了在引力波参数推断中使用精确偏心波形模型的重要性。
英文摘要：
With the expected large number of binary neutron star (BNS) observations through gravitational waves (GWs), third-generation GW detectors, Cosmic Explorer (CE) and Einstein Telescope (ET), will be able to constrain the tidal deformability, and hence the equation of state (EoS) of neutron star (NS) with exquisite precision. A subset of the detected BNS systems can retain residual eccentricity in the detector frequency band. We study the systematic errors due to unmodeled eccentricity in the tidal deformability measurement and its implications for NS EoS and redshift measurement via the Love siren method. We find that the systematic errors in the tidal deformability parameter exceed the statistical errors at an eccentricity of $\sim 10^{-3}$ ($\sim 3\times 10^{-4}$) at $10$Hz reference GW frequency for CE (ET). We show that these biases on tidal deformability parameter can significantly bias the NS EoS inference. Furthermore, the error on tidal deformability propagates to the source frame NS mass, which in turn biases the redshift inference. For CE, the redshift inference is significantly biased at an eccentricity of $\sim 10^{-3}$ (at a reference frequency of $10$Hz). We also study the implications of biased tidal deformability in testing the Kerr nature of black holes. Systematic error on the tidal deformability parameter leads to a non-zero value of tidal deformability for binary black holes, indicating a false deviation from the Kerr nature. Finally, we show that including eccentricity in the waveform model increases the statistical errors in tidal deformability measurement by a factor of $\lesssim 2$. Our study, therefore, highlights the importance of using accurate eccentric waveform models for GW parameter inference.
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