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arXiv 1304.7017gr-qc
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引力波螺旋信号的统计误差和系统误差:主成分分析

Statistical and systematic errors for gravitational-wave inspiral signals: A principal component analysis

Frank Ohme, Alex B. Nielsen, Drew Keppel, Andrew Lundgren

摘要:

仅从引力波测量中识别源参数受到我们区分来自不同源的信号的能力和搜索中采用的波形族的准确性的限制。在这里,我们在自适应坐标系的框架中解决了这两个问题,该自适应坐标系允许波形差的线性Fisher矩阵类型计算,其既准确又在计算上非常有效。我们调查统计误差,使用主成分分析的后牛顿(PN)的膨胀系数,这是良好的条件,尽管费舍尔矩阵成为病态的大量参数。我们确定的物理参数的组合是最有效的测量系统的中子星和黑洞对齐自旋的引力波探测器。我们确认的预期,inspiral波形的主导参数是啁啾质量。下一个主要参数取决于自旋和对称质量比的组合。此外,我们可以研究各种自旋贡献的PN定相在相同的参数化的系统效果,表明包括自旋-轨道校正下一个领先的顺序,但不一定是自旋-自旋贡献,是一个准确的inspiral波形模型的关键。这种对整个参数空间的波形结构的理解对于建立有效的搜索策略和正确解释未来的引力波观测是重要的。

英文摘要:

Identifying the source parameters from a gravitational-wave measurement alone is limited by our ability to discriminate signals from different sources and the accuracy of the waveform family employed in the search. Here we address both issues in the framework of an adapted coordinate system that allows for linear Fisher-matrix type calculations of waveform differences that are both accurate and computationally very efficient. We investigate statistical errors by using principal component analysis of the post-Newtonian (PN) expansion coefficients, which is well conditioned despite the Fisher matrix becoming ill conditioned for larger numbers of parameters. We identify which combinations of physical parameters are most effectively measured by gravitational-wave detectors for systems of neutron stars and black holes with aligned spin. We confirm the expectation that the dominant parameter of the inspiral waveform is the chirp mass. The next dominant parameter depends on a combination of the spin and the symmetric mass ratio. In addition, we can study the systematic effect of various spin contributions to the PN phasing within the same parametrization, showing that the inclusion of spin-orbit corrections up to next-to-leading order, but not necessarily of spin-spin contributions, is crucial for an accurate inspiral waveform model. This understanding of the waveform structure throughout the parameter space is important to set up an efficient search strategy and correctly interpret future gravitational-wave observations.

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