Importance of including small body spin effects in the modelling of extreme and intermediate mass-ratio inspirals
Importance of including small body spin effects in the modelling of extreme and intermediate mass-ratio inspirals
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DOI：
10.1103/physrevd.84.064023
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发表时间：
2011-05
影响因子：
5
通讯作者：
E. Huerta;J. Gair
中科院分区：
文献类型：
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作者：
E. Huerta;J. Gair
我们探索了未来低频引力波探测器测量恒星质量和中等质量黑洞自转的能力，这些黑洞激发到超大质量克尔黑洞(SMBH)上。在Saijo等人推导的运动方程的基础上，我们发展了一个杂乱无章的波形模型。[Phys Rev D 58,064005,1998]用于旋转BH双星，增加了来自微扰和后牛顿(PN)计算的自旋-轨道和自旋-自旋耦合，以及相关的保守自力修正，通过与PN结果的比较得出。我们使用精确的通量来模拟激发相，其中包括对激励体自旋的微扰修正、自旋-自旋耦合以及对Teukolsky方程的解的高阶拟合。我们给出了参数估计误差和当我们从波形模板中省略保守校正时产生的模型误差的蒙特卡罗模拟结果。对于信噪比为1000时观测到的5000+10^6太阳质量源，LISA将能够确定这两个质量的分数误差在~0.001以内，测量SMBH自旋星等Q和激励BH的自旋星等分别为0.0001和10%，并确定源在天空中的位置和SMBH自旋方向在0.0001斯特拉第以内。对于信噪比为30的10+10^6太阳质量系统，LISA将无法确定激励黑洞的自旋星等，尽管其他波形参数的测量不会因自旋的存在而显著降低。在质量比大于0.0001的情况下，由于忽略保守修正而产生的模型误差变得很大，但将这些修正包括到2PN数量级可能足以将这些系统误差减小到可接受的水平。
We explore the ability of future low-frequency gravitational wave detectors to measure the spin of stellar mass and intermediate mass black holes that inspiral onto super-massive Kerr black holes (SMBHs). We develop a kludge waveform model based on the equations of motion derived by Saijo et al. [Phys Rev D 58, 064005, 1998] for spinning BH binaries, augmented with spin-orbit and spin-spin couplings taken from perturbative and post-Newtonian (PN) calculations, and the associated conservative self-force corrections, derived by comparison to PN results. We model the inspiral phase using accurate fluxes which include perturbative corrections for the spin of the inspiralling body, spin-spin couplings and higher-order fits to solutions of the Teukolsky equation. We present results of Monte Carlo simulations of parameter estimation errors and of the model errors that arise when we omit conservative corrections from the waveform template. For a source 5000+10^6 solar mass observed with an SNR of 1000, LISA will be able to determine the two masses to within a fractional error of ~0.001, measure the SMBH spin magnitude, q, and the spin magnitude of the inspiralling BH to 0.0001, 10%, respectively, and determine the location of the source in the sky and the SMBH spin orientation to within 0.0001 steradians. For a 10+10^6 solar mass system observed with SNR of 30, LISA will not be able to determine the spin magnitude of the inspiralling BH, although the measurement of the other waveform parameters is not significantly degraded by the presence of spin. The model errors which arise from ignoring conservative corrections become significant for mass-ratios above 0.0001, but including these corrections up to 2PN order may be sufficient to reduce these systematic errors to an acceptable level.