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arXiv 0710.4369gr-qc
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交替LISA配置的灵敏度和参数估计精度

Sensitivity and parameter-estimation precision for alternate LISA configurations

Michele Vallisneri, Jeff Crowder, Massimo Tinto

摘要:

我们描述了一个简单的框架,以评估LISA的科学性能(更具体地说,其灵敏度和预期的参数估计精度为规定的引力波信号)的假设下失败的一个或两个航天器间的激光测量(链接)和一到四个航天器内的激光测量。我们将该框架应用于测量LISA对单色圆双星的敏感性的简单情况,以及这些系统的引力波偏振角的LISA参数估计精度。与六链路基线配置相比,五链路情况的特征在于LISA频带的高频部分中的信噪比(SNR)的小损失;四链路情况在低频下显示出sqrt(2)的因子减小,并且在高频下最多减小~2。在费雪矩阵形式主义中计算的极化估计的不确定性,在从六个链路移动到五个链路,然后移动到四个链路时也是不确定的:这可以通过这些配置中可用的SNR降低来解释(除了短于三个月的观测,其中即使在相同的SNR下,五个和六个链路也比四个链路更好)。此外,我们证明(通用信号)的SNR和Fisher矩阵是不变的TDI观测值的基础的选择,而是,它们只取决于其中的航天器间和航天器内的测量是可用的。

英文摘要:

We describe a simple framework to assess the LISA scientific performance (more specifically, its sensitivity and expected parameter-estimation precision for prescribed gravitational-wave signals) under the assumption of failure of one or two inter-spacecraft laser measurements (links) and of one to four intra-spacecraft laser measurements. We apply the framework to the simple case of measuring the LISA sensitivity to monochromatic circular binaries, and the LISA parameter-estimation precision for the gravitational-wave polarization angle of these systems. Compared to the six-link baseline configuration, the five-link case is characterized by a small loss in signal-to-noise ratio (SNR) in the high-frequency section of the LISA band; the four-link case shows a reduction by a factor of sqrt(2) at low frequencies, and by up to ~2 at high frequencies. The uncertainty in the estimate of polarization, as computed in the Fisher-matrix formalism, also worsens when moving from six to five, and then to four links: this can be explained by the reduced SNR available in those configurations (except for observations shorter than three months, where five and six links do better than four even with the same SNR). In addition, we prove (for generic signals) that the SNR and Fisher matrix are invariant with respect to the choice of a basis of TDI observables; rather, they depend only on which inter-spacecraft and intra-spacecraft measurements are available.

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